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WO2025068310A1 - Apparatus for generating a property associated with a chemical product - Google Patents

Apparatus for generating a property associated with a chemical product Download PDF

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Publication number
WO2025068310A1
WO2025068310A1 PCT/EP2024/076968 EP2024076968W WO2025068310A1 WO 2025068310 A1 WO2025068310 A1 WO 2025068310A1 EP 2024076968 W EP2024076968 W EP 2024076968W WO 2025068310 A1 WO2025068310 A1 WO 2025068310A1
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WO
WIPO (PCT)
Prior art keywords
quantum
solution
representation
electronic structure
computer
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Application number
PCT/EP2024/076968
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French (fr)
Inventor
Michael Kuehn
Peter PINSKI
Sebastian ZANKER
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BASF SE
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BASF SE
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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/20—Models of quantum computing, e.g. quantum circuits or universal quantum computers
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/80—Quantum programming, e.g. interfaces, languages or software-development kits for creating or handling programs capable of running on quantum computers; Platforms for simulating or accessing quantum computers, e.g. cloud-based quantum computing
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control

Definitions

  • the invention refers to an apparatus, a method and a computer program product for gen- erating a property associated with a chemical product. Further, the invention relates to a system generating a property associated with the chemical product comprising the appa- ratus.
  • Quantum computers generally are a completely new kind of computing system that allows utilizing the special behaviour of quantum mechanical systems for performing problem cal- culations that, under the right circumstances, are not performable by ordinary computers in any reasonable time.
  • chemical industry sells chemical products with specific technical application properties.
  • the core of any chemical product is the chemical molecule or the combination of chemical molecules, e.g. the chem- ical product includes one or more chemical molecules, which determines the properties of BASF SE 221032 221032WO01 the chemical product.
  • Properties of chemical monomers or oligomers may be determined to determine the properties of chemical polymers, e.g. through extrapolation.
  • Chemical products with one or more chemical molecules of one or more types are highly complex real-world systems containing multiple interacting electrons that make up the prop- erties of the chemical molecules and thus the properties of the chemical products.
  • Such highly complex molecular structures are commonly described by way of an electronic structure problem, such as by utilizing a Schrödinger equation utilizing a Hamiltonian operator.
  • an electronic structure problem such as by utilizing a Schrödinger equation utilizing a Hamiltonian operator.
  • approximations can be used.
  • the properties stemming from electron correlations may be inade- quately reflected in most systems.
  • the solution of the first part of the electronic structure representation and the solution of the second part of the electronic structure representation are computationally combined by generating an interaction representation that is based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the solution of the second part, independent of the computing systems utilized in the previous step the correlations between and within the first and second part of the elec- tronic structure representation can be determined again on a respective suitable computing system, in particular, a classical computer and/or a quantum computer depending on the respective problem.
  • a suitable computing system in particular, a classical computer and/or a quantum computer depending on the respective problem.
  • the most suitable com- puting system can be chosen independent of a computing system utilized for computing other parts of the solution. This allows for a very computer resource effective solving of complex electronic structure problems.
  • utilizing a reference state as defined above provides more information on an electronic structure system than, for instance, com- monly utilized reduced density matrices.
  • the reference state as defined above allows to utilize a plurality of effective and efficient solution methods that can only be utilized with respective information on the system and are independent of the methods utilized for de- termining the solution of the second part and the solution of the first part.
  • the respec- tive relevant electronic structure problems important for determination of a property asso- ciated with a chemical product can be solved with a higher efficiency and effectivity in the development of chemical products.
  • an apparatus for generating a prop- erty associated with a chemical product, wherein the chemical product includes one or more molecular structures
  • the apparatus comprises i) an electronic structure rep- resentation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the BASF SE 221032 221032WO01 electronic structure representation indicative of an active space including a part of the elec- tronic structure associated with a molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the elec- tronic structure associated with a molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) a solution determination unit for causing a quantum computer and/or a classical computer to generate and provide a solution of the first part of the electronic structure representation, and for causing a quantum computer and/or a classical computer to generate and provide and provide and provide and provide and provide a solution of the
  • the apparatus can be realized in form of software or hardware or a combination thereof, wherein the hardware can refer to any known dedicated or general classical com- puter hardware.
  • the apparatus can be realized as any known computational device, like a PC.
  • the apparatus can also be realized as a cloud environment, computational network, etc., such that at least parts of the apparatus can also be realized as a network solution and thus can be spread over a plurality of computational devices.
  • the chemical product can be any chemical product that includes, for example, consists of, one or more molecular structures. Molecular structures are structures that form at least a part of a molecule.
  • the molecular structure in a polymer consisting of a plurality of monomers, can be one of these monomers, but can also refer to a plurality of these monomers or even the complete polymer. Moreover, the molecular structure can also be one or more atoms in a molecule forming the chemical product. Generally, the molecular structure comprises an electronic structure that can be described by an electronic structure representation.
  • the apparatus being for generating a property is to be interpreted as being suitable for generating a property, in particular, in assisting in generating a property.
  • the generating of the property associated with the chemical product refers to determining or deriving and providing the respective property.
  • the property can generally be any property of a chemical BASF SE 221032 221032WO01 product that is related to a solution of an electronic structure representation, for instance, refers to or can be derived from a solution of the electronic structure representation, of a molecular structure forming the chemical product.
  • the property can be an electronic prop- erty of the electronic structure representation.
  • the property can preferably refer to any property of a chemical product that allows to assess a technical applicability of the respec- tive chemical product as provided after its production.
  • the technical application property comprises any of a chemical reactivity, spectra and spectroscopic property, mo- lecular property, activation and reaction energies for a predetermined chemical reaction.
  • the technical application property comprises at least one of mechanical proper- ties, spectroscopic properties, physicochemical properties, chemical properties and biolog- ical properties.
  • mechanical properties can refer to any of adhesion, tensile strength, stiffness, hardness, shrinkage, elongation, split tear, tear-strength, rebound, com- pressibility, abrasion, spillage, morphology, haptic properties, stress at break, elongation at break, granulometry and a degree of filling.
  • a spectroscopic property can generally com- prise any of coloration, turbidity, opaqueness, lucidity, reflection, appearance, absorption, scattering, color strength, colour hue, colour saturation, colour intensity, cloud point, mat- ting degree, optical density, spectra, refractive index, IR spectra, Raman spectra, NMR spectra, ESR spectra, and UV/Vis spectra.
  • a physicochemical property can refer to any of density, viscosity, K-value, molar weight, dispersity, molar mass distribution, par- ticle size distribution, solubility, partition coefficients, interfacial properties, surface tension, dispersibility, storage stability, odor, segregation, coagulation, electric conductivity, electric capacity, surface area, flow time, vapor pressure, VOC, solid content, hygroscopicity, mag- netism, miscibility, thixotropy, phase transition properties, glass transition temperature, cor- rosion inhibition, solvent separation, aggregation, self-heating ability, impact sensitivity, loss on drying, angle of response, electrostatic charge, minimum film-forming temperature, charge density, electrostatic multipole moments, and thermal conductivity.
  • the chemical property can comprise any of reaction thermodynamics, reaction kinetics, chemical re- sistance, reaction timing, demolding time, growing, hard/soft segment content, crystallinity, reaction temperature, reaction pressure, decomposition, thermal decomposition, photodeg- radation, acidity, pKa, pH, moisture/water content, flammability, burning rate, self-ignition, flash point, formation of flammable gases, reaction to fire, deflagration rate, residual mon- omer count, side product formation, degree of polymerization, salt content, temperature tolerance, oxidizing properties, reduction properties, reactivity, ash content, nonvolatile matter content, stability, chelating ability, calorific value, saponification value.
  • the biological property can comprise any of biodegradability, biological resistance, in particular, resistance against a pathogenic virus, bacterium, fungus, plant or animal or developmental stage of said pathogen, tolerance against environmental parameters, e.g. drought toler- BASF SE 221032 221032WO01 ance, resistance against enzymatic degradation, e.g.
  • the electronic structure representation providing unit is adapted to provide an electronic structure representation associated with at least one of the one or more molecular struc- tures of the chemical product.
  • the electronic structure representation providing unit can refer to a storage unit on which the electronic structure representation is already stored.
  • the electronic structure representation providing unit can also comprise an input unit with which, for instance, a user can indicate an electronic structure represen- tation to the electronic structure representation providing unit.
  • the electronic structure representation can be provided in any form that allows to determine the form of the electronic structure problem to be solved and the quantities defining the electronic structure problem and the form of interaction between these quantities.
  • the electronic structure representation refers to a mathematical description of an electronic structure problem to be solved, for example, to a mathematical description of the electronic structure problem utilizing an electronic structure Hamiltonian.
  • the electronic structure representation can also refer to any other unambiguous form of notation of a re- spective electronic structure problem.
  • the electronic structure representation is related to a molecular structure of the chemical product.
  • the molecular struc- ture of the chemical product to which the electronic structure representation is related to can define the electronic structure problem and the quantities of the electronic structure problem.
  • the electronic structure representation is associated with the technical application property.
  • the chemical product refers to a specific molecule for which a technical application property should be determined
  • the respective molecule and its struc- ture define the quantities and interactions of the quantum mechanical electronic structure problem indicated by the electronic structure representation.
  • the solution of the elec- tronic structure representation is indicative of the property.
  • providing a solution of the electronic structure representation refers to providing the respective property.
  • the property can be derived from the solution of the electronic structure problem.
  • the electronic structure representation comprises or is indicative of atomic positions, a basis set, charge, and spin multiplicity depending on the specific chemical product and/or quantum mechanical electronic structure problem.
  • an electronic structure representation can refer to problems that are associated with determining an electronic structure of an atom, molecule, crystal, or amorphous solid, etc.
  • electronic structure representations can be utilized for determining ener- getic ground states of atoms and/or molecules, etc. Based on solutions of the electronic structure representation, further properties of the atom, molecule, crystal, or amorphous solid can be derived.
  • the electronic structure representation can be mathemati- cally represented utilizing different classes of underlying electronic structure Hamiltonians.
  • Born-Oppenheimer Hamiltonians For example, Born-Oppenheimer Hamiltonians, non-Born-Oppenheimer Hamiltonians, Hamiltonians with additional one-electron potentials representing, e.g., electrostatic fields, two-component Hamiltonians including spin-orbit coupling, fully relativistic four-component Dirac-Hamiltonians, etc.
  • a plurality of properties of a respective chemical product can be derived.
  • Examples for such electronic structure repre- sentation that can advantageously be solved in this invention can refer to calculating a ground state energy of a molecule or general electronic system.
  • the electronic structure representation can also refer to calculating multipole moments of a chemical product. Such a calculation can be relevant for determining properties of the chemical product related to electrical and other technical application properties, e.g.
  • the determining of the value of the property based on the result of the solution of electronic structure representation is based on the respective property that should be determined and further based on the information that is provided by the solution of the electronic structure representation.
  • the electronic structure representation includes a first part of the problem and a second part of the problem. The first part of the electronic structure representation is indic- ative of an active space including a part of the electronic structure associated with the mo- lecular structure.
  • the second part of the electronic structure representation is indicative of BASF SE 221032 221032WO01 an inactive space including another part of the electronic structure representation associ- ated with the molecular structure.
  • the part of the electronic structure represen- tation associated with the molecular structure included in the second part is the remaining part of the electronic structure representation without the first part.
  • the active space and the inactive space of the electronic structure representation refer to subspaces of the Hilbert space of the electronic structure representation.
  • the basis of the Hilbert space of the electronic structure representation can be formed by electron orbitals and mathematically represented by antisymmetrized tensor products of the electron orbit- als and the inactive space and active space are defined by the electron orbitals to which they refer.
  • the active and the inactive space can also be defined in other mathe- matical representations, for instance, if the electronic structure representation is formulated in another space.
  • the first part and the second part are preferably defined based on the respective active or inactive space, i.e. are defined in the respective basis of the respective space, but can also comprise terms that are related to the orbitals representing the respec- tive other space, for example, terms that are related to electrons or electron orbitals that form the basis of the respective other space.
  • the first part and the second part of the electronic structure representation are determined based on the chemical product and the molecular structure to be described by the electronic structure representation.
  • the molecular structure of the chemical product defines the quantities and interrelations between the quantities of the electronic structure representation, it also de- fines how these quantities and interrelations are described with respect to the first part and the second part of the electronic structure representation.
  • the chemical product defines the electron orbitals in the electronic structure representation, and in par- ticular, which orbitals have the strongest correlations such that for an accurate solution of the electronic structure representation of this molecular structure of the chemical product these correlations should be accounted for more accurately, the chemical product deter- mines how the first part and the second part are defined.
  • the first part of the electronic structure representation is provided such that it allows to calculate parts of the electronic structure of the chemical product that are most relevant for a specific application with high accuracy using a quantum computer.
  • the first part is provided such that it is based on electron orbitals that are most relevant for a specific application, since these electron orbitals exhibit the strongest correlations in the molecular structure of the chemical product during a chemical reaction of the chemical product and/or change during the specific application, e.g. are involved in bond-breaking and/or -forming processes dur- ing a chemical reaction of the molecular structure of the chemical product.
  • the property associated with the chemical product depends on the active space and the inactive space.
  • the electronic structure repre- sentation comprises or is indicative of the number and identity of the electron orbitals in the active space, the number of electrons to be taken into account in the first part, and/or a coefficient matrix of initial electron orbitals.
  • the apparatus can further comprise or utilize a translation unit configured to translate the electronic structure representation into a representative operation description indicative of a sequence of operations to be applied to the quantum elements of the quan- tum computer.
  • the translation unit can be part of the apparatus, but can however also be omitted in the apparatus and can be part of the quantum computer, in particular, of a control unit of the quantum computer that automatically translates a provided electronic structure representation into a respective operation description.
  • the translation unit is con- figured to determine, in particular, a sequence of operations such that a quantum mechan- ical calculation of the first part and/or the second part can be performed on a quantum computer.
  • the translation unit can be configured to translate only the first part or only the second part, respectively, into a respective operation description depending on which part is to be computed on a quantum computer.
  • operations are performed by a quantum computer by manipulating the states of quantum elements of the quantum com- puter, wherein the quantum elements can refer to all elements of the quantum computer that are utilized for simulating the electronic structure representation, for instance, to quan- tum elements forming the qubits of a quantum computer but also to bosonic fields repre- senting bosonic modes during a calculation of the problem.
  • Methods for determining such operations for problems to be calculated on a quantum computer are generally known and can be utilized by the translation unit for determining the operation description for the first part or the second part, respectively, of the electronic structure representation.
  • QPE Quantum Phase Estimation
  • VHA Variational Hamiltonian Ansatz
  • VQE Variational Quantum Eigensolver
  • UCC Unitary Coupled Cluster
  • the FSIM network algorithm us- ing low-rank decomposition for the unitary evolution can be utilized for translating and pre- paring a calculation of a first part or second part, respectively, of the problem description on the quantum computer.
  • the solution determination unit can be adapted to cause a quantum computer to generate and provide a quantum computational solution of the first part of the electronic structure representation.
  • the solution determination unit is configured to cause a quantum computer to perform a quantum mechanical calculation based on the first part such that the result of the quantum mechanical calculation is indicative of the solution of the first part and then to generate the solution based on the result of the quantum mechan- ical calculation.
  • the apparatus comprises an optional translation unit that already provides a translation of the first part of the electronic structure representation into a representative operation description
  • the solution determination unit can be adapted to provide the repre- sentative operation description to the quantum computer in order to cause the quantum computer to perform the quantum mechanical calculation based on the determined repre- sentative operation description.
  • the solution determination unit can be adapted to provide the first part or the sec- ond part provided or indicated by the electronic structure representation to the quantum computer, wherein then a part of the quantum computer system, for instance, a control unit of the quantum computer system, can be configured to provide the translation of the first part or the second part into a respective operation description that provides operations that can be performed on the quantum computer to calculate a solution of the first part or second part.
  • the solution determination unit can be communicatively coupled with the quantum computer or a control unit of the quantum computer in order to cause the quantum computer to perform the quantum mechanical calculation and obtain a result that is indica- tive of the solution of the first part or second part.
  • the communicative coupling can also be an indirect coupling, for instance, via a storage unit like a cloud storage unit on which respective control signals that cause the quantum computer to perform the quantum mechanical calculation are stored and then send to the quantum computer.
  • the solution determination unit can also cause a classical computer to gener- ate and provide a solution of the first part of the electronic structure representation.
  • De- pending on the respective electronic structure representation utilizing a classical computer BASF SE 221032 221032WO01 for solving the first part of the electronic structure representation can be more effective and efficient. For example, for electronic structure representations with first parts that only rep- resent a small part of the electronic structure, for instance, only below a predetermined number of orbitals and electrons, it can be more resource efficient to utilize a classical computer.
  • the solution determination unit can be configured for causing a classical computer to generate and provide a solution to the second part of the electronic structure represen- tation.
  • the solution of the second part can be a representation of an electron configuration of the inactive space of the respective molecule.
  • the solution determination unit can be configured for causing a classical computer to generate and pro- vide a classical computational solution to the second part of the electronic structure repre- sentation.
  • the solution determination unit can be configured to prepare and control a classical computer using known methods for causing the classical computer for solving the respective second part.
  • the solution of the second part can be any kind of contribution of the second part to the solution of the electronic structure problem.
  • the solution can refer to any contribution of the inactive space that is taken into account for the interaction representation.
  • the solution determination unit can be configured to determine a solution of the second part based on respective known algo- rithms like Hartree-Fock or density functional theory (DFT).
  • DFT density functional theory
  • the solution of the second part is determined based on the solution of the first part.
  • an influence of the first part on the second part i.e. of the active space on the inactive space, can be taken into account.
  • a SCF solution is determined for the second part.
  • the solution of the second part hence is a better approx- imation to the overall solution and the interaction representation thus is based on an already quite accurate solution.
  • the electronic structure representa- tion is already provided such that the solution of the second part can be calculated on a classical computing device utilizing respective known calculation methods.
  • the solution determination unit can be configured for causing a quantum com- puter to generate and provide a quantum computational solution to the second part.
  • the same methods described above with respect to computing the first part on a quantum com- puter can also be applied to computing the second part on a quantum computer.
  • the solu- tion determination unit can for example be configured to cause a quantum computer to generate and provide a solution for at least one of the first part and the second part of the electronic structure representation.
  • the solution determination unit is BASF SE 221032 221032WO01 configured for causing a quantum computer to generate and provide a solution of at least one of the first and the second part.
  • the correlation computation unit is configured to generate a solution to the electronic struc- ture representation by combining the solution of the first part and the solution of the second part.
  • the computational solution of the first part and the computational solution of the second part are computationally combined to generate the property associated with the chemical product.
  • the correlation computation unit can be configured to utilize the measurement results provided by the quantum computer to determine the respective solu- tion.
  • a respective control unit of the quantum computer can be configured to utilize the measurement results to determine the respective solution.
  • the computationally combining includes generating an interaction representation associ- ated with the combination of active and inactive space.
  • the interaction representation is based on a reference state associated with a superposition of electron configurations and is generated based on the solution of the first part and the solution of the second part.
  • the reference state refers to a representation of the superposition of electron configurations that are utilized as basis for the determination of correlations between the active space and the electronic structure of the inactive space and optionally also within one or both of these spaces.
  • the reference state based on the solution of the first part and the solution of the second part represents the electron configurations in such a way that it can form a basis for the further calculations of the solution of the interaction representation.
  • solutions of the first part and solutions of the second part that are generated on a quantum computer refer to direct measurements of the electronic configuration states that are then directly constructed on the respective classical and/or quantum computer that is utilized for solving the interaction representation.
  • a solution for a first part and/or a second part prepared on a quantum computer is not measured by measuring, for instance, characterizing quantities of the respective state, for instance, an energy, a reduced density matrix or any other observable, but refers directly to the states measured for the quantum elements that represent the respective states of the electrons in the electronic structure.
  • the reference state therefore can be regarded as a mathemati- cal representation of the electron configuration of the molecular structure of the chemical product after solving the first and the second part of the electronic structure representation.
  • the reference state can be generated as a superposition of the electron configurations being part of the solution of the first and the second part, wherein each electron configura- tion is associated with a weight for weighting the contribution of the electron configuration BASF SE 221032 221032WO01 to the overall solution of the electronic structure problem. Determining the weights refers to determining the overall solution. For example, if the reference state is represented utilizing configuration interaction basis states the weights refer to configuration interaction coeffi- cients associated with respective configuration interaction basis states.
  • the utilized elec- tron configurations can comprise a part that represents the active space and a part that represents the inactive space.
  • an electron configuration can comprise elec- tron orbitals that are part of the first part, i.e.
  • the re- spective parts of the electron configurations utilized with the superposition in the reference state can be treated differently.
  • the parts of the electron configurations rep- resenting the active space can be more numerous than the parts of the electron configura- tions representing the inactive space.
  • the parts of the electron configurations representing the inactive space can be identical, whereas parts of the electron configura- tions representing the active space can be different.
  • the reference state can refer to a superposition of electron configurations wherein the different active parts of the electron configurations are combined, for instance linear combined, and the inactive parts are the same.
  • the interaction representation can then, during the respective computation, also allow for the generation of different inactive parts resulting from the correlation between the active parts and the inactive part.
  • the interaction repre- sentation generated based on the reference state then generally represents the correlation between the parts of the electronic structure representation represented by the first part and represented by the second part and further represents correlations within one or both parts, in particular, within the second part.
  • the interaction representation can include cor- relations between electron orbitals among which at least one electron orbital is a member of the inactive space.
  • the correlation computation unit is configured for causing a classical computer and/or quantum computer to provide a solution to the interaction representation.
  • the utilized classical and/or quantum computer can be the same or different from the clas- sical and/or quantum computer utilized by the solution determination unit.
  • the interaction representation includes correlations a) within the inactive space, and/or b) between the active space and the inactive space. Correlations occurring within the active space are determined when determining the solution of the first part.
  • BASF SE 221032 221032WO01 correlations between spaces are defined as correlations between quantities defined in these spaces.
  • the quantities refer to the quantities as defined in the first part of the electronic structure representation and the second part of the electronic structure repre- sentation.
  • the above preferred embodiment can therefore also be formulated as the inter- action representation including correlations a) within the second part of the electronic struc- ture representation, and/or b) between the first part and the second part of electronic struc- ture representation.
  • the solution of the electronic structure representation is indicative of the property of the chemical product.
  • the property can be a property that can be derived from a solution of the electronic structure representation for a chemical product.
  • the method can thus further comprise generating and providing the property of the chemical product based on the elec- tronic structure representation.
  • the generated property can be property of the electronic configuration of the chemical product, e.g.
  • the property can be an electronic property of the electronic structure of the chemical product.
  • the property can be a ground state and/or excitation state energy of the chemical product. Based on the respective property further properties can be derived. For example, based on a determined ground state energy of all molecular species occurring in a chemical reaction, as technical application property a reaction rate, the thermodynamic properties of the reaction, and the kinetic properties of the reaction can be generated. This understanding and the properties of the reaction can then again be utilized to optimize chemical production processes, for determination of a microstructure of polymers, for optimizing material properties, etc. Fur- ther, the property can also refer to multipole moments of a chemical product.
  • Such a cal- culation can be relevant for determining technical application properties of the chemical product related to electrical and other technical application properties, e.g. the dielectric behavior of the chemical product, but also properties resulting from intermolecular interac- tions which are strongly dependent on the polar nature of the chemical product – such technical application properties can range from solubility and compatibility with certain me- dia to complexation behavior of ions or impacts on spectroscopic properties, e.g. color.
  • the method comprises providing the property for monitoring and/or controlling a technical application including the chemical product, preferably, a chemical reaction in- cluding the chemical product and/or a synthesis of the chemical product.
  • the providing of the property is thus configured to be directly utilizable in the respective controlling and/or monitoring of the application.
  • the providing can comprise implementing the property into a respective control/monitoring system of the application.
  • the providing can comprise providing the property in a respective data format together with information on how to utilize the property in a controlling and/or monitoring of the application.
  • the method BASF SE 221032 221032WO01 can comprise providing control signals based on the property for monitoring and/or control- ling a technical application including the chemical product.
  • the technical application can be any application in a technical context that includes the chemical product.
  • the technical application can be a chemical reaction including the chemical product, for example, a cat- alyst.
  • the technical application can be a synthesis process for synthesizing the chemical product.
  • the technical application can be a product design screening process including a screening process for determining one or more properties of the chemical product.
  • the electronic structure representation is further associated with prede- fined electron orbitals, wherein the first part and the second part of the electronic structure representation are defined by the electron orbitals being part of the active space and the electron orbitals being part of the inactive space, respectively.
  • the molecular structure is defined by the respective electron orbitals of the molecule such that the elec- tronic structure representation of the molecular structure includes these electron orbitals.
  • the electron orbitals being part of the active space and the electron orbitals being part of the inactive space form the basis for the respective space.
  • the electron orbitals can refer to atomic or- bitals or electron orbitals, depending on the respective application, for example, depending on the molecular structure of the chemical product for which an electronic structure repre- sentation should be solved.
  • an electron orbital generally refers to a mathematical function that is indicative of the probability of finding an electron in a specific region in the atom or molecule.
  • the electron orbitals are adaptable with respect to a quantity of the first and/or second part of the electronic structure representation
  • the apparatus further comprises an iteration controlling unit adapted to control an iteration for minimizing or maximizing the quantity of the electronic structure representation with respect to the electron orbitals, wherein the iteration comprises providing starting electron orbitals and generating a solution for the first part and/or second part, respectively,, amending the start- ing electron orbitals based on the generated solution and generating a further solution for the amended electron orbitals and repeating the electron orbital amendment and solution generation until the quantity of the first and/or second part, respectively, of the electronic structure representation is maximized or minimized with respect to a given criterion.
  • This solution of the first and/or second part can then be utilized for generating the interaction representation, in particular, the reference state.
  • the solution of the first part can be generated iteratively as described above and then be utilized for generating the BASF SE 221032 221032WO01 reference state.
  • the quantity can refer to any quantity that is influenced by the electron orbitals, i.e. by the local probability density of the respective electrons in the atom, mole- cule, crystal, or amorphous solid related to the chemical product.
  • more than one quantity of the first and/or second part of the electronic structure representation can be optimized during the above iteration, for example, utilizing known methods and algorithms for multi-objective optimization, for example, Pareto optimization techniques, etc.
  • the quantity of the first and/or second part of the electronic structure representation can generally also refer to a quantity representing the solution of the first and/or second part, respectively, of the electronic structure representation.
  • the quantity to be optimized refers to an energy of the electronic structure defined by the first and/or second part, respectively, of the electronic structure representation, wherein it is in particular preferred to find the minimum energy for the electronic structure of the atom, molecule, crystal, or amorphous solid related to the chemical product.
  • the calculating of the solution of the first and/or second part of the electronic structure representation during the iteration comprises the calculation steps as described above with respect to the solution of the first and/or second part of an electronic structure representation.
  • the calculation of a solution of the first and/or second part of the electronic structure representation during the iteration comprises steps of providing a first and/or a second part of the electronic structure representation comprising or indicative of the respective electron orbitals of the current iteration step, causing a quantum computer and/or classical computer to perform a quantum mechanical and/ or classical calculation as already described above and calculating a solution of the first and/or second part of the electronic structure representation as already described above.
  • the starting electron orbit- als for the first iteration step are generally predetermined, for example, based on user ex- perience, already known approximate solutions of the electronic structure representation, for example, calculated utilizing a Hartree-Fock calculation, or based on theoretical consid- erations, for example, based on respective physical assumptions or approximate solutions of similar electronic structure representations.
  • the electron orbitals can be adapted based on predetermined rules, for example, based on respective physical relations or insights that can be formulated and implemented as re- spective rules, or can even be amended arbitrarily by amending one or more parameters influencing the respective electron orbital.
  • the optimization is per- formed with respect to a given criterion, wherein the given criterion can depend on the BASF SE 221032 221032WO01 respective quantity to be optimized and also on the respective property or application for which an electronic structure representation should be solved.
  • the criterion can refer to a minimizing of the energy and can be based, for example, on determining that the minimum of the energy is reached if a deviation between the energy determined between subsequent iteration steps lies below a predetermined threshold.
  • the criterion refers to a converging of the iteration to a mini- mum energy.
  • the criterion can also comprise an abortion criterion that indi- cates that the iteration is to be aborted if the abortion criterion is fulfilled.
  • the abortion criterion can refer to a predetermined number of iteration steps, wherein, if this predetermined number of iteration steps is exceeded, it can be assumed that no valid so- lution for the electronic structure problem will be found during the iteration and the iteration is to be aborted.
  • the quantity refers to an energy of the electronic structure defined by the first and/or second part, respectively, of the electronic structure representation, wherein the iteration refers to a minimization of the energy of the electronic structure for solving the electronic structure representation.
  • the electronic struc- ture i.e.
  • the electronic structure representation providing unit is adapted to de- termine a partitioning of the electronic structure representation into the first and second part of the electronic structure representation based on the electronic structure of the chem- ical product.
  • the electronic structure representation providing unit is adapted to determine a partitioning of the electronic structure representation into the first part of the problem and the second part of the problem before providing the electronic structure rep- resentation.
  • the determination can be performed completely or partly auto- mated.
  • predetermined rules can be automatically applied to the electronic structure representation to determine the first and second part of the electronic structure representation.
  • the determination can also comprise a user-machine interaction process.
  • the electronic structure representation providing unit can utilize first predetermined rules to determine a first part and/or second part, and can then present the BASF SE 221032 221032WO01 determined first part and/or second part to a user.
  • the electronic structure representation providing unit can be adapted to determine the partitioning not only based on the electronic structure representation itself but also based on further information, for instance, provided by a user.
  • the electronic structure representation of the chemical product provides infor- mation on the electronic structure of the respective chemical product.
  • active space selection procedures utilizing electron orbital entanglement infor- mation and single-orbital entropies that are calculated with, for example, a density matrix renormalization group (DMRG) method or other correlated methods, including exact and approximate full configuration interaction schemes can be utilized to determine a partition- ing of the problem into the first and second part of the problem.
  • DMRG density matrix renormalization group
  • AVAS atomic valence active space
  • the electronic structure represen- tation provides information on the correlation between electron orbitals or at least about assumed correlations between electron orbitals that can then be utilized to determine the partitioning of the electronic structure representation into the first and second part.
  • the partitioning of the electronic structure representation is determined based on chemical product information indicative of a correlation between electrons occu- pying different electron orbitals, in particular, information indicative of an electron orbital entanglement and entropies of the electron orbitals.
  • the elec- tronic structure representation providing unit is adapted to determine a partitioning of the problem into the first and second part of the electronic structure representation based on the number of quantum elements of the quantum computer.
  • the quantum elements can refer, in the context of this invention, to the physical quantum elements realized and ma- nipulated in the physical realization of the quantum computer but can also refer to the log- ical qubits that refer to the logical representations of one or more physical quantum ele- ments.
  • a logical qubit can comprise more than one physical quantum ele- ments, wherein some of the physical quantum elements of the logical qubit are used for example for error correction.
  • the partitioning of the problem is determined based on the number of utilizable quantum elements.
  • the number of utilizable quantum elements takes into account that depending on the respective quantum algorithm utilized for perform- ing the quantum mechanical calculation, at least some of the physical quantum elements but also the logical qubits have to be utilized for other purposes, for example, for error BASF SE 221032 221032WO01 correction, representation of bosonic fields, etc. In some cases some of the quantum ele- ments are idle in the quantum mechanical calculation, since an increase in the used num- ber of quantum elements would lead to an inacceptable error rate for a specific algorithm, etc.
  • the partitioning of the electronic structure representation can preferably also take into account information on physical characteristics of the quantum computer hardware, for example, on the type of quantum computer utilized, the general error rate of the respective quantum computer, the error rate of the quantum operations, the quality of the quantum elements of the quantum computer, or the general topology of the quantum computer.
  • the number of quantum elements of the quantum computer in par- ticular, the number of utilizable quantum elements that should be utilized for the quantum mechanical calculation of the first part and/or second part, determines the maximum num- ber of variables that during the partitioning are considered as being part of the first part and/or second part, respectively, of the electronic structure representation.
  • the number of quantum elements in particular, of utilizable quantum elements, preferably determines the maximum number of electron or- bitals considered, for example, as part of the first part of the active space. This allows to provide a partitioning of the electronic structure representation that optimally utilizes the advantages of the quantum computers available for the calculation but at the same time also mitigates the downsides of current and near-term quantum computer calculations, for example, high error rates, or respectively limited number of qubits that might necessitate a separation of the electronic structure representation into respectively feasible sub-prob- lems.
  • the reference state is represented with configuration interaction basis states and coefficients associated with the configuration interaction basis states, wherein the configuration interaction basis states are given by a fixed distribution of electrons among electron orbitals.
  • the configuration interaction basis states and configuration inter- action coefficients can be utilized to generate a superposition of the electron configurations mathematically representing the solution of the first part and the solution of the second part.
  • the reference state can be represented by a wavefunction described by a linear combination of Slater determinants representing the configuration interaction basis states, wherein the weights of the Slater determinants represent the configuration interac- tion coefficients.
  • the configuration interaction basis states can be constructed from a set of orthogonal spin orbitals.
  • the first part of the problem can be solved, for instance, using a respective configuration interaction method that directly pro- vides as solution the wavefunction in the basis of the configuration interaction basis states and the respective coefficients.
  • the second part can then be integrated into this configura- tion interaction solution of the first part to provide a respective reference state.
  • BASF SE 221032 221032WO01 determining the reference state based on the solution of the first part and second part comprises controlling a quantum computer to generate a representation of the solution of the first part on the quantum computer, wherein the reference state is determined based on the representation of the solution of the first part on the quantum computer.
  • the state on the quantum computer generated to solve the first part can be regarded as equivalent to the state of the active space of the reference state of the respective described molecule.
  • the quantum computer solution directly provides a representation of the active space part of the reference state on the quantum computer.
  • the controlling can comprise, for instance, utilizing the phase estimation algo- rithm or noisy intermediate-scale quantum (NISQ) algorithms like the variational quantum eigensolver (VQE) to generate the solution of the first part that can be utilized to prepare a representation of an active space of the reference state.
  • the determining of the reference state comprises determining an overlap between the prepared solution of the first part on the quantum computer and the respective configuration interaction basis states to determine the coefficients.
  • the overlap between the prepared solution of the first part on the quantum computer and the respective config- uration interaction basis states can refer to a projection of the prepared solution of the first part on the respective configuration interaction basis states.
  • respective projection operations can be utilized.
  • the absolute value of the configuration interaction coefficients can be determined, for instance, in form of squared absolute values.
  • the phase for example, determining the sign of the coefficient, can also be determined. This allows to reconstruct the representation of the respective reference state on any suitable computer hardware that should be utilized for solving the interaction repre- sentation.
  • determining the overlap comprises measuring the representation of the solution of the first part on the quantum computer corresponding to the distribution of the electrons among the electron orbitals in the active space, determining respective coefficients asso- ciated with the configuration interaction basis states from this measurement and repeating the process until a predetermined condition is met to generate a histogram of the coeffi- cients of the measured configuration interaction basis states and determining the reference state based on the histogram.
  • the process can be repeated until the gener- ated histogram converges with a predetermined accuracy for the respective coefficients of the histogram.
  • a predetermined fixed number of repetitions can be utilized for restricting the utilized computational resources.
  • the reference state representation on the quantum computer refers to a quantum state, it is based on a superposition of a plurality of possible quantum states referring to the configuration interaction basis states.
  • the superposition can be determined by utilizing the histogram that reflects the contribu- tions mathematically represented as the weights of the different quantum states contrib- uting to the superposition, if enough repetitions are performed.
  • the weights are mathemat- ically the square of the absolute value of the configuration interaction coefficients and can be determined based on the histogram.
  • the absolute values of the configuration interaction coefficients can then be determined based on the determined squared absolute values.
  • the reference state is determined based on the representation of the solution of the first part on the quantum computer by applying a projection operator to the representa- tion of the solution of the first part projecting the representation of the solution of the first part on a respective configuration interaction basis state representation and measuring the resulting states on the quantum computer based on the histogram.
  • the measurements of the resulting states refers to measuring as observable the projector on the respective state which refers to measuring the squared absolute value of the configuration interaction coef- ficients.
  • the histogram is determined as described above and based on the histogram it is determined which configuration interaction basis states are determined the most, i.e. above a predetermined threshold or cut-off.
  • the reference state can mathematically be represented by equation wherein are the configuration interaction basis states and are the configuration interaction coefficients, wherein the index ⁇ runs over all possible electron distributions among the electron orbitals in the active space.
  • the correlation computation unit is configured to cause a quantum computer to prepare a representation of the reference state on the quantum computer and to entangle quantum elements representing the correlations between the active space and the inactive space to provide a solution to the interaction representation.
  • the correlations within the active and/or inactive space and/or between the active and the inactive space are de- termined by entangling quantum elements on a quantum computer representing respective correlated electron orbitals.
  • the entangled quantum elements can be part of the same quantum computer or of different quantum computers, for instance, if the solution of the first part and the solution of the second part are prepared as reference state on different quantum computers.
  • a solution to the interaction representation is pro- vided by preparing the representation of a solution of the first part on a first quantum com- puter and preparing a representation of a solution of the second part on a second quantum computer and performing a quantum computation of the interaction representation in which the quantum elements of the first quantum computer and the quantum elements of the second quantum computer are entangled for representing the correlations between the active space and the inactive space.
  • a unitary correlation ansatz is combined with a variational quantum eigensolver for providing the solution to the interaction representation.
  • the variational quantum eigen- solver varies parameters of the specific utilized ansatz for minimizing an energy of a state resulting from applying an operator representing the utilized anthesis to the respective refer- ence state, wherein a solution of the interaction representation refers to a respective state with a minimal energy.
  • the interaction representation includes correlations between electron orbitals among which at least one electron orbital is a member of the inactive space by projecting the reference state on one or more predetermined configuration interaction basis states and generating the solution based on the result of the projection.
  • the solution of the first part and the second part refer to a superposition of electron configura- tions.
  • the correlation can be approximated by taking one or more of the configurations, i.e. only one or more predetermined states into account, and determining the correlations based on respective configurations.
  • a tailored coupled cluster method is utilized for generating a solution of the interaction representation.
  • a tailored coupled cluster method can be utilized for including the dynamic correlation of the inactive space and/or between the active space and the inactive space into the interaction representation. This method has the advantage that it can be performed on a classical computer and still provides reasonably accurate results.
  • a stochastic strongly contracted second-order n-electron valence state perturbation theory method is utilized for including correlations between electron orbitals among which at least one electron orbital is a member of the inactive space into the inter- action representation.
  • the solution determination unit and correlation computation unit are con- figured to cause a quantum computing system to compute the solution of the first part, the second part and/or the interaction representation, wherein the quantum computing system comprises at least two quantum computers with different fidelities, wherein the solution BASF SE 221032 221032WO01 determination unit and correlation computation unit are configured to distribute the compu- ting of the solution of the first part, the second part and/or the interaction representation to the at least two quantum computers based on the fidelity of the respective at least two quantum computers.
  • the fidelity of a quantum computer is a measure defining the quality with which the quan- tum computer performs a respective quantum computation, for instance, the operations, e.g. quantum gates, of an algorithm performed during a quantum computation.
  • the fidelity of a quantum computer can be based on quantum gate fidelities and/or decoherence times.
  • a quantum gate is a basic quantum operation usually generated through one or more con- trol pulses applied to a respective small number of qubits, wherein a plurality of quantum gates build a quantum circuit and thus can be regarded as an analogue to classical logical gates that build conventional digital circuits. Any multi-qubit operation can be generated from a sequence of one- and two-qubit operations.
  • a fidelity measures the quality with which a quantum gate realised on the quantum computer hardware resembles the theoretical quantum gate it is supposed to implement in the quantum computer.
  • the quantum gate fidelity measures the difference between the real operation performed by the real hardware and the perfect theoretical operation.
  • a decoherence time describes how long quantum information can be stored on the quantum computer before it is lost to the environment.
  • the decoherence times also have an influence on the quantum gate fidelities that are determined, for instance, by all small imperfections in the build, calibration and control of the quantum computer and also based on the specific decoherence time of the quantum computer.
  • the fidelity of a quantum computer can be determined utilizing known methods and measurements, for example, cross-entropy benchmarking, randomized benchmarking or full state tomography.
  • fidelity deter- mination methods More details on possible fidelity deter- mination methods can be found, for instance, in “Quantum supremacy using a programma- ble superconducting processor.”, Arute, F., Arya, K., Babbush, R. et al., Nature 574, 505– 510 (2019). In most cases the fidelity will be provided as general information by a provider of the quantum computer. For example, for causing a quantum computer to compute the solution of the first part, the second part and/or the interaction representation respective control signals can be gener- ated and provided to the quantum computing system.
  • control signals can be generated such that the fidelity determines on which of the at least two quantum com- puters the solution of the first part, the second part and/or the interaction representation is computed.
  • control signals are generated based on the fidelities of the respective at least two quantum computers.
  • the solution determination apparatus can be configured to cause a computation of the solution of the first part on a quantum computer BASF SE 221032 221032WO01 with a high fidelity, for instance, a fidelity above a predetermined threshold
  • the corre- lation computation unit can be configured cause a computation of the solution of the inter- action representation on a quantum computer with a lower fidelity, for example, a fidelity lower than the fidelity of the quantum computer used for computing the interaction repre- sentation.
  • the control signals can be generated such that the solution of the first part, the second part and/or the interaction representation are computed on a quantum computer with a respective fidelity most suitable from the available fidelities.
  • control signals can be configured, for example, for controlling a manipulation part of a quantum computer configured to manipulate the states of the quantum elements, in accordance with a corre- sponding sequence of manipulations.
  • the control signals can be adapted for controlling the controlling unit of the quantum computer.
  • the control signals can simply refer to a representation of a sequence of manipulations that can be interpreted by the controlling unit of the quantum computer to provide the respective control signals for controlling the parts of the quantum computer accordingly.
  • control signals can, in this case, also refer to generally known and interpretable control signals that are translated by the controlling unit of the quantum computer to respective dedicated control signals for controlling the specific hardware of the quantum computer.
  • at least two of the quantum computers are configured to be entangled and the control signals can be generated for further controlling the entanglement between the at least two quantum computers of the quantum computers of the quantum computing system during a parallel quantum computation of the solution of the first part, the second part and the interaction representation, wherein the entanglement of two quantum comput- ers is defined by at least one quantum element of each of the quantum computers being entangled.
  • An entanglement between two quantum computers can be realised, for in- stance, by configuring the quantum computers such that at least one quantum element of one quantum computer can interact with at least one quantum element of another quantum computer.
  • a photonic link or respective entanglement bus or another qubit can be utilized.
  • the details of the realisation strongly depend on the nature of the respective quantum computers, for instance, superconducting quantum computers, trapped-ion quantum computers, photonic quantum computers, etc.
  • the quantum states of the entangled quantum elements depend on each other such that the quantum elements can only be described together as if they were one object.
  • This state dependency of the entangled quantum elements leads to the distribution and sharing of information between the at least two quantum computers during the quantum computation during which the BASF SE 221032 221032WO01 states of the quantum elements utilised in the quantum computation are changed, for in- stance, due to respective quantum operations performed during the quantum computation.
  • an operation performed on one of the entangled quantum elements also has an effect on the state of the other of the entangled quantum elements influencing the calculation of the other quantum computer.
  • basis operations, intermediate results, and final results of a quantum computation performed on the first quantum computer can directly, i.e. without being read out and processed by a classical computer and then prepared on the other quantum computer, influence the quantum computation on the other quantum computer.
  • the entanglement allows to transfer a solution of the first part and/or the second part directly, e.g. without utilizing a classical computer in between, to another quantum computer to gen- erate the reference state as starting point for the calculation of the solution of the interaction representation.
  • different hardware solutions can be utilized depending on the respective type of quantum computer.
  • waveguides and transmission lines can be utilized, as de- scribed, for example, in the article “Quantum computer with superconducting circuits in the ultrastrong coupling regime”, Stassi, R., Cirio, M.
  • the solution of the first part, the second part and/or the interaction rep- resentation can be generated based on the fidelities of the quantum computing system. For example, if a higher fidelity quantum computer is available the first part can be derived to encompass more electron orbitals that can be calculated on the higher fidelity quantum computer.
  • a higher fidelity can be regarded as being higher with respect to a) the fidelity of at least one other quantum computer of the at least two quantum computers, b) the fidelity of all other quantum computers of the at least two quantum computers and/or c) a prede- termined fidelity threshold.
  • a lower fidelity can be regarded as being lower with respect to BASF SE 221032 221032WO01 a) the fidelity of at least one other quantum computer of the at least two quantum comput- ers, b) the fidelity of all other quantum computers of the at least two quantum computers and/or c) a predetermined fidelity threshold.
  • the first part required higher solution accuracy since it is more crucial to the solution of the problem.
  • control signals can be generated based on a computation algorithm to be utilized for solving the solution of the first part, the second part and/or the interaction representation, wherein the computation algorithm to be utilized determines a threshold for the fidelity of the quantum computer on which the computation algorithm can be performed.
  • computation algorithms to be performed generally on higher fidelity quantum computers since they are associated with a higher fidelity threshold, can refer to quantum Fourier transform, quantum phase estimation, Grover-type search algorithms, Shor-type factorization algorithms and Harrow-Hassidim-Lloyd-type algorithms.
  • relevant computation algorithms for lower fidelity quantum computers since they are associated with a lower fidelity threshold compared with the above algorithms, are variational algorithms, such as the variational quantum eigensolver and the quantum approximate optimization algorithm.
  • the distribution of the solution of the first part, the second part and/or the interaction represen- tation can also be based on the number of logical quantum elements provided by the re- spective at least two quantum computers.
  • Logical quantum elements are quantum ele- ments that can be operated during a quantum computation. For example, depending on the quantum algorithm utilised some quantum elements are utilised as ancillary quantum elements and thus cannot be utilised for representing quantities and aspects of a respective sub-problem.
  • the quantum computing system comprises at least one fault-tolerant quantum computer and one noisy intermediate-scale quantum computer, wherein the fault- tolerant quantum computer has a higher fidelity than the noisy intermediate-scale quantum computer.
  • noisy intermediate-scale quantum computers are generally sensitive to the en- vironment and prone to quantum decoherence such that they can only apply a finite number of gates or operations before too many errors have accumulated such that too much infor- mation is lost due to the noise and the computation becomes irrelevant. This limits the number of operations and thus also the size and complexity of sub-problems that can be computed on such a quantum computer.
  • Fault-tolerant quantum computers perform a quantum computation with a physical error rate below a predetermined threshold defined BASF SE 221032 221032WO01 by the quantum threshold theorem such that through the application of quantum error cor- rection the logical error rate can be suppressed to arbitrary low levels.
  • Fault-tolerant quantum com- puters can be realized by applying quantum error correction codes utilizing at least three physical quantum elements to represent one logical qubit.
  • An example is a surface code described in the article “Google Quantum AI. Suppressing quantum errors by scaling a surface code logical qubit.”, Nature 614, 676–681 (2023).
  • Other codes exist that exploit this principle. Many of these error correction codes are only applicable to quan- tum computers with a respective high number of qubits.
  • an apparatus for generating a property associated with a chemical product, wherein the chemical product includes one or more molecular structures, wherein the apparatus comprises i) an electronic structure rep- resentation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the electronic structure representation indicative of an active space including a part of the elec- tronic structure associated with a molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the elec- tronic structure associated with a molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) a solution determination unit for causing a quantum
  • an apparatus for generating a property associated with a chemical product, wherein the chemical product includes one or more molecular structures
  • the apparatus comprises i) an electronic structure rep- resentation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the electronic structure representation indicative of an active space including a part of the elec- tronic structure associated with a molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the elec- tronic structure associated with a molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) a solution determination unit for causing a quantum computer to generate and provide a solution of the first part of the electronic structure representation, and for causing a classical computer to generate and provide a solution to the second part of the electronic structure represen- tation, and
  • a system for generating a property asso- ciated with a chemical product, wherein the system comprises a) a quantum computer adapted to perform quantum mechanical calculations, and b) an apparatus as described above, wherein the apparatus is adapted to cause the quantum computer to perform a quantum mechanical calculation.
  • a computer-implemented method for gen- erating a property associated with a chemical product, wherein the chemical product in- cludes one or more molecular structures
  • the method comprises i) providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the electronic structure representation indicative of an active space including a part of the electronic structure associated with the molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the electronic structure associated with the molec- ular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) causing a quantum computer and/or a classical BASF SE 221032 221032WO01 computer to generate and provide a solution of the first part of the electronic structure rep- resentation, and for causing a quantum computer and/or a classical computer to generate and provide a solution to the second part of the electronic structure representation, and ii
  • a computer program product for generating a property associated with a chemical product comprises program code means for causing the apparatus as described above to execute the method as described above.
  • a use of an apparatus as described above for generating properties referring to at least one of a chemical reactivity, spectra and spectroscopic prop- erties, and molecular properties derivable from electronic structure problem calculations of a chemical product is presented.
  • a reaction energy refers to an energy difference between products and reactants.
  • the chemical reac- tion can be part of a complex reactive network, e.g. of a catalytic cycle.
  • Utilizing an appa- ratus as described above is in particular advantageous in cases where at least one chem- ical species of this reactive system a) contains one or more transition metal atoms, lantha- nide atoms and/or actinide atoms with unpaired electrons or b) exhibits an electronic struc- ture with a small energetic gap between occupied and unoccupied electron orbitals, i.e., an energetic gap that is equal or smaller than the gap of at least one of the molecules ozone, pentacene or para-quinodimethane calculated with the same electronic structure approach, i.e.
  • ⁇ diagnostic is determined based on the Frobenius norm of the am- plitudes for single excitations of a CCSD wave function based on a Hartree-Fock reference state scaled by the square root of the number of correlated electrons in the CCSD calcula- tion, and wherein the ⁇ ⁇ diagnostic is determined based on the matrix 2-norm of the ampli- tudes for single excitations of a CCSD or MP2 wave function based
  • an apparatus for determining a technical appli- cation property of a chemical product, wherein the apparatus comprises a) an input unit configured to receive an electronic structure representation associated with one or more molecular structures of the chemical product, b) an apparatus as described above, c) a property determination unit configured for generating the technical application property based on the solution of the interaction representation of the one or more molecular struc- tures.
  • a computer-implemented method for de- termining a technical application property of a chemical product, wherein the method com- prises a) receiving an electronic structure representation associated with one or more mo- lecular structures of the chemical product, b) utilizing an apparatus as described above to provide a solution of the interaction representation, c) generating the technical application property based on the solution of the interaction representation of the one or more molec- ular structures.
  • a computer program product is presented for determining a technical application property of a chemical product, wherein the computer program product com- prises program code means for causing the apparatus as described above to execute the method as described above.
  • an apparatus for determining a target chemical product comprising a target technical application property comprising a target technical application property
  • the apparatus com- prises a) a target property providing unit configured to provide a target technical application property and a potential chemical product, b) a property determination unit utilizing an ap- paratus as described above and/or a method as described above for determining a tech- nical application property of the potential chemical product, c) an iteration unit configured to compare the determined technical application property of the potential chemical product with the target technical application property and, based on the comparison, either i) deter- mining the potential chemical product as the target chemical product, or ii) providing a new potential chemical product and repeating the determination of the technical application property utilizing the new potential chemical product, and d) a control data generation unit configured to generate control data for producing the determined target chemical product.
  • a computer implemented method for determining a target chemical product comprising a target technical application property comprises a) providing a target technical application property and a potential chemical product, b) utilizing an apparatus as described above and/or a method as described above for determining a technical application property of the potential chem- ical product, c) comparing the determined technical application property of the potential chemical product with the target technical application property and, based on the compar- ison, either i) determining the potential chemical product as the target chemical product, or ii) providing a new potential chemical product and repeating the determination of the tech- nical application property utilizing the new potential chemical product, and d) generating control data for producing the determined target chemical product.
  • a computer program product for determining a target chem- ical product comprising a target technical application property
  • the computer pro- gram product comprises program code means for causing the apparatus as described above to execute the method as described above.
  • properties that can advantageously be generated in this invention can refer to calculating a ground state energy of a molecule or general electronic system. This allows, in particular, in the context of determining the ground state energy of all molecular species occurring in a chemical reaction to predict the reaction end products, the thermodynamic properties of the reaction, and the kinetic properties of the reaction.
  • the generated property can also refer to multipole moments of a chemical product.
  • Such a calculation can be relevant for determining properties of the chemical prod- uct related to electrical and other technical application properties, e.g. the dielectric behav- ior of the chemical product, but also properties resulting from intermolecular interactions which are strongly dependent on the polar nature of the chemical product – such technical application properties can range from solubility and compatibility with certain media to com- plexation behavior of ions or impacts on spectroscopic properties, e.g. color.
  • the providing of the target application property can refer to receiving the target application property from an input of a user applying, for instance, a respective input unit.
  • the providing can also refer to accessing a storage unit on which a target appli- cation property is already stored and providing the same.
  • the providing can also comprise receiving a target application property, for instance, via a network connection from other sources and providing the received target application property.
  • the target application property can refer to one target value, for instance, a specific hardness of a chemical product, or can refer to a value range that should be met by the chemical product.
  • the target application property can also refer to any kind of target func- tion, for instance, a timely sequence of a property under a changing environmental condi- tion, like a hardness under changing temperature conditions.
  • target application properties can be advantageous in cases in which the application of the chem- ical product comprises different environmental conditions, for example, different tempera- tures.
  • the target chemical product then refers to a chemical product that provides the re- spective target technical application property, i.e. meets the target technical application property within predetermined limits, when provided in a respective form, for example, as pure substance, or mixture.
  • the target chemical product provides the respec- tive target technical application property when produced according to a corresponding rec- ipe.
  • a potential chemical product can be provided in any digital representable format such that the potential chemical product and/or characteristics of the potential chemical product can be processed by the apparatus.
  • the providing of the potential chemical product BASF SE 221032 221032WO01 can also comprise providing a respective electronic structure representation for determin- ing the technical application property of the potential chemical product.
  • the re- spective electronic structure representation can also be selected automatically, for exam- ple, by the apparatus based on the potential chemical product and the provided target tech- nical application property.
  • a user can, for example, select a respective elec- tronic structure representation preferably based on a selection of a plurality of possible electronic structure representation presented to the user based on the potential chemical product and/or the target technical application property.
  • the comparison of the determined technical application property with the target technical application property allows to determine whether the determined technical application prop- erty fulfils a predetermined criterion, for example, that the determined technical application property meets the target technical application property within predetermined limits. If such a criterion is fulfilled, the potential target chemical product is determined as the target chem- ical product and the method proceeds to the next step. However, if the comparison indi- cates that the determined technical application property does not meet the target technical application property within the predetermined limits, a next iteration step utilizing a new potential chemical product can be performed.
  • a new potential chemical product is determined, preferably based on the previous potential chemical product, for instance, by amending one or more features of the previous chemical product, e.g. one or more constituents or other characteristics.
  • a new potential chemical product can also be generated by arbitrarily choosing a new potential chemical product, for example, from a large amount of previously generated potential chemical products.
  • more sophisticated methods can be utilized for selecting a new potential chemical product from a plurality of previously already generated potential chemical products.
  • the quantum computer is utilized for determining the technical application property and the such determined technical application property is again compared with the target technical application property such that the comparison can again lead to a further iteration step or if the respective criterion is fulfilled the respective new potential chemical product can be selected as the target chemical product.
  • an additional abortion cri- terion for the iteration can be selected, for instance, a number of iteration steps can be determined before the iteration is aborted with a notification to a user that no target chem- ical product could be found for the respective target technical application property.
  • the method can further comprise amending the target technical application property, for instance, by increasing the predetermined limits around the target technical application property and to repeat the iteration while utilizing the increased limits during the comparison.
  • amending the target technical application property for instance, by increasing the predetermined limits around the target technical application property and to repeat the iteration while utilizing the increased limits during the comparison.
  • the target chemical product can be provided, for instance, to a user via an output unit.
  • a recipe of the target chem- ical product is utilized to generate control data that can be utilized for controlling a produc- tion system for producing the target chemical product.
  • Fig.1 illustrates a state representation of a qubit as used in a quantum computing device
  • Fig.2 illustrates a schematic example of a quantum computing device with qubits as calculation unit
  • Fig.3 illustrates a schematic example method for generating a control signal to per- form operations on a quantum computing device and for processing measure- ment signals from the quantum computing device
  • Fig.4 illustrates a schematic example of a hybrid system including a classical and a quantum computing device
  • Fig.5 illustrates a schematic example of a quantum computing device based on su- perconductors
  • Fig.6 illustrates a schematic example of a quantum computing device based on trapped ions
  • Fig.7 shows schematically and exemplarily an embodiment of a system generating a property associated with a chemical product
  • Fig.8 shows schematically and exemplarily a flow chart of a method generating a property associated with a chemical product
  • Fig.9 shows schematically and exemplar
  • Representations of the machine-readable instructions may include binary or hexadecimal representations. Based on such machine-readable instructions, the operations are performed on the processor of a classical computing device.
  • Quantum computation is a relatively new computation method that uses quantum effects, such as superposition and entanglement, to perform certain computations more efficiently than classical digital computers.
  • quantum computing devices i.e. quantum computers
  • qubits i.e. quantum bits
  • Quantum computing devices are based on quantum elements adhering to the physics of quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, particle spins, bosons or the like. These quantum elements may be manipulated in a controlled manner to perform operations. Although qubits and their manipulation may be described in terms of their mathematical properties, each such qubit may be implemented in a physical quantum element in any of a variety of different ways.
  • quantum elements include superconducting materials, trapped ions, photons, optical cavities, individual electrons trapped within quan- tum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond), molecules (e.g., alanine, vanadium complexes), or any medium that exhibits qubit behavior comprising quantum states and transitions therebetween that can be controllably induced or detected.
  • point defects in solids e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond
  • molecules e.g., alanine, vanadium complexes
  • any medium that exhibits qubit behavior comprising quantum states and transitions therebetween that can be controllably induced or detected.
  • any of a variety of properties of that physical unit may be chosen to implement the qubit.
  • the x, y or z component of an electron spin degree of freedom can be chosen as the property of such electrons to represent the states of such qubits.
  • the physical quantum elements can be controllably put in a state of superposition or entanglement and measurements can then be taken in the chosen degree of freedom to obtain readouts of qubit values.
  • each quantum element of quantum computing devices can not only take the basis states ⁇ or ⁇ but also any superposition of such basis states, such as state ⁇ .
  • the state of each quantum element is represented by a state of a quantum bit, i.e. qubit, as illustrated in the two-dimensional simplification of Fig.1.
  • Dirac notation is commonly used in quantum mechanics.
  • a state in a n dimensional, complex vector space, such as a Hilbert space is represented in braket notation, for example ⁇ .
  • braket notation for example ⁇ .
  • the superposition of “0” and “1” states in a quantum computing device can be represented as ⁇ ⁇ ⁇ .
  • the states “0” and “1” or bits of the classical computing device are similar to the basis states ⁇ ⁇ ⁇ and ⁇ ⁇ ⁇ or quantum bits of the quantum computing device, respec- tively.
  • the value ⁇ ⁇ represents the probability that the qubit will be measured in the ⁇ state
  • the value ⁇ ⁇ ⁇ represents the probability that the qubit will be measured in the ⁇ state.
  • Entan- glement means that the state of one qubit is dependent on the state of at least one other qubit and vice versa, wherein further in the entangled state the respective qubits cannot be regarded as individual qubits anymore.
  • a register of ⁇ qubits in a quantum com- puter can be put into a superposition of basis states at once whereas a register of ⁇ clas- sical bits can only be in a single basis state at once.
  • the computational method to solve a given problem may be translated into qubit manipulations, which may be translated into control signals for manipulating qubits.
  • Representations of the machine-readable in- structions may include common quantum mechanical representations of operations in the Hilbert space.
  • different rep- resentations of the qubit states may be chosen. Any state preparation on the quantum computing device may be represented by a manipulation acting on the qubit states.
  • a ma- nipulation may be translated into control signals to control a respective part of the quantum computer, which depend on the type of quantum computing device used.
  • a one-qubit operation may change the state of one qubit e.g., into a specific superposition which corresponds to a rotation of the vector ⁇ as illustrated in Fig 1.
  • a multi-qubit operation may create entanglement between two or more qubits.
  • This projection usually happens in the ⁇ ⁇ eigenbasis of the qubits which is also used to define the computational basis stats “0” and “1” of the qubit.
  • this measurement is achieved by applying a hardware-specific readout protocol of a series of readout manipulations including control pulses and monitoring the response to control pulses.
  • a superconducting qubit may be coupled to a hardware resonator. The measured shift of the resonator frequency allows to determine the state of the qubit as this shift depends on the state of the coupled qubit.
  • an optical readout may be used, e.g.
  • the quantum compu- ting device 100 shown in Fig.2 includes a quantum register 104 configured to perform the quantum computation, a manipulation part 106 configured to manipulate the quantum reg- ister, in particular, quantum elements forming the qubits, and a readout part 108 configured to collect measurement signals from the quantum register 104 for reading out the qubits after a quantum mechanical calculation.
  • Such optical quantum computing devices may include lasers that generate photons that are provided to a waveguide.
  • a beam splitter can be provided for manipulating the photon states based on manipulation signals such as a mechanical rotation applied to a mirror.
  • the measurement part 108 can in such an embod- iment be a photon detector, and the measurement signals can be photons.
  • BASF SE 221032 221032WO01 In other embodiments of gate-based quantum computers the qubits can be implemented by electronic states of ions trapped in a magnetic field.
  • the manipulation part 106 can in such a case utilize a laser, and the manipulation signals can cause the providing of control laser pulses.
  • the readout part 108 can be a photon detector com- bined with read-out laser pulses, and the measurement signals 102 may be photons.
  • Other qubit implementations may be based on superconductors as quantum elements, semicon- ducting material with anyons as quantum elements, or the like.
  • Fig.3 illustrates a schematic exemplary method for generating a control signal to perform manipulations on the quantum computing device and for processing measurement signals from the quantum computing device.
  • the control signals for the quantum computing device are prepared on a classical computing device and the measurement signals provided by the quantum com- puting device are further processed on the classical computing device.
  • Other embodiments are, however, conceivable as quantum computing devices mature.
  • the quantum computer refers to a gate-based quantum computer for which the manip- ulations refer to operations on the quantum elements of the quantum computer.
  • the problem to be solved with the aid of the quantum computing device is provided in step S10, preferably, in a mathematical description.
  • Such problem may for instance include de- termining a material property based on the mathematical description of the material’s elec- tronic structure.
  • Other problems may include optimization problems and associated objec- tive functions.
  • an operation description of the problem or a sub-problem may be generated in step S12, wherein the operation description com- prises the operations to be applied to the qubits of the quantum computer to solve the problem in the quantum mechanical calculation.
  • the operation description can in- clude a reference state that allows to generate a representation of an initial qubit state on the quantum computer on which the further operations are then applied by manipulating the qubit states.
  • control signals can then be generated in step S14 to control the quantum computer, for instance, by providing the control signals to the manipulation unit that can then manipulate the qubit states based on the control signals.
  • step S16 the manipulation unit then applies the manipulation operations to indi- vidual or multiple qubits of the quantum computer, wherein based on the manipulation op- erations the qubits perform the quantum mechanical calculation.
  • measurement signals can be generated to determine the result of the quantum mechanical calculation in step S18.
  • This step can include a read-out, i.e. measurement, of the qubit BASF SE 221032 221032WO01 states after applying the manipulation operations to the initial qubit states.
  • the measure- ment signals can in step S20 then be translated into a measured quantity on the classical computer and in case of a sub-problem fed back into the problem to be solved.
  • the result of the problem calculation including the quantum mechanical calculation can be pro- vided on the classical computing device in step S22.
  • Fig.4 illustrates a schematic example of a hybrid system including a classical and a quan- tum computing device.
  • quan- tum computing devices are often used in connection with classical computing devices.
  • a problem preparation system e.g. control signal generation apparatus, can be realized as a classical computing device 110 performing, for instance, steps S10, S12, S20, S22 of the method illustrated in Fig.3.
  • a controlling unit can then be provided as interface between the classical computing device 110 and the quantum computer 100, wherein the controlling unit can also be a classical computing device, for instance, perform- ing step S14.
  • the control unit can then be communicatively coupled with the manipulation part 106 that can control the manipulators of the quantum computing device.
  • the ma- nipulation part 106 can be realized as a classical computing device, for instance, a classical controlling hardware for the control of specific hardware components of the quantum com- puter that perform the manipulation of the qubits.
  • the manipulation part 106 is generally regarded as part of the quantum computer, since it directly influences the quan- tum register.
  • the quantum computing device 100 is adapted to perform the quantum oper- ation S16, in particular, by the manipulation of the qubits of the quantum register.
  • the measurement part 108 that is also generally regarded as part of the quantum computing device can then perform the step S18 by utilizing classical hardware.
  • Fig.5 illustrates a schematic example of a quantum computing device based on supercon- ductors.
  • Superconducting quantum computing devices are one of the solid-state quantum computing technologies.
  • the quantum register 104 can include superconducting cir- cuits 520, 522, 524 based on Josephson junctions.
  • the qubits can then, for instance, refer to charge, flux, transmon, or phase qubits depending on the quantity of the superconduct- ing circuits that are chosen to represent the qubits.
  • Fig.5 refers to a simplified illustration of a superconducting quantum computer utilizing charge qubits.
  • the dif- ferent states of the qubit are represented by an integer number of Cooper pairs on a su- perconducting island.
  • quantum manipulations can then be performed by manipulating the qubits through microwave pulses.
  • Resonators BASF SE 221032 221032WO01 512, 514, 516 can be utilized to manipulate the state of the qubits by applying the micro- waves or for reading out the state of the qubits by measuring respective microwaves, wherein generally different resonators are used for the manipulation of the state of the qubits and the readout of the qubits.
  • resonator 518 can be utilized for applying microwaves that entangle the qubits.
  • the entanglement can also be achieved by an inductive or capacitive coupling of the superconducting circuits or even by providing another qubit, here a superconducting circuit, between the to be en- tangled qubits.
  • a superconducting circuit On an operational level such systems are maintained at extremely low temperatures, e.g., in the tens of mK. The extreme cooling of the systems keeps superconducting materials below their critical temperature and helps to avoid unwanted state transitions. To maintain such low temperatures, the quantum information processing systems may be operated within a cryostat, such as a dilution refrigerator.
  • control signals are generated in higher-temperature environments, and are transmitted to the quantum computer using shielded impedance-controlled GHz capable transmission lines, such as coaxial cables.
  • the state measurement of superconducting qubits is achieved using a dispersive detection scheme.
  • a probing signal e.g., a travelling microwave, may be excited along a readout transmission line coupled to the qubit via a respective readout resonator.
  • the fre- quency of the probing signal can be in the vicinity of the resonance frequency of the readout resonator.
  • the intensity or phase of the probing signal transmitted along the readout transmission line may be al- tered because the reflectivity of the readout resonator coupled to the qubit changes de- pending on the state of the qubit.
  • This allows for the state detection of the qubits, wherein during the readout of a qubit state the state of the qubit collapses, i.e. is projected with the respective probability onto one of the basis states.
  • Fig.6 illustrates a schematic example of a quantum computing device based on ions in an ion trap. Similar to neutral atom traps ion traps with, e.g. positively charged Calcium ions, can be used to implement the quantum computing device. Here ions 626 are trapped in an oscillating electromagnetic field 624 inside a high or ultra-high vacuum. The ions 626 are laser cooled and held in the oscillating electrical field 624. For qubit manipulation such as superposition or entanglement laser light 628 at different frequencies may be used.
  • BASF SE 221032 221032WO01 Generally, based on the above described quantum computer realizations gate-based type calculations can be performed on a quantum computer hardware architecture.
  • the gate- based type calculation is based on quantum gates.
  • quantum gates In contrast to classical gates, there is an infinite number of possible single-qubit quantum gates that can change the state vector of a qubit. Changing the state of a qubit state vector typically is referred to as a single qubit rotation, and may also be referred to herein as a state change or a single-qubit quantum gate operation.
  • a rotation, state change, or single-qubit quantum gate operation can be represented mathematically by a unitary 2 x 2 matrix with complex elements.
  • a rotation corresponds to a rotation of a qubit state within its Hilbert space, which can be conceptu- alized as a rotation of a vector on the Bloch sphere, wherein the Bloch sphere is generally known as a geometrical representation of the space of the pure states of a qubit.
  • Multi- qubit gates alter the quantum state of a set of qubits. For example, two-qubit gates rotate the state of two qubits as a rotation in the four-dimensional Hilbert space of the two qubits, wherein, as generally known, the Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete, i.e.
  • the term operation description refers to a representation of a problem that comprises a sequence of quantum operations that should be applied during a quantum mechanical calculation of the problem.
  • quantum operation can include in the context of this invention all types of quantum gates as described above and more generally all manipulations known for quantum elements on any quantum computer hardware. More- over, the term can also include operations performed on components of the quantum com- puter representing a coupling between the quantum elements forming the qubits and bosonic fields and, optionally, components representing the bosonic fields themselves.
  • quantum operations then refer to any kind of change of the state of the coupling or bosonic field representing components, for example, a turning of a coupling on and off, or the change of a field frequency, etc.
  • the quantum operations can also include measurement operations. This allows to implement algorithms using a meas- urement feedback.
  • a quantum computer can execute the quantum gates defined by the sequence of quantum operations and then measure only a subset, i.e., fewer than all, of the qubits or other calculation elements, like the bosonic field states, in the quantum computer, and then decide which further quantum manipula- tions to execute next based on the outcome of the one or more measurements.
  • measurement feedback can be useful for performing quantum error correction, but is not limited to use in performing quantum error correction.
  • BASF SE 221032 221032WO01 Not all quantum computers are gate-based quantum computers.
  • Embodiments of the pre- sent invention are not limited to utilizing gate-based quantum computers.
  • embodiments of the present invention can also utilize, in whole or in part, a quan- tum computer that is implemented using a quantum annealing paradigm which is an alter- native to the gate-based quantum computing paradigm. More specifically, quantum anneal- ing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctua- tions.
  • quantum annealing is closely related to adiabatic quantum computing.
  • quantum annealing procedures start with utilizing a classical computer providing or generating an initial Hamiltonian and a final Hamiltonian based on a computa- tional problem to be solved, and providing the initial Hamiltonian, the final Hamiltonian and an annealing schedule as input to a quantum computer.
  • the final Hamiltonian refers to an Ising Hamiltonian representing the optimization problem, or to a good approximation of the ground state of the Ising Hamiltonian representing the optimization problem.
  • the quantum computer is then adapted, for instance, by utilizing a respective control unit controlling a manipulation part of the quantum computer, to prepare a relatively easy to prepare initial state, such as a quantum-mechanical superposition of all possible states, e.g. candidate states, with equal weights, based on the initial Hamiltonian.
  • a relatively easy to prepare initial state such as a quantum-mechanical superposition of all possible states, e.g. candidate states, with equal weights, based on the initial Hamiltonian.
  • the initial state is then evolved according to the an- nealing schedule following a time-dependent Schroedinger equation referring to a natural quantum-mechanical evolution of the physical system of the quantum computer. More spe- cifically, the state of the quantum computer undergoes time evolution under a time-depend- ent Hamiltonian, which starts from the initial Hamiltonian and terminates at the final Hamil- tonian.
  • the system stays close to the ground state of the instantaneous Hamiltonian.
  • the set of qubits, i.e. quan- tum elements, on the quantum annealer is in a final state, which is expected to be close to the ground state of the Ising Hamiltonian that corresponds to a solution to the original prob- lem, referring, for instance, to an optimization problem.
  • the final state of the quantum com- puter can then be measured, thereby producing results that can be utilized for solving the original problem.
  • the measurement operation can be performed, for example, in any of the ways described already above.
  • a classical computer can then perform postprocessing on the measurement results to produce an output representing a solution to the original com- putational problem.
  • a quantum annealer as described above can, for instance, be realized on a superconducting quantum computer hardware.
  • BASF SE 221032 221032WO01 Moreover, embodiments of the present invention can also utilize, in whole or in part, quan- tum computers that are implemented using a one-way quantum computing architecture, also referred to as a measurement-based quantum computing architecture. More specifi- cally, the one-way or measurement-based quantum computer refers to a method of quan- tum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it.
  • the system 700 can, in addition to the apparatus 720, further comprise an input unit 710 and/or a quantum computer system 730.
  • the production plant 740 and in particular the production system 741 can also be part of the system, but can also be omitted or only provided as communicatively coupled to the apparatus 720.
  • the apparatus 720 comprises an electronic structure representation providing unit 721, a solution determination unit 722 and a correlation computation unit 723.
  • the ap- paratus 720 further comprises an iteration unit and a control data generation unit (not shown in Fig.7).
  • the apparatus 720 can optionally also comprise a translation unit 724.
  • the translation unit 724 can also be part of the quantum computer system 730 or can be a standalone device communicatively coupled to the apparatus 720 and the quantum computer system 730.
  • the apparatus 720 can be realized as any known classical computing system.
  • the function provided by the units can be performed by one or more processors on one or more classical computing devices.
  • the apparatus 720 can also be realized as distributed computing framework, for example, as a cloud or network environment, in which more than one computing device or processor is utilized for performing the functions of the apparatus.
  • the electronic structure representation providing unit 721 is configured for providing an electronic structure representation associated with a molecular structure of the chemical product.
  • the problem providing unit 721 can be coupled with the input unit 710 to allow a user to indicate, for instance, select from a respective provided selection, the respective electronic structure representation to be solved.
  • the electronic structure representation providing unit 721 can refer to or be communicatively coupled to a storage unit on which the respective problem description is already stored.
  • the electronic structure representation if solved, allows to derive a technical application prop- erty of a respective chemical product.
  • the electronic structure representation if solved, can allow to determine one or more production process parameters, for example, allows to determine a specific catalyst suitable for producing the chemical product, a re- spective reaction temperature, a respective reaction energy, etc.
  • the electronic structure representation is further indicative of a first part indicative of an active space and a second part indicative of an inactive space.
  • the active space and the inactive space of the problem can refer to subspaces of the Hilbert space of the electronic structure repre- sentation and can be determined based on the chemical product and/or the property, for example, based on an already known approximated electronic structure of the chemical product. Further details on the first and the second part including preferred examples and embodiments will be described, for instance, with respect to Fig.12.
  • the electronic structure representation can be provided, generally, in any form that allows the apparatus 720 to derive respective information from the electronic structure represen- tation for solving the electronic structure representation.
  • the electronic struc- ture representation is preferably provided in a digital format.
  • the electronic structure representation is provided in a mathematical formulation.
  • the electronic structure representation can also be provided in any other format from which the electronic structure representation providing unit 721 or optionally also the translation unit 724 can derive a respective mathematical formulation of the electronic structure rep- resentation.
  • the electronic structure representation providing unit 721 can then be config- ured to provide the electronic structure representation to the solution determination unit 722.
  • the solution determination unit 722 can be configured to cause the quantum computer 730 to perform a quantum mechanical calculation based on the first part of the electronic struc- ture representation such that the result of the quantum mechanical calculation is indicative of the solution of the first part.
  • the solution determination unit 722 can be communicatively coupled to the quantum computer 730, for example, to provide respective BASF SE 221032 221032WO01 control signals to the quantum computer 730 that cause the quantum mechanical calcula- tion.
  • the electronic structure representation or the first part of the electronic structure representation can be provided to a translation unit 724.
  • a respective problem is trans- lated into a respective operation description indicative of a sequence of operations to be applied to the quantum computer for solving the problem.
  • the sequence of operations is determined such that the quantum mechanical calculation of the first part defined on the active space is performed on the quantum computer.
  • This translation of the first part and thus also the translation unit 724 can be part of the apparatus 720, for exam- ple, as a respective unit that translates the electronic structure representation or the first part of the electronic structure representation provided by the electronic structure repre- sentation providing unit, wherein then the solution determination unit 722 can directly utilize the determined representative operation description for causing the quantum computer 730 to perform the quantum mechanical calculation of the first part.
  • the translation unit 724 can also be provided as an independent unit or as a unit that is part of the quantum computer system 730 and receives from the solution determination unit 722 the respective electronic structure representation or first part of the electronic structure representation for translation.
  • algorithms and methods for translating an electronic structure representation into respective operations to be performed on the quantum computer system 730 in order to perform a quantum mechanical calculation are already known.
  • the respective translation depends strongly on the quantum computer system 730 utilized for determining the solution of the problem. For example, for a quantum computer based on superconductors other operations might be necessary than for a quantum computer based on trapped ions. More- over, the respective operation description can also refer to the manipulations performed on a quantum annealer in order to solve the respective electronic structure representation.
  • the respective operation description will differ from an operation de- scription utilized, for instance, for other quantum computer systems, like gate-based quan- tum computing systems.
  • the translation unit 724 is part of the quantum computer system 730 allowing for a higher flexibility of the ap- paratus 720 to utilize different quantum computing systems 730, wherein in each case the respective translation unit 724 can be specialized and specifically adapted for optimally translating the electronic structure representation into a representative operation descrip- tion that is in particular suitable for the respective quantum computing system to which the respective translation unit refers.
  • the respective result of the calculation can again be provided to the apparatus 720.
  • the such determined result of the calculation is indicative of the solution of the first part of the electronic structure representation.
  • respective known algorithms and methods can be utilized to determine from the results of the measurements of the states of the quantum elements of the quantum computer 730 the respective solution of the calculated first part.
  • This determination of the solution of the first part can be performed, for instance, by a part of the quantum computer system 730 comprising a classical computer before providing the respective result, in this case, the solution of the first part, to the apparatus 720 or can also be performed by the apparatus 720 itself, for example, by the correlation computation unit 723.
  • the solution determination unit 722 can be configured to cause a classical computer to perform a respective calculation based on the first part of the electronic struc- ture representation such that the result of the classical calculation is indicative of the solu- tion of the first part.
  • the correlation computation unit 723 is configured to generating a solution to the electronic structure representation by combining the solution of the first and the solution of the second part, wherein the solution to the first part and the solution to the second part are computa- tionally combined to generate the property associated with the chemical product.
  • computationally combining includes generating an interaction representation associ- ated with the combination of active and inactive space.
  • the interaction representation is based on a reference state associated with a superposition of electron configurations gen- erated based on the solution of the first part and the solution for the second part.
  • the BASF SE 221032 221032WO01 interaction representation allows to calculate the solution of the electronic structure repre- sentation by combining i) a solution of the second part in the inactive space and ii) the solution of the first part in the active space.
  • the generating of the interaction problem for combining the solution of the first part and the solution of the second part can depend on the respective provided electronic structure representation itself but can also depend on a method that is utilized to solve the electronic structure representation. Some of the preferred methods and algorithms for gen- erating the interaction representation and combining solution of the first part and the sec- ond part will be described later in more detail.
  • the interaction representation can then be solved by a classical computer and/or quantum computer.
  • the solution of the electronic structure representation is related to a property of a chemical product 750
  • the solution can then be utilized to generate respective control data for controlling a pro- duction system 741 for producing the chemical product 750, for example, using a respec- tive control data generation unit.
  • control data can refer to a recipe or specification of the respective chemical product, to preferably used production process pa- rameters for producing the chemical product, to control margins for controlling the produc- tion of the chemical product, etc.
  • the apparatus 720 is configured to determine the tech- nical application property of the chemical product.
  • the control data can then be generated, for example, based on the determined technical application property.
  • the apparatus 720 comprises additionally an iteration unit (not shown in Fig. 7) that allows to control an iteration based on the solution of the electronic structure repre- sentation related to a chemical product.
  • a target technical application property is provided to the apparatus 720, for instance, utilizing input unit 710, and that the technical application property determined based on the solution of the elec- tronic structure representation is then compared to the target technical application property.
  • a further iteration step can then be initiated, for instance, by amending one or more characteristics of the chemical product and thus the respective electronic structure representation, or it can be determined that the respective chemical product meets the target technical application property and thus is the target chemical product that should be produced by production system 741.
  • control data can be generated that causes the production system 741 to produce the target chemical prod- uct 750.
  • BASF SE 221032 221032WO01 Further details on this and on respective other embodiments of a method that can be per- formed by the apparatus 720 will be described in the following with respect to Fig.8.
  • Fig.8 shows schematically and exemplarily a method generating a property associated with a chemical product.
  • the main part of the method 800 comprises providing an electronic struc- ture representation related to the chemical product that is indicative of or includes a first part of the electronic structure representation and a second part of the electronic structure representation, as already described above, for example, with respect to the electronic structure representation providing unit 721. Further, the method 800 comprises utilizing a quantum computer system like quantum computer system 730 to perform a quantum me- chanical calculation, wherein the result of the quantum mechanical calculation is indicative of the solution of the first part and/or the second part.
  • a solution of the first part and/or the second part can be calculated. Alternatively, the calculating of the first part or the second part can be performed by a classical computer.
  • the method 800 comprises generating and solving an interaction representation for combining a solution of the first part and a solution of the second part, for example, as described with respect to the problem correlation computation unit 723.
  • the method can comprise additional steps, in particular, related to the produc- tion of the chemical product. These optionally additional steps 810 are illustrated in Fig.8 in the form of dotted and dashed boxes.
  • the additional steps refer to determining a technical application property of a chemical product based on the determined solution of the electronic structure representation.
  • the additional steps can also refer to determining one or more production process parameters for control- ling a production process of a chemical product. For example, such production process parameters can be determined based on the calculated technical application properties.
  • production process parameters can also refer, for example, to a catalyst or reactant utilized in the production of the chemical product and can thus be determined based on solving respective electronic structure representations that allow to derive and predict respective reaction parameters for potential catalysts or reactants.
  • Examples for specific preferred applications of the method 800 but also of the method 810 will be pro- vided in the following description with respect to some more detailed embodiments.
  • the method 810 can further comprise providing a target technical application property for a chemical product, wherein in this case the electronic structure representation is provided based on a potential chemical product for which it should be determined whether or not it meets the respective target technical application property.
  • the target tech- nical application property can then be compared with the determined technical application BASF SE 221032 221032WO01 property and it can be determined whether or not the determined technical application prop- erty meets the target technical application property.
  • This comparison can be utilized in an iteration algorithm, in which the comparison is performed in each iteration step. If the de- termined technical application property does not meet the target technical application prop- erty within predetermined limits, in a next iteration step the potential chemical product can be amended, for example, by amending one or more aspects or characteristics of the re- spective potential chemical product and a new electronic structure representation can be provided based on the new potential chemical product.
  • the steps of utilizing the quantum computer for solving the first part or second part, of combining the solution of the first part and the second part to determine the solution of the electronic structure representation and the determination of the technical application prop- erty can then be repeated in each iteration step. If in one iteration step it is determined during the comparison that the determined technical application property meets the target technical application property within the predetermined limits, it can be determined that the respective potential chemical product is the target chemical product and respective control data for producing the target chemical product can be generated for the target chemical product. It is noted that the respective control data can also be generated without the iter- ation for example, only based on the determined technical application property.
  • control data can then refer to control data that allows to control, for example, a produc- tion system 741 for producing the chemical product 750, for instance, the target chemical product.
  • control data can refer to a recipe or specification, for example, a synthe- sis specification, of the target chemical product.
  • control data can also refer to production process parameters that are determined, for instance, based on the deter- mined technical application property. Further details and embodiments are described in the following.
  • Quantum computing is an emerging technology that exploits quantum-mechanical phenomena to perform computa- tional tasks. Quantum computers are expected to solve certain computational problems substantially faster than classical computers.
  • a parameterized quantum state is prepared on the NISQ computer
  • a target function is measured on the NISQ computer
  • the parameters are optimized on the classical computer to minimize or maximize the target function. This procedure is repeated with the updated parameters until the value of the target function converges and thus becomes minimal or maximal, respectively.
  • post-processing can be carried out on the classical computer. Both the number and fidelities of the qubits are expected to continuously increase.
  • a logical qubit can be formed by one or more physical quantum elements of the respective quantum computer hardware.
  • a quan- tum device comprised of several of those logical qubits is termed a fault-tolerant (FT) quan- tum computer.
  • FT fault-tolerant
  • the error rate of such a FT quantum computer depends on the error-correction code and the number of physical qubits used. As a rule of thumb, the more physical qubits of a certain quality are used the more errors are suppressed.
  • Such a FT quantum computer is able to accommodate deep quantum circuits that allow for highly accurate or exact solutions of many highly relevant computational problems which cannot be obtained on classical computers in reasonable time or with reasonable energy cost.
  • some FT quantum computers remain rather restricted with regard to the number of logical qubits and thus the size, e.g. dimension, of the computational problem that can be solved.
  • fault-tolerant quantum computers e.g. fault-tolerant quantum processing units (FT-QPUs)
  • FT-QPUs fault-tolerant quantum processing units
  • NISQ-QPUs noisy interme- diate-scale quantum processing units
  • NISQ-QPUs in many cases are able to accommodate wider quantum circuits, i.e. utilizing more qubits but fewer gate operations than in case of FT-QPUs, to provide approximate but still accurate solutions for many problems.
  • NISQ-QPUs with a wide range of fidelities exist that allow for calculations with different accuracies or for quantum circuits with different depths.
  • the above described method, for instance, with respect to Figs.7 and 8, for solving elec- tronic structure problems can be performed on a plurality of different hardware combina- tions. For example, the method can be performed purely on one or more classical comput- ers.
  • the quantum computing system can be a BASF SE 221032 221032WO01 triple hybrid quantum computing system that combines FT-QPUs, NISQ-QPUs and classi- cal central processing units (CPUs) or other conventional computational devices wherein computational operations are carried out wherever most advantageous for solving the prob- lem.
  • the quantum computing system can also combine different NISQ-QPUs with different fidelities and CPUs or other conventional hardware without using FT-QPUs.
  • Fig. 9 two examples of respective quantum computing systems that can be advanta- geously utilized are shown. The examples are shown with respect to quantum computing systems comprising FT-QPUs and NISQ-QPUs. However, additionally or alternatively to FT-QPUs also NISQ-QPUs with higher fidelities can be used with the same exemplary principles described below.
  • the term “higher fidelity NISQ-QPUs” is utilized with the meaning that a higher fidelity NISQ-QPU can have a higher fidelity compared to a) all other NISQ-QPUs of the quantum computing system, b) higher fidelity than at least on other NISQ-QPU of the quantum computing system and/or c) higher fidelity than a prede- termined threshold.
  • any combination of these three criteria can be defined a NISQ-QPU that can be utilized for computing a sub-problem as described in the following.
  • the threshold can be based for instance, on previous consideration, experience with a respective problem type, an algorithm to be utilized, a specific problem type, a to be achieved accuracy of a solution, etc.
  • the higher fidelity NISQ-QPU simply refers to the NISQ-QPU with the highest fidelity of the NISQ-QPUs of the quantum computing system, wherein in this case the respective sub-problem is derived such that it can be computed by the higher fidelity NISQ-QPU.
  • the FT-QPU(s) referred to are optional and can also be replaced by higher-fidelity NISQ-QPU(s) or can be used together with higher-fidelity NISQ-QPU(s).
  • One example comprises controlling the FT-QPU(s), and/or higher-fidelity NISQ-QPU(s), and the NISQ-QPU(s) and exchange data via the CPU(s).
  • Another example comprises a quantum computing system where FT-CPU(s), and/or higher-fidelity NISQ-QPU(s), and NISQ-QPUs are additionally entangled in a way that quantum information is distributed and shared among the entangled QPU(s) and can also be directly transferred between the re- spective QPU(s).
  • the FT-CPU(s), or higher-fidelity NISQ- QPU(s), and NISQ-QPU(s) are on the same chip to facilitate entanglement.
  • a quantum bus such as optical fibers and photons, spatially separated QPUs can also be entangled.
  • the principles of the described methods can also be performed utilizing generally known hybrid computing systems comprising a quantum com- puter and a classical computer instead of a quantum computing system comprising quan- tum computers with different fidelities.
  • the electronic structure representation can be defined on a classical computing system, for instance, by a user using a user inter- face.
  • Typical electronic structure representations refer to the electronic structure of mole- cules, solids and materials.
  • the electronic structure representation can comprise or can be divided on the classical computing system into sub-problems, for in- stance, a first part of the electronic structure representation indicative of an active space including a part of the electronic structure associated with the molecular structure and a second part of the electronic structure representation indicative of an inactive space includ- ing another part of the electronic structure associated with the molecular structure.
  • the fidelities of the FT-QPU(s), and/or NISQ-QPU(s) of the quantum computing system on which the sub-problems are to be solved are taken into account.
  • FT-QPUs or higher-fidelity NISQ-QPU(s) are best used to solve smaller computational sub-problems for which exact or highly accurate solutions are desired that can be efficiently obtained neither on low-fidelity NISQ-QPUs nor on CPUs. Also sub-problems for which the solution requires deeper quantum algorithms exceeding the capabilities of lower-fidelity NISQ-QPU(s) and CPUs can be derived to be solved on the higher-fidelity NISQ-QPU(s) or FT-QPU(s).
  • the dimension of the sub-problem, for in- stance, of the first part can accordingly be chosen to be less or equal than the dimension of the Hilbert space spanned by the qubits of the FT-QPU(s) or higher-fidelity NISQ- QPU(s).
  • the lower-fidelity NISQ-QPU(s) are best used to solve larger computational sub- problems where accurate solutions are desired that cannot be efficiently obtained on clas- sical computers, e.g. CPU(s), or where the solution requires wide rather than deep quantum algorithms utilizing a larger number of qubits, for instance, for the second part.
  • CPUs are used for all remaining tasks and controlling of the entangled or unentangled quantum com- puters.
  • control signals are provided that cause to prepare and run respective quantum circuits on the quantum computing system for calculating and solving the respec- tive sub-problems.
  • the quantum circuits can contain parameters, which are typ- ically used in the context of variational procedures.
  • an initial set of parameters is provided in the first iteration step.
  • the sub-problem is encoded into qubits, the quantum circuit is compiled, and control signals are provided, for instance, to either the FT-QPU(s), higher-fidelity NISQ-QPU(s) or the NISQ-QPU(s), all simultaneously or to the entangled FT-QPU(s), higher-fidelity NISQ-QPU(s), and NISQ-QPU(s) systems.
  • BASF SE 221032 221032WO01 This is also done in all subsequent iteration steps with an appropriately updated set of parameters.
  • a fourth step the quantum circuit of the current iteration step is executed on either the FT-QPU(s), higher-fidelity NISQ-QPU(s) or the NISQ-QPU(s), all simultaneously or on the entangled FT-QPU(s), higher-fidelity NISQ-QPU(s), and NISQ-QPU(s) to prepare the re- spective sub-problem solutions.
  • relevant algorithms for FT-QPU(s) are quan- tum Fourier transform, quantum phase estimation (QPE), Grover-type search algorithms, Shor-type factorization algorithms and Harrow-Hassidim-Lloyd-type algorithms.
  • NISQ-QPU(s) or NISQ- QPU(s) examples are the variational quantum eigensolver (VQE) and the quantum approximate op- timization algorithm (QAOA). Respective quantum gate operations are carried out on the qubit registers. In case of an entangled FT- or higher-fidelity NISQ- and NISQ-QPU system the solutions of sub-problems can be directly transferred between the two types of QPU(s).
  • relevant observables of the sub-problems can be measured on either the FT- QPU(s), the higher-fidelity NISQ-QPU(s), or the NISQ-QPU(s), all simultaneously or the entangled FT-, or higher-fidelity NISQ-, and NISQ-QPU systems and provided to the CPU(s).
  • Examples for observables that can be measured are qubit occupation numbers, reduced density matrices and energies.
  • the target function and/or quantity and if needed its derivatives or other dependent quantities can be evaluated on the CPU(s) based on the measured observables. Examples for target functions and/or quantities are the total energy of the electronic structure problem and classical loss functions.
  • feed- back calculations connecting iteration steps of the algorithm like self-consistency conditions can be invoked, or, in case of variational procedures, optimization approaches such as quasi-Newton methods can be invoked to obtain a new set of parameters to minimize or maximize the target function and/or quantity.
  • the iteration can return to the second or third step or if one or more stop criteria are fulfilled, e.g., the target function and/or quan- tity has converged, the iteration can terminate the feedback loop and proceed with the next step.
  • optional post-processing steps e.g.
  • the result e.g., error mitiga- tion or error correction
  • the CPU(s) may be carried out on the CPU(s) for instance by the correlation computation unit. If necessary for this, further observables can be measured on the QPU(s).
  • the results of the sub-problems are further combined either in this post-processing or during the iteration, depending on the interactions between the sub-problem results. Lastly, the final result is provided to the user as solution of the processed problem.
  • BASF SE 221032 221032WO01 In the following an example of a method is described utilizing a hybrid quantum-classical approach.
  • the following exemplary method refers to an “active space” that is solved pref- erably on a quantum computing system and wherein the result is then used to adjust elec- tron orbitals, preferably, both in an “inactive” and the “active space”, on a classical computer or a quantum computer.
  • an “inactive space” or the influence of the “active space” on the “inactive space” can be solved on a quantum computer system. The procedure is iteratively repeated until convergence of the molecular orbitals and total energy can be achieved.
  • This method can be referred to as the “complete active space self-consistent field” (CASSCF) method.
  • a related method is “complete active space configuration interaction” (CASCI), which can be viewed as a special case of CASSCF that neglects the adjustment of the electron orbitals to the “active space” solution.
  • CASCI complete active space configuration interaction
  • CASSCF complete active space configuration interaction
  • both methods are referred to as “CAS meth- ods”.
  • a solution of this computation can then be utilized for generating the interaction rep- resentation and solving the respective electronic structure problem more accurately.
  • the method is particularly advantageous for the simulation of so-called statically correlated molecular systems, such as transition metal compounds that are relevant for improving and designing, e.g., new catalysts and chelating agents, which is typically very challenging for traditional methods utilizing CPUs both with respect to computational effort and accuracy.
  • statically correlated molecular systems such as transition metal compounds that are relevant for improving and designing, e.g., new catalysts and chelating agents, which is typically very challenging for traditional methods utilizing CPUs both with respect to computational effort and accuracy.
  • the first and the second part, respectively, of the problem is compliant with the general procedure depicted in Fig.10 above wherein the type of quantum computer utilized can be determined based on the fidelity of the respective available quantum computers before the quantum computation and can remaining fixed throughout the whole iterative procedure.
  • the steps in Fig.10 are detailed in the following.
  • the specific electronic-structure problem to be solved is provided as a molecular system specified by atomic positions, basis sets, electric charge and spin on a CPU. This is in analogy to the first step in the general process in Fig.10.
  • an initial set of electron orbitals is specified, e.g. from a Hartree-Fock calculation on a CPU.
  • a fixed “active space” is defined BASF SE 221032 221032WO01 for example by electron orbitals and electrons that constitute the “active space”, wherein the active space defines a first part.
  • These steps are performed on a CPU, in analogy to the second step in the general process in Fig.10.
  • the matrix elements of the effective Hamiltonian of the “active space” in the electron orbital basis are set up on a CPU defining the first part further. This is in analogy to the third step in the general process in Fig. 10.
  • the effective “active space” Hamiltonian operator which is fermi- onic/electronic in nature, is encoded, i.e.
  • the quantum circuit to solve the “active space” part is then compiled on a CPU such that it can be performed on a quantum computer.
  • the “active space” part is then prepared and solved on a quantum computer, for example, a higher-fidelity NISQ-QPU, or FT-QPU, for instance, by a so-called quantum phase estima- tion algorithm (QPE).
  • QPE quantum phase estima- tion algorithm
  • the “active space” part can be solved on a NISQ-QPU, e.g. by a so-called variational quantum eigensolver (VQE), in the step above.
  • VQE variational quantum eigensolver
  • typically approximate but accurate solutions, for instance as eigenfunctions of the “active space” part can be prepared on the NISQ-QPU.
  • step five the one- and two-particle reduced density matrices would then be measured on the NISQ-QPU in the step above.
  • the energy can then be calculated from the one- and two-particle reduced density matrices on a CPU.
  • the gradient with respect to variation of the elec- tron orbitals can be calculated on a CPU, wherein this step is only performed in case of CASSCF but not for CASCI.
  • step six in the general process in Fig.10.
  • step seven in Fig.10 if energy and gradient are converged, it can be pro- ceeded with the final step.
  • step seven can be omitted and there is no self-consistency loop, and thus it can be proceeded directly to the next step in that case. Further steps performed to determine a solution of the problem are described in the following.
  • MC-PDFT multiconfiguration pair-density functional theory
  • NAVPT2 second-order n-electron valence state perturbation theory
  • these methods are in particular suited to be utilized in with the method and quantum computing system described above taking the fidelities of the quan- tum computers into account when solving sub-problems.
  • the first step is, as described above, to determine a solution of the first part and the second part.
  • the result can then be expressed, for instance, as a CAS wavefunction, ⁇ ⁇ ⁇ that can be utilized as reference state for an interaction representation that allows to combine the results of the first and the second part.
  • relevant specifics of the CAS wavefunction determined as described above can be read out from the QPU(s) in order to be reconstructed or approximated on a different hardware device, for instance, CPU(s) or a different QPU(s), e.g. with a different fidelity, that is most suited for the multireference dynamic correlation treatment.
  • a reconstruction of the CAS wavefunction on a different hardware device is not required and thus the methods for the readout of the CAS wave- function can be omitted.
  • the CAS wavefunction as exemplary reference state for the interaction representation that is determined based on the solution of the active space part, i.e. first part, and the solution of the second part, i.e. second part, obtained as described above can be expanded as the basis states, e.g. Slater determinants, adhering to the “active space” definition. More precisely, those basis states can be so-called configuration interaction (CI) states given by a fixed distribution of the electrons among the electron orbitals in the “active space” part and the inactive space part. The index ⁇ runs over all possible electron distri- butions among the electron orbitals in the “active space” and “inactive space” part.
  • CI configuration interaction
  • the expansion coefficients are then the so-called CI coefficients, which are utilized to recon- struct the CAS wavefunction on a different QPU or CPU that is most suited for the next computational step, for instance, a multireference dynamic correlation treatment based on an interaction representation.
  • the following method can be utilized to determine the CI coefficients of a CAS wavefunction based on the solution of the active space part that has been prepared on a quantum com- puter, for instance, as described above.
  • CI coefficients associated with inactive space can be determined, for instance, as solution of the second part, utilizing a mean field approxi- mation and are in most cases determined utilizing known method on a classical computer.
  • an absolute value of CI coefficients can be measured on the respective QPU.
  • the absolute value of the CI coefficients can be measured by deter- mination of an overlap of the CAS wavefunction and the defined basis states, for instance according to:
  • the CAS wavefunction, ⁇ ⁇ ⁇ can be prepared on the QPU as the result of the preceding CAS calculation of the active space part.
  • the CAS wavefunction can be prepared on the QPU and a projective meas- urement on all qubits can be performed. Since no basis rotations of the qubit states are required, all qubits can be measured simultaneously.
  • Slater determinant is given by ⁇ ⁇ ⁇ and the histogram translates directly to these absolute values.
  • a significant advantage of running the CAS method and measuring the result using a quantum computer is that it directly provides the most important basis states, e.g. Slater determinants, to span a relevant por- tion of the Hilbert space. This information is used in the following steps below. On a CPU, the CAS method would need to search for the relevant basis states, e.g. Slater determi- nants, which are not known a priori.
  • the absolute value can be additionally directly measured in a second step where the CAS wavefunction is projected onto the basis states for instance, via the projection operator: ( 3) ⁇ ⁇ ⁇ being the unitary operator that prepares the basis state from the vacuum state
  • the above described step only determines the absolute value of the complex-valued CI coefficients but not the phase, which, can be crucial to reconstruct the CAS wavefunction according to Eq. (1).
  • To determine the phase of the CI coefficients the following steps can be carried out. Since the ⁇ absolute value ⁇ ⁇ ⁇ can be measured on the QPU(s) it can be determined which basis states have the largest CI coefficient and are therefore most important for the reconstruc- tion of the CAS wavefunction. Those basis states can then be selected.
  • the number of determined CI coefficients can be predetermined, for example, such that the measure- ments lead to a manageable number of basis states and also to a sufficient representation of a sufficiently large portion of the CAS wavefunction. Truncating the summation in Eq.
  • (1) to a predetermined number of basis states leads to a more efficient calculation of the prob- lem.
  • a representation of a Hamiltonian ⁇ ⁇ for example, which defines the molecule that is simulated, is reconstructed in a small subspace spanned by the most im- portant basis states selected in the previous step.
  • the Hamiltonian in this sufficiently small subspace has a reduced size compared to the full Hamiltonian and can therefore be effi- ciently diagonalized, e.g. through power iterations or by the Davidson method.
  • the CI coefficients with their absolute value and phase within that subspace can be obtained.
  • ⁇ ⁇ ⁇ as the absolute values ⁇ ⁇ ⁇ are already known from the preceding CAS cal- culation on the QPU(s) and the measurement of the CI coefficients described above, in case of real CI coefficients ⁇ ⁇ , a variant of Eq. (4) could comprise fixing the absolute values ⁇ ⁇ ⁇ and only modifying the signs, e.g. in the framework of a Monte-Carlo-like procedure that flips the signs randomly: define ⁇ ⁇ as a vector of the values on the left-hand side of Eq.
  • the CI coefficients change when the number of measurements is increased and/or if the ratios of important CI coefficients change when the number of measurements is increased.
  • the CAS wave- function of a problem can also be determined by a traditional CAS, RAS (“restricted active space”, such as RASSCF or RASCI) or GAS (“generalized active space”, such as GASSCF or GASCI) calculation running entirely on CPU(s) without any quantum computing part.
  • RAS restricted active space
  • GAS generalized active space
  • GASSCF generalized active space
  • the first embodiment leverages a NISQ-QPU that is not entangled with the FT-QPU or higher-fidelity NISQ-QPU used for the CAS wavefunction calculation BASF SE 221032 221032WO01 and thus this is compatible with the unentangled quantum computing system described with respect to Fig.9.
  • a further embodiment leverages a NISQ-QPU that is entangled with the FT-QPU or higher-fidelity NISQ-QPU used for the CAS wavefunction calculation thus this is compatible with the entangled quantum computing system described with respect to Fig.9.
  • the remaining two embodiments are focused on post-processing on a CPU.
  • Fig.14 shows an overview of the four embodiments that will be discussed in the following.
  • the following sections treat the CAS method as separating between predominantly static correlation within the “active space” on the one hand, and dynamic correlation among elec- trons in all electron orbitals, both active and inactive, on the other hand.
  • the methods described below can also be applied in an embedding context.
  • the CASCI method can be used to calculate both the static and dynamic correlation of electrons in electron orbitals located on a fragment of a molecular system or material, and a dynamic correlation method can be used to calculate the interaction between the CASCI fragment and the surrounding electron orbitals.
  • a fragment refers to a spatially connected part of the molecular system comprising the respective electron orbitals associated with this part of the molecular system and is independent of the active and inactive space sub-problems.
  • a fragment can be associated with spatially connected atoms of the molecular system and comprise the electron orbitals of these atoms.
  • a separation between electron orbitals inside and outside of the CASCI fragment can be achieved through orbital locali- zation methods, which can be aided by other techniques such as natural orbitals, natural orbitals for orbital pairs or subsets, orbital-specific virtual orbitals, and domains of projected atomic orbitals or other functions.
  • a molecule or material can also contain multiple frag- ments that are treated at CASCI level with approximate interaction, for example at mean- field level, between the fragments. Afterwards, a correlated interaction is calculated using the dynamic correlation methods described below.
  • NISQ-UDC NISQ unitary dynamic correlation
  • Such a hard- ware setting is ideally suited to combine a CAS calculation, wherein a FT-QPU or a higher- fidelity NISQ-QPU is used to solve the “active space” part at a high level of accuracy, with an approximate dynamic correlation method for the “inactive space” part and to approxi- mately account for dynamic correlation within the “inactive space” sub-problem and be- tween “active space” and “inactive space” sub-problems utilizing a NISQ-QPU.
  • an interaction representation can be gen- erated and solved by applying a unitary dynamic correlation (UDC) ansatz in combination with the variational quantum eigensolver (VQE) or the variational Hamiltonian ansatz (VHA) to approximately account for dynamic correlation utilizing a NISQ-QPU.
  • UDC unitary dynamic correlation
  • VQE variational quantum eigensolver
  • VHA variational Hamiltonian ansatz
  • the solution can also be generated al- ready taking a solution of the “active space” part into account, for example, adapting the electron orbitals of the “inactive space” part based on a solution of the “active space” part.
  • This solution of the “inactive space” part can then be integrated into the CAS wavefunction as part of the interaction representation.
  • the method can be represented by a parameterized unitary operator ⁇ ⁇ that acts both on the “inactive space” and “active space” parts of the previously determined CAS wavefunction forming an example of an interaction representation as follows: with ⁇ being a set of parameters that are optimized within a variational procedure, e.g. VQE or VHA.
  • ⁇ ⁇ ⁇ is a unitary coupled cluster (UCC) op- erator.
  • the method can be referred to as an “internally contracted multireference unitary coupled cluster method” (ic-MR-UCC).
  • ic-MR-UCC internally contracted multireference unitary coupled cluster method
  • the expansion only includes the singles and doubles term as explicitly shown above leading to the UCCSD operator and thus the ic-MR-UCCSD method.
  • the method can also be systematically extended to higher-order excitations like triple, quadruple, etc. excitations leading to ic-MR-UCCSDT, ic-MR-UCCSDTQ, etc. vari- ants.
  • ⁇ ⁇ ⁇ and ⁇ ⁇ are electronic creation and annihilation operators, respectively.
  • Restrictions can be applied to the indices ⁇ in the singles term, the indices ⁇ in the doubles term, BASF SE 221032 221032WO01 or the corresponding indices in higher-order terms. Examples for possible restrictions on the indices include the following.
  • only the “active space” part is solved on the FT-QPU or higher-fidelity NISQ-QPU which means that typically as many logical qubits as there are electron orbitals in the “active space” can be used to represent the solution of the “active space” part.
  • additional qubits can be required to implement the algorithm, e.g., ancilla qubits for the QPE algorithm.
  • a NISQ-QPU and, e.g., the variational quantum eigensolver, VQE) to solve the “active space” part can be used in this step.
  • the CAS or alternatively RAS or GAS
  • the dynamic correlation treatment on a NISQ-QPU.
  • the CI coefficients can be determined as described above.
  • the CAS wavefunction or the most relevant CI coefficients that were read out, can be stored on the CPU and kept fixed throughout all of the following steps as part of the reference state.
  • the dynamic correlation of the “inactive space” and among “active space” and “inactive space” can be taken into account utilizing a NISQ-QPU by executing again parts of the process depicted in Fig.10 as described in the following.
  • a representation of the CAS wavefunction is prepared on a quantum computer with a suitable fidelity, for ex- ample, a NISQ-QPU.
  • the entire CAS wavefunction, and not only the “active space” solution can be reconstructed according to Eq. (1), for example, using the most relevant CI coefficients as described above, on the NISQ-QPU via where the summation over ⁇ is restricted to the ⁇ most important basis states, e.g. Slater ⁇ determinants, as described above, e.g. the ones where ⁇ ⁇ ⁇ is larger than a predetermined threshold.
  • a UDC operator ⁇ ⁇ can be applied to generate as an interaction representation a trial state according to Eq. (5) with ⁇ being a set of variational parameters that will be adjusted on the CPU later within a VQE or VHA procedure.
  • unitary operator is the unitary coupled cluster (UCC) operator described above, where ⁇ ⁇ and ⁇ ⁇ are the sets of variational parameters.
  • parameters can be either chosen randomly or by means of other com- putationally inexpensive traditional methods, e.g. based on perturbation theory, that are run on a CPU in advance.
  • the electronic creation and annihilation operators can be en- coded in qubit operators, namely Pauli operators, e.g. by means of the Jordan-Wigner or Bravyi-Kitaev transformation.
  • the encoded UDC operator, ⁇ ⁇ is then translated into quantum gates that are applied to the previously reconstructed CAS wavefunction on the quantum computer to prepare a parameterized trial state according to Eq. (5) as interaction representation.
  • Strategies like the FSIM network algorithm using low-rank decomposition or the CZ algorithm can be used.
  • the one- and two-particle reduced density matrices can then be measured on the quantum computer.
  • the measured quantities allow for the eval- uation of the energy of the trial state ⁇ ⁇ ⁇ with respect to the molecular Hamiltonian ⁇ ⁇ on a classical computer, e.g.
  • a CPU according to: If the energy and the variational parameters are not converged yet, the iteration continues by updating the set of variational parameters such that the energy ⁇ is minimized in a var- iational procedure on the classical computer. If the energy and the variational parameters are converged, the iteration proceeds with the final step. The final energy and further prop- erties of the solution can then be provided to the user. Also, further post-processing on a BASF SE 221032 221032WO01 classical computer, e.g. a CPU, can be performed including application to real-world prob- lems related to chemical products like molecules, solids, materials, etc.
  • multireference dynamic correlation approaches have an advantage over the CAS method as they account for dynamic correlation across the “active space” and “inactive space”.
  • the ic-MR-UCC method provides a more systematic ap- proach to compute observable quantities compared to MC-PDFT, as it does not rely on the choice of a pair density functional as MC-PDFT.
  • the accuracy can be in- creased systematically by going from ic-MR-UCCSD to ic-MR-UCCSDT to ic-MR- UCCSDTQ etc.
  • ic-MR-UCC over perturbative methods such as CASPT2 and NEVPT2 is its increased accuracy, analogous to the well-documented ad- vantages of CCSD and UCCSD over second-order M ⁇ ller-Plesset perturbation theory (MP2) and to the advantages of traditional multireference coupled cluster over perturbative multireference methods.
  • MP2 M ⁇ ller-Plesset perturbation theory
  • FT-NISQ unitary dynamic correlation FT-NISQ-UDC
  • FT-NISQ-UDC FT-NISQ unitary dynamic correlation
  • the latter information can be used to represent the electron orbitals defining the “inactive space” part on a NISQ-QPU with a respective fidelity using a state that can easily be prepared on the NISQ-QPU, ⁇ ⁇ ⁇ ⁇ , e.g. by initializing a qubit in state 1 if the inactive electron orbital is oc- cupied and in state 0 if the inactive electron orbital is unoccupied according to the Jordan- Wigner transformation.
  • the FT-, higher-fidelity NISQ- and/or the NISQ-QPU are located on the same chip to facilitate entanglement in a later step.
  • ⁇ ⁇ ⁇ is a unitary coupled cluster (UCC) operator.
  • UCC unitary coupled cluster
  • Those electronic excitations/transitions that involve at least one active and at least one inactive electron orbital will create entanglement between the respective quantum comput- ers, e.g. a term ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ with ⁇ referring to an active electron orbital that has been mapped onto a FT-QPU or a higher fidelity NISQ-QPU and ⁇ , ⁇ , ⁇ referring to occupied or unoccupied inactive electron orbitals that have been mapped onto the NISQ-QPU will cre- ate entanglement between qubits located on two different QPUs.
  • the method can comprise the following steps.
  • a first step the CAS method and process as described above is performed using, for example, a FT-QPU of higher-fidelity NISQ- QPU and, e.g., a quantum phase estimation algorithm (QPE) to determine the exact or a near-exact solution of the “active space” part.
  • QPE quantum phase estimation algorithm
  • the electron orbitals can be stored on a CPU as part of the reference state.
  • the dynamic correlation of the “inactive space” and be- tween “active space” and “inactive space” is accounted for by using an entangled quantum computing system in combination with a variational approach similar to the general proce- dure exemplarily depicted in Fig.11.
  • the solution of the “active space” part can be prepared on a higher-fidelity NISQ-QPU or FT-QPU resulting in ⁇ ⁇ ⁇ ⁇ , e.g.
  • the electron orbitals that are stored on the CPU can be utilized, to prepare a wavefunction describing the “inactive space” part on a NISQ-QPU resulting in ⁇ ⁇ ⁇ ⁇ as part of the ref- erence state. This can require as many qubits on the NISQ-QPU as there are electron orbitals in the “inactive space”.
  • QPE quantum phase estimation
  • the entire CAS wavefunction is prepared on the QPUs of the quantum computing system as reference state.
  • ⁇ being a set of varia- tional parameters that is adjusted on the CPU within, e.g., a VQE procedure.
  • ⁇ being a set of varia- tional parameters that is adjusted on the CPU within, e.g., a VQE procedure.
  • UDC operator unitary coupled cluster (UCC) operator described above.
  • parameters can be either chosen randomly or by means of other computationally inexpensive traditional methods, e.g.
  • the method performes a respective iteration of the above steps after updating the set of varia- tional parameters on the CPU such that the energy is minimized, e.g. in a variational pro- cedure. If the energy and the variational parameters are converged, the method can pro- ceed with the final step.
  • the electron orbitals that are stored on the CPU as a result of the CAS calculation are kept fixed during the procedure, i.e. the CAS wavefunction that serves as a reference for the dynamic correlation treatment is not varied any more.
  • the electron orbitals within optional self-consistent field (SCF) steps.
  • SCF self-consistent field
  • the final energy and further properties of the solution can then be pro- vided to the user.
  • further post-processing on the CPU can be performed including application to real-world problems related to a chemical product like molecules, solids, ma- terials, etc.
  • the multireference dynamic correlation approach described above exhibits very similar ad- vantages over other methods as described already with respect to the NISQ-UDC method above.
  • the FT-NISQ-UDC method described above neither relies on the measurement of CI coefficients nor on the approximate recon- struction of the CAS wavefunction on a different hardware device. This brings the ad- vantage that the unitary operator accounting for dynamic correlation is applied to the exact CAS wavefunction and not an approximately reconstructed one. Such an approach may help to eliminate problems that can result from an approximate reconstruction of the CAS wavefunction, such as intruder states.
  • TCC tailored coupled cluster
  • CC complementary multi- reference coupled cluster
  • TCC is a modification of the widely used single-reference CC approach to incorporate the effects of static correlation directly into the coupled cluster exponential operator, which is then applied to a single-reference wavefunction ⁇ ⁇ ⁇ to generate an interaction representation of the form: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ (9)
  • ⁇ ⁇ ⁇ is a single basis state such as the one constructed from the natural or canonical orbitals of a CAS wavefunction and not a linear combination of multiple basis states like in Eq.
  • ⁇ ⁇ can be partitioned into a sum of two commuting operators, ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ .
  • ⁇ ⁇ is a coupled cluster operator which is of similar form as the one already discussed with regard to Eq. (5).
  • it is directly determined from the preceding CAS calculation on a QPU via the CI coefficients described above, e.g. in case of the TCCSD method the CI coefficients for the singly and doubly excited basis states, ⁇ ⁇ ⁇ and ⁇ ⁇ , are connected to the coupled cluster operator ⁇ ⁇ via the relation
  • ⁇ ⁇ focuses on static correlation and is restricted to act on electron orbitals within the “active space”.
  • the parameters that determine the oper- ator ⁇ ⁇ can be calculated from the CI coefficients according to Eq. (10) as part of the interaction representation. If applying the TCCSD method, only the singles and doubles CI coefficients are needed. Furthermore, ⁇ ⁇ ⁇ can be constructed, e.g., from the natural or canonical orbitals of the CAS wavefunction. Both quantities, ⁇ ⁇ and ⁇ ⁇ , can be kept fixed throughout all of the following steps. Then, the modified coupled cluster equations, Eq. (11) as part of the interaction representation, are iteratively solved on a CPU to deter- mine the parameters contained in ⁇ ⁇ , thus accounting for dynamic correlation across all electron orbitals.
  • the final energy can be evaluated on the CPU according to Eq. (12).
  • further properties can be calculated.
  • the final outcome can be provided to the user.
  • Further post-processing and application to real-world problems related to a chemical product like molecules, solids, materials, etc. is possible.
  • the TCC method is simpler and computationally less expensive com- pared to traditional genuine multireference approaches for CPUs that aim at including dy- namic correlation on top of a statically correlated reference wavefunction and thus typically require the calculation of higher-order reduced density matrices as already described above.
  • the s-sc-NEVPT2 energy correction which is a second-order perturbative energy correction to the CAS energy can be used as interaction representation in this case and can read: ( 13) s trongly contracted perturber function repre- senting the subspace ⁇ ⁇ ⁇ is the projection operator onto the subspace .
  • ⁇ is the ⁇ ⁇ number of electrons added to or removed from the “active space”.
  • ⁇ labels the occupied and virtual electron orbitals in the “inactive space” that electrons are removed from or added BASF SE 221032 221032WO01 to, respectively.
  • BASF SE 221032 221032WO01 BASF SE 221032 221032WO01
  • ⁇ ⁇ ⁇ is the unperturbed reference wavefunction obtained by the CAS calcu- lation in the previous step as reference state.
  • ⁇ ⁇ ⁇ is the energy of the perturber state: which is calculated as the expectation value of the so-called Dyall Hamiltonian ⁇ ⁇ ⁇ .
  • the denominator and numerator in Eq. (14) are: denote the CI states defined in Eq. (1) and the respective CI coefficients are calculated via the overlap of the CAS wavefunction with the CI states, see Eq. (2) and following.
  • the preceding CAS procedure on the QPU naturally provides a stochastic sam- ple of the CI states, with probability distribution by measuring qubits repeatedly. This result can then be put into Eqs.
  • the CI coefficients can be determined as also already described above.
  • the absolute values and phases of the most relevant CI coefficients can then be stored on a CPU as part of the reference state.
  • dynamic correlation is accounted for by evaluating the sec- ond order energy correction according to Eq. (13) as interaction representation, for in- stance, on a CPU.
  • the CAS wavefunction can be reconstructed according to Eq. (1) using the most relevant CI coefficients, as described above.
  • the CAS wavefunction is normalized ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ .
  • the CAS energy, ⁇ ⁇ ⁇ can also be put into Eq. (13).
  • the reaction free en- thalpy is indicative of whether a chemical reaction can occur in principle or not and the free enthalpy of activation is indicative of the rate, i.e. speed, of a chemical reaction.
  • the most important and difficult to calculate contributions to the respectively required free en- thalpies are energy differences between reactants, products and the transition state, e.g. the highest point in energy along the reaction pathway from reactants to products.
  • the reaction energy which is one of the main contributions to chemical thermody- namics, is obtained by subtracting the sum of the total energies of all reactants from the sum of the total energies of all products.
  • the activation energy which is one of the main contributions to chemical kinetics, is obtained by subtracting the sum of the total BASF SE 221032 221032WO01 energies of all educts from the total energy of the transition state.
  • the total energies of respective products, reactants and transition states can advantageously be calculated uti- lizing the methods of the invention as described above.
  • a highly accurate calculation of all species within a chemical reactive network i.e.
  • calculating the differences in total energies between dif- ferent electronic states e.g., between the ground state and one or more electronically ex- cited states, e.g., with particular spin multiplicities or electronic configurations that are dif- ferent from the ground state
  • the calculation of electronically excited states is furthermore a prerequisite for the computational design of, e.g., dyes or photoinitiators as well as more complex assem- blies like organic electronic materials.
  • Another example for technical application properties that can be determined with the above described methods are molecular properties beyond energies, for example, electrostatic multipole moments, hyperfine couplings, electrical fields and their gradients relevant for Mössbauer spectroscopy, diamagnetic shieldings relevant for nuclear magnetic resonance (NMR) spectroscopy, etc.
  • the calculation of physico-chemical properties is im- portant for molecular structure and property elucidation.
  • the above described invention is particularly advantageous for the solving of problems in molecular systems that exhibit strong static correlation. Nevertheless, the in- vention is not limited to solving statically correlated electronic structure problems and can be applied to all electronic structure problems.
  • Statically correlated molecular systems usu- ally comprise parts that exhibit a complex electronic structure which makes high-accuracy calculations often prohibitively expensive on classical computers already for small problem sizes.
  • Examples for molecular systems that exhibit strong static correlation commonly in- clude metal-organic compounds that contain transition metals such as iron, nickel, rhodium, palladium, etc., or contain lanthanides and actinides.
  • the examples for molecular systems that exhibit strong static correlation include statically correlated homonuclear or oligonuclear center in weakly correlated environments, wherein the term “nuclear” refers to transition metal, lanthanide or actinide ions or atoms therein plus optionally single ions or single atoms of the ligands.
  • transition metal compounds are of key importance for the design of new catalysts, chelating agents, homogenously catalyzed fine chemicals, en- zymes, etc. Furthermore, static correlation also occurs outside of transition metal chemis- try, e.g., during chemical reactions of organic molecules in bond-breaking and/or -forming situations, e.g. in certain transition states, and also occurs in certain common main-group- element molecules like ozone. Specific industry-relevant chemical products to which the invention can be applied are, for example, catalysts.
  • Catalysts play a crucial role in enabling or accelerating chemical reac- tions under mild conditions, e.g., mild temperatures and mild pressures, by interacting with the transition state and lowering its energy thus reducing the activation energy and increas- ing the rate of the chemical reaction.
  • catalysts are often used that contain 4d or 5d transition metals like rhodium and palladium, which are highly expensive, like the rhodium- based Wilkinson catalyst for hydroformylation.
  • the goal of many technical objectives is to substitute those catalysts by catalysts that are cheaper to produce containing, e.g., cheaper 3d transition metals cobalt or iron.
  • the above described invention can be particularly ad- vantageous in the area of homogenous catalysis, e.g., for calculating oxidation reactions, reduction reactions, hydrogenations, carbonylations, etc. in large-scale chemical produc- tion processes such as the chemical production process of polymers but also in the syn- thesis of homogenously catalyzed basic chemicals.
  • energies for a predetermined catalytic cycle including unde- sired side reactions can be calculated for a set of predetermined catalysts before their syn- thesis in the laboratory. As described above, those activation energies contribute to the calculation of chemical kinetics, in particular chemical reaction rates.
  • deter- mined chemical reaction rates of the potential catalyst can be compared with target chem- ical reaction rates and, based on the comparison, either i) a respective potential catalyst BASF SE 221032 221032WO01 can be determined as target catalyst, or ii) a new potential catalyst can be provided and the determination of the reaction rates according to the invention can be repeated.
  • a respective potential catalyst BASF SE 221032 221032WO01 can be determined as target catalyst
  • ii) a new potential catalyst can be provided and the determination of the reaction rates according to the invention can be repeated.
  • a complex formation constant is a thermodynamic quantity that indicates how thermodynam- ically stable the resulting complex of the metal ion and chelating agent is.
  • a reliable com- putational prediction typically requires a highly accurate calculation of total energies of the respective ions and molecules which is particularly challenging for the case of transition- metal ions.
  • a reliable prediction of the selectivity of chelating agents is chal- lenging, since both its experimental determination and its computational prediction are dif- ficult.
  • Selectivity is a means that describes how strongly a particular chelating agent pref- erably binds to a specific metal ion compared to other metal ions, which can be derived from respective complex formation constants.
  • a very well-known example for a chelating agent is ethylenediaminetetraacetic acid (EDTA) which can be used, e.g., for the solubili- sation of a Fe 3+ ion.
  • EDTA ethylenediaminetetraacetic acid
  • the goal of many technical objectives is to design new chelating agents with a predetermined selectivity that exhibit favorable properties like biodegradability or are less hazardous to water organisms.
  • Chelating agents are used in a large variety of tech- nical applications, e.g., to suppress the undesired influence of metal ions in washing and cleaning processes. Furthermore, chelating agents are also used in mining for selective extraction of metals. For example, using the above described invention reaction energies for a predetermined chelating agent can be calculated that ultimately contribute to the cal- culation of complex formation constants and thus the selectivity with respect to different transition metal ions. These calculations are done, e.g., for a set of predetermined chelating agents before their synthesis in the laboratory.
  • determined selectivities of the potential chelating agent can be compared with target selectivities and, based on the com- parison, either i) a respective potential chelating agent can be determined as target chelat- ing agent, or ii) a new potential chelating agent can be provided and the determination of the selectivities according to the invention can be repeated.
  • a respective potential chelating agent can be determined as target chelat- ing agent
  • a new potential chelating agent can be provided and the determination of the selectivities according to the invention can be repeated.
  • excited-state properties obtained as solution to the electronic struc- ture problem can be used.
  • energies of electronically excited states i.e. ener- gies of states with predefined spin multiplicities or electronic orbital configurations that are different from the ground state, and the energy of the respective electronic ground state, for instance, both obtained by utilizing a gate-based quantum computer, can be used.
  • vibrational contributions such as Franck-Condon profiles obtained by utilizing, e.g., a boson sampling photonic quantum computer as well as other contribu- tions, such as line widths obtained via approximate calculations on a classical computer or as input from a user
  • vibrational contributions such as Franck-Condon profiles obtained by utilizing, e.g., a boson sampling photonic quantum computer as well as other contribu- tions, such as line widths obtained via approximate calculations on a classical computer or as input from a user
  • technical application properties related to spectroscopy can be calculated that can be directly related to experimentally accessible properties and thus support solving the real-world chemistry or material problem.
  • electronic absorption spectra can be computed, that directly refer to, e.g., experi- mentally accessible UV/Vis spectra.
  • UV/Vis spectroscopy uses light in the visible and adjacent ranges, wherein the absorption or reflectance of the light in the visible range by a chemical product or material directly affects the perceived color of that chemical product or material.
  • computed electronic absorption spectra can support, for instance, the design of new dyes.
  • photoinitiators which are molecules that create reactive species, such as free radicals, when exposed to radiation in the UV or visible range. The reactive species can then initiate, for instance, polymerization to create a polymer.
  • the difference in computed energies between the energetically lowest electronically excited state and the electronic ground state directly relates to the required wavelength of a laser irradiating the photoinitiator to initiate this polymerization process.
  • Electronic emission spectra can be computed, that directly refer to, e.g., ex- perimentally accessible fluorescence spectra.
  • Electronic emission spectra are complemen- tary to electronic absorption spectra, in that the former deal with transitions of electrons from an excited state to the ground state induced by emission of photons while the latter deals with transitions of electrons from the ground state to excited states induced by ab- sorption of photons.
  • the differ- ence in computed energies between an electronically excited state and the electronic ground state of a molecule or material is directly related to the color of the emitted light.
  • the color of the emitted light of a new potential organic light emitting diode material can be computed before actually synthesizing the material.
  • IR infrared
  • the derivatives of the total ground state energy w.r.t to nuclear positions obtained as described above can be used.
  • the second derivates are used, which can be either calculated entirely analytically, entirely numerically, or by using the analytically calculated first derivatives to calculate the second derivates numerically in a subsequent step.
  • the calculated spectra which are also referred to as vibrational spectra within the rigid rotor/harmonic oscillator approximation as they refer to molecular vibrations, can be directly related to experimentally accessible IR spectra.
  • IR spectroscopy can be used to characterize new chemical and/or materials or to identify and verify known and unknown samples. Furthermore, vibronic spectra can be computed, that take into account simultaneous changes in electronic and vibrational energy levels of a chemical product or material due to the absorption of emission of a photon of the appropriate energy. Vibronic spectroscopy may provide information, such as bond-length, on electronic excited states of a molecule. To facilitate the comparison of the above mentioned computed spectra with respective ex- perimentally determined spectra, the calculated spectra are typically visualized by plotting calculated transition intensities or related quantities, such as absorbance, against the re- spectively calculated transition energies or related quantities, such as transition wave- lengths.
  • the reaction free enthalpy is indicative of whether a chemical re- action can occur in principle or not and the free enthalpy of activation is indicative of the rate, i.e. speed, of a chemical reaction.
  • the reaction free enthalpy, ⁇ ⁇ can be calculated by subtracting the sum of the free en- thalpies of all reactants – ⁇ and ⁇ in the example above – from the sum of the free en- thalpies of all products – ⁇ and ⁇ in the example above according to ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ wherein the free enthalpy in solution, ⁇ ⁇ , of each individual chemical species is weighted by its respective stochiometric weight ⁇ .
  • the free enthalpy of activation, ⁇ ⁇ can be obtained by subtracting the sum of the stochiometrically weighted free enthalpies of all reactants from the free enthalpy of the transition state – ⁇ in the example above – which is the highest point in free enthalpy along the reaction pathway from reactants to products, according to ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ Since chemical reactions typically happen in solution, e.g. in water, and not in the gas phase, all free enthalpies are preferably calculated considering the influence of a solvent. However, also a calculation omitting the influence of the solvent can be a reasonable ap- proximation for many application cases.
  • the following example takes the solvent into ac- count, but can also be applied to approximations without taking the solvent into account by removing the solvent components accordingly.
  • the free enthalpy in solution, ⁇ ⁇ of an individual chemical species, e.g. a reactant ⁇ or ⁇ , a transition state ⁇ of product ⁇ or ⁇ , can be obtained as the sum of the free enthalpy in the gas phase, ⁇ ⁇ , and the free en- thalpy of solvation, ⁇ ⁇ , according to ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ It is noted that sometimes the free enthalpy in solution is also named Gibbs free energy in solution.
  • the free enthalpy in the gas phase is obtained at a predetermined temperature ⁇ according to ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ wherein ⁇ is the electronic energy.
  • the high-level energy can be generated utilizing the method described above, for instance, utilizing a quantum computer. It is noted, that this energy can – depending on the electronic state of interest – both refer to the electronic ground state and an electronically excited state.
  • ⁇ is the vibrational zero-point energy
  • ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ are the translational/rotational/vibrational partition functions, respec- tively.
  • Both the ⁇ and ⁇ ⁇ can be calculated from a vibrational spectrum, which can be generated, for instance, using a spectroscopy workflow as described above, in particular, the IR spectroscopy workflow, utilizing a quantum computer as described above.
  • these quantities can also be obtained utilizing a classical computer in combination with generally less accurate methods such as density functional theory (DFT).
  • DFT density functional theory
  • ⁇ is the Avogadro gas constant.
  • the free enthalpy of solvation, ⁇ ⁇ , of a molecule in a predefined solvent can be obtained via solvation models such as the conductor like screening model for real solvents (COSMO-RS) utilizing a classical computer.
  • the electron density, which is indicative of the distribution of the electric charge in the molecule, obtained utilizing a quantum computer as described above can be used to cal- culate the screening charge density ⁇ on the surface of the molecule.
  • this information can be used to calculate the chemical potential ⁇ of the molecule in the prede- termined liquid solvent or mixture. The resulting chemical potential ⁇ is then used to calcu- late the free enthalpy of solvation.
  • reaction free enthalpies and free enthalpies of activation in solution for all potential reaction pathways i.e., for multiple chemical reactions taking into account all possible transition states, intermediates and products
  • i.e., reactants i.e., reactants
  • the highly accurate energy computation for all species of a chemical reactive network i.e.
  • Catalysts play a crucial role in enabling or accelerating chemical reactions under mild con- ditions, e.g., mild temperatures and mild pressures, by interacting with the transition state and lowering its energy thus reducing the free enthalpy of activation and increasing the rate of the chemical reaction.
  • catalysts are often used that contain 4d or 5d transition metals like rhodium and palladium, which are highly expensive, like the rhodium-based Wilkinson catalyst for hydroformylation.
  • the goal of many technical objectives is to substi- tute those catalysts by catalysts that are cheaper to produce containing, e.g., cheaper 3d transition metals like cobalt or iron.
  • the chemical reactivity workflow can be particularly advantageous in the area of homogenous catalysis, e.g., for calculating oxidation reactions, reduction reactions, hydrogenations, carbonylations, etc. in large-scale chemical produc- tion processes such as the chemical production process of polymers but also in the syn- thesis of homogenously catalyzed fine chemicals.
  • utilizing the chemical re- activity workflow free enthalpies of activation for a predetermined catalytic cycle including undesired side reactions can be calculated for a set of predetermined catalysts before their BASF SE 221032 221032WO01 synthesis in the laboratory. As described above, those free enthalpies of activation contrib- ute to the calculation of chemical kinetics, in particular chemical reaction rates.
  • determined chemical reaction rates of the potential catalyst can be compared with target chemical reaction rates and, based on the comparison, either i) a respective potential cat- alyst can be determined as target catalyst, or ii) a new potential catalyst can be provided and the determination of the reaction rates according to the invention can be repeated.
  • a re- spective reaction process can also be controlled such that the catalyst is utilized in the reaction, for example, a feet to a reactor can be controlled accordingly.
  • chelating agents as shown in Fig. 17.
  • a complex formation constant is a thermodynamic quantity that indicates how thermodynamically stable the resulting complex of the metal ion and chelating agent is. It can be calculated using the reaction free enthalpy for the reaction of chelating agent and metal ion to form the respective chelate complex in solution.
  • a reliable computational determination is preferably based on an accurate calculation of the reaction free enthalpy which is particularly challenging for reactions of transitional metal ions.
  • Selectivity is a means that describes how strongly a particular chelating agent preferably binds to a specific metal ion compared to other metal ions, which can be derived from respective complex formation constants.
  • a very well-known example for a chelating agent is ethylenediaminetetraacetic acid (EDTA) which can be used, e.g., for the solubilisation of a Fe 3+ ion.
  • the goal of many technical objectives is to design new chelating agents with a predetermined selectivity that exhibit favorable properties like biodegradability or are less hazardous to water organisms.
  • Chelating agents are used in a large variety of technical applications, e.g., to suppress the undesired influence of metal ions in washing and clean- ing processes.
  • chelating agents are also used in mining for selective extrac- tion of metals. For example, using the chemical reactivity workflow described above reac- tion free enthalpies for a predetermined chelating agent can be calculated to obtain respec- tive complex formation constants and thus the selectivity with respect to different transition metal ions.
  • chelating agents that fulfill certain predetermined criteria/technical application properties, e.g., with respect to selectivity, are finally selected for synthesis and further investigation in the la- boratory, for instance, by providing control data that causes a respective synthesis of the respective chelating agent.
  • a respective reaction process can also be controlled such that the chelating agent is utilized in the reaction, for example, a feet to a reactor can be controlled accordingly.
  • further technical application properties such as activity coefficients, solubility, partition coefficients and vapor pressure can be calculated using a slightly amended work- flow as described above based on the COSMO-RS method.
  • the equilibrium vapor pres- sure for example, is also an experimentally accessible quantity and defined as the pres- sure exerted by a vapor in thermodynamic equilibrium with its condensed phases (liquid or solid) at a given temperature in a closed environment and is an indication of a liquid’s or solid’s evaporation rate.
  • the computation of the vapor pressure is important, e.g., to quantify the volatility of a hazardous or toxic chemical product at a given tempera- ture before or instead of carrying out real-world experiments.
  • the potentially haz- ardous or toxic chemical product is volatile, i.e., has a high vapor pressure, which would result in a high concentration of the chemical product in the breathing zone, additional safety measures can be established.
  • a further exemplary embodiment refers to quantitative structure-activity relationship (QSAR) or quantitative structure-property relationship (QSPR).
  • QSAR or QSPR models are regression or classification models that relate a set of predictor variables, also called “de- scriptors”, to one or more output variables, e.g., the potency of a response variable in case of a regression model, in particular a partial least squares regression model, or to a cate- gorical value in case of a classification model.
  • neural networks can also be used as model.
  • the predictor variables can refer to a set of solutions of electronic structure problem of electronic structure systems, e.g., molecules, wherein at BASF SE 221032 221032WO01 least one of the electronic structure properties that is generated based on the solution of the electronic structure problem is calculated utilizing a quantum computer.
  • the predictor variables can also refer to a set of technical application properties of real-world chemistry or material problems that are obtained by processing the electronic structure properties as described above. Furthermore, a combination with predictor variables ob- tained from other sources like chemoinformatic processing of structural information or ex- perimental physico-chemical properties is possible as well.
  • the predictor variables can be electronic, geometric, structural or physico-chemical properties and/or molecular de- scriptors and thus refer to quantities that are obtainable by one of the above described approaches or similar approaches, whereas the output variables refer to technical applica- tion properties of real-world chemistry or material problems, such as a biological activity or a chemical property of a molecule, that are not directly accessible by the above described or similar approaches.
  • the QSAR/QSPR model mathematically summarizes a supposed relationship between the selected set of predictor variables and the output variables. After the construction of the model, it is carefully validated with regard to robustness, prediction performance and its applicability domain. After successful validation, the QSAR/QSPR model can then finally be used to determine the output variables, e.g., technical application properties, of new real-world chemistry or material problems for a set of predictor variables that are obtained as described above utilizing a quantum computer. Since the quality of the prediction signif- icantly depends on the accuracy of the provided predictor variables the utilization of a quan- tum computer is expected to be advantageous.
  • the quality of the prediction also depends on other factors such as the selection of appropriate predictor variables, the used QSAR/QSPR model as well as its validation.
  • a specific technical application property that can be calculated using the above described QSAR/QSPR workflow is, for example, the biological activity of a chemical product such as a drug, toxicant or environmental pollutant using respective computed electronic structure properties or above described technical application properties as predictor variables. Bio- logical activity can be expressed quantitatively as the concentration of a chemical product required to give a certain biological response including desirable therapeutic effects and undesirable side effects.
  • the QSAR/QSPR workflow can be used for a com- putational toxicological assessment of a new chemical product.
  • a single unit or device may fulfill the functions of several items recited in the claims.
  • the mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
  • Procedures like the providing of an electronic structure representation, causing a quantum computer and/or a classical computer to generate and provide a solution, generating a solution to the electronic structure representation, etc. performed by one or several units or devices can be performed by any other number of units or devices.
  • These procedures can be implemented as program code means of a computer program and/or as dedicated hardware.
  • a computer program product may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.
  • Any units described herein may be processing units that are part of a classical computing system. Processing units may include a general-purpose processor and may also include a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other specialized circuit.
  • Any memory may be a physical system memory, which may be volatile, non-volatile, or some combination of the two.
  • the term “memory” may include any computer-readable storage media such as a non-volatile mass storage.
  • the computing system may include multiple structures as “executable com- ponents”.
  • executable component is a structure well understood in the field of computing as being a structure that can be software, hardware, or a combination thereof.
  • BASF SE 221032 221032WO01 stand that the structure of an executable component may include software objects, rou- tines, methods, and so forth, that may be executed on the computing system. This may include both an executable component in the heap of a computing system, or on computer- readable storage media.
  • the structure of the executable component may exist on a com- puter-readable medium such that, when interpreted by one or more processors of a com- puting system, e.g., by a processor thread, the computing system is caused to perform a function.
  • Such structure may be computer readable directly by the processors, for instance, as is the case if the executable component were binary, or it may be structured to be inter- pretable and/or compiled, for instance, whether in a single stage or in multiple stages, so as to generate such binary that is directly interpretable by the processors.
  • structures may be hard coded or hard wired logic gates, that are implemented exclusively or near-exclusively in hardware, such as within a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other specialized circuit.
  • FPGA field programmable gate array
  • ASIC application specific integrated circuit
  • executable component is a term for a structure that is well under- stood by those of ordinary skill in the art of computing, whether implemented in software, hardware, or a combination. Any embodiments herein are described with reference to acts that are performed by one or more processing units of the computing system. If such acts are implemented in software, one or more processors direct the operation of the computing system in response to having executed computer-executable instructions that constitute an executable component.
  • Computing system may also contain communication channels that allow the computing system to communicate with other computing systems over, for exam- ple, network.
  • a “network” is defined as one or more data links that enable the transport of electronic data between computing systems and/or modules and/or other electronic de- vices.
  • Transmission media can include a network and/or data links which can be used to carry desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general-purpose or special- purpose computing system or combinations.
  • the computing system includes a user interface sys- tem for use in interfacing with a user.
  • User interfaces act as input or output mechanism to users for instance via displays.
  • Those skilled in the art will appreciate that at least parts of the invention may be practiced in network computing environments with many types of computing system configurations, including, personal computers, desktop computers, laptop computers, message proces- BASF SE 221032 221032WO01 sors, hand-held devices, multi-processor systems, microprocessor-based or programma- ble consumer electronics, network PCs, minicomputers, mainframe computers, mobile tel- ephones, PDAs, pagers, routers, switches, datacenters, wearables, such as glasses, and the like.
  • the invention may also be practiced in distributed system environments where local and remote computing system, which are linked, for example, either by hardwired data links, wireless data links, or by a combination of hardwired and wireless data links, through a network, both perform tasks.
  • program mod- ules may be located in both local and remote memory storage devices.
  • at least parts of the invention may be prac- ticed in a cloud computing environment.
  • Cloud computing environments may be distributed, although this is not required. When distributed, cloud computing environments may be dis- tributed internationally within an organization and/or have components possessed across multiple organizations.
  • cloud computing is defined as a model for enabling on-demand network access to a shared pool of configura- ble computing resources, e.g., networks, servers, storage, applications, and services.
  • the definition of “cloud computing” is not limited to any of the other numerous advantages that can be obtained from such a model when deployed.
  • the computing systems of the figures include various components or functional blocks that may implement the various embodi- ments disclosed herein as explained.
  • the various components or functional blocks may be implemented on a local computing system or may be implemented on a distributed com- puting system that includes elements resident in the cloud or that implement aspects of cloud computing.
  • the various components or functional blocks may be implemented as software, hardware, or a combination of software and hardware.
  • the computing systems shown in the figures may include more or less than the components illustrated in the figures and some of the components may be combined as circumstances warrant. Any reference signs in the claims should not be construed as limiting the scope.
  • the invention refers to an apparatus for generating a property associated with a chemical product.
  • a providing unit provides an electronic structure representation including a) a first part indicative of an active space and b) a second part indicative of an inactive space. The property depends on the active space and the inactive space.
  • a determination unit causes a quantum computer and/or a classical computer to generate a solution of the first part and a solution to the second part.
  • a computation unit generates a solution to the electronic structure representation by combining the solution of the first part and the second part to generate the property.
  • the combining includes generating an interaction representation based on a reference state associated with a superposition of electron configurations gen- erated based on the solution of the first part and the second part.

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Abstract

The invention refers to an apparatus (720) for generating a property associated with a chemical product. A providing unit (721) provides an electronic structure representation including a) a first part indicative of an active space and b) a second part indicative of an inactive space. The property depends on the active space and the inactive space. A determination unit (722) causes a quantum computer and/or a classical computer to generate a solution of the first part and a solution to the second part. A computation unit (723) generates a solution to the electronic structure representation by combining the solution of the first part and the second part to generate the property. The combining includes generating an interaction representation based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the second part.

Description

BASF SE Carl-Bosch-Straße 38, 67056 Ludwigshafen am Rhein Germany Apparatus for generating a property associated with a chemical product FIELD OF THE INVENTION The invention refers to an apparatus, a method and a computer program product for gen- erating a property associated with a chemical product. Further, the invention relates to a system generating a property associated with the chemical product comprising the appa- ratus. BACKGROUND OF THE INVENTION Quantum computers generally are a completely new kind of computing system that allows utilizing the special behaviour of quantum mechanical systems for performing problem cal- culations that, under the right circumstances, are not performable by ordinary computers in any reasonable time. SUMMARY OF THE INVENTION It is an object of the present invention to provide apparatuses, methods, systems and com- puter program products that allow to increase the efficiency and effectivity, i.e. allow to decrease the computational time and required computational resources with the same re- sulting quality, for calculations of problems related to chemical products, for instance, elec- tronic structure problems, utilizing a quantum computer. Moreover, chemical industry sells chemical products with specific technical application properties. The core of any chemical product is the chemical molecule or the combination of chemical molecules, e.g. the chem- ical product includes one or more chemical molecules, which determines the properties of BASF SE 221032 221032WO01 the chemical product. Properties of chemical monomers or oligomers may be determined to determine the properties of chemical polymers, e.g. through extrapolation. Chemical products with one or more chemical molecules of one or more types are highly complex real-world systems containing multiple interacting electrons that make up the prop- erties of the chemical molecules and thus the properties of the chemical products. Hence, it is utterly important to capture the complexity of chemical molecules in calculations by reflecting the atom types, the chemical bonds between the atoms of the same and/or dif- ferent types, the three-dimensional structure of the atom arrangement, the interactions be- tween multiple atoms in that three-dimensional arrangement and in particular the sub-atom structure made up by electrons and the electron density. Such highly complex molecular structures are commonly described by way of an electronic structure problem, such as by utilizing a Schrödinger equation utilizing a Hamiltonian operator. To allow for a solution of such complex electronic structure problems approximations can be used. However, through approximation the properties stemming from electron correlations may be inade- quately reflected in most systems. Hence there is a need to include as much of the electron correlations of the real-world system as possible to arrive at results that are as close to the real-world technical application properties of the chemical molecule as possible. This is particularly important for the chemical industry, which produces chemical products based on the generation of chemical molecules, their properties and the production recipes lead- ing to a respective real-world chemical product with respective properties. Electronic structure calculations are essential in a process for designing an experimental setup, wherein often the number of experiments that lead to the real-world chemical mole- cule with desired properties depends on the accuracy of the result of the calculated elec- tronic structure problem and the accuracy of the properties determined by the result. Ob- taining a highly accurate solution can be a NP hard problem – meaning more than multiple ten years for a classical computer to solve. Hence, it is impossible in many real-world sce- narios of developing practically relevant chemical molecules with enhanced or new prop- erties to generate such accurate solutions. This leads to more intense laboratory work, which is inefficient and increases the time for developing new chemical molecules. With the environmental impacts of chemical developments and the speed at which chemi- cal industries have to adapt their chemistry backbones and chemical products, it is advan- tageous to improve the development of new or enhanced chemical products specifically via more accurate solutions to the electronic structure problems. Embedding quantum compu- ting into such development cycles may provide for a solution to such problems. However, BASF SE 221032 221032WO01 the embedding of quantum computing is a challenge on its own. As a result, the apparat- uses, systems, methods and computer program products disclosed herein allow for more efficient and effective use of quantum computing to enhance the development of new or enhanced chemical products. Since causing a quantum computer and/or a classical computer to generate and provide a solution of a first part of an electronic structure representation and causing a quantum com- puter and/or a classical computer to generate and provide a solution to a second part of an electronic structure representation, for each of the parts of the electronic structure repre- sentation respective most suitable computing systems can be utilized including quantum computing systems, classical computing systems and combinations thereof. This allows to adapt the utilized computation systems specifically to the to be solved problem. Moreover, since the solution of the first part of the electronic structure representation and the solution of the second part of the electronic structure representation are computationally combined by generating an interaction representation that is based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the solution of the second part, independent of the computing systems utilized in the previous step the correlations between and within the first and second part of the elec- tronic structure representation can be determined again on a respective suitable computing system, in particular, a classical computer and/or a quantum computer depending on the respective problem. Thus, for each part of the solution computation the most suitable com- puting system can be chosen independent of a computing system utilized for computing other parts of the solution. This allows for a very computer resource effective solving of complex electronic structure problems. Moreover, utilizing a reference state as defined above provides more information on an electronic structure system than, for instance, com- monly utilized reduced density matrices. Thus, the reference state as defined above allows to utilize a plurality of effective and efficient solution methods that can only be utilized with respective information on the system and are independent of the methods utilized for de- termining the solution of the second part and the solution of the first part. Thus, the respec- tive relevant electronic structure problems important for determination of a property asso- ciated with a chemical product can be solved with a higher efficiency and effectivity in the development of chemical products. In a first aspect of the present invention, an apparatus is presented for generating a prop- erty associated with a chemical product, wherein the chemical product includes one or more molecular structures, wherein the apparatus comprises i) an electronic structure rep- resentation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the BASF SE 221032 221032WO01 electronic structure representation indicative of an active space including a part of the elec- tronic structure associated with a molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the elec- tronic structure associated with a molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) a solution determination unit for causing a quantum computer and/or a classical computer to generate and provide a solution of the first part of the electronic structure representation, and for causing a quantum computer and/or a classical computer to generate and provide a solu- tion to the second part of the electronic structure representation, and iii) a correlation com- putation unit for generating a solution to the electronic structure representation by combin- ing the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate the property associated with the chemical product, wherein computationally combining in- cludes generating an interaction representation based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the solution for the second part, and causing a classical computer and/or quantum computer to provide a solution to the interaction representation. Generally, the apparatus can be realized in form of software or hardware or a combination thereof, wherein the hardware can refer to any known dedicated or general classical com- puter hardware. For example, the apparatus can be realized as any known computational device, like a PC. However, the apparatus can also be realized as a cloud environment, computational network, etc., such that at least parts of the apparatus can also be realized as a network solution and thus can be spread over a plurality of computational devices. The chemical product can be any chemical product that includes, for example, consists of, one or more molecular structures. Molecular structures are structures that form at least a part of a molecule. For example, in a polymer consisting of a plurality of monomers, the molecular structure can be one of these monomers, but can also refer to a plurality of these monomers or even the complete polymer. Moreover, the molecular structure can also be one or more atoms in a molecule forming the chemical product. Generally, the molecular structure comprises an electronic structure that can be described by an electronic structure representation. The apparatus being for generating a property is to be interpreted as being suitable for generating a property, in particular, in assisting in generating a property. The generating of the property associated with the chemical product refers to determining or deriving and providing the respective property. The property can generally be any property of a chemical BASF SE 221032 221032WO01 product that is related to a solution of an electronic structure representation, for instance, refers to or can be derived from a solution of the electronic structure representation, of a molecular structure forming the chemical product. The property can be an electronic prop- erty of the electronic structure representation. The property can preferably refer to any property of a chemical product that allows to assess a technical applicability of the respec- tive chemical product as provided after its production. Preferably, the technical application property comprises any of a chemical reactivity, spectra and spectroscopic property, mo- lecular property, activation and reaction energies for a predetermined chemical reaction. Preferably, the technical application property comprises at least one of mechanical proper- ties, spectroscopic properties, physicochemical properties, chemical properties and biolog- ical properties. Generally, mechanical properties can refer to any of adhesion, tensile strength, stiffness, hardness, shrinkage, elongation, split tear, tear-strength, rebound, com- pressibility, abrasion, spillage, morphology, haptic properties, stress at break, elongation at break, granulometry and a degree of filling. A spectroscopic property can generally com- prise any of coloration, turbidity, opaqueness, lucidity, reflection, appearance, absorption, scattering, color strength, colour hue, colour saturation, colour intensity, cloud point, mat- ting degree, optical density, spectra, refractive index, IR spectra, Raman spectra, NMR spectra, ESR spectra, and UV/Vis spectra. Moreover, a physicochemical property can refer to any of density, viscosity, K-value, molar weight, dispersity, molar mass distribution, par- ticle size distribution, solubility, partition coefficients, interfacial properties, surface tension, dispersibility, storage stability, odor, segregation, coagulation, electric conductivity, electric capacity, surface area, flow time, vapor pressure, VOC, solid content, hygroscopicity, mag- netism, miscibility, thixotropy, phase transition properties, glass transition temperature, cor- rosion inhibition, solvent separation, aggregation, self-heating ability, impact sensitivity, loss on drying, angle of response, electrostatic charge, minimum film-forming temperature, charge density, electrostatic multipole moments, and thermal conductivity. The chemical property can comprise any of reaction thermodynamics, reaction kinetics, chemical re- sistance, reaction timing, demolding time, growing, hard/soft segment content, crystallinity, reaction temperature, reaction pressure, decomposition, thermal decomposition, photodeg- radation, acidity, pKa, pH, moisture/water content, flammability, burning rate, self-ignition, flash point, formation of flammable gases, reaction to fire, deflagration rate, residual mon- omer count, side product formation, degree of polymerization, salt content, temperature tolerance, oxidizing properties, reduction properties, reactivity, ash content, nonvolatile matter content, stability, chelating ability, calorific value, saponification value. Further, the biological property can comprise any of biodegradability, biological resistance, in particular, resistance against a pathogenic virus, bacterium, fungus, plant or animal or developmental stage of said pathogen, tolerance against environmental parameters, e.g. drought toler- BASF SE 221032 221032WO01 ance, resistance against enzymatic degradation, e.g. protease resistance, lipase re- sistance, amylase resistance, hydrolase resistance, pesticide resistance, toxicity, biotrans- formation, ecotoxicology, sensitization, in particular, allergenicity, bacterial count, enzyme activity, substrate specificity, cofactor dependence, product specificity, substrate and/or product inhibition, dissociation constant, Michaelis-Menten-kinetics values, activity/stability at or in different: pH, temperature, pressure, organic solvent concentration, carrier formu- lations, encapsulation formulations; distribution in environment, compartimentalisation, bi- oaccumulation, biological exposure LD50, mutagenicity. The electronic structure representation providing unit is adapted to provide an electronic structure representation associated with at least one of the one or more molecular struc- tures of the chemical product. In particular, the electronic structure representation providing unit can refer to a storage unit on which the electronic structure representation is already stored. However, the electronic structure representation providing unit can also comprise an input unit with which, for instance, a user can indicate an electronic structure represen- tation to the electronic structure representation providing unit. Generally, the electronic structure representation can be provided in any form that allows to determine the form of the electronic structure problem to be solved and the quantities defining the electronic structure problem and the form of interaction between these quantities. Preferably, the electronic structure representation refers to a mathematical description of an electronic structure problem to be solved, for example, to a mathematical description of the electronic structure problem utilizing an electronic structure Hamiltonian. However, the electronic structure representation can also refer to any other unambiguous form of notation of a re- spective electronic structure problem. Generally, the electronic structure representation is related to a molecular structure of the chemical product. In particular, the molecular struc- ture of the chemical product to which the electronic structure representation is related to can define the electronic structure problem and the quantities of the electronic structure problem. The electronic structure representation is associated with the technical application property. For example, if the chemical product refers to a specific molecule for which a technical application property should be determined, the respective molecule and its struc- ture define the quantities and interactions of the quantum mechanical electronic structure problem indicated by the electronic structure representation. Thus, the solution of the elec- tronic structure representation is indicative of the property. Thus, providing a solution of the electronic structure representation refers to providing the respective property. In particular, the property can be derived from the solution of the electronic structure problem. Prefera- bly, the electronic structure representation comprises or is indicative of atomic positions, a basis set, charge, and spin multiplicity depending on the specific chemical product and/or quantum mechanical electronic structure problem. BASF SE 221032 221032WO01 Generally, an electronic structure representation can refer to problems that are associated with determining an electronic structure of an atom, molecule, crystal, or amorphous solid, etc. For example, electronic structure representations can be utilized for determining ener- getic ground states of atoms and/or molecules, etc. Based on solutions of the electronic structure representation, further properties of the atom, molecule, crystal, or amorphous solid can be derived. Generally, the electronic structure representation can be mathemati- cally represented utilizing different classes of underlying electronic structure Hamiltonians. For example, Born-Oppenheimer Hamiltonians, non-Born-Oppenheimer Hamiltonians, Hamiltonians with additional one-electron potentials representing, e.g., electrostatic fields, two-component Hamiltonians including spin-orbit coupling, fully relativistic four-component Dirac-Hamiltonians, etc. From the solution of the electronic structure representation a plurality of properties of a respective chemical product can be derived. Examples for such electronic structure repre- sentation that can advantageously be solved in this invention can refer to calculating a ground state energy of a molecule or general electronic system. This allows, in particular, in the context of determining the ground state energy of all molecular species occurring in a chemical reaction to predict the reaction end products, the thermodynamic properties of the reaction, and the kinetic properties of the reaction. This understanding and the proper- ties of the reaction can then again be utilized to optimize chemical production processes, for prediction of a microstructure of polymers, for optimizing material properties, etc. Fur- ther, the electronic structure representation can also refer to calculating multipole moments of a chemical product. Such a calculation can be relevant for determining properties of the chemical product related to electrical and other technical application properties, e.g. the dielectric behavior of the chemical product, but also properties resulting from intermolecular interactions which are strongly dependent on the polar nature of the chemical product – such technical application properties can range from solubility and compatibility with certain media to complexation behavior of ions or impacts on spectroscopic properties, e.g. color. Accordingly, the determining of the value of the property based on the result of the solution of electronic structure representation is based on the respective property that should be determined and further based on the information that is provided by the solution of the electronic structure representation. Further, the electronic structure representation includes a first part of the problem and a second part of the problem. The first part of the electronic structure representation is indic- ative of an active space including a part of the electronic structure associated with the mo- lecular structure. The second part of the electronic structure representation is indicative of BASF SE 221032 221032WO01 an inactive space including another part of the electronic structure representation associ- ated with the molecular structure. Preferably, the part of the electronic structure represen- tation associated with the molecular structure included in the second part is the remaining part of the electronic structure representation without the first part. Preferably, the active space and the inactive space of the electronic structure representation refer to subspaces of the Hilbert space of the electronic structure representation. In particular, the basis of the Hilbert space of the electronic structure representation can be formed by electron orbitals and mathematically represented by antisymmetrized tensor products of the electron orbit- als and the inactive space and active space are defined by the electron orbitals to which they refer. However, the active and the inactive space can also be defined in other mathe- matical representations, for instance, if the electronic structure representation is formulated in another space. The first part and the second part are preferably defined based on the respective active or inactive space, i.e. are defined in the respective basis of the respective space, but can also comprise terms that are related to the orbitals representing the respec- tive other space, for example, terms that are related to electrons or electron orbitals that form the basis of the respective other space. Generally, the first part and the second part of the electronic structure representation are determined based on the chemical product and the molecular structure to be described by the electronic structure representation. In particular, since the molecular structure of the chemical product defines the quantities and interrelations between the quantities of the electronic structure representation, it also de- fines how these quantities and interrelations are described with respect to the first part and the second part of the electronic structure representation. In particular, since the chemical product defines the electron orbitals in the electronic structure representation, and in par- ticular, which orbitals have the strongest correlations such that for an accurate solution of the electronic structure representation of this molecular structure of the chemical product these correlations should be accounted for more accurately, the chemical product deter- mines how the first part and the second part are defined. For example, the first part of the electronic structure representation is provided such that it allows to calculate parts of the electronic structure of the chemical product that are most relevant for a specific application with high accuracy using a quantum computer. In such cases, the first part is provided such that it is based on electron orbitals that are most relevant for a specific application, since these electron orbitals exhibit the strongest correlations in the molecular structure of the chemical product during a chemical reaction of the chemical product and/or change during the specific application, e.g. are involved in bond-breaking and/or -forming processes dur- ing a chemical reaction of the molecular structure of the chemical product. The property associated with the chemical product depends on the active space and the inactive space. In particular, the property depends on the electronic structure represented BASF SE 221032 221032WO01 by the first and the second part and thus on the solution of the first and the second part of the electronic structure representation. Generally, the electronic structure representation can directly provide the first part and the second part. However, the electronic structure representation can also be provided such that it only indicates how to define the first and the second part, for example, by indicating the active and the inactive space or by indicating respectively which electron orbitals of the electronic structure problem indicated by the electronic structure representation should be part of the active and the inactive space. The first part and the second part of the electronic structure representation can then be derived by the information provided by the electronic structure representation, for example, by uti- lizing known mathematical rules and methods. Preferably, the electronic structure repre- sentation comprises or is indicative of the number and identity of the electron orbitals in the active space, the number of electrons to be taken into account in the first part, and/or a coefficient matrix of initial electron orbitals. Optionally, the apparatus can further comprise or utilize a translation unit configured to translate the electronic structure representation into a representative operation description indicative of a sequence of operations to be applied to the quantum elements of the quan- tum computer. Generally, the translation unit can be part of the apparatus, but can however also be omitted in the apparatus and can be part of the quantum computer, in particular, of a control unit of the quantum computer that automatically translates a provided electronic structure representation into a respective operation description. The translation unit is con- figured to determine, in particular, a sequence of operations such that a quantum mechan- ical calculation of the first part and/or the second part can be performed on a quantum computer. Thus, the translation unit can be configured to translate only the first part or only the second part, respectively, into a respective operation description depending on which part is to be computed on a quantum computer. Generally, operations are performed by a quantum computer by manipulating the states of quantum elements of the quantum com- puter, wherein the quantum elements can refer to all elements of the quantum computer that are utilized for simulating the electronic structure representation, for instance, to quan- tum elements forming the qubits of a quantum computer but also to bosonic fields repre- senting bosonic modes during a calculation of the problem. Methods for determining such operations for problems to be calculated on a quantum computer are generally known and can be utilized by the translation unit for determining the operation description for the first part or the second part, respectively, of the electronic structure representation. For exam- ple, Quantum Phase Estimation (QPE) or variational algorithms such as the Variational Hamiltonian Ansatz (VHA) or the Variational Quantum Eigensolver (VQE) with the Unitary Coupled Cluster (UCC) ansatz in combination with the Jordan-Wigner or the Bravyi-Kitaev BASF SE 221032 221032WO01 transformation and the CZ algorithm or similar algorithms, the FSIM network algorithm us- ing low-rank decomposition for the unitary evolution can be utilized for translating and pre- paring a calculation of a first part or second part, respectively, of the problem description on the quantum computer. An example for such a translation can be found, for example, in the articles “Quantum Computational Chemistry”, S. McArdle et. al., Rev. Mod. Phys.92, (2020), “Quantum Algorithms for Quantum Chemistry and Quantum Materials Science”, B. Bauer et. al., Chem. Rev. (2020), and “Quantum Chemistry in the Age of Quantum Com- puting”, Y. Cao, et al., Chem. Rev. (2019). The solution determination unit can be adapted to cause a quantum computer to generate and provide a quantum computational solution of the first part of the electronic structure representation. In an example, the solution determination unit is configured to cause a quantum computer to perform a quantum mechanical calculation based on the first part such that the result of the quantum mechanical calculation is indicative of the solution of the first part and then to generate the solution based on the result of the quantum mechan- ical calculation. If the apparatus comprises an optional translation unit that already provides a translation of the first part of the electronic structure representation into a representative operation description, the solution determination unit can be adapted to provide the repre- sentative operation description to the quantum computer in order to cause the quantum computer to perform the quantum mechanical calculation based on the determined repre- sentative operation description. However, if the apparatus does not comprise the transla- tion unit, the solution determination unit can be adapted to provide the first part or the sec- ond part provided or indicated by the electronic structure representation to the quantum computer, wherein then a part of the quantum computer system, for instance, a control unit of the quantum computer system, can be configured to provide the translation of the first part or the second part into a respective operation description that provides operations that can be performed on the quantum computer to calculate a solution of the first part or second part. In particular, the solution determination unit can be communicatively coupled with the quantum computer or a control unit of the quantum computer in order to cause the quantum computer to perform the quantum mechanical calculation and obtain a result that is indica- tive of the solution of the first part or second part. However, the communicative coupling can also be an indirect coupling, for instance, via a storage unit like a cloud storage unit on which respective control signals that cause the quantum computer to perform the quantum mechanical calculation are stored and then send to the quantum computer. Alternatively, the solution determination unit can also cause a classical computer to gener- ate and provide a solution of the first part of the electronic structure representation. De- pending on the respective electronic structure representation, utilizing a classical computer BASF SE 221032 221032WO01 for solving the first part of the electronic structure representation can be more effective and efficient. For example, for electronic structure representations with first parts that only rep- resent a small part of the electronic structure, for instance, only below a predetermined number of orbitals and electrons, it can be more resource efficient to utilize a classical computer. In such a case methods like full configuration interaction, density matrix renor- malization group theory, Møller-Plesset perturbation theory or coupled cluster theory can be utilized. Further, the solution determination unit can be configured for causing a classical computer to generate and provide a solution to the second part of the electronic structure represen- tation. For example, the solution of the second part can be a representation of an electron configuration of the inactive space of the respective molecule. In particular, the solution determination unit can be configured for causing a classical computer to generate and pro- vide a classical computational solution to the second part of the electronic structure repre- sentation. In particular, the solution determination unit can be configured to prepare and control a classical computer using known methods for causing the classical computer for solving the respective second part. The solution of the second part can be any kind of contribution of the second part to the solution of the electronic structure problem. For ex- ample, the solution can refer to any contribution of the inactive space that is taken into account for the interaction representation. For example, the solution determination unit can be configured to determine a solution of the second part based on respective known algo- rithms like Hartree-Fock or density functional theory (DFT). In a preferred embodiment, the solution of the second part is determined based on the solution of the first part. Thus, al- ready in this step an influence of the first part on the second part, i.e. of the active space on the inactive space, can be taken into account. In a preferred embodiment a SCF solution is determined for the second part. The solution of the second part hence is a better approx- imation to the overall solution and the interaction representation thus is based on an already quite accurate solution. In particular, it is preferred that the electronic structure representa- tion is already provided such that the solution of the second part can be calculated on a classical computing device utilizing respective known calculation methods. Alternatively, the solution determination unit can be configured for causing a quantum com- puter to generate and provide a quantum computational solution to the second part. The same methods described above with respect to computing the first part on a quantum com- puter can also be applied to computing the second part on a quantum computer. The solu- tion determination unit can for example be configured to cause a quantum computer to generate and provide a solution for at least one of the first part and the second part of the electronic structure representation. In an embodiment, the solution determination unit is BASF SE 221032 221032WO01 configured for causing a quantum computer to generate and provide a solution of at least one of the first and the second part. The correlation computation unit is configured to generate a solution to the electronic struc- ture representation by combining the solution of the first part and the solution of the second part. In particular, the computational solution of the first part and the computational solution of the second part are computationally combined to generate the property associated with the chemical product. If the solution of the first part and/or the second part is generated using a quantum computer, the correlation computation unit can be configured to utilize the measurement results provided by the quantum computer to determine the respective solu- tion. However, also a respective control unit of the quantum computer can be configured to utilize the measurement results to determine the respective solution. The computationally combining includes generating an interaction representation associ- ated with the combination of active and inactive space. The interaction representation is based on a reference state associated with a superposition of electron configurations and is generated based on the solution of the first part and the solution of the second part. The reference state refers to a representation of the superposition of electron configurations that are utilized as basis for the determination of correlations between the active space and the electronic structure of the inactive space and optionally also within one or both of these spaces. Thus, the reference state based on the solution of the first part and the solution of the second part represents the electron configurations in such a way that it can form a basis for the further calculations of the solution of the interaction representation. For example, for generating the reference state, solutions of the first part and solutions of the second part that are generated on a quantum computer refer to direct measurements of the electronic configuration states that are then directly constructed on the respective classical and/or quantum computer that is utilized for solving the interaction representation. Thus, a solution for a first part and/or a second part prepared on a quantum computer is not measured by measuring, for instance, characterizing quantities of the respective state, for instance, an energy, a reduced density matrix or any other observable, but refers directly to the states measured for the quantum elements that represent the respective states of the electrons in the electronic structure. The reference state therefore can be regarded as a mathemati- cal representation of the electron configuration of the molecular structure of the chemical product after solving the first and the second part of the electronic structure representation. The reference state can be generated as a superposition of the electron configurations being part of the solution of the first and the second part, wherein each electron configura- tion is associated with a weight for weighting the contribution of the electron configuration BASF SE 221032 221032WO01 to the overall solution of the electronic structure problem. Determining the weights refers to determining the overall solution. For example, if the reference state is represented utilizing configuration interaction basis states the weights refer to configuration interaction coeffi- cients associated with respective configuration interaction basis states. The utilized elec- tron configurations can comprise a part that represents the active space and a part that represents the inactive space. For example, an electron configuration can comprise elec- tron orbitals that are part of the first part, i.e. active space, and electron orbitals that are part of the second part, i.e. inactive space. Depending on the respective problem, the re- spective parts of the electron configurations utilized with the superposition in the reference state can be treated differently. For example, the parts of the electron configurations rep- resenting the active space can be more numerous than the parts of the electron configura- tions representing the inactive space. In particular, the parts of the electron configurations representing the inactive space can be identical, whereas parts of the electron configura- tions representing the active space can be different. Thus, the reference state can refer to a superposition of electron configurations wherein the different active parts of the electron configurations are combined, for instance linear combined, and the inactive parts are the same. Based on this reference state the interaction representation can then, during the respective computation, also allow for the generation of different inactive parts resulting from the correlation between the active parts and the inactive part. The interaction repre- sentation generated based on the reference state then generally represents the correlation between the parts of the electronic structure representation represented by the first part and represented by the second part and further represents correlations within one or both parts, in particular, within the second part. The interaction representation can include cor- relations between electron orbitals among which at least one electron orbital is a member of the inactive space. The correlation computation unit is configured for causing a classical computer and/or quantum computer to provide a solution to the interaction representation. The utilized classical and/or quantum computer can be the same or different from the clas- sical and/or quantum computer utilized by the solution determination unit. Although it is preferred that a quantum computer is utilized for the calculation of the interaction represen- tation, in an embodiment also a classical computer can be utilized or a combination of both can be utilized. The solution computed on the classical and/or quantum computer can then be provided. The providing can refer to providing the solution to the apparatus but also providing the solution to other computer hardware separate from the apparatus that is then configured to determine the property from the solution. Preferably, the interaction representation includes correlations a) within the inactive space, and/or b) between the active space and the inactive space. Correlations occurring within the active space are determined when determining the solution of the first part. Generally, BASF SE 221032 221032WO01 correlations between spaces are defined as correlations between quantities defined in these spaces. Thus, the quantities refer to the quantities as defined in the first part of the electronic structure representation and the second part of the electronic structure repre- sentation. The above preferred embodiment can therefore also be formulated as the inter- action representation including correlations a) within the second part of the electronic struc- ture representation, and/or b) between the first part and the second part of electronic struc- ture representation. The solution of the electronic structure representation is indicative of the property of the chemical product. The property can be a property that can be derived from a solution of the electronic structure representation for a chemical product. The method can thus further comprise generating and providing the property of the chemical product based on the elec- tronic structure representation. In particular the generated property can be property of the electronic configuration of the chemical product, e.g. the property can be an electronic property of the electronic structure of the chemical product. For instance, the property can be a ground state and/or excitation state energy of the chemical product. Based on the respective property further properties can be derived. For example, based on a determined ground state energy of all molecular species occurring in a chemical reaction, as technical application property a reaction rate, the thermodynamic properties of the reaction, and the kinetic properties of the reaction can be generated. This understanding and the properties of the reaction can then again be utilized to optimize chemical production processes, for determination of a microstructure of polymers, for optimizing material properties, etc. Fur- ther, the property can also refer to multipole moments of a chemical product. Such a cal- culation can be relevant for determining technical application properties of the chemical product related to electrical and other technical application properties, e.g. the dielectric behavior of the chemical product, but also properties resulting from intermolecular interac- tions which are strongly dependent on the polar nature of the chemical product – such technical application properties can range from solubility and compatibility with certain me- dia to complexation behavior of ions or impacts on spectroscopic properties, e.g. color. Preferably, the method comprises providing the property for monitoring and/or controlling a technical application including the chemical product, preferably, a chemical reaction in- cluding the chemical product and/or a synthesis of the chemical product. The providing of the property is thus configured to be directly utilizable in the respective controlling and/or monitoring of the application. For example, the providing can comprise implementing the property into a respective control/monitoring system of the application. The providing can comprise providing the property in a respective data format together with information on how to utilize the property in a controlling and/or monitoring of the application. The method BASF SE 221032 221032WO01 can comprise providing control signals based on the property for monitoring and/or control- ling a technical application including the chemical product. The technical application can be any application in a technical context that includes the chemical product. The technical application can be a chemical reaction including the chemical product, for example, a cat- alyst. The technical application can be a synthesis process for synthesizing the chemical product. The technical application can be a product design screening process including a screening process for determining one or more properties of the chemical product. In an embodiment, the electronic structure representation is further associated with prede- fined electron orbitals, wherein the first part and the second part of the electronic structure representation are defined by the electron orbitals being part of the active space and the electron orbitals being part of the inactive space, respectively. In particular, the molecular structure is defined by the respective electron orbitals of the molecule such that the elec- tronic structure representation of the molecular structure includes these electron orbitals. The electron orbitals being part of the active space and the electron orbitals being part of the inactive space form the basis for the respective space. Since electrons being associ- ated with electron orbitals in an inactive space can also influence electrons in electron or- bitals in the active space, this influence can be taken into account also as part of the first part of the problem and vice versa. Generally, the electron orbitals can refer to atomic or- bitals or electron orbitals, depending on the respective application, for example, depending on the molecular structure of the chemical product for which an electronic structure repre- sentation should be solved. Moreover, an electron orbital generally refers to a mathematical function that is indicative of the probability of finding an electron in a specific region in the atom or molecule. In a preferred embodiment, the electron orbitals are adaptable with respect to a quantity of the first and/or second part of the electronic structure representation, wherein the apparatus further comprises an iteration controlling unit adapted to control an iteration for minimizing or maximizing the quantity of the electronic structure representation with respect to the electron orbitals, wherein the iteration comprises providing starting electron orbitals and generating a solution for the first part and/or second part, respectively,, amending the start- ing electron orbitals based on the generated solution and generating a further solution for the amended electron orbitals and repeating the electron orbital amendment and solution generation until the quantity of the first and/or second part, respectively, of the electronic structure representation is maximized or minimized with respect to a given criterion. This solution of the first and/or second part can then be utilized for generating the interaction representation, in particular, the reference state. For example, the solution of the first part can be generated iteratively as described above and then be utilized for generating the BASF SE 221032 221032WO01 reference state. The quantity can refer to any quantity that is influenced by the electron orbitals, i.e. by the local probability density of the respective electrons in the atom, mole- cule, crystal, or amorphous solid related to the chemical product. Moreover, also more than one quantity of the first and/or second part of the electronic structure representation can be optimized during the above iteration, for example, utilizing known methods and algorithms for multi-objective optimization, for example, Pareto optimization techniques, etc. Further- more, the quantity of the first and/or second part of the electronic structure representation can generally also refer to a quantity representing the solution of the first and/or second part, respectively, of the electronic structure representation. For example, it is preferred that the quantity to be optimized refers to an energy of the electronic structure defined by the first and/or second part, respectively, of the electronic structure representation, wherein it is in particular preferred to find the minimum energy for the electronic structure of the atom, molecule, crystal, or amorphous solid related to the chemical product. Generally, the calculating of the solution of the first and/or second part of the electronic structure representation during the iteration comprises the calculation steps as described above with respect to the solution of the first and/or second part of an electronic structure representation. In particular, the calculation of a solution of the first and/or second part of the electronic structure representation during the iteration comprises steps of providing a first and/or a second part of the electronic structure representation comprising or indicative of the respective electron orbitals of the current iteration step, causing a quantum computer and/or classical computer to perform a quantum mechanical and/ or classical calculation as already described above and calculating a solution of the first and/or second part of the electronic structure representation as already described above. The starting electron orbit- als for the first iteration step are generally predetermined, for example, based on user ex- perience, already known approximate solutions of the electronic structure representation, for example, calculated utilizing a Hartree-Fock calculation, or based on theoretical consid- erations, for example, based on respective physical assumptions or approximate solutions of similar electronic structure representations. During the iteration for each iteration step, the electron orbitals can be adapted based on predetermined rules, for example, based on respective physical relations or insights that can be formulated and implemented as re- spective rules, or can even be amended arbitrarily by amending one or more parameters influencing the respective electron orbital. Moreover, during an iteration step, only one elec- tron orbital can be amended or a plurality of electron orbitals can be amended at the same time. Preferably, quasi-Newton methods, gradient descent methods or gradient-free meth- ods, like the Nelder-Mead method, are utilized for amending the respective electron orbitals based on the results of the respective iteration steps. Generally, the optimization is per- formed with respect to a given criterion, wherein the given criterion can depend on the BASF SE 221032 221032WO01 respective quantity to be optimized and also on the respective property or application for which an electronic structure representation should be solved. For example, if the quantity refers to an energy of the electronic structure defined by the electronic structure represen- tation, the criterion can refer to a minimizing of the energy and can be based, for example, on determining that the minimum of the energy is reached if a deviation between the energy determined between subsequent iteration steps lies below a predetermined threshold. In particular, it is preferred that the criterion refers to a converging of the iteration to a mini- mum energy. Furthermore, the criterion can also comprise an abortion criterion that indi- cates that the iteration is to be aborted if the abortion criterion is fulfilled. For example, the abortion criterion can refer to a predetermined number of iteration steps, wherein, if this predetermined number of iteration steps is exceeded, it can be assumed that no valid so- lution for the electronic structure problem will be found during the iteration and the iteration is to be aborted. Preferably, as already described above, the quantity refers to an energy of the electronic structure defined by the first and/or second part, respectively, of the electronic structure representation, wherein the iteration refers to a minimization of the energy of the electronic structure for solving the electronic structure representation. Generally, the electronic struc- ture, i.e. the electrons provided in the different electron orbitals of the atom, molecule, crys- tal, or amorphous solid and their interactions, defines the electronic structure representa- tion. The energy then refers to the total energy of this electronic structure and comprises the kinetic energy of the electrons, the energy of the Coulomb interaction between the electrons, the energy of the Coulomb interaction between the electrons and the atomic nuclei. In particular, the total energy can be defined mathematically as expectation value of the respectively utilized Hamiltonian. In an embodiment, the electronic structure representation providing unit is adapted to de- termine a partitioning of the electronic structure representation into the first and second part of the electronic structure representation based on the electronic structure of the chem- ical product. Preferably, the electronic structure representation providing unit is adapted to determine a partitioning of the electronic structure representation into the first part of the problem and the second part of the problem before providing the electronic structure rep- resentation. In particular, the determination can be performed completely or partly auto- mated. For example, predetermined rules can be automatically applied to the electronic structure representation to determine the first and second part of the electronic structure representation. Moreover, the determination can also comprise a user-machine interaction process. For example, the electronic structure representation providing unit can utilize first predetermined rules to determine a first part and/or second part, and can then present the BASF SE 221032 221032WO01 determined first part and/or second part to a user. The user can then provide further infor- mation as input that can then also be taken into account during the partitioning and/or the user can amend the determined first and second part based on his/her experience. Gener- ally, the electronic structure representation providing unit can be adapted to determine the partitioning not only based on the electronic structure representation itself but also based on further information, for instance, provided by a user. Generally, the electronic structure representation of the chemical product provides infor- mation on the electronic structure of the respective chemical product. Based on the infor- mation on the chemical product available, in particular, based on the electronic structure information, active space selection procedures utilizing electron orbital entanglement infor- mation and single-orbital entropies that are calculated with, for example, a density matrix renormalization group (DMRG) method or other correlated methods, including exact and approximate full configuration interaction schemes can be utilized to determine a partition- ing of the problem into the first and second part of the problem. Furthermore, also localiza- tion procedures, population analysis, atomic valence active space (AVAS) procedures and/or natural orbital occupations can be utilized to determine a partitioning of the problem into the first and second part of the problem. Generally, the electronic structure represen- tation provides information on the correlation between electron orbitals or at least about assumed correlations between electron orbitals that can then be utilized to determine the partitioning of the electronic structure representation into the first and second part. Thus, it is preferred that the partitioning of the electronic structure representation is determined based on chemical product information indicative of a correlation between electrons occu- pying different electron orbitals, in particular, information indicative of an electron orbital entanglement and entropies of the electron orbitals. Additionally or alternatively, the elec- tronic structure representation providing unit is adapted to determine a partitioning of the problem into the first and second part of the electronic structure representation based on the number of quantum elements of the quantum computer. The quantum elements can refer, in the context of this invention, to the physical quantum elements realized and ma- nipulated in the physical realization of the quantum computer but can also refer to the log- ical qubits that refer to the logical representations of one or more physical quantum ele- ments. For example, a logical qubit can comprise more than one physical quantum ele- ments, wherein some of the physical quantum elements of the logical qubit are used for example for error correction. Preferably, the partitioning of the problem is determined based on the number of utilizable quantum elements. The number of utilizable quantum elements takes into account that depending on the respective quantum algorithm utilized for perform- ing the quantum mechanical calculation, at least some of the physical quantum elements but also the logical qubits have to be utilized for other purposes, for example, for error BASF SE 221032 221032WO01 correction, representation of bosonic fields, etc. In some cases some of the quantum ele- ments are idle in the quantum mechanical calculation, since an increase in the used num- ber of quantum elements would lead to an inacceptable error rate for a specific algorithm, etc. Furthermore, the partitioning of the electronic structure representation can preferably also take into account information on physical characteristics of the quantum computer hardware, for example, on the type of quantum computer utilized, the general error rate of the respective quantum computer, the error rate of the quantum operations, the quality of the quantum elements of the quantum computer, or the general topology of the quantum computer. Preferably, the number of quantum elements of the quantum computer, in par- ticular, the number of utilizable quantum elements that should be utilized for the quantum mechanical calculation of the first part and/or second part, determines the maximum num- ber of variables that during the partitioning are considered as being part of the first part and/or second part, respectively, of the electronic structure representation. In particular, if the variables refer to electron orbitals, the number of quantum elements, in particular, of utilizable quantum elements, preferably determines the maximum number of electron or- bitals considered, for example, as part of the first part of the active space. This allows to provide a partitioning of the electronic structure representation that optimally utilizes the advantages of the quantum computers available for the calculation but at the same time also mitigates the downsides of current and near-term quantum computer calculations, for example, high error rates, or respectively limited number of qubits that might necessitate a separation of the electronic structure representation into respectively feasible sub-prob- lems. In an embodiment, the reference state is represented with configuration interaction basis states and coefficients associated with the configuration interaction basis states, wherein the configuration interaction basis states are given by a fixed distribution of electrons among electron orbitals. The configuration interaction basis states and configuration inter- action coefficients can be utilized to generate a superposition of the electron configurations mathematically representing the solution of the first part and the solution of the second part. For example, the reference state can be represented by a wavefunction described by a linear combination of Slater determinants representing the configuration interaction basis states, wherein the weights of the Slater determinants represent the configuration interac- tion coefficients. In this case, the configuration interaction basis states can be constructed from a set of orthogonal spin orbitals. In an example, the first part of the problem can be solved, for instance, using a respective configuration interaction method that directly pro- vides as solution the wavefunction in the basis of the configuration interaction basis states and the respective coefficients. The second part can then be integrated into this configura- tion interaction solution of the first part to provide a respective reference state. BASF SE 221032 221032WO01 In an embodiment, determining the reference state based on the solution of the first part and second part comprises controlling a quantum computer to generate a representation of the solution of the first part on the quantum computer, wherein the reference state is determined based on the representation of the solution of the first part on the quantum computer. In this embodiment, the state on the quantum computer generated to solve the first part can be regarded as equivalent to the state of the active space of the reference state of the respective described molecule. Thus, the quantum computer solution directly provides a representation of the active space part of the reference state on the quantum computer. The controlling can comprise, for instance, utilizing the phase estimation algo- rithm or noisy intermediate-scale quantum (NISQ) algorithms like the variational quantum eigensolver (VQE) to generate the solution of the first part that can be utilized to prepare a representation of an active space of the reference state. In an embodiment, the determining of the reference state comprises determining an overlap between the prepared solution of the first part on the quantum computer and the respective configuration interaction basis states to determine the coefficients. The overlap between the prepared solution of the first part on the quantum computer and the respective config- uration interaction basis states can refer to a projection of the prepared solution of the first part on the respective configuration interaction basis states. For this, respective projection operations can be utilized. Based on the projection, the absolute value of the configuration interaction coefficients can be determined, for instance, in form of squared absolute values. Further, also the phase, for example, determining the sign of the coefficient, can also be determined. This allows to reconstruct the representation of the respective reference state on any suitable computer hardware that should be utilized for solving the interaction repre- sentation. Preferably, determining the overlap comprises measuring the representation of the solution of the first part on the quantum computer corresponding to the distribution of the electrons among the electron orbitals in the active space, determining respective coefficients asso- ciated with the configuration interaction basis states from this measurement and repeating the process until a predetermined condition is met to generate a histogram of the coeffi- cients of the measured configuration interaction basis states and determining the reference state based on the histogram. For example, the process can be repeated until the gener- ated histogram converges with a predetermined accuracy for the respective coefficients of the histogram. However, also other conditions can be utilized for determining the amount of repetitions, for instance, a predetermined fixed number of repetitions can be utilized for restricting the utilized computational resources. Since the reference state representation on the quantum computer refers to a quantum state, it is based on a superposition of a plurality of possible quantum states referring to the configuration interaction basis states. The superposition can be determined by utilizing the histogram that reflects the contribu- tions mathematically represented as the weights of the different quantum states contrib- uting to the superposition, if enough repetitions are performed. The weights are mathemat- ically the square of the absolute value of the configuration interaction coefficients and can be determined based on the histogram. The absolute values of the configuration interaction coefficients can then be determined based on the determined squared absolute values. Preferably, the reference state is determined based on the representation of the solution of the first part on the quantum computer by applying a projection operator to the representa- tion of the solution of the first part projecting the representation of the solution of the first part on a respective configuration interaction basis state representation and measuring the resulting states on the quantum computer based on the histogram. The measurements of the resulting states refers to measuring as observable the projector on the respective state which refers to measuring the squared absolute value of the configuration interaction coef- ficients. For example, the histogram is determined as described above and based on the histogram it is determined which configuration interaction basis states are determined the most, i.e. above a predetermined threshold or cut-off. Then a projection measurement as described above is performed for the determined configuration interaction basis states for determining the coefficients. In an embodiment, the reference state can mathematically be represented by equation
Figure imgf000023_0001
wherein are the configuration interaction basis states and
Figure imgf000023_0002
are the configuration interaction coefficients, wherein the index ^ runs over all possible electron distributions among the electron orbitals in the active space. Preferably, the correlation computation unit is configured to cause a quantum computer to prepare a representation of the reference state on the quantum computer and to entangle quantum elements representing the correlations between the active space and the inactive space to provide a solution to the interaction representation. Thus, the correlations within the active and/or inactive space and/or between the active and the inactive space are de- termined by entangling quantum elements on a quantum computer representing respective correlated electron orbitals. The entangled quantum elements can be part of the same quantum computer or of different quantum computers, for instance, if the solution of the first part and the solution of the second part are prepared as reference state on different quantum computers. In an embodiment, a solution to the interaction representation is pro- vided by preparing the representation of a solution of the first part on a first quantum com- puter and preparing a representation of a solution of the second part on a second quantum computer and performing a quantum computation of the interaction representation in which the quantum elements of the first quantum computer and the quantum elements of the second quantum computer are entangled for representing the correlations between the active space and the inactive space. Preferably, a unitary correlation ansatz, more prefer- ably a unitary coupled cluster ansatz, is combined with a variational quantum eigensolver for providing the solution to the interaction representation. The variational quantum eigen- solver varies parameters of the specific utilized ansatz for minimizing an energy of a state resulting from applying an operator representing the utilized ansatz to the respective refer- ence state, wherein a solution of the interaction representation refers to a respective state with a minimal energy. In an embodiment, the interaction representation includes correlations between electron orbitals among which at least one electron orbital is a member of the inactive space by projecting the reference state on one or more predetermined configuration interaction basis states and generating the solution based on the result of the projection. Generally, the solution of the first part and the second part refer to a superposition of electron configura- tions. The correlation can be approximated by taking one or more of the configurations, i.e. only one or more predetermined states into account, and determining the correlations based on respective configurations. Preferably, a tailored coupled cluster method is utilized for generating a solution of the interaction representation. For example, a tailored coupled cluster method can be utilized for including the dynamic correlation of the inactive space and/or between the active space and the inactive space into the interaction representation. This method has the advantage that it can be performed on a classical computer and still provides reasonably accurate results. In an embodiment, a stochastic strongly contracted second-order n-electron valence state perturbation theory method is utilized for including correlations between electron orbitals among which at least one electron orbital is a member of the inactive space into the inter- action representation. In an embodiment the solution determination unit and correlation computation unit are con- figured to cause a quantum computing system to compute the solution of the first part, the second part and/or the interaction representation, wherein the quantum computing system comprises at least two quantum computers with different fidelities, wherein the solution BASF SE 221032 221032WO01 determination unit and correlation computation unit are configured to distribute the compu- ting of the solution of the first part, the second part and/or the interaction representation to the at least two quantum computers based on the fidelity of the respective at least two quantum computers. The fidelity of a quantum computer is a measure defining the quality with which the quan- tum computer performs a respective quantum computation, for instance, the operations, e.g. quantum gates, of an algorithm performed during a quantum computation. The fidelity of a quantum computer can be based on quantum gate fidelities and/or decoherence times. A quantum gate is a basic quantum operation usually generated through one or more con- trol pulses applied to a respective small number of qubits, wherein a plurality of quantum gates build a quantum circuit and thus can be regarded as an analogue to classical logical gates that build conventional digital circuits. Any multi-qubit operation can be generated from a sequence of one- and two-qubit operations. In this context a fidelity measures the quality with which a quantum gate realised on the quantum computer hardware resembles the theoretical quantum gate it is supposed to implement in the quantum computer. Thus, the quantum gate fidelity measures the difference between the real operation performed by the real hardware and the perfect theoretical operation. A decoherence time describes how long quantum information can be stored on the quantum computer before it is lost to the environment. Thus, the decoherence times also have an influence on the quantum gate fidelities that are determined, for instance, by all small imperfections in the build, calibration and control of the quantum computer and also based on the specific decoherence time of the quantum computer. Generally, the fidelity of a quantum computer can be determined utilizing known methods and measurements, for example, cross-entropy benchmarking, randomized benchmarking or full state tomography. More details on possible fidelity deter- mination methods can be found, for instance, in “Quantum supremacy using a programma- ble superconducting processor.”, Arute, F., Arya, K., Babbush, R. et al., Nature 574, 505– 510 (2019). In most cases the fidelity will be provided as general information by a provider of the quantum computer. For example, for causing a quantum computer to compute the solution of the first part, the second part and/or the interaction representation respective control signals can be gener- ated and provided to the quantum computing system. In particular, the control signals can be generated such that the fidelity determines on which of the at least two quantum com- puters the solution of the first part, the second part and/or the interaction representation is computed. Thus, the control signals are generated based on the fidelities of the respective at least two quantum computers. For example, the solution determination apparatus can be configured to cause a computation of the solution of the first part on a quantum computer BASF SE 221032 221032WO01 with a high fidelity, for instance, a fidelity above a predetermined threshold, and the corre- lation computation unit can be configured cause a computation of the solution of the inter- action representation on a quantum computer with a lower fidelity, for example, a fidelity lower than the fidelity of the quantum computer used for computing the interaction repre- sentation. Thus, the control signals can be generated such that the solution of the first part, the second part and/or the interaction representation are computed on a quantum computer with a respective fidelity most suitable from the available fidelities. Generally, in case of control signals referring to the controlling of a quantum computing system, the control signal can be configured, for example, for controlling a manipulation part of a quantum computer configured to manipulate the states of the quantum elements, in accordance with a corre- sponding sequence of manipulations. However, if the quantum computer itself already pro- vides a controlling unit that is adapted to control the manipulation part such that the states of the quantum elements are manipulated, the control signals can be adapted for controlling the controlling unit of the quantum computer. In this case, for instance, the control signals can simply refer to a representation of a sequence of manipulations that can be interpreted by the controlling unit of the quantum computer to provide the respective control signals for controlling the parts of the quantum computer accordingly. However, the control signals can, in this case, also refer to generally known and interpretable control signals that are translated by the controlling unit of the quantum computer to respective dedicated control signals for controlling the specific hardware of the quantum computer. In an embodiment at least two of the quantum computers are configured to be entangled and the control signals can be generated for further controlling the entanglement between the at least two quantum computers of the quantum computers of the quantum computing system during a parallel quantum computation of the solution of the first part, the second part and the interaction representation, wherein the entanglement of two quantum comput- ers is defined by at least one quantum element of each of the quantum computers being entangled. An entanglement between two quantum computers can be realised, for in- stance, by configuring the quantum computers such that at least one quantum element of one quantum computer can interact with at least one quantum element of another quantum computer. For achieving this a photonic link or respective entanglement bus or another qubit can be utilized. The details of the realisation strongly depend on the nature of the respective quantum computers, for instance, superconducting quantum computers, trapped-ion quantum computers, photonic quantum computers, etc. The quantum states of the entangled quantum elements depend on each other such that the quantum elements can only be described together as if they were one object. This state dependency of the entangled quantum elements leads to the distribution and sharing of information between the at least two quantum computers during the quantum computation during which the BASF SE 221032 221032WO01 states of the quantum elements utilised in the quantum computation are changed, for in- stance, due to respective quantum operations performed during the quantum computation. Thus, an operation performed on one of the entangled quantum elements also has an effect on the state of the other of the entangled quantum elements influencing the calculation of the other quantum computer. In this way basis operations, intermediate results, and final results of a quantum computation performed on the first quantum computer can directly, i.e. without being read out and processed by a classical computer and then prepared on the other quantum computer, influence the quantum computation on the other quantum computer. This allows for a true parallel computation of the solution of the first part, the second part and the interaction representation that depend on each other. Moreover, the entanglement allows to transfer a solution of the first part and/or the second part directly, e.g. without utilizing a classical computer in between, to another quantum computer to gen- erate the reference state as starting point for the calculation of the solution of the interaction representation. For realizing the entanglement different hardware solutions can be utilized depending on the respective type of quantum computer. For example, for superconducting based quantum computers waveguides and transmission lines can be utilized, as de- scribed, for example, in the article “Quantum computer with superconducting circuits in the ultrastrong coupling regime”, Stassi, R., Cirio, M. & Nori, F. Scalable, npj Quantum Inf 6, 67 (2020) incorporated herein by reference. Further, photonic links as described in the ar- ticle “Modular entanglement of atomic qubits using photons and phonons.”, Hucul, D., Inlek, I., Vittorini, G. et al., Nature Phys 11, 37–42 (2015) incorporated herein by reference can be used. For ion trap based quantum computing architectures the ion can be transported between respective quantum computers as disclosed, for instance, in the article “A high- fidelity quantum matter-link between ion-trap microchip modules.”, Akhtar, M., Bonus, F., Lebrun-Gallagher, F.R. et al., Nat Commun 14, 531 (2023), or electron shuffling can be utilized as described in the article “Conveyor-mode single-electron shuttling in Si/SiGe for a scalable quantum computing architecture.”, Seidler, I., Struck, T., Xue, R. et al., npj Quan- tum Inf 8, 100 (2022) both incorporated herein by reference. In an embodiment, the solution of the first part, the second part and/or the interaction rep- resentation can be generated based on the fidelities of the quantum computing system. For example, if a higher fidelity quantum computer is available the first part can be derived to encompass more electron orbitals that can be calculated on the higher fidelity quantum computer. A higher fidelity can be regarded as being higher with respect to a) the fidelity of at least one other quantum computer of the at least two quantum computers, b) the fidelity of all other quantum computers of the at least two quantum computers and/or c) a prede- termined fidelity threshold. A lower fidelity can be regarded as being lower with respect to BASF SE 221032 221032WO01 a) the fidelity of at least one other quantum computer of the at least two quantum comput- ers, b) the fidelity of all other quantum computers of the at least two quantum computers and/or c) a predetermined fidelity threshold. In an example, the first part required higher solution accuracy since it is more crucial to the solution of the problem. Further, the control signals can be generated based on a computation algorithm to be utilized for solving the solution of the first part, the second part and/or the interaction representation, wherein the computation algorithm to be utilized determines a threshold for the fidelity of the quantum computer on which the computation algorithm can be performed. For example, computation algorithms to be performed generally on higher fidelity quantum computers, since they are associated with a higher fidelity threshold, can refer to quantum Fourier transform, quantum phase estimation, Grover-type search algorithms, Shor-type factorization algorithms and Harrow-Hassidim-Lloyd-type algorithms. Examples for relevant computation algorithms for lower fidelity quantum computers, since they are associated with a lower fidelity threshold compared with the above algorithms, are variational algorithms, such as the variational quantum eigensolver and the quantum approximate optimization algorithm. Moreover, the distribution of the solution of the first part, the second part and/or the interaction represen- tation can also be based on the number of logical quantum elements provided by the re- spective at least two quantum computers. Logical quantum elements are quantum ele- ments that can be operated during a quantum computation. For example, depending on the quantum algorithm utilised some quantum elements are utilised as ancillary quantum elements and thus cannot be utilised for representing quantities and aspects of a respective sub-problem. Additionally taking the number of logical quantum elements on a respective quantum computer into account when deriving the sub-problems allows to specifically adapt the sub-problems to the respective quantum computers on which they are to be cal- culated allowing to utilise more efficient and effective quantum algorithms for the computa- tion of the sub-problems on the respective quantum computers. In an embodiment, the quantum computing system comprises at least one fault-tolerant quantum computer and one noisy intermediate-scale quantum computer, wherein the fault- tolerant quantum computer has a higher fidelity than the noisy intermediate-scale quantum computer. Noisy intermediate-scale quantum computers are generally sensitive to the en- vironment and prone to quantum decoherence such that they can only apply a finite number of gates or operations before too many errors have accumulated such that too much infor- mation is lost due to the noise and the computation becomes irrelevant. This limits the number of operations and thus also the size and complexity of sub-problems that can be computed on such a quantum computer. Fault-tolerant quantum computers perform a quantum computation with a physical error rate below a predetermined threshold defined BASF SE 221032 221032WO01 by the quantum threshold theorem such that through the application of quantum error cor- rection the logical error rate can be suppressed to arbitrary low levels. This allows to per- form arbitrarily long quantum computations, i.e. to apply an arbitrary number of gates and operations, leading to much higher precision and accuracy of calculation and allowing to calculate more complex sub-problems with more variables. Fault-tolerant quantum com- puters can be realized by applying quantum error correction codes utilizing at least three physical quantum elements to represent one logical qubit. An example is a surface code described in the article “Google Quantum AI. Suppressing quantum errors by scaling a surface code logical qubit.”, Nature 614, 676–681 (2023). However, also other codes exist that exploit this principle. Many of these error correction codes are only applicable to quan- tum computers with a respective high number of qubits. However, also codes which utilize only three physical quantum elements for representing one logical qubit exist, like the Steane code. These might not lead to fully fault-tolerant quantum computers for all cases but strongly increase the fidelity, and can thus lead to a higher fidelity quantum computer. In a further aspect of the present invention, an apparatus is presented for generating a property associated with a chemical product, wherein the chemical product includes one or more molecular structures, wherein the apparatus comprises i) an electronic structure rep- resentation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the electronic structure representation indicative of an active space including a part of the elec- tronic structure associated with a molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the elec- tronic structure associated with a molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) a solution determination unit for causing a quantum computer or a classical computer to generate and provide a solution of the first part of the electronic structure representation, and for causing a quantum computer or a classical computer to generate and provide a solution to the second part of the electronic structure representation, and iii) a correlation computation unit for generating a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate the property as- sociated with the chemical product, wherein computationally combining includes generat- ing an interaction representation based on a reference state associated with a superposi- tion of electron configurations generated based on the solution of the first part and the solution for the second part, and causing a classical computer and/or quantum computer to provide a solution to the interaction representation. BASF SE 221032 221032WO01 In a further aspect of the present invention, an apparatus is presented for generating a property associated with a chemical product, wherein the chemical product includes one or more molecular structures, wherein the apparatus comprises i) an electronic structure rep- resentation providing unit for providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the electronic structure representation indicative of an active space including a part of the elec- tronic structure associated with a molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the elec- tronic structure associated with a molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) a solution determination unit for causing a quantum computer to generate and provide a solution of the first part of the electronic structure representation, and for causing a classical computer to generate and provide a solution to the second part of the electronic structure represen- tation, and iii) a correlation computation unit for generating a solution to the electronic struc- ture representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computa- tionally combined to generate the property associated with the chemical product, wherein computationally combining includes generating an interaction representation based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the solution for the second part, and causing a classical computer and/or quantum computer to provide a solution to the interaction representation. In a further aspect of the invention, a system is presented for generating a property asso- ciated with a chemical product, wherein the system comprises a) a quantum computer adapted to perform quantum mechanical calculations, and b) an apparatus as described above, wherein the apparatus is adapted to cause the quantum computer to perform a quantum mechanical calculation. In a further aspect of the invention, a computer-implemented method is presented for gen- erating a property associated with a chemical product, wherein the chemical product in- cludes one or more molecular structures, wherein the method comprises i) providing an electronic structure representation associated with the molecular structure of the chemical product and including a) a first part of the electronic structure representation indicative of an active space including a part of the electronic structure associated with the molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the electronic structure associated with the molec- ular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, ii) causing a quantum computer and/or a classical BASF SE 221032 221032WO01 computer to generate and provide a solution of the first part of the electronic structure rep- resentation, and for causing a quantum computer and/or a classical computer to generate and provide a solution to the second part of the electronic structure representation, and iii) generating a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate the property as- sociated with the chemical product, wherein computationally combining includes generat- ing an interaction representation based on a reference state associated with a superposi- tion of electron configurations generated based on the solution of the first part and the solution for the second part, and causing a classical computer and/or quantum computer to provide a solution to the interaction representation. In a further aspect of the invention, a computer program product for generating a property associated with a chemical product is presented, wherein the computer program product comprises program code means for causing the apparatus as described above to execute the method as described above. In a further aspect of the invention, a use of an apparatus as described above for generating properties referring to at least one of a chemical reactivity, spectra and spectroscopic prop- erties, and molecular properties derivable from electronic structure problem calculations of a chemical product is presented. In a further aspect of the invention, a use of an apparatus as described above is presented, for generating properties related to at least one of metalorganic compounds containing transition metals including lanthanides and actinides, chelating agents interacting with met- als, catalysts, biomolecules with active centers, macromolecular systems and transition metal compounds in solution or embedded in an environment. In a further aspect of the invention, a use of an apparatus as described above is presented for determining activation and/or reaction energies for a predetermined chemical reaction. Preferably, an apparatus as described above is used for generating as property activation and/or reaction energies for a predetermined chemical reaction. Generally, an activation energy refers to an energy difference between a transition state and reactants. A reaction energy refers to an energy difference between products and reactants. The chemical reac- tion can be part of a complex reactive network, e.g. of a catalytic cycle. Utilizing an appa- ratus as described above is in particular advantageous in cases where at least one chem- ical species of this reactive system a) contains one or more transition metal atoms, lantha- nide atoms and/or actinide atoms with unpaired electrons or b) exhibits an electronic struc- ture with a small energetic gap between occupied and unoccupied electron orbitals, i.e., an energetic gap that is equal or smaller than the gap of at least one of the molecules ozone, pentacene or para-quinodimethane calculated with the same electronic structure approach, i.e. same basis set, same self-consistent field (SCF) method, e.g. Hartree-Fock, etc. or c) exhibits a multi-reference diagnostic that exceeds a predetermined limit, e.g. ^^(CCSD) greater than 0.02 and/or ^^(CCSD) greater than 0.05 and/or ^^(MP2) greater than 0.04 and/or ^ଶ(MP2/CCSD) greater than 0.18 and/or ^^^^^ greater than 0.1 and/or %TAE greater than 10, wherein the ^^ diagnostic is determined based on the Frobenius norm of the am- plitudes for single excitations of a CCSD wave function based on a Hartree-Fock reference state scaled by the square root of the number of correlated electrons in the CCSD calcula- tion, and wherein the ^^ diagnostic is determined based on the matrix 2-norm of the ampli- tudes for single excitations of a CCSD or MP2 wave function based on a Hartree-Fock reference state, and wherein the ^ଶ diagnostic is determined analogously to the ^^ diag- nostic but refers to double excitations, and wherein the ^^^^^ diagnostic is determined based on orbital-entanglement information obtained from an approximate correlated wave func- tion such as a partially converged but qualitatively correct density matrix renormalization group (DMRG) wave function, and wherein the %TAE diagnostic is determined based on the difference of total atomization energies obtained with CCSD(T) and CCSD relative to the total atomization energy obtained with CCSD(T). In an aspect of the invention, a use of an apparatus as described above is presented for generating a property related to activation energies for a predetermined catalytic cycle and/or for determining reaction energies for a predetermined chelating agent. In an aspect of the invention, an apparatus is presented for determining a technical appli- cation property of a chemical product, wherein the apparatus comprises a) an input unit configured to receive an electronic structure representation associated with one or more molecular structures of the chemical product, b) an apparatus as described above, c) a property determination unit configured for generating the technical application property based on the solution of the interaction representation of the one or more molecular struc- tures. In a further aspect of the invention, a computer-implemented method is presented for de- termining a technical application property of a chemical product, wherein the method com- prises a) receiving an electronic structure representation associated with one or more mo- lecular structures of the chemical product, b) utilizing an apparatus as described above to provide a solution of the interaction representation, c) generating the technical application property based on the solution of the interaction representation of the one or more molec- ular structures. In a further aspect a computer program product is presented for determining a technical application property of a chemical product, wherein the computer program product com- prises program code means for causing the apparatus as described above to execute the method as described above. In a further aspect of the invention, an apparatus for determining a target chemical product comprising a target technical application property is presented, wherein the apparatus com- prises a) a target property providing unit configured to provide a target technical application property and a potential chemical product, b) a property determination unit utilizing an ap- paratus as described above and/or a method as described above for determining a tech- nical application property of the potential chemical product, c) an iteration unit configured to compare the determined technical application property of the potential chemical product with the target technical application property and, based on the comparison, either i) deter- mining the potential chemical product as the target chemical product, or ii) providing a new potential chemical product and repeating the determination of the technical application property utilizing the new potential chemical product, and d) a control data generation unit configured to generate control data for producing the determined target chemical product. In a further aspect of the invention, a computer implemented method for determining a target chemical product comprising a target technical application property is presented, wherein the method comprises a) providing a target technical application property and a potential chemical product, b) utilizing an apparatus as described above and/or a method as described above for determining a technical application property of the potential chem- ical product, c) comparing the determined technical application property of the potential chemical product with the target technical application property and, based on the compar- ison, either i) determining the potential chemical product as the target chemical product, or ii) providing a new potential chemical product and repeating the determination of the tech- nical application property utilizing the new potential chemical product, and d) generating control data for producing the determined target chemical product. In a further aspect a computer program product is presented for determining a target chem- ical product comprising a target technical application property, wherein the computer pro- gram product comprises program code means for causing the apparatus as described above to execute the method as described above. BASF SE 221032 221032WO01 Examples for properties that can advantageously be generated in this invention can refer to calculating a ground state energy of a molecule or general electronic system. This allows, in particular, in the context of determining the ground state energy of all molecular species occurring in a chemical reaction to predict the reaction end products, the thermodynamic properties of the reaction, and the kinetic properties of the reaction. This understanding and the properties of the reaction can then again be utilized to optimize chemical production processes, for prediction of a microstructure of polymers, for optimizing material properties, etc. Further, the generated property can also refer to multipole moments of a chemical product. Such a calculation can be relevant for determining properties of the chemical prod- uct related to electrical and other technical application properties, e.g. the dielectric behav- ior of the chemical product, but also properties resulting from intermolecular interactions which are strongly dependent on the polar nature of the chemical product – such technical application properties can range from solubility and compatibility with certain media to com- plexation behavior of ions or impacts on spectroscopic properties, e.g. color. In particular, the providing of the target application property can refer to receiving the target application property from an input of a user applying, for instance, a respective input unit. Moreover, the providing can also refer to accessing a storage unit on which a target appli- cation property is already stored and providing the same. Further, the providing can also comprise receiving a target application property, for instance, via a network connection from other sources and providing the received target application property. Generally, the target application property can refer to one target value, for instance, a specific hardness of a chemical product, or can refer to a value range that should be met by the chemical product. Moreover, the target application property can also refer to any kind of target func- tion, for instance, a timely sequence of a property under a changing environmental condi- tion, like a hardness under changing temperature conditions. Such more complex target application properties can be advantageous in cases in which the application of the chem- ical product comprises different environmental conditions, for example, different tempera- tures. The target chemical product then refers to a chemical product that provides the re- spective target technical application property, i.e. meets the target technical application property within predetermined limits, when provided in a respective form, for example, as pure substance, or mixture. In particular, the target chemical product provides the respec- tive target technical application property when produced according to a corresponding rec- ipe. A potential chemical product can be provided in any digital representable format such that the potential chemical product and/or characteristics of the potential chemical product can be processed by the apparatus. Moreover, the providing of the potential chemical product BASF SE 221032 221032WO01 can also comprise providing a respective electronic structure representation for determin- ing the technical application property of the potential chemical product. However, the re- spective electronic structure representation can also be selected automatically, for exam- ple, by the apparatus based on the potential chemical product and the provided target tech- nical application property. However, also a user can, for example, select a respective elec- tronic structure representation preferably based on a selection of a plurality of possible electronic structure representation presented to the user based on the potential chemical product and/or the target technical application property. The comparison of the determined technical application property with the target technical application property allows to determine whether the determined technical application prop- erty fulfils a predetermined criterion, for example, that the determined technical application property meets the target technical application property within predetermined limits. If such a criterion is fulfilled, the potential target chemical product is determined as the target chem- ical product and the method proceeds to the next step. However, if the comparison indi- cates that the determined technical application property does not meet the target technical application property within the predetermined limits, a next iteration step utilizing a new potential chemical product can be performed. In particular, for each iteration step of the iteration a new potential chemical product is determined, preferably based on the previous potential chemical product, for instance, by amending one or more features of the previous chemical product, e.g. one or more constituents or other characteristics. However, a new potential chemical product can also be generated by arbitrarily choosing a new potential chemical product, for example, from a large amount of previously generated potential chemical products. Moreover, also more sophisticated methods can be utilized for selecting a new potential chemical product from a plurality of previously already generated potential chemical products. Based on the new potential chemical product, in each iteration step again the quantum computer is utilized for determining the technical application property and the such determined technical application property is again compared with the target technical application property such that the comparison can again lead to a further iteration step or if the respective criterion is fulfilled the respective new potential chemical product can be selected as the target chemical product. Moreover, also an additional abortion cri- terion for the iteration can be selected, for instance, a number of iteration steps can be determined before the iteration is aborted with a notification to a user that no target chem- ical product could be found for the respective target technical application property. How- ever, alternatively, after a predetermined amount of iteration steps the method can further comprise amending the target technical application property, for instance, by increasing the predetermined limits around the target technical application property and to repeat the iteration while utilizing the increased limits during the comparison. This can allow to find a target chemical product that meets the target technical application property as much as possible, even if a meeting of the original goal might not be possible. After the target chem- ical product has been determined as described above, the target chemical product can be provided, for instance, to a user via an output unit. Preferably, a recipe of the target chem- ical product is utilized to generate control data that can be utilized for controlling a produc- tion system for producing the target chemical product. It shall be understood that the apparatuses as described above, the methods as described above, the systems as described above and the computer program products as described above have similar and/or identical preferred embodiments, in particular, as defined in the dependent claims. It shall be understood that a preferred embodiment of the present invention can also be any combination of the dependent claims or above embodiments with the respective inde- pendent claim. These and other aspects of the invention will be apparent from and elucidated with refer- ence to the embodiments described hereafter. BRIEF DESCRIPTION OF THE DRAWINGS In the following drawings: Fig.1 illustrates a state representation of a qubit as used in a quantum computing device, Fig.2 illustrates a schematic example of a quantum computing device with qubits as calculation unit, Fig.3 illustrates a schematic example method for generating a control signal to per- form operations on a quantum computing device and for processing measure- ment signals from the quantum computing device, Fig.4 illustrates a schematic example of a hybrid system including a classical and a quantum computing device, Fig.5 illustrates a schematic example of a quantum computing device based on su- perconductors, Fig.6 illustrates a schematic example of a quantum computing device based on trapped ions, Fig.7 shows schematically and exemplarily an embodiment of a system generating a property associated with a chemical product, Fig.8 shows schematically and exemplarily a flow chart of a method generating a property associated with a chemical product, Fig.9 shows schematically and exemplarily examples of quantum computing sys- tems with quantum computers comprising different fidelities, Figs.10, 11 show schematically and exemplarily flowcharts of exemplary implementations of computational methods on the quantum computer system, Fig.12 shows schematically and exemplarily an illustration of an electron orbital en- ergy diagram, Fig.13 shows schematically and exemplary a quantum circuit diagram of a Hadamard overlap measurement, Fig.14 shows schematically and exemplary an overview over different embodiments of methods using the quantum computer system, and Fig.15 – 17 show schematically and exemplarily further applications of the method for de- termining a solution. DETAILD DESCRIPTION OF DRAWINGS In the following first a short introduction into the general basic principles of quantum com- puters and the performance of calculations of quantum computers will be provided. Further, general principles can also be found in “Quantum Computation and Quantum Information: 10th Anniversary Edition”, M. A. Nielsen and I. L. Chuang (2010). Classical computing devices use processors which are based on transistors. The state of each transistor has two controllable states 1 or 0 representing a digital binary or a bit. To perform operations on a classical computing device a human readable program code is translated via a compiler into machine-readable instructions. Machine-readable instruc- tions are control signals, e.g. voltage settings, for each transistor. Representations of the machine-readable instructions may include binary or hexadecimal representations. Based on such machine-readable instructions, the operations are performed on the processor of a classical computing device. Quantum computation is a relatively new computation method that uses quantum effects, such as superposition and entanglement, to perform certain computations more efficiently than classical digital computers. In contrast to digital computers, which represent infor- mation in the form of bits (e.g., “1” or “0”), as described above, quantum computing devices, i.e. quantum computers, use qubits, i.e. quantum bits, to represent information. Quantum computing devices are based on quantum elements adhering to the physics of quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, particle spins, bosons or the like. These quantum elements may be manipulated in a controlled manner to perform operations. Although qubits and their manipulation may be described in terms of their mathematical properties, each such qubit may be implemented in a physical quantum element in any of a variety of different ways. Examples of such quantum elements include superconducting materials, trapped ions, photons, optical cavities, individual electrons trapped within quan- tum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond), molecules (e.g., alanine, vanadium complexes), or any medium that exhibits qubit behavior comprising quantum states and transitions therebetween that can be controllably induced or detected. Generally, for any given physical quantum element that implements a qubit, any of a variety of properties of that physical unit may be chosen to implement the qubit. For example, if electrons are chosen to implement qubits, then the x, y or z component of an electron spin degree of freedom can be chosen as the property of such electrons to represent the states of such qubits. For any particular degree of freedom, the physical quantum elements can be controllably put in a state of superposition or entanglement and measurements can then be taken in the chosen degree of freedom to obtain readouts of qubit values. In contrast to transistors of classical computing devices each quantum element of quantum computing devices can not only take the basis states ȁ^ۧ or ȁ^ۧ but also any superposition of such basis states, such as state ȁ^ۧ. The state of each quantum element is represented by a state of a quantum bit, i.e. qubit, as illustrated in the two-dimensional simplification of Fig.1. To represent such states Dirac notation is commonly used in quantum mechanics. In Dirac notation a state in a n dimensional, complex vector space, such as a Hilbert space, is represented in braket notation, for example ȁ^ۧ. According to conventional terminology, the superposition of “0” and “1” states in a quantum computing device can be represented as ^ȁ^ۧ ^ ^ȁ^ۧ^. The states “0” and “1” or bits of the classical computing device are similar to the basis states ȁ ^ ۧ and ȁ ^ ۧ or quantum bits of the quantum computing device, respec- tively. The value ȁ^ȁଶ represents the probability that the qubit will be measured in the ȁ^ۧ state, while the value ȁ^ȁଶ represents the probability that the qubit will be measured in the ȁ^ۧ state. If more than one qubit is present, two or more qubits may be entangled. Entan- glement means that the state of one qubit is dependent on the state of at least one other qubit and vice versa, wherein further in the entangled state the respective qubits cannot be regarded as individual qubits anymore. Generally, a register of ^ qubits in a quantum com- puter can be put into a superposition of basis states at once whereas a register of ^ clas- sical bits can only be in a single basis state at once. Thus, in contrast to classical computing devices on a quantum computing device ʹே basis states can be manipulated and pro- cessed simultaneously allowing for exponential intrinsic parallelism. To perform operations on the quantum computing device the computational method to solve a given problem may be translated into qubit manipulations, which may be translated into control signals for manipulating qubits. Representations of the machine-readable in- structions may include common quantum mechanical representations of operations in the Hilbert space. Depending on a specific realization of the quantum computer different rep- resentations of the qubit states may be chosen. Any state preparation on the quantum computing device may be represented by a manipulation acting on the qubit states. A ma- nipulation may be translated into control signals to control a respective part of the quantum computer, which depend on the type of quantum computing device used. This way based on the manipulation acting on the qubit states, operations may be performed on the quan- tum equivalent of a classical processor as part of the quantum computing device. In gate-based quantum computer systems the manipulations acting on the qubit states may generally be one- or multi-qubit operations. A one-qubit operation may change the state of one qubit e.g., into a specific superposition which corresponds to a rotation of the vector ȁ^ۧ as illustrated in Fig 1. For example, in a superconducting quantum computer this can be accomplished by microwave pulses or in a trapped-ion quantum computer by irradiation of the ion with a laser beam. A multi-qubit operation may create entanglement between two or more qubits. For example, in a superconducting quantum computer this may be achieved by connecting qubits via an intermediate electrical coupling circuit or in a trapped-ion quan- tum computer via controlling the collective vibrations of the trapped ions. Generally, to prepare manipulations for solving a given problem a respective quantum me- chanical representation of the problem may be translated into qubit manipulations, which are carried out to prepare a solution of the given problem. After the preparation of the pre- determined solution, i.e. after the application of the operations to the qubits of the quantum computer, a projective measurement of all individual qubits is carried out returning either 0 or 1 for each qubit. This projection usually happens in the ^௭ eigenbasis of the qubits which is also used to define the computational basis stats “0” and “1” of the qubit. This means that only operators that are products of ^௭ Pauli operators or can be directly transformed into such operators can be measured concurrently. On the quantum computing device this measurement is achieved by applying a hardware-specific readout protocol of a series of readout manipulations including control pulses and monitoring the response to control pulses. For example, a superconducting qubit may be coupled to a hardware resonator. The measured shift of the resonator frequency allows to determine the state of the qubit as this shift depends on the state of the coupled qubit. In case of trapped ions, for example, an optical readout may be used, e.g. the state of the qubit is 1 if the ion emits light or 0 if the ion does not emit light or vice versa. This way qubits may be used to implement logical circuits or gates as in classical computing devices. In Fig.2 a schematic example of a quantum computer is illustrated. The quantum compu- ting device 100 shown in Fig.2 includes a quantum register 104 configured to perform the quantum computation, a manipulation part 106 configured to manipulate the quantum reg- ister, in particular, quantum elements forming the qubits, and a readout part 108 configured to collect measurement signals from the quantum register 104 for reading out the qubits after a quantum mechanical calculation. The manipulation part 106, in particular, provides manipulation signals for manipulating the quantum register, wherein the manipulation sig- nals are generated based on received control signals that are determined based on the respective operations that should be performed on the qubits. In some embodiment a feed- back loop between the manipulation part 106 and measurement part 108 can be provided. In contrast to classical computing, where one measurement cycle provides the state of a transistor, quantum computing includes performing multiple measurement cycles to provide a probability density or a probability for the qubit states in case of gate-based quantum computers. The quantum register 104 can be based on different quantum elements representing the qubits. In some embodiments of gate-based quantum computers the qubits may be imple- mented by photons as quantum elements. Such optical quantum computing devices may include lasers that generate photons that are provided to a waveguide. A beam splitter can be provided for manipulating the photon states based on manipulation signals such as a mechanical rotation applied to a mirror. The measurement part 108 can in such an embod- iment be a photon detector, and the measurement signals can be photons. BASF SE 221032 221032WO01 In other embodiments of gate-based quantum computers the qubits can be implemented by electronic states of ions trapped in a magnetic field. The manipulation part 106 can in such a case utilize a laser, and the manipulation signals can cause the providing of control laser pulses. Moreover, in this case, the readout part 108 can be a photon detector com- bined with read-out laser pulses, and the measurement signals 102 may be photons. Other qubit implementations may be based on superconductors as quantum elements, semicon- ducting material with anyons as quantum elements, or the like. Fig.3 illustrates a schematic exemplary method for generating a control signal to perform manipulations on the quantum computing device and for processing measurement signals from the quantum computing device. In most embodiments of quantum computing devices known to date, the control signals for the quantum computing device are prepared on a classical computing device and the measurement signals provided by the quantum com- puting device are further processed on the classical computing device. Other embodiments are, however, conceivable as quantum computing devices mature. In the following exam- ple, the quantum computer refers to a gate-based quantum computer for which the manip- ulations refer to operations on the quantum elements of the quantum computer. For generating the control signal to perform operations on the quantum computing device, the problem to be solved with the aid of the quantum computing device is provided in step S10, preferably, in a mathematical description. Such problem may for instance include de- termining a material property based on the mathematical description of the material’s elec- tronic structure. Other problems may include optimization problems and associated objec- tive functions. Based on the problem to be solved, an operation description of the problem or a sub-problem may be generated in step S12, wherein the operation description com- prises the operations to be applied to the qubits of the quantum computer to solve the problem in the quantum mechanical calculation. Further, the operation description can in- clude a reference state that allows to generate a representation of an initial qubit state on the quantum computer on which the further operations are then applied by manipulating the qubit states. Based on the operation description control signals can then be generated in step S14 to control the quantum computer, for instance, by providing the control signals to the manipulation unit that can then manipulate the qubit states based on the control signals. In step S16 the manipulation unit then applies the manipulation operations to indi- vidual or multiple qubits of the quantum computer, wherein based on the manipulation op- erations the qubits perform the quantum mechanical calculation. After the manipulation, measurement signals can be generated to determine the result of the quantum mechanical calculation in step S18. This step can include a read-out, i.e. measurement, of the qubit BASF SE 221032 221032WO01 states after applying the manipulation operations to the initial qubit states. The measure- ment signals can in step S20 then be translated into a measured quantity on the classical computer and in case of a sub-problem fed back into the problem to be solved. Finally, the result of the problem calculation including the quantum mechanical calculation can be pro- vided on the classical computing device in step S22. Fig.4 illustrates a schematic example of a hybrid system including a classical and a quan- tum computing device. As described with respect to the method illustrated in Fig.3, quan- tum computing devices are often used in connection with classical computing devices. As shown in Fig. 4 a problem preparation system, e.g. control signal generation apparatus, can be realized as a classical computing device 110 performing, for instance, steps S10, S12, S20, S22 of the method illustrated in Fig.3. A controlling unit can then be provided as interface between the classical computing device 110 and the quantum computer 100, wherein the controlling unit can also be a classical computing device, for instance, perform- ing step S14. The control unit can then be communicatively coupled with the manipulation part 106 that can control the manipulators of the quantum computing device. Also, the ma- nipulation part 106 can be realized as a classical computing device, for instance, a classical controlling hardware for the control of specific hardware components of the quantum com- puter that perform the manipulation of the qubits. However, the manipulation part 106 is generally regarded as part of the quantum computer, since it directly influences the quan- tum register. The quantum computing device 100 is adapted to perform the quantum oper- ation S16, in particular, by the manipulation of the qubits of the quantum register. The measurement part 108 that is also generally regarded as part of the quantum computing device can then perform the step S18 by utilizing classical hardware. The measurement part 108 can then be communicatively coupled to the preparation system 110 for further processing of the measurement signals. Fig.5 illustrates a schematic example of a quantum computing device based on supercon- ductors. Superconducting quantum computing devices are one of the solid-state quantum computing technologies. Here the quantum register 104 can include superconducting cir- cuits 520, 522, 524 based on Josephson junctions. The qubits can then, for instance, refer to charge, flux, transmon, or phase qubits depending on the quantity of the superconduct- ing circuits that are chosen to represent the qubits. Fig.5 refers to a simplified illustration of a superconducting quantum computer utilizing charge qubits. For charge qubits the dif- ferent states of the qubit are represented by an integer number of Cooper pairs on a su- perconducting island. In case of gate-based quantum computing quantum manipulations can then be performed by manipulating the qubits through microwave pulses. Resonators BASF SE 221032 221032WO01 512, 514, 516 can be utilized to manipulate the state of the qubits by applying the micro- waves or for reading out the state of the qubits by measuring respective microwaves, wherein generally different resonators are used for the manipulation of the state of the qubits and the readout of the qubits. Moreover, resonator 518 can be utilized for applying microwaves that entangle the qubits. However, instead of resonator 518 the entanglement can also be achieved by an inductive or capacitive coupling of the superconducting circuits or even by providing another qubit, here a superconducting circuit, between the to be en- tangled qubits. On an operational level such systems are maintained at extremely low temperatures, e.g., in the tens of mK. The extreme cooling of the systems keeps superconducting materials below their critical temperature and helps to avoid unwanted state transitions. To maintain such low temperatures, the quantum information processing systems may be operated within a cryostat, such as a dilution refrigerator. In some implementations, control signals are generated in higher-temperature environments, and are transmitted to the quantum computer using shielded impedance-controlled GHz capable transmission lines, such as coaxial cables. In some implementations, the state measurement of superconducting qubits is achieved using a dispersive detection scheme. In order to read out or detect the state of any qubit, a probing signal, e.g., a travelling microwave, may be excited along a readout transmission line coupled to the qubit via a respective readout resonator. The fre- quency of the probing signal can be in the vicinity of the resonance frequency of the readout resonator. Depending on the internal quantum mechanical state of the qubit, the intensity or phase of the probing signal transmitted along the readout transmission line may be al- tered because the reflectivity of the readout resonator coupled to the qubit changes de- pending on the state of the qubit. This allows for the state detection of the qubits, wherein during the readout of a qubit state the state of the qubit collapses, i.e. is projected with the respective probability onto one of the basis states. By performing the quantum mechanical calculation and the readout a plurality of times the respective probabilities can be deter- mined. Further details for superconducting quantum devices are described e.g. in docu- ments EP 3830867 A1, EP 3449427 A1, US 2020272925 A1, CN 212061223 U and US 2019019099 A1. Fig.6 illustrates a schematic example of a quantum computing device based on ions in an ion trap. Similar to neutral atom traps ion traps with, e.g. positively charged Calcium ions, can be used to implement the quantum computing device. Here ions 626 are trapped in an oscillating electromagnetic field 624 inside a high or ultra-high vacuum. The ions 626 are laser cooled and held in the oscillating electrical field 624. For qubit manipulation such as superposition or entanglement laser light 628 at different frequencies may be used. BASF SE 221032 221032WO01 Generally, based on the above described quantum computer realizations gate-based type calculations can be performed on a quantum computer hardware architecture. The gate- based type calculation is based on quantum gates. In contrast to classical gates, there is an infinite number of possible single-qubit quantum gates that can change the state vector of a qubit. Changing the state of a qubit state vector typically is referred to as a single qubit rotation, and may also be referred to herein as a state change or a single-qubit quantum gate operation. A rotation, state change, or single-qubit quantum gate operation can be represented mathematically by a unitary 2 x 2 matrix with complex elements. A rotation corresponds to a rotation of a qubit state within its Hilbert space, which can be conceptu- alized as a rotation of a vector on the Bloch sphere, wherein the Bloch sphere is generally known as a geometrical representation of the space of the pure states of a qubit. Multi- qubit gates alter the quantum state of a set of qubits. For example, two-qubit gates rotate the state of two qubits as a rotation in the four-dimensional Hilbert space of the two qubits, wherein, as generally known, the Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete, i.e. there are enough limits in the space to allow the tech- niques of calculus to be used. In the following the term operation description refers to a representation of a problem that comprises a sequence of quantum operations that should be applied during a quantum mechanical calculation of the problem. The term “quantum operation” can include in the context of this invention all types of quantum gates as described above and more generally all manipulations known for quantum elements on any quantum computer hardware. More- over, the term can also include operations performed on components of the quantum com- puter representing a coupling between the quantum elements forming the qubits and bosonic fields and, optionally, components representing the bosonic fields themselves. These operations then refer to any kind of change of the state of the coupling or bosonic field representing components, for example, a turning of a coupling on and off, or the change of a field frequency, etc. Further, in some applications the quantum operations can also include measurement operations. This allows to implement algorithms using a meas- urement feedback. For example, in such an algorithm a quantum computer can execute the quantum gates defined by the sequence of quantum operations and then measure only a subset, i.e., fewer than all, of the qubits or other calculation elements, like the bosonic field states, in the quantum computer, and then decide which further quantum manipula- tions to execute next based on the outcome of the one or more measurements. In particu- lar, measurement feedback can be useful for performing quantum error correction, but is not limited to use in performing quantum error correction. BASF SE 221032 221032WO01 Not all quantum computers are gate-based quantum computers. Embodiments of the pre- sent invention are not limited to utilizing gate-based quantum computers. As an alternative example, embodiments of the present invention can also utilize, in whole or in part, a quan- tum computer that is implemented using a quantum annealing paradigm which is an alter- native to the gate-based quantum computing paradigm. More specifically, quantum anneal- ing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctua- tions. In particular, quantum annealing is closely related to adiabatic quantum computing. Generally, also quantum annealing procedures start with utilizing a classical computer providing or generating an initial Hamiltonian and a final Hamiltonian based on a computa- tional problem to be solved, and providing the initial Hamiltonian, the final Hamiltonian and an annealing schedule as input to a quantum computer. In case of an annealing procedure in which an optimization problem is solved, preferably, the final Hamiltonian refers to an Ising Hamiltonian representing the optimization problem, or to a good approximation of the ground state of the Ising Hamiltonian representing the optimization problem. The quantum computer is then adapted, for instance, by utilizing a respective control unit controlling a manipulation part of the quantum computer, to prepare a relatively easy to prepare initial state, such as a quantum-mechanical superposition of all possible states, e.g. candidate states, with equal weights, based on the initial Hamiltonian. After the preparation of the initial state on the quantum computer, the initial state is then evolved according to the an- nealing schedule following a time-dependent Schroedinger equation referring to a natural quantum-mechanical evolution of the physical system of the quantum computer. More spe- cifically, the state of the quantum computer undergoes time evolution under a time-depend- ent Hamiltonian, which starts from the initial Hamiltonian and terminates at the final Hamil- tonian. If the evolution rate is slow enough, the system stays close to the ground state of the instantaneous Hamiltonian. At the end of the time evolution, the set of qubits, i.e. quan- tum elements, on the quantum annealer is in a final state, which is expected to be close to the ground state of the Ising Hamiltonian that corresponds to a solution to the original prob- lem, referring, for instance, to an optimization problem. The final state of the quantum com- puter can then be measured, thereby producing results that can be utilized for solving the original problem. The measurement operation can be performed, for example, in any of the ways described already above. A classical computer can then perform postprocessing on the measurement results to produce an output representing a solution to the original com- putational problem. A quantum annealer as described above can, for instance, be realized on a superconducting quantum computer hardware. BASF SE 221032 221032WO01 Moreover, embodiments of the present invention can also utilize, in whole or in part, quan- tum computers that are implemented using a one-way quantum computing architecture, also referred to as a measurement-based quantum computing architecture. More specifi- cally, the one-way or measurement-based quantum computer refers to a method of quan- tum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements. In such an architecture, the outcome of each individual measurement is random, but they are related in such a way that the com- putation always succeeds. In general, the choices of basis for later measurements need to depend on the results of earlier measurements, and hence the measurements cannot all be performed at the same time. Fig.7 shows schematically and exemplarily a system for generating a property associated with a chemical product and also optionally for producing the chemical product. In particu- lar, system 700 comprises an apparatus 720 for generating a property associated with a chemical product to be produced by production plant 740, for example, in production sys- tem 741. In particular, the property allows to determine the chemical product, e.g. a target chemical product comprising a predetermined target technical application property, to be produced. Generally, the property associated with a chemical product 750 can be derived from a solution of an electronic structure representation and thus can be solved based on information related to the electronic structure of the chemical product 750. The system 700 can, in addition to the apparatus 720, further comprise an input unit 710 and/or a quantum computer system 730. Generally, the production plant 740 and in particular the production system 741 can also be part of the system, but can also be omitted or only provided as communicatively coupled to the apparatus 720. The apparatus 720 comprises an electronic structure representation providing unit 721, a solution determination unit 722 and a correlation computation unit 723. Optionally, the ap- paratus 720 further comprises an iteration unit and a control data generation unit (not shown in Fig.7). Further, the apparatus 720 can optionally also comprise a translation unit 724. However, the translation unit 724 can also be part of the quantum computer system 730 or can be a standalone device communicatively coupled to the apparatus 720 and the quantum computer system 730. Generally, the apparatus 720 can be realized as any known classical computing system. For example, the function provided by the units can be performed by one or more processors on one or more classical computing devices. In par- ticular, the apparatus 720 can also be realized as distributed computing framework, for example, as a cloud or network environment, in which more than one computing device or processor is utilized for performing the functions of the apparatus. BASF SE 221032 221032WO01 The electronic structure representation providing unit 721 is configured for providing an electronic structure representation associated with a molecular structure of the chemical product. For example, the problem providing unit 721 can be coupled with the input unit 710 to allow a user to indicate, for instance, select from a respective provided selection, the respective electronic structure representation to be solved. However, the electronic structure representation providing unit 721 can refer to or be communicatively coupled to a storage unit on which the respective problem description is already stored. Generally, the electronic structure representation, if solved, allows to derive a technical application prop- erty of a respective chemical product. Moreover, the electronic structure representation, if solved, can allow to determine one or more production process parameters, for example, allows to determine a specific catalyst suitable for producing the chemical product, a re- spective reaction temperature, a respective reaction energy, etc. Generally, the electronic structure representation is further indicative of a first part indicative of an active space and a second part indicative of an inactive space. The active space and the inactive space of the problem can refer to subspaces of the Hilbert space of the electronic structure repre- sentation and can be determined based on the chemical product and/or the property, for example, based on an already known approximated electronic structure of the chemical product. Further details on the first and the second part including preferred examples and embodiments will be described, for instance, with respect to Fig.12. The electronic structure representation can be provided, generally, in any form that allows the apparatus 720 to derive respective information from the electronic structure represen- tation for solving the electronic structure representation. In particular, the electronic struc- ture representation is preferably provided in a digital format. Moreover, it is preferred that the electronic structure representation is provided in a mathematical formulation. However, the electronic structure representation can also be provided in any other format from which the electronic structure representation providing unit 721 or optionally also the translation unit 724 can derive a respective mathematical formulation of the electronic structure rep- resentation. The electronic structure representation providing unit 721 can then be config- ured to provide the electronic structure representation to the solution determination unit 722. The solution determination unit 722 can be configured to cause the quantum computer 730 to perform a quantum mechanical calculation based on the first part of the electronic struc- ture representation such that the result of the quantum mechanical calculation is indicative of the solution of the first part. In particular, the solution determination unit 722 can be communicatively coupled to the quantum computer 730, for example, to provide respective BASF SE 221032 221032WO01 control signals to the quantum computer 730 that cause the quantum mechanical calcula- tion. Optionally, before the solution determination unit 722 causes the quantum computer 730 to perform the quantum mechanical calculation, the electronic structure representation or the first part of the electronic structure representation can be provided to a translation unit 724. Generally, for a quantum mechanical calculation a respective problem is trans- lated into a respective operation description indicative of a sequence of operations to be applied to the quantum computer for solving the problem. In this case, the sequence of operations is determined such that the quantum mechanical calculation of the first part defined on the active space is performed on the quantum computer. This translation of the first part and thus also the translation unit 724 can be part of the apparatus 720, for exam- ple, as a respective unit that translates the electronic structure representation or the first part of the electronic structure representation provided by the electronic structure repre- sentation providing unit, wherein then the solution determination unit 722 can directly utilize the determined representative operation description for causing the quantum computer 730 to perform the quantum mechanical calculation of the first part. However, the translation unit 724 can also be provided as an independent unit or as a unit that is part of the quantum computer system 730 and receives from the solution determination unit 722 the respective electronic structure representation or first part of the electronic structure representation for translation. Generally, algorithms and methods for translating an electronic structure representation into respective operations to be performed on the quantum computer system 730 in order to perform a quantum mechanical calculation are already known. The respective translation depends strongly on the quantum computer system 730 utilized for determining the solution of the problem. For example, for a quantum computer based on superconductors other operations might be necessary than for a quantum computer based on trapped ions. More- over, the respective operation description can also refer to the manipulations performed on a quantum annealer in order to solve the respective electronic structure representation. In particular, in this case the respective operation description will differ from an operation de- scription utilized, for instance, for other quantum computer systems, like gate-based quan- tum computing systems. Thus, in many applications it is preferred that the translation unit 724 is part of the quantum computer system 730 allowing for a higher flexibility of the ap- paratus 720 to utilize different quantum computing systems 730, wherein in each case the respective translation unit 724 can be specialized and specifically adapted for optimally translating the electronic structure representation into a representative operation descrip- tion that is in particular suitable for the respective quantum computing system to which the respective translation unit refers. Details on the algorithms used for preparing the quantum BASF SE 221032 221032WO01 mechanical calculation are provided for preferred examples and embodiments, for in- stance, with respect to Figs.10 and 11. After the quantum computer 730 has performed the quantum mechanical calculation, the respective result of the calculation can again be provided to the apparatus 720. Generally, the such determined result of the calculation is indicative of the solution of the first part of the electronic structure representation. In particular, depending on the specific first part, respective known algorithms and methods can be utilized to determine from the results of the measurements of the states of the quantum elements of the quantum computer 730 the respective solution of the calculated first part. This determination of the solution of the first part can be performed, for instance, by a part of the quantum computer system 730 comprising a classical computer before providing the respective result, in this case, the solution of the first part, to the apparatus 720 or can also be performed by the apparatus 720 itself, for example, by the correlation computation unit 723. Alternatively, the solution determination unit 722 can be configured to cause a classical computer to perform a respective calculation based on the first part of the electronic struc- ture representation such that the result of the classical calculation is indicative of the solu- tion of the first part. Moreover, the solution determination unit 722 can be configured to cause the quantum computer 730 to perform a quantum mechanical calculation based on the second part of the electronic structure representation such that the result of the quan- tum mechanical calculation is indicative of the solution of the second part. The same prin- ciples and embodiments as described above with respect to calculating a solution of the first part can be applied when causing a quantum computer to calculate the solution of the second part. Alternatively, the solution determination unit 722 can be configured to cause a classical computer to perform a respective calculation based on the second part of the electronic structure representation such that the result of the classical calculation is indic- ative of the solution of the second part. It is preferred that at least one of the first and the second part are calculated on a quantum computer. The correlation computation unit 723 is configured to generating a solution to the electronic structure representation by combining the solution of the first and the solution of the second part, wherein the solution to the first part and the solution to the second part are computa- tionally combined to generate the property associated with the chemical product. Prefera- bly, computationally combining includes generating an interaction representation associ- ated with the combination of active and inactive space. The interaction representation is based on a reference state associated with a superposition of electron configurations gen- erated based on the solution of the first part and the solution for the second part. Thus, the BASF SE 221032 221032WO01 interaction representation allows to calculate the solution of the electronic structure repre- sentation by combining i) a solution of the second part in the inactive space and ii) the solution of the first part in the active space. Generally, the generating of the interaction problem for combining the solution of the first part and the solution of the second part can depend on the respective provided electronic structure representation itself but can also depend on a method that is utilized to solve the electronic structure representation. Some of the preferred methods and algorithms for gen- erating the interaction representation and combining solution of the first part and the sec- ond part will be described later in more detail. The interaction representation can then be solved by a classical computer and/or quantum computer. Generally, since the solution of the electronic structure representation is related to a property of a chemical product 750, the solution can then be utilized to generate respective control data for controlling a pro- duction system 741 for producing the chemical product 750, for example, using a respec- tive control data generation unit. For example, such control data can refer to a recipe or specification of the respective chemical product, to preferably used production process pa- rameters for producing the chemical product, to control margins for controlling the produc- tion of the chemical product, etc. Preferably, based on the solution of the electronic structure representation related to the property of the chemical product, the apparatus 720 is configured to determine the tech- nical application property of the chemical product. The control data can then be generated, for example, based on the determined technical application property. In a further preferred embodiment, the apparatus 720 comprises additionally an iteration unit (not shown in Fig. 7) that allows to control an iteration based on the solution of the electronic structure repre- sentation related to a chemical product. In particular, it is preferred that a target technical application property is provided to the apparatus 720, for instance, utilizing input unit 710, and that the technical application property determined based on the solution of the elec- tronic structure representation is then compared to the target technical application property. Based on the comparison, a further iteration step can then be initiated, for instance, by amending one or more characteristics of the chemical product and thus the respective electronic structure representation, or it can be determined that the respective chemical product meets the target technical application property and thus is the target chemical product that should be produced by production system 741. In this case, control data can be generated that causes the production system 741 to produce the target chemical prod- uct 750. BASF SE 221032 221032WO01 Further details on this and on respective other embodiments of a method that can be per- formed by the apparatus 720 will be described in the following with respect to Fig.8. Fig.8 shows schematically and exemplarily a method generating a property associated with a chemical product. The main part of the method 800 comprises providing an electronic struc- ture representation related to the chemical product that is indicative of or includes a first part of the electronic structure representation and a second part of the electronic structure representation, as already described above, for example, with respect to the electronic structure representation providing unit 721. Further, the method 800 comprises utilizing a quantum computer system like quantum computer system 730 to perform a quantum me- chanical calculation, wherein the result of the quantum mechanical calculation is indicative of the solution of the first part and/or the second part. By utilizing the quantum computer system, for example, as already described above with respect to the solution determination unit 722, a solution of the first part and/or the second part can be calculated. Alternatively, the calculating of the first part or the second part can be performed by a classical computer. Further, the method 800 comprises generating and solving an interaction representation for combining a solution of the first part and a solution of the second part, for example, as described with respect to the problem correlation computation unit 723. Optionally, the method can comprise additional steps, in particular, related to the produc- tion of the chemical product. These optionally additional steps 810 are illustrated in Fig.8 in the form of dotted and dashed boxes. In a preferred embodiment, the additional steps refer to determining a technical application property of a chemical product based on the determined solution of the electronic structure representation. However, the additional steps can also refer to determining one or more production process parameters for control- ling a production process of a chemical product. For example, such production process parameters can be determined based on the calculated technical application properties. However, such production process parameters can also refer, for example, to a catalyst or reactant utilized in the production of the chemical product and can thus be determined based on solving respective electronic structure representations that allow to derive and predict respective reaction parameters for potential catalysts or reactants. Examples for specific preferred applications of the method 800 but also of the method 810 will be pro- vided in the following description with respect to some more detailed embodiments. Preferably, the method 810 can further comprise providing a target technical application property for a chemical product, wherein in this case the electronic structure representation is provided based on a potential chemical product for which it should be determined whether or not it meets the respective target technical application property. The target tech- nical application property can then be compared with the determined technical application BASF SE 221032 221032WO01 property and it can be determined whether or not the determined technical application prop- erty meets the target technical application property. This comparison can be utilized in an iteration algorithm, in which the comparison is performed in each iteration step. If the de- termined technical application property does not meet the target technical application prop- erty within predetermined limits, in a next iteration step the potential chemical product can be amended, for example, by amending one or more aspects or characteristics of the re- spective potential chemical product and a new electronic structure representation can be provided based on the new potential chemical product. The steps of utilizing the quantum computer for solving the first part or second part, of combining the solution of the first part and the second part to determine the solution of the electronic structure representation and the determination of the technical application prop- erty can then be repeated in each iteration step. If in one iteration step it is determined during the comparison that the determined technical application property meets the target technical application property within the predetermined limits, it can be determined that the respective potential chemical product is the target chemical product and respective control data for producing the target chemical product can be generated for the target chemical product. It is noted that the respective control data can also be generated without the iter- ation for example, only based on the determined technical application property. Generally, the control data can then refer to control data that allows to control, for example, a produc- tion system 741 for producing the chemical product 750, for instance, the target chemical product. Thus, the control data can refer to a recipe or specification, for example, a synthe- sis specification, of the target chemical product. However, the control data can also refer to production process parameters that are determined, for instance, based on the deter- mined technical application property. Further details and embodiments are described in the following. Quantum computing is an emerging technology that exploits quantum-mechanical phenomena to perform computa- tional tasks. Quantum computers are expected to solve certain computational problems substantially faster than classical computers. They can be used for example to simulate quantum mechanical problems such as electronic structure problems including but not lim- ited to molecules, crystals, and amorphous solids. In an industrial environment such simu- lations of electronic structure problems are important for the discovery of new materials and chemicals, the improvement of chemical processes, the tailoring of molecules, solids and materials to desired properties and, generally, for making the development and pro- duction of a new product more efficient by reducing the number of required lab and produc- tion trials that are often resource expensive. Additionally, optimization problems, machine BASF SE 221032 221032WO01 learning and artificial intelligence are further exemplary application fields of quantum com- puting. Quantum computing is expected to significantly surpass classical computing with regard to treatable problem size, required computation time, in terms of energy costs, and/or achievable accuracy in the above mentioned fields. The fundamental processing unit of a quantum computer is a quantum mechanical bit (qubit) that can be represented on the quantum computer hardware by one or more quan- tum elements. By executing a suitable quantum circuit via control pulses that act on the qubits a solution to one of the abovementioned problems or a specific sub-problem can be prepared on the qubit register and finally measured within a hardware-specific readout pro- tocol. Both the number of logical qubits formed by one or more physical quantum elements and their quality, e.g. error rates or fidelities, mainly determine the maximum size, e.g. dimension, and maximum complexity of the problem that can be solved by a respective quantum computer. Currently both the number and the fidelities of the qubits are rather restricted resulting in so-called noisy intermediate-scale quantum (NISQ) computers. Typically, those NISQ com- puters are combined with classical computers, like a classical high-performance computer (HPC). Within this so-called hybrid quantum-classical framework components of algorithms are run on the computing architecture which can best resolve the specific components of the problem. In this context typically variational approaches are used, wherein the quantum computer is controlled by a classical computer. For example, after preprocessing and prep- aration of the problem on a classical computer, in a second step a parameterized quantum state is prepared on the NISQ computer, in a third step a target function is measured on the NISQ computer and in a fourth step the parameters are optimized on the classical computer to minimize or maximize the target function. This procedure is repeated with the updated parameters until the value of the target function converges and thus becomes minimal or maximal, respectively. In the last step post-processing can be carried out on the classical computer. Both the number and fidelities of the qubits are expected to continuously increase. As soon as a certain threshold is reached, several hundred or thousands, the exact number de- pends on the specific error-correction code, with two examples being the “surface code” and the “color code” for error correction, of such so-called physical qubits can be entangled to form a single error-free so-called logical qubit. A logical qubit can be formed by one or more physical quantum elements of the respective quantum computer hardware. A quan- tum device comprised of several of those logical qubits is termed a fault-tolerant (FT) quan- tum computer. It is noted, that the FT quantum computers mentioned in the following em- bodiments are not restrict to fully FT quantum computers, but also include such FT quantum computers that still exhibit sufficiently small errors. The error rate of such a FT quantum computer depends on the error-correction code and the number of physical qubits used. As a rule of thumb, the more physical qubits of a certain quality are used the more errors are suppressed. Such a FT quantum computer is able to accommodate deep quantum circuits that allow for highly accurate or exact solutions of many highly relevant computational problems which cannot be obtained on classical computers in reasonable time or with reasonable energy cost. However, due to the massive overhead in physical qubits required to build one logical qubit, some FT quantum computers remain rather restricted with regard to the number of logical qubits and thus the size, e.g. dimension, of the computational problem that can be solved. As a consequence, for many practically relevant computational problems the prob- lem dimension will exceed the dimension of the Hilbert space that is spanned by the quan- tum computer. In such cases, the computational problem cannot be solved on a FT quan- tum computer in a straightforward manner. Further, more specific examples of problems from the area of electronic-structure problems that can be solved utilizing the invention as described herein are described below. Although fault-tolerant quantum computers, e.g. fault-tolerant quantum processing units (FT-QPUs), outperform noisy intermediate-scale quantum computers, e.g. noisy interme- diate-scale quantum processing units (NISQ-QPUs), with respect to accuracy as they are able to accommodate deeper quantum circuits, i.e. more gate operations, NISQ-QPUs in many cases are able to accommodate wider quantum circuits, i.e. utilizing more qubits but fewer gate operations than in case of FT-QPUs, to provide approximate but still accurate solutions for many problems. Moreover, even without FT-QPUs NISQ-QPUs with a wide range of fidelities exist that allow for calculations with different accuracies or for quantum circuits with different depths. The above described method, for instance, with respect to Figs.7 and 8, for solving elec- tronic structure problems can be performed on a plurality of different hardware combina- tions. For example, the method can be performed purely on one or more classical comput- ers. In a more advantageous embodiment, at least one of the first part, the second part and the interaction representation is calculated on one or more quantum computers. Moreover, utilizing a quantum computing system comprising at least two quantum computers and a classical computer, wherein the at least two quantum computers comprise different fideli- ties is particularly advantageous. For example, the quantum computing system can be a BASF SE 221032 221032WO01 triple hybrid quantum computing system that combines FT-QPUs, NISQ-QPUs and classi- cal central processing units (CPUs) or other conventional computational devices wherein computational operations are carried out wherever most advantageous for solving the prob- lem. However, the quantum computing system can also combine different NISQ-QPUs with different fidelities and CPUs or other conventional hardware without using FT-QPUs. In Fig. 9 two examples of respective quantum computing systems that can be advanta- geously utilized are shown. The examples are shown with respect to quantum computing systems comprising FT-QPUs and NISQ-QPUs. However, additionally or alternatively to FT-QPUs also NISQ-QPUs with higher fidelities can be used with the same exemplary principles described below. In the following the term “higher fidelity NISQ-QPUs” is utilized with the meaning that a higher fidelity NISQ-QPU can have a higher fidelity compared to a) all other NISQ-QPUs of the quantum computing system, b) higher fidelity than at least on other NISQ-QPU of the quantum computing system and/or c) higher fidelity than a prede- termined threshold. In particular, any combination of these three criteria can be defined a NISQ-QPU that can be utilized for computing a sub-problem as described in the following. The threshold can be based for instance, on previous consideration, experience with a respective problem type, an algorithm to be utilized, a specific problem type, a to be achieved accuracy of a solution, etc. However, in most cases the higher fidelity NISQ-QPU simply refers to the NISQ-QPU with the highest fidelity of the NISQ-QPUs of the quantum computing system, wherein in this case the respective sub-problem is derived such that it can be computed by the higher fidelity NISQ-QPU. In the following examples, the FT-QPU(s) referred to are optional and can also be replaced by higher-fidelity NISQ-QPU(s) or can be used together with higher-fidelity NISQ-QPU(s). One example comprises controlling the FT-QPU(s), and/or higher-fidelity NISQ-QPU(s), and the NISQ-QPU(s) and exchange data via the CPU(s). Another example comprises a quantum computing system where FT-CPU(s), and/or higher-fidelity NISQ-QPU(s), and NISQ-QPUs are additionally entangled in a way that quantum information is distributed and shared among the entangled QPU(s) and can also be directly transferred between the re- spective QPU(s). In this case it is preferred, that the FT-CPU(s), or higher-fidelity NISQ- QPU(s), and NISQ-QPU(s) are on the same chip to facilitate entanglement. However, by using a quantum bus such as optical fibers and photons, spatially separated QPUs can also be entangled. Both setups depicted in Fig.9 in principle allow to solve practically rel- evant computational problems with a problem size, e.g. dimension, that exceeds the di- mension of the Hilbert space of a FT-QPU or higher-fidelity NISQ-QPU by optimally distrib- uting computational tasks. BASF SE 221032 221032WO01 An exemplary detailed method for solving a problem as described above is shown in Fig. 10 utilizing an unentangled quantum computing system and in Fig.11 utilizing an entangled quantum computing system. However, the principles of the described methods can also be performed utilizing generally known hybrid computing systems comprising a quantum com- puter and a classical computer instead of a quantum computing system comprising quan- tum computers with different fidelities. In a first step the electronic structure representation can be defined on a classical computing system, for instance, by a user using a user inter- face. Typical electronic structure representations refer to the electronic structure of mole- cules, solids and materials. In a second step the electronic structure representation can comprise or can be divided on the classical computing system into sub-problems, for in- stance, a first part of the electronic structure representation indicative of an active space including a part of the electronic structure associated with the molecular structure and a second part of the electronic structure representation indicative of an inactive space includ- ing another part of the electronic structure associated with the molecular structure. Prefer- ably, for the defining of the first and the second part the fidelities of the FT-QPU(s), and/or NISQ-QPU(s) of the quantum computing system on which the sub-problems are to be solved are taken into account. FT-QPUs or higher-fidelity NISQ-QPU(s) are best used to solve smaller computational sub-problems for which exact or highly accurate solutions are desired that can be efficiently obtained neither on low-fidelity NISQ-QPUs nor on CPUs. Also sub-problems for which the solution requires deeper quantum algorithms exceeding the capabilities of lower-fidelity NISQ-QPU(s) and CPUs can be derived to be solved on the higher-fidelity NISQ-QPU(s) or FT-QPU(s). The dimension of the sub-problem, for in- stance, of the first part, can accordingly be chosen to be less or equal than the dimension of the Hilbert space spanned by the qubits of the FT-QPU(s) or higher-fidelity NISQ- QPU(s). The lower-fidelity NISQ-QPU(s) are best used to solve larger computational sub- problems where accurate solutions are desired that cannot be efficiently obtained on clas- sical computers, e.g. CPU(s), or where the solution requires wide rather than deep quantum algorithms utilizing a larger number of qubits, for instance, for the second part. CPUs are used for all remaining tasks and controlling of the entangled or unentangled quantum com- puters. In a third step control signals are provided that cause to prepare and run respective quantum circuits on the quantum computing system for calculating and solving the respec- tive sub-problems. Optionally, the quantum circuits can contain parameters, which are typ- ically used in the context of variational procedures. In this case an initial set of parameters is provided in the first iteration step. In the next step, the sub-problem is encoded into qubits, the quantum circuit is compiled, and control signals are provided, for instance, to either the FT-QPU(s), higher-fidelity NISQ-QPU(s) or the NISQ-QPU(s), all simultaneously or to the entangled FT-QPU(s), higher-fidelity NISQ-QPU(s), and NISQ-QPU(s) systems. BASF SE 221032 221032WO01 This is also done in all subsequent iteration steps with an appropriately updated set of parameters. In a fourth step the quantum circuit of the current iteration step is executed on either the FT-QPU(s), higher-fidelity NISQ-QPU(s) or the NISQ-QPU(s), all simultaneously or on the entangled FT-QPU(s), higher-fidelity NISQ-QPU(s), and NISQ-QPU(s) to prepare the re- spective sub-problem solutions. Examples for relevant algorithms for FT-QPU(s) are quan- tum Fourier transform, quantum phase estimation (QPE), Grover-type search algorithms, Shor-type factorization algorithms and Harrow-Hassidim-Lloyd-type algorithms. Examples for relevant algorithms that can also be used on higher-fidelity NISQ-QPU(s) or NISQ- QPU(s) are the variational quantum eigensolver (VQE) and the quantum approximate op- timization algorithm (QAOA). Respective quantum gate operations are carried out on the qubit registers. In case of an entangled FT- or higher-fidelity NISQ- and NISQ-QPU system the solutions of sub-problems can be directly transferred between the two types of QPU(s). In a fifth step relevant observables of the sub-problems can be measured on either the FT- QPU(s), the higher-fidelity NISQ-QPU(s), or the NISQ-QPU(s), all simultaneously or the entangled FT-, or higher-fidelity NISQ-, and NISQ-QPU systems and provided to the CPU(s). Examples for observables that can be measured are qubit occupation numbers, reduced density matrices and energies. In a sixth step the target function and/or quantity and if needed its derivatives or other dependent quantities can be evaluated on the CPU(s) based on the measured observables. Examples for target functions and/or quantities are the total energy of the electronic structure problem and classical loss functions. Then, feed- back calculations connecting iteration steps of the algorithm like self-consistency conditions can be invoked, or, in case of variational procedures, optimization approaches such as quasi-Newton methods can be invoked to obtain a new set of parameters to minimize or maximize the target function and/or quantity. Finally, the iteration can return to the second or third step or if one or more stop criteria are fulfilled, e.g., the target function and/or quan- tity has converged, the iteration can terminate the feedback loop and proceed with the next step. In the next step after convergence has been achieved, optional post-processing steps, e.g. to enhance the overall accuracy or further process the result, e.g., error mitiga- tion or error correction, may be carried out on the CPU(s) for instance by the correlation computation unit. If necessary for this, further observables can be measured on the QPU(s). The results of the sub-problems are further combined either in this post-processing or during the iteration, depending on the interactions between the sub-problem results. Lastly, the final result is provided to the user as solution of the processed problem. BASF SE 221032 221032WO01 In the following an example of a method is described utilizing a hybrid quantum-classical approach. The following exemplary method refers to an “active space” that is solved pref- erably on a quantum computing system and wherein the result is then used to adjust elec- tron orbitals, preferably, both in an “inactive” and the “active space”, on a classical computer or a quantum computer. However, also other distributions are possible depending on the problem and the determined “active space” and “inactive space” as sub-problems. For ex- ample, also an “inactive space” or the influence of the “active space” on the “inactive space” can be solved on a quantum computer system. The procedure is iteratively repeated until convergence of the molecular orbitals and total energy can be achieved. This method can be referred to as the “complete active space self-consistent field” (CASSCF) method. A related method is “complete active space configuration interaction” (CASCI), which can be viewed as a special case of CASSCF that neglects the adjustment of the electron orbitals to the “active space” solution. In the following both methods are referred to as “CAS meth- ods”. A solution of this computation can then be utilized for generating the interaction rep- resentation and solving the respective electronic structure problem more accurately. By means of the described partitioning into an “active space” and an “inactive space”, the method allows solving electronic-structure problems with a size, e.g. dimension, that would otherwise exceed the dimension of a quantum computer, e.g., in terms of available qubits onto which the electron orbitals are mapped and/or in terms of gate operations that are needed to prepare the solution, as only the electron orbitals comprising the “active space” are explicitly treated on the quantum computer. The method is particularly advantageous for the simulation of so-called statically correlated molecular systems, such as transition metal compounds that are relevant for improving and designing, e.g., new catalysts and chelating agents, which is typically very challenging for traditional methods utilizing CPUs both with respect to computational effort and accuracy. Generally, the procedure for solving the “active space” and the “inactive space” parts, i.e. the first and the second part, respectively, of the problem is compliant with the general procedure depicted in Fig.10 above wherein the type of quantum computer utilized can be determined based on the fidelity of the respective available quantum computers before the quantum computation and can remaining fixed throughout the whole iterative procedure. In summary, for the specific case of the hybrid quantum-classical CAS method the steps in Fig.10 are detailed in the following. In the first step the specific electronic-structure problem to be solved is provided as a molecular system specified by atomic positions, basis sets, electric charge and spin on a CPU. This is in analogy to the first step in the general process in Fig.10. Further, an initial set of electron orbitals is specified, e.g. from a Hartree-Fock calculation on a CPU. Along with these electron orbitals, a fixed “active space” is defined BASF SE 221032 221032WO01 for example by electron orbitals and electrons that constitute the “active space”, wherein the active space defines a first part. These steps are performed on a CPU, in analogy to the second step in the general process in Fig.10. In a next step, the matrix elements of the effective Hamiltonian of the “active space” in the electron orbital basis are set up on a CPU defining the first part further. This is in analogy to the third step in the general process in Fig. 10. Moreover, the effective “active space” Hamiltonian operator, which is fermi- onic/electronic in nature, is encoded, i.e. translated, in qubit operators, e.g., via the Jordan- Wigner or Bravyi-Kitaev transformation. The quantum circuit to solve the “active space” part is then compiled on a CPU such that it can be performed on a quantum computer. The “active space” part is then prepared and solved on a quantum computer, for example, a higher-fidelity NISQ-QPU, or FT-QPU, for instance, by a so-called quantum phase estima- tion algorithm (QPE). This way the exact or a near-exact solution, for example, an exact or near-exact eigenfunction, of the “active space” sub-problem, for instance, the “active space” Hamiltonian, is prepared on the quantum computer. This is in analogy to the fourth step in the general process in Fig.10. The one- and two-particle reduced density matrices can then be measured on the quantum computer as solution of the first problem. This is in analogy to the fifth step in the general process in Fig.10. Alternatively and also according to step four in Fig.10, the “active space” part can be solved on a NISQ-QPU, e.g. by a so- called variational quantum eigensolver (VQE), in the step above. Depending on the chosen ansatz, typically approximate but accurate solutions, for instance as eigenfunctions of the “active space” part can be prepared on the NISQ-QPU. According to step five the one- and two-particle reduced density matrices would then be measured on the NISQ-QPU in the step above. The energy can then be calculated from the one- and two-particle reduced density matrices on a CPU. Furthermore, the gradient with respect to variation of the elec- tron orbitals can be calculated on a CPU, wherein this step is only performed in case of CASSCF but not for CASCI. This is in analogy to step six in the general process in Fig.10. In analogy to step seven in Fig.10, if energy and gradient are converged, it can be pro- ceeded with the final step. If not converged yet, it can be proceeded with updating the electron orbitals on the CPU as in step eight in Fig.10, such that the energy is minimized until convergence of the iterative procedure is obtained. In case of CASCI step seven can be omitted and there is no self-consistency loop, and thus it can be proceeded directly to the next step in that case. Further steps performed to determine a solution of the problem are described in the following. Although these CAS-like approaches are well suited to capture static correlation in an “ac- tive space”, for real-world applications the accuracy of the results is often not sufficient, even if the “active space” is solved exactly on a FT-QPU, because the “inactive space” has been treated only at a very basic level often comparable to the Hartree-Fock level that BASF SE 221032 221032WO01 completely neglects correlations of the electron orbitals in the “inactive space” and between electron orbitals in the “active space” and “inactive space”. In the following, this problem is solved by utilizing multireference dynamic correlation methods which account for dynamic correlation of the “inactive space” and among “active space” and “inactive space” both more systematically than e.g. multiconfiguration pair-density functional theory (MC-PDFT) and more efficiently than e.g. second-order n-electron valence state perturbation theory (NEVPT2). Moreover, these methods are in particular suited to be utilized in with the method and quantum computing system described above taking the fidelities of the quan- tum computers into account when solving sub-problems. In all approaches discussed below, the first step is, as described above, to determine a solution of the first part and the second part. The result can then be expressed, for instance, as a CAS wavefunction, ȁ^େ^ୗ ۧ that can be utilized as reference state for an interaction representation that allows to combine the results of the first and the second part. In the following it is described how to proceed from this reference state referring to a CAS wave- function. First it is described how the CAS wavefunction can be read out from a quantum computer in order to be reconstructed on a different hardware device. Then it is explained how to add, for instance, dynamic correlations of the “active space” and “inactive space” to generate the interaction representation from the CAS wavefunction. For an overview see also Fig.14. For all multireference dynamic correlation methods utilizing an interaction representation for combining a result of a calculation of an active space with a result of a calculation of an inactive space that will be discussed below that leverage unentangled quantum computing systems, relevant specifics of the CAS wavefunction determined as described above can be read out from the QPU(s) in order to be reconstructed or approximated on a different hardware device, for instance, CPU(s) or a different QPU(s), e.g. with a different fidelity, that is most suited for the multireference dynamic correlation treatment. In case of entan- gled quantum computing systems a reconstruction of the CAS wavefunction on a different hardware device is not required and thus the methods for the readout of the CAS wave- function can be omitted. The CAS wavefunction as exemplary reference state for the interaction representation that is determined based on the solution of the active space part, i.e. first part, and the solution of the second part, i.e. second part, obtained as described above can be expanded as
Figure imgf000060_0001
the basis states, e.g. Slater determinants, adhering to the “active space” definition. More precisely, those basis states can be so-called configuration interaction (CI) states given by a fixed distribution of the electrons among the electron orbitals in the “active space” part and the inactive space part. The index ^^runs over all possible electron distri- butions among the electron orbitals in the “active space” and “inactive space” part. The expansion coefficients
Figure imgf000061_0001
are then the so-called CI coefficients, which are utilized to recon- struct the CAS wavefunction on a different QPU or CPU that is most suited for the next computational step, for instance, a multireference dynamic correlation treatment based on an interaction representation. The following method can be utilized to determine the CI coefficients of a CAS wavefunction based on the solution of the active space part that has been prepared on a quantum com- puter, for instance, as described above. CI coefficients associated with inactive space can be determined, for instance, as solution of the second part, utilizing a mean field approxi- mation and are in most cases determined utilizing known method on a classical computer. Thus, the following focuses on the more complex determination of the CI coefficients of the “active space” part. In a first step an absolute value of CI coefficients can be measured on the respective QPU. The absolute value of the CI coefficients can be measured by deter- mination of an overlap of the CAS wavefunction and the defined basis states, for instance according to:
Figure imgf000061_0002
The CAS wavefunction, ȁ^େ^ୗۧ, can be prepared on the QPU as the result of the preceding CAS calculation of the active space part. Thus, in a previous step, the CAS wavefunction can be prepared on the QPU and a projective meas- urement on all qubits can be performed. Since no basis rotations of the qubit states are required, all qubits can be measured simultaneously. The measurement result (either 1 or 0 for each qubit) directly corresponds to the distribution of the electrons among the electron orbitals in the “active space”, wherein the measurement is 0 if an electron orbital is unoc- cupied and 1 if an electron orbital is occupied in case the Jordan-Wigner transformation is used. From this the corresponding basis state, e.g. Slater determinant, can be easily de- duced. The count of the respectively measured basis state, e.g. Slater determinant, can be increased by one and the process is repeated until a histogram of how often which basis state, e.g. Slater determinant, has been measured can be recorded. According to Eq. (2) ଶ the probability to measure a basis state, e.g. Slater determinant, is given by ห^ఓห and the histogram translates directly to these absolute values. A significant advantage of running the CAS method and measuring the result using a quantum computer is that it directly provides the most important basis states, e.g. Slater determinants, to span a relevant por- tion of the Hilbert space. This information is used in the following steps below. On a CPU, the CAS method would need to search for the relevant basis states, e.g. Slater determi- nants, which are not known a priori. Optionally, if the absolute values of selected, important CI coefficients are required to be determined with higher precision than achievable by the step above alone, the absolute value can be additionally directly measured in a second step where the CAS wavefunction is projected onto the basis states
Figure imgf000062_0001
for instance, via the projection operator: (3)
Figure imgf000062_0002
^^ ^ ^being the unitary operator that prepares the basis state
Figure imgf000062_0003
from the vacuum state |vacۧ, i.e. the state where each qubit is in state 0, according to
Figure imgf000062_0004
by exciting some qubits to state 1 such that the distribution of the electrons among the electron orbitals in the “active space” is reflected in the qubit register, where a qubit in state 0 indicates an empty electron orbital in the “active space” and a qubit in state 1 indicates an electron orbital occupied by one electron in the “active space” in case of the Jordan- Wigner transformation. Furthermore, in Eq. (3), ^^ ^ୟୡ ൌ
Figure imgf000062_0005
the unitary elementary operators
Figure imgf000062_0006
and ^^ ^ directly translate into unitary elementary operations acting on the qubits. In a further step for reconstructing the CAS wavefunction the phase of the CI coefficients can be determined in a post-processing step on a CPU. The above described step only determines the absolute value
Figure imgf000062_0007
of the complex-valued CI coefficients
Figure imgf000062_0008
but not the phase, which, can be crucial to reconstruct the CAS wavefunction according to Eq. (1). To determine the phase of the CI coefficients the following steps can be carried out. Since the ଶ absolute value ห^ఓห can be measured on the QPU(s) it can be determined which basis states have the largest CI coefficient and are therefore most important for the reconstruc- tion of the CAS wavefunction. Those basis states
Figure imgf000062_0009
can then be selected. The number of determined CI coefficients can be predetermined, for example, such that the measure- ments lead to a manageable number of basis states and also to a sufficient representation of a sufficiently large portion of the CAS wavefunction. Truncating the summation in Eq. (1) to a predetermined number of basis states leads to a more efficient calculation of the prob- lem. In a next step a representation of a Hamiltonian ^^, for example, which defines the molecule that is simulated, is reconstructed in a small subspace spanned by the most im- portant basis states selected in the previous step. The Hamiltonian in this sufficiently small subspace has a reduced size compared to the full Hamiltonian and can therefore be effi- ciently diagonalized, e.g. through power iterations or by the Davidson method. As a result, the CI coefficients
Figure imgf000063_0001
with their absolute value and phase within that subspace can be obtained. Optionally, to increase the accuracy, if needed, further CI coefficients that have not been included in the previous step can be obtained self-consistently using the results of the previous step as input via:
Figure imgf000063_0002
ଶ Alternatively, as the absolute values ห^ఓห are already known from the preceding CAS cal- culation on the QPU(s) and the measurement of the CI coefficients described above, in case of real CI coefficients ^ఓ, a variant of Eq. (4) could comprise fixing the absolute values ห^ఓห and only modifying the signs, e.g. in the framework of a Monte-Carlo-like procedure that flips the signs randomly: define ۱^ as a vector of the values on the left-hand side of Eq. (4), which are obtained by evaluating the right-hand side of Eq. (4) with a given set of CI coefficients ۱. One possible target of the sign-finding procedure is to minimize the deviation between the vectors ۱ ^ and ۱, for example by minimizing ห۱ ^ െ ۱ห with respect to the signs, ^ఓ ൌ േห^ఓห . Another possible target of the sign-finding procedure is to minimize the energy expectation value of the Hamiltonian with respect to the signs. Instead of the process described above a direct measurement of the CI coefficients with absolute value and phase is possible using, e.g., a Hadamard overlap measurement as shown in Fig.13. The Hadamard test requires controlled application of the entire quantum state preparation on the QPU. This algorithm is thus not feasible on NISQ-QPU devices but can be executed on a FT-QPU if part of the quantum computer system. This expensive measurement can be combined with predetermination of important determinants as de- scribed above. Alternatively, there are other elaborate measurement schemes like shadow tomography that can be used to measure the absolute value and phase of the CI coeffi- cients. After a sufficiently large number of CI coefficients has been determined to adequately rep- resent the CAS wavefunction according to Eq. (1), the CAS wavefunction can be recon- structed as reference state on a different computing device, i.e. a different QPU or a CPU, that is most suited for the subsequent multireference dynamic correlation treatment. To BASF SE 221032 221032WO01 determine how many of the most important CI coefficients are sufficient to adequately rep- resent the CAS wavefunction the following rules can be implemented. For example, it can be monitored how the energy, i.e. the expectation value of the Hamiltonian operator, con- verges with the number of included CI coefficients and thus basis states. For example, if an additional CI coefficient leads to a change in the energy below a predetermined thresh- old, then it can be determined that enough CI coefficients have been included. Additionally ଶ or alternatively the stability of the probability distribution and thus the ห^ఓห can be obtained, as described in the following. During the measurement of the CI coefficients it can be de- termined if the CI coefficients change when the number of measurements is increased and/or if the ratios of important CI coefficients change when the number of measurements is increased. Depending on the result it can be determined which CI coefficients to include. Additionally or alternatively, it can be determined how much the absolute values of the CI coefficients determined after the reconstruction of the Hamiltonian in a reduced subspace as described above differ from the absolute values of the CI coefficients obtained during the original measurement. Additionally or alternatively, it can be determined, if the absolute values are kept fixed in Eq. (4), how much the values
Figure imgf000064_0001
resulting from evaluating the right- hand side of Eq. (4) differ from the values ^ఓ. Based on the respective results it can be determined if the relevant CI coefficients are included in the reconstructed CAS wavefunc- tion. Alternatively, to the method described above utilizing a quantum computer the CAS wave- function of a problem can also be determined by a traditional CAS, RAS (“restricted active space”, such as RASSCF or RASCI) or GAS (“generalized active space”, such as GASSCF or GASCI) calculation running entirely on CPU(s) without any quantum computing part. Thus, the first part in in this case calculated on a classical computer. In this case a quantum computer can be utilized for the dynamic correlation treatment of the “inactive space” part, i.e. second part, in a further computational step. However, using traditional CAS, RAS or GAS methods utilizing CPU(s) can be computationally more expensive than using the method described above utilizing a quantum computer in combination with the procedure describe above to determine the CI coefficients. In the following the multireference dynamic correlation treatment, in which the CAS wave- function is used as a reference state and thus as fixed starting point is described. The CAS wavefunction is used as a reference state that is not varied anymore. The following meth- ods account for dynamic correlation of the “inactive space” and among “active space” and “inactive space” in a further computational step. In the following, four exemplary embodi- ments are presented. The first embodiment leverages a NISQ-QPU that is not entangled with the FT-QPU or higher-fidelity NISQ-QPU used for the CAS wavefunction calculation BASF SE 221032 221032WO01 and thus this is compatible with the unentangled quantum computing system described with respect to Fig.9. A further embodiment leverages a NISQ-QPU that is entangled with the FT-QPU or higher-fidelity NISQ-QPU used for the CAS wavefunction calculation thus this is compatible with the entangled quantum computing system described with respect to Fig.9. The remaining two embodiments are focused on post-processing on a CPU. Fig.14 shows an overview of the four embodiments that will be discussed in the following. The following sections treat the CAS method as separating between predominantly static correlation within the “active space” on the one hand, and dynamic correlation among elec- trons in all electron orbitals, both active and inactive, on the other hand. However, the methods described below can also be applied in an embedding context. For example, the CASCI method can be used to calculate both the static and dynamic correlation of electrons in electron orbitals located on a fragment of a molecular system or material, and a dynamic correlation method can be used to calculate the interaction between the CASCI fragment and the surrounding electron orbitals. A fragment refers to a spatially connected part of the molecular system comprising the respective electron orbitals associated with this part of the molecular system and is independent of the active and inactive space sub-problems. For example, a fragment can be associated with spatially connected atoms of the molecular system and comprise the electron orbitals of these atoms. A separation between electron orbitals inside and outside of the CASCI fragment can be achieved through orbital locali- zation methods, which can be aided by other techniques such as natural orbitals, natural orbitals for orbital pairs or subsets, orbital-specific virtual orbitals, and domains of projected atomic orbitals or other functions. A molecule or material can also contain multiple frag- ments that are treated at CASCI level with approximate interaction, for example at mean- field level, between the fragments. Afterwards, a correlated interaction is calculated using the dynamic correlation methods described below. In the following a method referring to a NISQ unitary dynamic correlation (NISQ-UDC) ap- proach leveraging the unentangled quantum computing system is described. For relevant molecules, such as transition metal compounds, the number of electron orbitals that are assigned to the “active space” defining an “active space” part is typically significantly smaller than the number of electron orbitals remaining in the “inactive space” defining the “inactive space” part. As discussed above, FT-QPU(s) and/or higher-fidelity NISQ-QPU(s) with only a small number of available qubits can be utilized together with larger NISQ- QPU(s), i.e. NISQ-QPU(s) with a larger number of qubits but a lower fidelity. Such a hard- ware setting is ideally suited to combine a CAS calculation, wherein a FT-QPU or a higher- fidelity NISQ-QPU is used to solve the “active space” part at a high level of accuracy, with an approximate dynamic correlation method for the “inactive space” part and to approxi- mately account for dynamic correlation within the “inactive space” sub-problem and be- tween “active space” and “inactive space” sub-problems utilizing a NISQ-QPU. Based on the preceding CAS calculation determining the CAS wavefunction as described above as reference state, in a further computational step an interaction representation can be gen- erated and solved by applying a unitary dynamic correlation (UDC) ansatz in combination with the variational quantum eigensolver (VQE) or the variational Hamiltonian ansatz (VHA) to approximately account for dynamic correlation utilizing a NISQ-QPU. The “inactive space” part can further be solved utilizing known methods. In many cases the solution of the “inactive space” part can be trivial. Moreover, the solution can also be generated al- ready taking a solution of the “active space” part into account, for example, adapting the electron orbitals of the “inactive space” part based on a solution of the “active space” part. This solution of the “inactive space” part can then be integrated into the CAS wavefunction as part of the interaction representation. In more detail the method can be represented by a parameterized unitary operator ^^^^^ that acts both on the “inactive space” and “active space” parts of the previously determined CAS wavefunction forming an example of an interaction representation as follows:
Figure imgf000066_0001
with ^ being a set of parameters that are optimized within a variational procedure, e.g. VQE or VHA. One specific example is that ^^^^^ ൌ
Figure imgf000066_0002
is a unitary coupled cluster (UCC) op- erator. The method can be referred to as an “internally contracted multireference unitary coupled cluster method” (ic-MR-UCC). For an introductory overview on MR-CC methods, see the article “Perspective: Multireference coupled cluster theories of dynamical electron correlation, F. A. Evangelista, The Journal of Chemical Physics: Vol 149, No 3” incorpo- rated herein by reference. The cluster operator
Figure imgf000066_0003
^ ڮdescribes ex- citations from arbitrary electron orbitals ^, ^ to arbitrary electron orbitals ^, ^ to account for dynamic correlation. Usually, the expansion only includes the singles and doubles term as explicitly shown above leading to the UCCSD operator and thus the ic-MR-UCCSD method. However, the method can also be systematically extended to higher-order excitations like triple, quadruple, etc. excitations leading to ic-MR-UCCSDT, ic-MR-UCCSDTQ, etc. vari- ants. ^^ற ^ and^^^ are electronic creation and annihilation operators, respectively. Restrictions can be applied to the indices ^^ in the singles term, the indices ^^^^ in the doubles term, BASF SE 221032 221032WO01 or the corresponding indices in higher-order terms. Examples for possible restrictions on the indices include the following. Whenever both indices ^, ^ in σ ^^ ^^^ ^^ற ^ ^^^ refer to inactive electron orbitals, the term can be restricted to include only contributions
Figure imgf000067_0001
with occupied inactive electron orbitals ^^and unoccupied inactive electron orbitals ^. Whenever all indices ^,
Figure imgf000067_0002
^^ refer to inactive electron orbitals, the term can be restricted to include only contributions ற ற
Figure imgf000067_0003
^^^^^ ^^^ ^^^ ^^^ ^^^ with occupied inactive electron orbitals ^, ^ and unoccupied inactive electron orbitals ^, ^. No terms σ ற ௧௨ ^௧௨ ^^௨ ^^௧ or σ௧௨௩௪ ^௧௨௩௪ ^^ற ௨ ^^ற ௪ ^^௩ ^^௪ with all indices ^, ^, ^, ^ referring exclusively to active electron orbit- als can be included. Terms including at least one creation operator and at least one anni- hilation operator in the occupied inactive space can be excluded. Terms with at least one creation and at least one annihilation operator in the unoccupied inactive space can be excluded. Examples for such excluded terms include σ^^^^ ^^^^^ ^^ற ற ^ ^^^ ^^^ ^^^ and σ^^^^ ^^^^^ ^^ற ^ ^^ற ^ ^^^ ^^^ with inactive occupied electron orbitals ^, ^, inactive unoccupied elec- tron orbitals ^, ^ and arbitrary orbitals ^, ^. The method can then be performed as described in the following. In a first step the CAS method and process described above using a FT-QPU or higher-fidelity NISQ-QPU and the quantum phase estimation (QPE) algorithm is applied to determine the exact or a near- exact solution of the “active space” part in form of the CAS wavefunction as reference state. In an embodiment, only the “active space” part is solved on the FT-QPU or higher-fidelity NISQ-QPU which means that typically as many logical qubits as there are electron orbitals in the “active space” can be used to represent the solution of the “active space” part. De- pending on the algorithm additional qubits can be required to implement the algorithm, e.g., ancilla qubits for the QPE algorithm. Alternatively a NISQ-QPU (and, e.g., the variational quantum eigensolver, VQE) to solve the “active space” part can be used in this step. Alter- natively, it is also possible to run the CAS (or alternatively RAS or GAS) method entirely on a CPU, and proceed with the step described below, e.g. the dynamic correlation treatment on a NISQ-QPU. In the second step the CI coefficients can be determined as described above. The CAS wavefunction or the most relevant CI coefficients that were read out, can be stored on the CPU and kept fixed throughout all of the following steps as part of the reference state. In the third step the dynamic correlation of the “inactive space” and among “active space” and “inactive space” can be taken into account utilizing a NISQ-QPU by executing again parts of the process depicted in Fig.10 as described in the following. First a representation of the CAS wavefunction is prepared on a quantum computer with a suitable fidelity, for ex- ample, a NISQ-QPU. For example, the entire CAS wavefunction, and not only the “active space” solution, can be reconstructed according to Eq. (1), for example, using the most relevant CI coefficients as described above, on the NISQ-QPU via
Figure imgf000068_0001
where the summation over ^ is restricted to the ^ most important basis states, e.g. Slater ଶ determinants, as described above, e.g. the ones where ห^ఓห is larger than a predetermined threshold. This typically requires as many qubits as there are electron orbitals in the mole- cule, for example, electron orbitals in the “active space” plus electron orbitals in the “inactive space”. Depending on the algorithm used to prepare the CAS wavefunction on the respec- tive quantum computer additional quits can be required for the preparation step, e.g., ancilla qubits to prepare sums of states. In a next step a UDC operator ^^^^^ can be applied to generate as an interaction representation a trial state according to Eq. (5) with Θ being a set of variational parameters that will be adjusted on the CPU later within a VQE or VHA procedure. One example of such a unitary operator is the unitary coupled cluster (UCC) operator described above, where ^^^ and ^^^^^ are the sets of variational parameters. In the first iteration step, parameters can be either chosen randomly or by means of other com- putationally inexpensive traditional methods, e.g. based on perturbation theory, that are run on a CPU in advance. Next, the electronic creation and annihilation operators can be en- coded in qubit operators, namely Pauli operators, e.g. by means of the Jordan-Wigner or Bravyi-Kitaev transformation. The encoded UDC operator, ^^^^^, is then translated into quantum gates that are applied to the previously reconstructed CAS wavefunction on the quantum computer to prepare a parameterized trial state according to Eq. (5) as interaction representation. Strategies like the FSIM network algorithm using low-rank decomposition or the CZ algorithm can be used. The one- and two-particle reduced density matrices can then be measured on the quantum computer. The measured quantities allow for the eval- uation of the energy of the trial state ȁ^^୍ୗ^ି^ୈେ^ with respect to the molecular Hamiltonian ^^ on a classical computer, e.g. a CPU, according to:
Figure imgf000068_0002
If the energy and the variational parameters are not converged yet, the iteration continues by updating the set of variational parameters such that the energy ^ is minimized in a var- iational procedure on the classical computer. If the energy and the variational parameters are converged, the iteration proceeds with the final step. The final energy and further prop- erties of the solution can then be provided to the user. Also, further post-processing on a BASF SE 221032 221032WO01 classical computer, e.g. a CPU, can be performed including application to real-world prob- lems related to chemical products like molecules, solids, materials, etc. As mentioned above multireference dynamic correlation approaches have an advantage over the CAS method as they account for dynamic correlation across the “active space” and “inactive space”. In particular, the ic-MR-UCC method provides a more systematic ap- proach to compute observable quantities compared to MC-PDFT, as it does not rely on the choice of a pair density functional as MC-PDFT. Additionally, the accuracy can be in- creased systematically by going from ic-MR-UCCSD to ic-MR-UCCSDT to ic-MR- UCCSDTQ etc. Traditional internally contracted multireference methods for CPUs, such as second-order complete active space perturbation theory (CASPT2), NEVPT2, ic-MRCI or ic-MRCC, require computation of three-particle, four-particle or even higher-order reduced density matrices. Needing to compute these reduced density matrices in calculations on CPUs, or to measure these reduced density matrices in calculations on QPUs, renders such methods extremely expensive or entirely unfeasible when used in combination with large “active spaces”. As there is no need to determine reduced density matrices of high order for the above described ic-MR-UCC method, it permits larger electronic-structure problems, e.g. larger molecules, to be simulated with higher accuracy than previously pos- sible. Another specific advantage of ic-MR-UCC over perturbative methods such as CASPT2 and NEVPT2 is its increased accuracy, analogous to the well-documented ad- vantages of CCSD and UCCSD over second-order Møller-Plesset perturbation theory (MP2) and to the advantages of traditional multireference coupled cluster over perturbative multireference methods. Unlike in MRCI, where the accuracy of results deteriorates with an increasing number of atoms due to lack of size consistency and size extensivity, the quality of ic-MR-UCC results is retained. In the following a FT-NISQ unitary dynamic correlation (FT-NISQ-UDC) method utilizing an entangled quantum computing system is described, wherein the FT-QPU can also be re- placed by a higher-fidelity NISQ-QPU. As an alternative to the exemplary method described above it is also possible to utilize an entangled quantum computing system to account for dynamic correlation. As a result of a successfully converged CAS calculation using a re- spective quantum computing system as described above a highly accurate solution, for example, highly accurate eigenfunctions, ȁ^ୟୡ^୧^^ۧ^^ି^^^, of the “active space” part, for in- stance, “active space” Hamiltonian, is available on the respective quantum computer, pref- erably, a FT-QPU or higher-fidelity NISQ-QPU. Furthermore, all resulting electron orbitals can be stored on a classical computer, e.g. a CPU. The latter information can be used to represent the electron orbitals defining the “inactive space” part on a NISQ-QPU with a respective fidelity using a state that can easily be prepared on the NISQ-QPU, ȁ^୧୬ୟୡ^୧^^ۧ^୍ୗ^ି^^^, e.g. by initializing a qubit in state 1 if the inactive electron orbital is oc- cupied and in state 0 if the inactive electron orbital is unoccupied according to the Jordan- Wigner transformation. It is noted that, preferably, the FT-, higher-fidelity NISQ- and/or the NISQ-QPU are located on the same chip to facilitate entanglement in a later step. However, using a quantum bus such as optical fibers and photons, spatially separated QPUs can be entangled as well. To approximately account for dynamic correlation within the “inactive space” part and be- tween “active space” and “inactive space” parts by using an entangled quantum computing system a parameterized unitary dynamic correlation (UDC) operator, ^^ ^୬^^^^, that entan- gles quantum computers with different fidelities can be applied leading to an interaction representation according to:
Figure imgf000070_0001
with Θ being a set of variational parameters within a variational procedure, e.g. within the variational quantum eigensolver (VQE) or a variational Hamiltonian ansatz (VHA). One specific example is that ^^ ^୬^^^^ ൌ
Figure imgf000070_0002
is a unitary coupled cluster (UCC) operator. Such a choice would also result in an ic-MR-UCC method, wherein the difference to the analo- gous method described above with respect to the unentangles quantum computing system is that here the entangled quantum computing system is used. Further details on the oper- ator, possible truncations and possible restrictions on indices are already described above and can also be applied in this embodiment. By describing electronic excitations/transitions between electron orbitals, the coupled cluster operator ^^ ^accounts for dynamic correlation. Those electronic excitations/transitions that involve at least one active and at least one inactive electron orbital will create entanglement between the respective quantum comput- ers, e.g. a term ^ ற ற ^^^^ ^^^ ^^^ ^^^ ^^^ with ^ referring to an active electron orbital that has been mapped onto a FT-QPU or a higher fidelity NISQ-QPU and ^, ^, ^ referring to occupied or unoccupied inactive electron orbitals that have been mapped onto the NISQ-QPU will cre- ate entanglement between qubits located on two different QPUs. The method can comprise the following steps. In a first step the CAS method and process as described above is performed using, for example, a FT-QPU of higher-fidelity NISQ- QPU and, e.g., a quantum phase estimation algorithm (QPE) to determine the exact or a near-exact solution of the “active space” part. Note, that only the “active space” part is solved on the FT-QPU or higher-fidelity NISQ-QPU which means that typically as many BASF SE 221032 221032WO01 logical qubits as there are electron orbitals in the “active space” part can be used to repre- sent the solution of the “active space” part. Depending on the algorithm additional qubits can be required to implement the algorithm, e.g., ancilla qubits for the QPE algorithm. After the CAS procedure is finished the electron orbitals can be stored on a CPU as part of the reference state. In the next step the dynamic correlation of the “inactive space” and be- tween “active space” and “inactive space” is accounted for by using an entangled quantum computing system in combination with a variational approach similar to the general proce- dure exemplarily depicted in Fig.11. For example, the solution of the “active space” part can be prepared on a higher-fidelity NISQ-QPU or FT-QPU resulting in ȁ^ୟୡ^୧^^ۧ^^ି^^^ , e.g. by applying the quantum phase estimation (QPE) algorithm using the electron orbitals that are stored on the CPU. If a CASSCF has been used, since the optimized electron orbitals are stored, it is not necessary to run the entire iterative CASSCF procedure again but a preparation of the solution of the “active space” part is sufficient, i.e. a single CASCI calculation using the optimized and stored electron orbitals. Simultaneously, the electron orbitals that are stored on the CPU can be utilized, to prepare a wavefunction describing the “inactive space” part on a NISQ-QPU resulting in ȁ^୧୬ୟୡ^୧^^ۧ^୍ୗ^ି^^^ as part of the ref- erence state. This can require as many qubits on the NISQ-QPU as there are electron orbitals in the “inactive space”. In summary, the entire CAS wavefunction is prepared on the QPUs of the quantum computing system as reference state. A UDC operator ^^ ^୬^^^^ that entangles the respective quantum computers on which the sub-problems, here wave- functions of the “active space” and “inactive space”, are prepared, is applied to generate as interaction representation a trial state according to Eq. (8) with Θ being a set of varia- tional parameters that is adjusted on the CPU within, e.g., a VQE procedure. One example of such a UDC operator is a unitary coupled cluster (UCC) operator described above. In the first iteration step, parameters can be either chosen randomly or by means of other computationally inexpensive traditional methods, e.g. based on perturbation theory, that are run on a CPU in advance. The one- and two-particle reduced density matrices can then be measured on the QPUs as result of the computation and the energy of the trial state ȁ^^^ି^୍ୗ^ି^ୈେ^ with respect to the molecular Hamiltonian can be evaluated on the CPU in analogy to Eq. (7). If the energy and the variational parameters are not converged yet, the method performes a respective iteration of the above steps after updating the set of varia- tional parameters on the CPU such that the energy is minimized, e.g. in a variational pro- cedure. If the energy and the variational parameters are converged, the method can pro- ceed with the final step. Preferably the electron orbitals that are stored on the CPU as a result of the CAS calculation are kept fixed during the procedure, i.e. the CAS wavefunction that serves as a reference for the dynamic correlation treatment is not varied any more. However, it is also possible to adjust the electron orbitals within optional self-consistent field (SCF) steps. The final energy and further properties of the solution can then be pro- vided to the user. Also, further post-processing on the CPU can be performed including application to real-world problems related to a chemical product like molecules, solids, ma- terials, etc. The multireference dynamic correlation approach described above exhibits very similar ad- vantages over other methods as described already with respect to the NISQ-UDC method above. Furthermore, in comparison to the NISQ-UDC method that leverages the unentan- gled quantum computing system there are additional advantages of the FT-NISQ-UDC method. In comparison to the NISQ-UDC method, the FT-NISQ-UDC method described above neither relies on the measurement of CI coefficients nor on the approximate recon- struction of the CAS wavefunction on a different hardware device. This brings the ad- vantage that the unitary operator accounting for dynamic correlation is applied to the exact CAS wavefunction and not an approximately reconstructed one. Such an approach may help to eliminate problems that can result from an approximate reconstruction of the CAS wavefunction, such as intruder states. Furthermore, whereas in case of the unentangled quantum computing system the entire CAS wavefunction comprising both “active space” and “inactive space” is represented on a NISQ-QPU, in the method described above it is sufficient to only represent the wavefunction of the “inactive space” on the NISQ-QPU re- sulting in a reduced requirement with respect to the number of qubits on the NISQ-QPU. In the following a tailored coupled cluster (TCC) approach is described. The “tailored cou- pled cluster” (TCC) method aims at accounting for dynamic correlation within the “inactive space” and between “active space” and “inactive space” utilizing the CAS wavefunction as a reference state for post-processing on a CPU after a CAS calculation. Genuine multi- reference coupled cluster (CC) approaches apply the coupled cluster exponential operator to a CAS-like multireference wavefunction ȁ^େ^ୗ ۧ, see, e.g. Eq. (5). TCC, on the other hand, is a modification of the widely used single-reference CC approach to incorporate the effects of static correlation directly into the coupled cluster exponential operator, which is then applied to a single-reference wavefunction ȁ^^ ۧ to generate an interaction representation of the form: ^^େେۧ ൌ ^ ^்^ిిȁ^^ۧ ൌ ^ ^்^౮౪^ ^்ి^^ȁ^^ۧ (9) As mentioned, ȁ^^ ۧ is a single basis state such as the one constructed from the natural or canonical orbitals of a CAS wavefunction and not a linear combination of multiple basis states like in Eq. (1). Other choices than canonical or natural orbitals are possible. ^^ ^େେ can be partitioned into a sum of two commuting operators, ^^ ^େେ ൌ ^^ ^^^ ^ ^^ େ^ୗ. ^^ ^^ௌ is a coupled cluster operator which is of similar form as the one already discussed with regard to Eq. (5). Here, it is directly determined from the preceding CAS calculation on a QPU via the CI coefficients described above, e.g. in case of the TCCSD method the CI coefficients for the singly and doubly excited basis states, ^ఓభ^and ^ఓమ , are connected to the coupled cluster operator ^^ େ^ୗ via the relation
Figure imgf000073_0001
Thus, ^^ େ^ୗ focuses on static correlation and is restricted to act on electron orbitals within the “active space”. Once determined via the preceding CAS calculation, ^^ େ^ୗ is kept fixed throughout the entire TCC procedure on the CPU. All other possible excitations that include at least one electron orbital outside the “active space” are part of the coupled cluster oper- ator ^^ ^^^ which focuses on dynamic correlation within the “inactive space” and between the “active space” and “inactive space”. The parameters contained in ^^ ^^^ are determined by solving coupled cluster equations on a CPU:
Figure imgf000073_0002
In Eq. (11) the parameter equations for single and double excitations are shown, resulting in the TCCSD method. An extension to higher-order excitations is straightforward but com- putationally more expensive. Indices ^, ^ describe occupied and indices ^, ^^describe unoc- cupied electron orbitals in a single determinant ȁ^^ۧ but not directly in the CAS wavefunc- tion. After convergence of the parameters contained in ^^ ^^^ , the final energy is evaluated on the CPU according to:
Figure imgf000073_0003
The entire process can then be described as follows. In a first step the CAS method and process described above can be utilized to solve the “active space” part. In a second step the CI coefficients can be determined as also already described above as reference state. In a third step dynamic correlation within the “inactive space” and between “active space” and “inactive space” can be accounted for while approximately including static correlation by means of the TCC method entirely on a CPU. The parameters that determine the oper- ator ^^ େ^ୗ can be calculated from the CI coefficients according to Eq. (10) as part of the interaction representation. If applying the TCCSD method, only the singles and doubles CI coefficients are needed. Furthermore, ȁ^^ ۧ can be constructed, e.g., from the natural or canonical orbitals of the CAS wavefunction. Both quantities, ^^ େ^ୗ and ȁ^^ ۧ , can be kept fixed throughout all of the following steps. Then, the modified coupled cluster equations, Eq. (11) as part of the interaction representation, are iteratively solved on a CPU to deter- mine the parameters contained in ^^ ^^^, thus accounting for dynamic correlation across all electron orbitals. After convergence of the parameters, the final energy can be evaluated on the CPU according to Eq. (12). Optionally, further properties can be calculated. The final outcome can be provided to the user. Further post-processing and application to real-world problems related to a chemical product like molecules, solids, materials, etc. is possible. Overall, in comparison to genuine multireference (MR) approaches, that directly build upon a CAS wavefunction, the TCC method is simpler and computationally less expensive com- pared to traditional genuine multireference approaches for CPUs that aim at including dy- namic correlation on top of a statically correlated reference wavefunction and thus typically require the calculation of higher-order reduced density matrices as already described above. After the CAS wavefunction has been prepared on the QPU and all required quan- tities have been measured, the computational effort of TCC on the CPU is comparable to that of the well-known traditional coupled cluster method. In the following a stochastic strongly contracted NEVPT2 (s-sc-NEVPT2) approach is de- scribed. Similar to TCC, the s-sc-NEVPT2 method aims at accounting for dynamic correla- tion within the “inactive space” and between “active space” and “inactive space” utilizing the CAS wavefunction as a reference state for post-processing on a CPU after a CAS cal- culation. The s-sc-NEVPT2 energy correction, which is a second-order perturbative energy correction to the CAS energy can be used as interaction representation in this case and can read: (13) strongly contracted perturber function repre-
Figure imgf000074_0001
senting the subspace
Figure imgf000074_0002
^^ ௌ^ೖ is the projection operator onto the subspace . ^ is the ^ҧ^
Figure imgf000074_0003
number of electrons added to or removed from the “active space”. ^ labels the occupied and virtual electron orbitals in the “inactive space” that electrons are removed from or added BASF SE 221032 221032WO01 to, respectively. As usual, by those excitations/transitions of electrons within the “inactive space”, or between the “active space” and the “inactive space” dynamic correlation is ac- counted for. ȁ^^^ௌۧ is the unperturbed reference wavefunction obtained by the CAS calcu- lation in the previous step as reference state. ^ ^^^ ^ is the energy of the perturber state:
Figure imgf000075_0001
which is calculated as the expectation value of the so-called Dyall Hamiltonian ^^ ୈ. The denominator and numerator in Eq. (14) are:
Figure imgf000075_0002
Figure imgf000075_0003
denote the CI states defined in Eq. (1) and
Figure imgf000075_0004
the respective CI coefficients are calculated via the overlap of the CAS wavefunction with the CI states, see Eq. (2) and following. The preceding CAS procedure on the QPU naturally provides a stochastic sam- ple of the CI states,
Figure imgf000075_0006
with probability distribution
Figure imgf000075_0005
by measuring qubits repeatedly. This result can then be put into Eqs. (15) and (16), which can be evalu- ated as part of the interaction representation on a CPU. Furthermore, the CI coefficients, ^ఓ, can be obtained as described above and also enter Eqs. (15) and (16). The CI coeffi- cients are also used to reconstruct the CAS wavefunction, ȁ^େ^ୗۧ. The accuracy depends on the number of utilized CI coefficients
Figure imgf000075_0008
and associated basis states
Figure imgf000075_0007
the matrix elements
Figure imgf000075_0009
ห^ఔ^ in Eqs. (15) and (16) can be efficiently calculated on a as they are only matrix elements between the basis states, e.g. Slater determinants. An exemplary method can then be described as follows. In a first step the CAS method and process described above is utilized to solve the “active space” part. In a second step the CI coefficients can be determined as also already described above. The absolute values and phases of the most relevant CI coefficients can then be stored on a CPU as part of the reference state. In a third step dynamic correlation is accounted for by evaluating the sec- ond order energy correction according to Eq. (13) as interaction representation, for in- stance, on a CPU. The CAS wavefunction can be reconstructed according to Eq. (1) using the most relevant CI coefficients, as described above. The CAS wavefunction is normalized^ ۦ^େ^ୗȁ^େ^ୗۧ ൌ ^. Furthermore, the CAS energy, ^ ^^^ ^ , can also be put into Eq. (13). The matrix elements
Figure imgf000076_0001
หǥ ห^ఔ^ in Eqs. (15) and (16) can be calculated on a CPU. Those equa- tions can be finally evaluated by using the previously determined most relevant CI coeffi- ଶ cients, ^ఓ, and their squares, ห^ఓห . The final s-sc-NEVPT2 energy correction, see Eq. (13), can then be added to the CAS energy, ^ ^^^ ^ , to obtain the final total energy of the electronic- structure problem on a CPU that is provided to the user. Further post-processing and ap- plication to real-world problems related to a chemical product like molecules, solids, mate- rials, etc. is possible. In contrast to conventional NEVPT2 and also other MR methods on a CPU and a potential straightforward implementation of NEVPT2 using a QPU, in s-sc- NEVPT2 the expensive calculation of higher-order reduced density matrices is circum- vented, thus allowing for simulation of larger electronic-structure problems, e.g. larger mol- ecules. In the following some preferred applications of the above described embodiments are pro- vided. As a result of the methods described above using a quantum computer, total ener- gies and properties of the electronic structure of a chemical product, e.g., molecular and, optionally, periodic materials can be calculated and provided to a user. Using those com- putational results it is possible to predict relevant quantities for real-world applications such as technical application properties of chemical products, e.g., molecules. From those, rec- ommendations can be derived to discover new materials and chemicals, improve chemical processes, tailor molecules, solids and materials to desired properties and make research activities more efficient by reducing the number of required expensive lab and production trials. An important example for a technical application property that can be determined is the chemical reactivity, wherein the prediction of thermodynamic and kinetic quantities of chemical reactions relies on the calculation of free enthalpies such as reaction free en- thalpies and free enthalpies of activation, respectively. For example, the reaction free en- thalpy is indicative of whether a chemical reaction can occur in principle or not and the free enthalpy of activation is indicative of the rate, i.e. speed, of a chemical reaction. Among the most important and difficult to calculate contributions to the respectively required free en- thalpies are energy differences between reactants, products and the transition state, e.g. the highest point in energy along the reaction pathway from reactants to products. For ex- ample, the reaction energy, which is one of the main contributions to chemical thermody- namics, is obtained by subtracting the sum of the total energies of all reactants from the sum of the total energies of all products. In analogy, the activation energy, which is one of the main contributions to chemical kinetics, is obtained by subtracting the sum of the total BASF SE 221032 221032WO01 energies of all educts from the total energy of the transition state. The total energies of respective products, reactants and transition states can advantageously be calculated uti- lizing the methods of the invention as described above. The calculation of the free en- thalpies of all potential reaction pathways, i.e., taking into account all possible transition states, intermediates and products, ultimately allows to predict the outcome if molecules are brought to reaction by identifying the one or more energetically most favorable reaction pathways. A highly accurate calculation of all species within a chemical reactive network, i.e. reactants, products, transition states and intermediates, and their total energies is in- dispensable for a reliable prediction of thermodynamic and kinetic quantities of chemical reactions, such as reaction free enthalpies and free enthalpies of activation; this highly accurate calculation is one requirement for the computational design of new chemical prod- ucts and improvement of industrial chemical production processes as well as for other tech- nical application areas like the understanding and based on that the suppression of the degradation of chemical products, the prediction of the microstructure of polymeric chemi- cal products and thus the computational fine-tuning of technical application properties of chemical products. Further examples for technical application properties that can be determined are spectra and spectroscopic properties, e.g., referring to electronically excited states of electronic structure problems. For example, calculating the differences in total energies between dif- ferent electronic states, e.g., between the ground state and one or more electronically ex- cited states, e.g., with particular spin multiplicities or electronic configurations that are dif- ferent from the ground state, allow the prediction of spectra and spectroscopic properties of chemical products, which are relevant to understand the influence of radiation on a chemical product, e.g. in photovoltaics and photochemical synthesis as well as degradation processes. The calculation of electronically excited states is furthermore a prerequisite for the computational design of, e.g., dyes or photoinitiators as well as more complex assem- blies like organic electronic materials. Another example for technical application properties that can be determined with the above described methods are molecular properties beyond energies, for example, electrostatic multipole moments, hyperfine couplings, electrical fields and their gradients relevant for Mössbauer spectroscopy, diamagnetic shieldings relevant for nuclear magnetic resonance (NMR) spectroscopy, etc. Generally, the calculation of physico-chemical properties is im- portant for molecular structure and property elucidation. BASF SE 221032 221032WO01 Moreover, the above described invention is particularly advantageous for the solving of problems in molecular systems that exhibit strong static correlation. Nevertheless, the in- vention is not limited to solving statically correlated electronic structure problems and can be applied to all electronic structure problems. Statically correlated molecular systems usu- ally comprise parts that exhibit a complex electronic structure which makes high-accuracy calculations often prohibitively expensive on classical computers already for small problem sizes. Examples for molecular systems that exhibit strong static correlation commonly in- clude metal-organic compounds that contain transition metals such as iron, nickel, rhodium, palladium, etc., or contain lanthanides and actinides. Thus, the examples for molecular systems that exhibit strong static correlation include statically correlated homonuclear or oligonuclear center in weakly correlated environments, wherein the term “nuclear” refers to transition metal, lanthanide or actinide ions or atoms therein plus optionally single ions or single atoms of the ligands. Such transition metal compounds are of key importance for the design of new catalysts, chelating agents, homogenously catalyzed fine chemicals, en- zymes, etc. Furthermore, static correlation also occurs outside of transition metal chemis- try, e.g., during chemical reactions of organic molecules in bond-breaking and/or -forming situations, e.g. in certain transition states, and also occurs in certain common main-group- element molecules like ozone. Specific industry-relevant chemical products to which the invention can be applied are, for example, catalysts. Catalysts play a crucial role in enabling or accelerating chemical reac- tions under mild conditions, e.g., mild temperatures and mild pressures, by interacting with the transition state and lowering its energy thus reducing the activation energy and increas- ing the rate of the chemical reaction. Today, catalysts are often used that contain 4d or 5d transition metals like rhodium and palladium, which are highly expensive, like the rhodium- based Wilkinson catalyst for hydroformylation. The goal of many technical objectives is to substitute those catalysts by catalysts that are cheaper to produce containing, e.g., cheaper 3d transition metals cobalt or iron. The above described invention can be particularly ad- vantageous in the area of homogenous catalysis, e.g., for calculating oxidation reactions, reduction reactions, hydrogenations, carbonylations, etc. in large-scale chemical produc- tion processes such as the chemical production process of polymers but also in the syn- thesis of homogenously catalyzed basic chemicals. For example, utilizing the above de- scribed invention activation, energies for a predetermined catalytic cycle including unde- sired side reactions can be calculated for a set of predetermined catalysts before their syn- thesis in the laboratory. As described above, those activation energies contribute to the calculation of chemical kinetics, in particular chemical reaction rates. In particular, deter- mined chemical reaction rates of the potential catalyst can be compared with target chem- ical reaction rates and, based on the comparison, either i) a respective potential catalyst BASF SE 221032 221032WO01 can be determined as target catalyst, or ii) a new potential catalyst can be provided and the determination of the reaction rates according to the invention can be repeated. Thus, only those catalysts for which the chemical reaction rate is larger than a predetermined threshold and for which no major undesired side reactions are predicted are finally selected for synthesis and further investigation in the laboratory, for instance, by providing control data that causes a respective synthesis of the respective catalyst. Other specific industry-relevant chemical products to which the invention can be applied are chelating agents. The development of chelating agents, which are tailored towards cer- tain metal ions, can be enhanced by the calculation of complex formation constants. A complex formation constant is a thermodynamic quantity that indicates how thermodynam- ically stable the resulting complex of the metal ion and chelating agent is. A reliable com- putational prediction typically requires a highly accurate calculation of total energies of the respective ions and molecules which is particularly challenging for the case of transition- metal ions. Additionally, a reliable prediction of the selectivity of chelating agents is chal- lenging, since both its experimental determination and its computational prediction are dif- ficult. Selectivity is a means that describes how strongly a particular chelating agent pref- erably binds to a specific metal ion compared to other metal ions, which can be derived from respective complex formation constants. A very well-known example for a chelating agent is ethylenediaminetetraacetic acid (EDTA) which can be used, e.g., for the solubili- sation of a Fe3+ ion. The goal of many technical objectives is to design new chelating agents with a predetermined selectivity that exhibit favorable properties like biodegradability or are less hazardous to water organisms. Chelating agents are used in a large variety of tech- nical applications, e.g., to suppress the undesired influence of metal ions in washing and cleaning processes. Furthermore, chelating agents are also used in mining for selective extraction of metals. For example, using the above described invention reaction energies for a predetermined chelating agent can be calculated that ultimately contribute to the cal- culation of complex formation constants and thus the selectivity with respect to different transition metal ions. These calculations are done, e.g., for a set of predetermined chelating agents before their synthesis in the laboratory. In particular, determined selectivities of the potential chelating agent can be compared with target selectivities and, based on the com- parison, either i) a respective potential chelating agent can be determined as target chelat- ing agent, or ii) a new potential chelating agent can be provided and the determination of the selectivities according to the invention can be repeated. Thus, only those chelating agents that fulfill certain predetermined criteria/technical application properties, e.g., with respect to selectivity, are finally selected for synthesis and further investigation in the la- boratory, for instance, by providing control data that causes a respective synthesis of the respective chelating agent. BASF SE 221032 221032WO01 Further specific industry-relevant chemical products to which the invention can be applied include (bio-)macromolecular systems as well as large biomolecules with active centers, e.g., enzymes like peptidases and esterases. More detailed examples how the above described properties can be calculated are pro- vided in the following. One example refers to the application to spectroscopy shown sche- matically and exemplarily in Fig.15. Spectroscopy is a non-invasive way of experimentally studying a system, either in comparison with other systems or in different environments and/or under different physico-chemical conditions to elucidate the system’s molecular structure, properties and chemical reactivity. Different experimental spectroscopic tech- niques spanning different ranges of the electromagnetic spectrum and their combination can lead to a more comprehensive picture of investigated systems such as molecules and materials. However, the growing sophistication of these experimental techniques makes it increasingly complex to interpret spectroscopic results without the help of computational chemistry. For example, oftentimes the experimental results do not allow to directly deduce the desired information, e.g., in some cases from a measured spectrum the molecular structure cannot be directly deduced. However, the experimental results can be compared to computational results to obtain the desired information, e.g. the measured spectrum can be compared to a variety of computed spectra assuming different molecular structures to determine the molecular structure for which the measured and computed spectra agree best. In the following a determining of technical application properties related to spectroscopy from the above described solution of the electronic structure problem is described. In UV/Vis spectroscopy, excited-state properties obtained as solution to the electronic struc- ture problem can be used. In particular, energies of electronically excited states, i.e. ener- gies of states with predefined spin multiplicities or electronic orbital configurations that are different from the ground state, and the energy of the respective electronic ground state, for instance, both obtained by utilizing a gate-based quantum computer, can be used. Ad- ditionally and optionally, vibrational contributions, such as Franck-Condon profiles obtained by utilizing, e.g., a boson sampling photonic quantum computer as well as other contribu- tions, such as line widths obtained via approximate calculations on a classical computer or as input from a user, can be used. As output, technical application properties related to spectroscopy can be calculated that can be directly related to experimentally accessible properties and thus support solving the real-world chemistry or material problem. For in- stance, electronic absorption spectra can be computed, that directly refer to, e.g., experi- mentally accessible UV/Vis spectra. UV/Vis spectroscopy uses light in the visible and adjacent ranges, wherein the absorption or reflectance of the light in the visible range by a chemical product or material directly affects the perceived color of that chemical product or material. Thus, computed electronic absorption spectra can support, for instance, the design of new dyes. Another example refers to photoinitiators, which are molecules that create reactive species, such as free radicals, when exposed to radiation in the UV or visible range. The reactive species can then initiate, for instance, polymerization to create a polymer. In this context, the difference in computed energies between the energetically lowest electronically excited state and the electronic ground state directly relates to the required wavelength of a laser irradiating the photoinitiator to initiate this polymerization process. Further examples of real-world chem- istry and material problems refer to photovoltaics and photochemical synthesis. Furthermore, electronic emission spectra can be computed, that directly refer to, e.g., ex- perimentally accessible fluorescence spectra. Electronic emission spectra are complemen- tary to electronic absorption spectra, in that the former deal with transitions of electrons from an excited state to the ground state induced by emission of photons while the latter deals with transitions of electrons from the ground state to excited states induced by ab- sorption of photons. For example, as an important technical application property, the differ- ence in computed energies between an electronically excited state and the electronic ground state of a molecule or material is directly related to the color of the emitted light. For example, using this workflow, the color of the emitted light of a new potential organic light emitting diode material can be computed before actually synthesizing the material. In infrared (IR) spectroscopy, the derivatives of the total ground state energy w.r.t to nuclear positions obtained as described above can be used. In particular, the second derivates are used, which can be either calculated entirely analytically, entirely numerically, or by using the analytically calculated first derivatives to calculate the second derivates numerically in a subsequent step. The calculated spectra, which are also referred to as vibrational spectra within the rigid rotor/harmonic oscillator approximation as they refer to molecular vibrations, can be directly related to experimentally accessible IR spectra. IR spectroscopy can be used to characterize new chemical and/or materials or to identify and verify known and unknown samples. Furthermore, vibronic spectra can be computed, that take into account simultaneous changes in electronic and vibrational energy levels of a chemical product or material due to the absorption of emission of a photon of the appropriate energy. Vibronic spectroscopy may provide information, such as bond-length, on electronic excited states of a molecule. To facilitate the comparison of the above mentioned computed spectra with respective ex- perimentally determined spectra, the calculated spectra are typically visualized by plotting calculated transition intensities or related quantities, such as absorbance, against the re- spectively calculated transition energies or related quantities, such as transition wave- lengths. Further details on computational spectroscopy prediction in general, are described in the article “Computational molecular spectroscopy”, Vincenzo Barone et al., Nature Re- views Methods Primers 1, 38 (2021). A preferred example for a technical application property that can be determined is the chemical reactivity, wherein the prediction of thermodynamic and kinetic quantities of a single chemical reaction such as ்ௌ ^^^ ^ ^^^^ ^՜^ ^^େ^ ^ ^ୈ^ relies on the calculation of reaction free enthalpies and free enthalpies of activation, re- spectively. For example, the reaction free enthalpy is indicative of whether a chemical re- action can occur in principle or not and the free enthalpy of activation is indicative of the rate, i.e. speed, of a chemical reaction. The reaction free enthalpy, ^^୰, can be calculated by subtracting the sum of the free en- thalpies of all reactants – ^ and ^ in the example above – from the sum of the free en- thalpies of all products – ^ and ^ in the example above according to ^^୰ ൌ ^େ^^୭୪ ^ ^ ^ ^ ^ୈ^^୭୪ ^ ^ ^ െ ^ ^^^^୭୪ ^ ^ ^ ^ ^^^^୭୪ ^ ^ ^^ wherein the free enthalpy in solution, ^^୭୪, of each individual chemical species is weighted by its respective stochiometric weight ^. Analogously, the free enthalpy of activation, ^^ஷ, can be obtained by subtracting the sum of the stochiometrically weighted free enthalpies of all reactants from the free enthalpy of the transition state – ^^ in the example above – which is the highest point in free enthalpy along the reaction pathway from reactants to products, according to ^^ ஷ ൌ ^^୭୪^^^^ െ ^ ^^^^୭୪^^^ ^ ^^^^୭୪^^^ ^ Since chemical reactions typically happen in solution, e.g. in water, and not in the gas phase, all free enthalpies are preferably calculated considering the influence of a solvent. However, also a calculation omitting the influence of the solvent can be a reasonable ap- proximation for many application cases. The following example takes the solvent into ac- count, but can also be applied to approximations without taking the solvent into account by removing the solvent components accordingly. The free enthalpy in solution, ^^୭୪, of an individual chemical species, e.g. a reactant ^ or ^, a transition state ^^ of product ^ or ^, can be obtained as the sum of the free enthalpy in the gas phase, ^^ୟ^, and the free en- thalpy of solvation, ^^^୭୪^ୟ^୧୭୬, according to ^^୭୪ ൌ ^^ୟ^ ^ ^^^୭୪^ୟ^୧୭୬ It is noted that sometimes the free enthalpy in solution is also named Gibbs free energy in solution. The free enthalpy in the gas phase is obtained at a predetermined temperature ^ according to ^^ୟ^ ^ൌ ^^^ ^ ^^^^^ െ ^^ ^ ^^^^^୰ୟ୬^ ^ ^୰୭^ ^ ^^୧ୠ^ wherein ^ is the electronic energy. The high-level energy can be generated utilizing the method described above, for instance, utilizing a quantum computer. It is noted, that this energy can – depending on the electronic state of interest – both refer to the electronic ground state and an electronically excited state. ^^^ is the vibrational zero-point energy, and ^^୰ୟ୬^ ^ ^୰୭^ ^ ^^୧ୠ are the translational/rotational/vibrational partition functions, respec- tively. Both the ^^^ and ^^୧ୠ can be calculated from a vibrational spectrum, which can be generated, for instance, using a spectroscopy workflow as described above, in particular, the IR spectroscopy workflow, utilizing a quantum computer as described above. However, these quantities can also be obtained utilizing a classical computer in combination with generally less accurate methods such as density functional theory (DFT). ^ is the Avogadro gas constant. The free enthalpy of solvation, ^^^୭୪^ୟ^୧୭୬, of a molecule in a predefined solvent can be obtained via solvation models such as the conductor like screening model for real solvents (COSMO-RS) utilizing a classical computer. Within the COSMO-RS approach, in a first step, the electron density, which is indicative of the distribution of the electric charge in the molecule, obtained utilizing a quantum computer as described above can be used to cal- culate the screening charge density σ on the surface of the molecule. In a second step, this information can be used to calculate the chemical potential μ of the molecule in the prede- termined liquid solvent or mixture. The resulting chemical potential μ is then used to calcu- late the free enthalpy of solvation. Further information on the COSMO-RS approach can BASF SE 221032 221032WO01 be found in the book “COSMO-RS: From Quantum Chemistry to fluid phase thermodynam- ics and drug design”, Andreas Klamt, Elsevier (2005). It is noted that by including the influ- ence of the solvent on the technical application properties, such as the reaction free en- thalpies and free enthalpies of activation, implicitly via the COSMO-RS approach rather than straightforwardly calculating the technical application properties in solution by con- structing a supersystem that explicitly includes solvent molecules, the computational cost can be significantly reduced. The calculation of the reaction free enthalpies and free enthalpies of activation in solution for all potential reaction pathways, i.e., for multiple chemical reactions taking into account all possible transition states, intermediates and products, ultimately allows to determine the outcome if predefined molecules, i.e., reactants, are mixed in a test tube or vessel by iden- tifying the one or more energetically most favorable reaction pathways. In particular, the highly accurate energy computation for all species of a chemical reactive network, i.e. re- actants, products, transition states and intermediates, is indispensable for reliable determi- nations and thus for the design of new chemical products and materials and the improve- ment of industrial chemical processes as well as for other technical application areas like the understanding and, based on that the suppression of the degradation of chemical prod- ucts, the determination of the microstructure of polymeric chemical products and thus the computational fine-tuning of technical application properties of chemical products. Specific industry-relevant chemical products to which the chemical reactivity, i.e. reaction rate, workflow can preferably be applied are, for example, catalysts, as shown in Fig.16. Catalysts play a crucial role in enabling or accelerating chemical reactions under mild con- ditions, e.g., mild temperatures and mild pressures, by interacting with the transition state and lowering its energy thus reducing the free enthalpy of activation and increasing the rate of the chemical reaction. Today, catalysts are often used that contain 4d or 5d transition metals like rhodium and palladium, which are highly expensive, like the rhodium-based Wilkinson catalyst for hydroformylation. The goal of many technical objectives is to substi- tute those catalysts by catalysts that are cheaper to produce containing, e.g., cheaper 3d transition metals like cobalt or iron. The chemical reactivity workflow can be particularly advantageous in the area of homogenous catalysis, e.g., for calculating oxidation reactions, reduction reactions, hydrogenations, carbonylations, etc. in large-scale chemical produc- tion processes such as the chemical production process of polymers but also in the syn- thesis of homogenously catalyzed fine chemicals. For example, utilizing the chemical re- activity workflow free enthalpies of activation for a predetermined catalytic cycle including undesired side reactions can be calculated for a set of predetermined catalysts before their BASF SE 221032 221032WO01 synthesis in the laboratory. As described above, those free enthalpies of activation contrib- ute to the calculation of chemical kinetics, in particular chemical reaction rates. In particular, determined chemical reaction rates of the potential catalyst can be compared with target chemical reaction rates and, based on the comparison, either i) a respective potential cat- alyst can be determined as target catalyst, or ii) a new potential catalyst can be provided and the determination of the reaction rates according to the invention can be repeated. Thus, only those catalysts for which the chemical reaction rate is larger than a predeter- mined threshold and for which no major undesired side reactions are predicted are finally selected for synthesis and further investigation in the laboratory, for instance, by providing control data that causes a respective synthesis of the respective catalyst. Moreover, a re- spective reaction process can also be controlled such that the catalyst is utilized in the reaction, for example, a feet to a reactor can be controlled accordingly. Other specific industry-relevant chemical products to which the chemical reactivity workflow can be applied are chelating agents as shown in Fig. 17. The development of chelating agents, which are tailored towards certain metal ions, can be enhanced by the calculation of complex formation constants. A complex formation constant is a thermodynamic quantity that indicates how thermodynamically stable the resulting complex of the metal ion and chelating agent is. It can be calculated using the reaction free enthalpy for the reaction of chelating agent and metal ion to form the respective chelate complex in solution. A reliable computational determination is preferably based on an accurate calculation of the reaction free enthalpy which is particularly challenging for reactions of transitional metal ions. Addi- tionally, a reliable determination of the selectivity of chelating agents is challenging, since both its experimental determination and its computational determination are difficult. How- ever, utilizing a quantum computer as described above allows for such accurate solutions. Selectivity is a means that describes how strongly a particular chelating agent preferably binds to a specific metal ion compared to other metal ions, which can be derived from respective complex formation constants. A very well-known example for a chelating agent is ethylenediaminetetraacetic acid (EDTA) which can be used, e.g., for the solubilisation of a Fe3+ ion. The goal of many technical objectives is to design new chelating agents with a predetermined selectivity that exhibit favorable properties like biodegradability or are less hazardous to water organisms. Chelating agents are used in a large variety of technical applications, e.g., to suppress the undesired influence of metal ions in washing and clean- ing processes. Furthermore, chelating agents are also used in mining for selective extrac- tion of metals. For example, using the chemical reactivity workflow described above reac- tion free enthalpies for a predetermined chelating agent can be calculated to obtain respec- tive complex formation constants and thus the selectivity with respect to different transition metal ions. These calculations can be done, e.g., for a set of predetermined chelating BASF SE 221032 221032WO01 agents before their synthesis in the laboratory. In particular, determined selectivities of the potential chelating agent can be compared with target selectivities and, based on the com- parison, either i) a respective potential chelating agent can be determined as target chelat- ing agent, or ii) a new potential chelating agent can be provided and the determination of the selectivities according to the invention can be repeated. Thus, only those chelating agents that fulfill certain predetermined criteria/technical application properties, e.g., with respect to selectivity, are finally selected for synthesis and further investigation in the la- boratory, for instance, by providing control data that causes a respective synthesis of the respective chelating agent. Moreover, a respective reaction process can also be controlled such that the chelating agent is utilized in the reaction, for example, a feet to a reactor can be controlled accordingly. Additionally, further technical application properties such as activity coefficients, solubility, partition coefficients and vapor pressure can be calculated using a slightly amended work- flow as described above based on the COSMO-RS method. The equilibrium vapor pres- sure, for example, is also an experimentally accessible quantity and defined as the pres- sure exerted by a vapor in thermodynamic equilibrium with its condensed phases (liquid or solid) at a given temperature in a closed environment and is an indication of a liquid’s or solid’s evaporation rate. For example, the computation of the vapor pressure is important, e.g., to quantify the volatility of a hazardous or toxic chemical product at a given tempera- ture before or instead of carrying out real-world experiments. In case the potentially haz- ardous or toxic chemical product is volatile, i.e., has a high vapor pressure, which would result in a high concentration of the chemical product in the breathing zone, additional safety measures can be established. Further information on generally determining the aforementioned technical application properties can be found in the article “Predicting ac- curate absolute binding energies in aqueous solution: thermodynamic considerations for electronic structure methods”, Jan H. Jensen, Phys. Chem. Chem. Phys.17, 12441 (2015). A further exemplary embodiment refers to quantitative structure-activity relationship (QSAR) or quantitative structure-property relationship (QSPR). QSAR or QSPR models are regression or classification models that relate a set of predictor variables, also called “de- scriptors”, to one or more output variables, e.g., the potency of a response variable in case of a regression model, in particular a partial least squares regression model, or to a cate- gorical value in case of a classification model. Furthermore, neural networks can also be used as model. In the context of this invention the predictor variables can refer to a set of solutions of electronic structure problem of electronic structure systems, e.g., molecules, wherein at BASF SE 221032 221032WO01 least one of the electronic structure properties that is generated based on the solution of the electronic structure problem is calculated utilizing a quantum computer. However, the predictor variables can also refer to a set of technical application properties of real-world chemistry or material problems that are obtained by processing the electronic structure properties as described above. Furthermore, a combination with predictor variables ob- tained from other sources like chemoinformatic processing of structural information or ex- perimental physico-chemical properties is possible as well. The predictor variables can be electronic, geometric, structural or physico-chemical properties and/or molecular de- scriptors and thus refer to quantities that are obtainable by one of the above described approaches or similar approaches, whereas the output variables refer to technical applica- tion properties of real-world chemistry or material problems, such as a biological activity or a chemical property of a molecule, that are not directly accessible by the above described or similar approaches. The QSAR/QSPR model mathematically summarizes a supposed relationship between the selected set of predictor variables and the output variables. After the construction of the model, it is carefully validated with regard to robustness, prediction performance and its applicability domain. After successful validation, the QSAR/QSPR model can then finally be used to determine the output variables, e.g., technical application properties, of new real-world chemistry or material problems for a set of predictor variables that are obtained as described above utilizing a quantum computer. Since the quality of the prediction signif- icantly depends on the accuracy of the provided predictor variables the utilization of a quan- tum computer is expected to be advantageous. Furthermore, the quality of the prediction also depends on other factors such as the selection of appropriate predictor variables, the used QSAR/QSPR model as well as its validation. A specific technical application property that can be calculated using the above described QSAR/QSPR workflow is, for example, the biological activity of a chemical product such as a drug, toxicant or environmental pollutant using respective computed electronic structure properties or above described technical application properties as predictor variables. Bio- logical activity can be expressed quantitatively as the concentration of a chemical product required to give a certain biological response including desirable therapeutic effects and undesirable side effects. For example, the QSAR/QSPR workflow can be used for a com- putational toxicological assessment of a new chemical product. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the dis- closure, and the appended claims. For the processes and methods disclosed herein, the operations performed in the pro- cesses and methods may be implemented in differing order. Furthermore, the outlined op- erations are only provided as examples, and some of the operations may be optional, com- bined into fewer steps and operations, supplemented with further operations, or expanded into additional operations without detracting from the essence of the disclosed embodi- ments. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single unit or device may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Procedures like the providing of an electronic structure representation, causing a quantum computer and/or a classical computer to generate and provide a solution, generating a solution to the electronic structure representation, etc. performed by one or several units or devices can be performed by any other number of units or devices. These procedures can be implemented as program code means of a computer program and/or as dedicated hardware. A computer program product may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium, supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any units described herein may be processing units that are part of a classical computing system. Processing units may include a general-purpose processor and may also include a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other specialized circuit. Any memory may be a physical system memory, which may be volatile, non-volatile, or some combination of the two. The term “memory” may include any computer-readable storage media such as a non-volatile mass storage. If the computing system is distributed, the processing and/or memory capability may be distrib- uted as well. The computing system may include multiple structures as “executable com- ponents”. The term “executable component” is a structure well understood in the field of computing as being a structure that can be software, hardware, or a combination thereof. For instance, when implemented in software, one of ordinary skill in the art would under- BASF SE 221032 221032WO01 stand that the structure of an executable component may include software objects, rou- tines, methods, and so forth, that may be executed on the computing system. This may include both an executable component in the heap of a computing system, or on computer- readable storage media. The structure of the executable component may exist on a com- puter-readable medium such that, when interpreted by one or more processors of a com- puting system, e.g., by a processor thread, the computing system is caused to perform a function. Such structure may be computer readable directly by the processors, for instance, as is the case if the executable component were binary, or it may be structured to be inter- pretable and/or compiled, for instance, whether in a single stage or in multiple stages, so as to generate such binary that is directly interpretable by the processors. In other in- stances, structures may be hard coded or hard wired logic gates, that are implemented exclusively or near-exclusively in hardware, such as within a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other specialized circuit. Accordingly, the term “executable component” is a term for a structure that is well under- stood by those of ordinary skill in the art of computing, whether implemented in software, hardware, or a combination. Any embodiments herein are described with reference to acts that are performed by one or more processing units of the computing system. If such acts are implemented in software, one or more processors direct the operation of the computing system in response to having executed computer-executable instructions that constitute an executable component. Computing system may also contain communication channels that allow the computing system to communicate with other computing systems over, for exam- ple, network. A “network” is defined as one or more data links that enable the transport of electronic data between computing systems and/or modules and/or other electronic de- vices. When information is transferred or provided over a network or another communica- tions connection, for example, either hardwired, wireless, or a combination of hardwired or wireless, to a computing system, the computing system properly views the connection as a transmission medium. Transmission media can include a network and/or data links which can be used to carry desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general-purpose or special- purpose computing system or combinations. While not all computing systems require a user interface, in some embodiments, the computing system includes a user interface sys- tem for use in interfacing with a user. User interfaces act as input or output mechanism to users for instance via displays. Those skilled in the art will appreciate that at least parts of the invention may be practiced in network computing environments with many types of computing system configurations, including, personal computers, desktop computers, laptop computers, message proces- BASF SE 221032 221032WO01 sors, hand-held devices, multi-processor systems, microprocessor-based or programma- ble consumer electronics, network PCs, minicomputers, mainframe computers, mobile tel- ephones, PDAs, pagers, routers, switches, datacenters, wearables, such as glasses, and the like. The invention may also be practiced in distributed system environments where local and remote computing system, which are linked, for example, either by hardwired data links, wireless data links, or by a combination of hardwired and wireless data links, through a network, both perform tasks. In a distributed system environment, program mod- ules may be located in both local and remote memory storage devices. Those skilled in the art will also appreciate that at least parts of the invention may be prac- ticed in a cloud computing environment. Cloud computing environments may be distributed, although this is not required. When distributed, cloud computing environments may be dis- tributed internationally within an organization and/or have components possessed across multiple organizations. In this description and the following claims, “cloud computing” is defined as a model for enabling on-demand network access to a shared pool of configura- ble computing resources, e.g., networks, servers, storage, applications, and services. The definition of “cloud computing” is not limited to any of the other numerous advantages that can be obtained from such a model when deployed. The computing systems of the figures include various components or functional blocks that may implement the various embodi- ments disclosed herein as explained. The various components or functional blocks may be implemented on a local computing system or may be implemented on a distributed com- puting system that includes elements resident in the cloud or that implement aspects of cloud computing. The various components or functional blocks may be implemented as software, hardware, or a combination of software and hardware. The computing systems shown in the figures may include more or less than the components illustrated in the figures and some of the components may be combined as circumstances warrant. Any reference signs in the claims should not be construed as limiting the scope. The invention refers to an apparatus for generating a property associated with a chemical product. A providing unit provides an electronic structure representation including a) a first part indicative of an active space and b) a second part indicative of an inactive space. The property depends on the active space and the inactive space. A determination unit causes a quantum computer and/or a classical computer to generate a solution of the first part and a solution to the second part. A computation unit generates a solution to the electronic structure representation by combining the solution of the first part and the second part to generate the property. The combining includes generating an interaction representation based on a reference state associated with a superposition of electron configurations gen- erated based on the solution of the first part and the second part.

Claims

BASF SE 221032 221032WO01 Claims: 1. An apparatus for generating a property associated with a chemical product, wherein the chemical product includes one or more molecular structures, wherein the apparatus comprises: an electronic structure representation providing unit for providing an electronic struc- ture representation associated with a molecular structure of the chemical product and in- cluding a) a first part of the electronic structure representation indicative of an active space including a part of the electronic structure associated with the molecular structure and b) a second part of the electronic structure representation indicative of an inactive space includ- ing another part of the electronic structure associated with the molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, a solution determination unit for causing a quantum computer and/or a classical com- puter to generate and provide a solution of the first part of the electronic structure repre- sentation, and for causing a quantum computer and/or a classical computer to generate and provide a solution to the second part of the electronic structure representation, and a correlation computation unit for generating a solution to the electronic structure representation by combining the solution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computa- tionally combined to generate the property associated with the chemical product, wherein computationally combining includes generating an interaction representation based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the solution for the second part, and causing a classical computer and/or quantum computer to provide a solution to the interaction representation. 2. The apparatus according to claim 1, wherein the reference state is represented with configuration interaction basis states and coefficients associated with the configuration in- teraction basis states, wherein the configuration interaction basis states are given by a fixed distribution of electrons among electron orbitals. 3. The apparatus according to any of claims 1 and 2, wherein determining the reference state based on the solution of the first part and second part comprises controlling a quan- tum computer to generate a representation of the solution of the first part on the quantum computer, wherein the reference state is determined based on the representation of the solution of the first part on the quantum computer. 4. The apparatus according to claim 3, wherein the determining of the reference state comprises determining an overlap between the prepared solution of the first part on the quantum computer and the respective configuration interaction basis states to determine the coefficients. 5. The apparatus according to claim 4, wherein determining the overlap comprises measuring the representation of the solution of the first part on the quantum computer cor- responding to the distribution of the electrons among the electron orbitals in the active space, determining respective coefficients associated with the configuration interaction ba- sis states from this measurement and repeating the process until a predetermined condition is met to generate a histogram of the coefficients of the measured configuration interaction basis states and determining the reference state based on the histogram. 6. The apparatus according to claim 5, wherein the reference state is determined based on the representation of the solution of the first part on the quantum computer by applying a projection operator to the representation of the solution of the first part projecting the representation of the solution of the first part on a respective configuration interaction basis state representation and measuring the resulting states on the quantum computer based on the histogram. 7. The apparatus according to any of the preceding claims, wherein the interaction rep- resentation includes correlations between electron orbitals among which at least one elec- tron orbital is a member of the inactive space. 8. The apparatus according to any of the preceding claims, wherein the correlation computation unit is configured to cause a quantum computer to prepare a representation of the reference state on the quantum computer and to entangle quantum elements repre- senting the correlations between the active space and the inactive space to provide a so- lution to the interaction representation. 9. The apparatus according to any of the preceding claims, wherein a solution to the interaction representation is provided by preparing the representation of a solution of the first part on a first quantum computer and preparing a representation of a solution of the second part on a second quantum computer and performing a quantum computation of the interaction representation in which the quantum elements of the first quantum computer and the quantum elements of the second quantum computer are entangled for representing the correlations between the active space and the inactive space. 10. The apparatus according to any of the preceding claims, wherein the interaction rep- resentation includes correlations between electron orbitals among which at least one elec- tron orbital is a member of the inactive space by projecting the reference state on one or more predetermined configuration interaction basis states and generating the solution based on the result of the projection. 11. The apparatus according to claim 10, wherein a tailored coupled cluster method is utilized for generating a solution of the interaction representation. 12. The apparatus according to any of the preceding claims, wherein a stochastic strongly contracted second-order n-electron valence state perturbation theory method is utilized for including correlations between electron orbitals among which at least one elec- tron orbital is a member of the inactive space into the interaction representation. 13. A system for generating a property associated with a chemical product, wherein the system comprises: a quantum computer adapted to perform quantum mechanical calculations, and an apparatus according to any of the preceding claims, wherein the apparatus is adapted to cause the quantum computer to perform a quantum mechanical calculation. 14. A computer-implemented method for generating a property associated with a chem- ical product, wherein the chemical product includes one or more molecular structures, wherein the method comprises: providing an electronic structure representation associated with the molecular struc- ture of the chemical product and including a) a first part of the electronic structure repre- sentation indicative of an active space including a part of the electronic structure associated with the molecular structure and b) a second part of the electronic structure representation indicative of an inactive space including another part of the electronic structure associated with the molecular structure, wherein the property associated with the chemical product depends on the active space and the inactive space, causing a quantum computer and/or a classical computer to generate and provide a solution of the first part of the electronic structure representation, and for causing a quan- tum computer and/or a classical computer to generate and provide a solution to the second part of the electronic structure representation, and BASF SE 221032 221032WO01 generating a solution to the electronic structure representation by combining the so- lution of the first part and the solution of the second part, wherein the solution of the first part and the solution of the second part are computationally combined to generate the property associated with the chemical product, wherein computationally combining in- cludes generating an interaction representation based on a reference state associated with a superposition of electron configurations generated based on the solution of the first part and the solution for the second part, and causing a classical computer and/or quantum computer to provide a solution to the interaction representation. 15. A computer program product for generating a property associated with a chemical product, wherein the computer program product comprises program code means for caus- ing the apparatus according to any of claims 1 to 12 to execute the method according to claim 14.
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