CN115790822A - Method and device for determining molecular vibration frequency - Google Patents

Abstract

The invention discloses a method and device for determining the vibration frequency of a molecule. The method includes: obtaining the test state of the molecule to be determined, calculating the energy expectation corresponding to the current test state, and judging whether the energy expectation corresponding to the test state satisfies the ground state energy of the molecule to be determined If so, then based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix, otherwise, update the test state, calculate the energy expectation corresponding to the updated test state, and continue to execute the judgment corresponding to the test state The step of whether the energy expectation meets the calculation termination condition of the molecular ground state energy to be determined, until the ground state energy of the molecule to be determined meeting the calculation termination condition and the Hessian matrix of the molecular ground state energy to be determined are obtained, according to the Hessian matrix of the molecular ground state energy to be determined , calculate the vibration frequency of the molecule to be determined, use the quantum correlation characteristics to speed up the solution process of the molecular vibration frequency, optimize the solution method and increase the solution speed.

Description

A method and device for determining the vibrational frequency of a molecule

technical field

The invention belongs to the technical field of quantum computing, in particular to a method and a device for determining the molecular vibration frequency.

Background technique

Quantum computing simulation is an analog computing that follows the laws of quantum mechanics by means of numerical computing and computer science. As a simulation program, it uses the high-speed computing capabilities of computers to describe the spatiotemporal evolution of quantum states based on the basic laws of qubits in quantum mechanics. .

With the continuous improvement of quantum chemistry theory, computational chemistry has become an important tool for chemists to explain experimental phenomena, predict experimental results, and guide experimental design. However, in the face of the huge amount of calculation involved in computational chemistry, classical computers appear to have limited capabilities in terms of calculation accuracy and calculation size, which limits the development of computational chemistry to a certain extent, which leads users to simulate target molecular systems The application of calculation is not strong, which affects the further development of quantum chemical simulation applications.

Molecular vibration frequency is an important physical quantity, which can reflect the vibration direction and amplitude of molecules, help to study the law of molecular motion, and can also calculate infrared spectra, thermodynamic quantities (such as entropy and free energy), etc., which are used in chemical reaction simulation, material research and other fields. When performing molecular simulation on a classical computer, the calculation amount of the ground state energy of the system increases exponentially with the increase of the number of electrons in the system, and the classical computer faces great difficulties in calculation accuracy and calculation range. Quantum computers are a new approach to this problem.

Therefore, it is an urgent problem to propose a new method for calculating the molecular vibration frequency to overcome the above-mentioned defects in the prior art.

Contents of the invention

The purpose of the present invention is to provide a method and device for determining the molecular vibration frequency to solve the deficiencies in the prior art. It proposes a new method for determining the molecular vibration frequency and utilizes quantum correlation characteristics to accelerate the molecular vibration frequency. The solution process optimizes the solution method and improves the solution speed.

One embodiment of the present application provides a method for determining the vibrational frequency of a molecule, the method comprising:

Obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state;

Judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets the accuracy;

If so, then based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the energy corresponding to the updated test state Expecting, continue to execute the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the ground state energy of the molecule to be determined that satisfies the calculation termination condition and the Describe the Hessian matrix of the molecular ground state energy to be determined;

According to the Hessian matrix of the ground state energy of the molecule to be determined, the vibration frequency of the molecule to be determined is calculated.

Optionally, said obtaining the test state of the molecule to be determined includes:

According to the pre-selected hypothetical mode and the determined Hartree Fock state of the molecule to be determined, the test state of the molecule to be determined is obtained.

Optionally, the calculation of the energy expectation corresponding to the current test state includes:

The energy expectation corresponding to the test state is calculated by the following formula:

为待确定分子的哈密顿量，h_α为电子积分相关系数，

为泡利字符串形式的算符。Among them, n represents the number of cycles for calculating the energy expectation corresponding to the test state, E(n) is the energy expectation corresponding to the current test state |Ψ(n)>,

is the Hamiltonian of the molecule to be determined, h _α is the electron integral correlation coefficient,

is an operator in Pauli string form.

Optionally, the calculation of the Hessian matrix of the ground state energy of the molecule to be determined includes:

Calculate the Hessian matrix of the molecular ground state energy to be determined by the following formula:

where R is the coordinates of the molecule.

Optionally, calculating the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined includes:

According to the Hessian matrix of the molecular ground state energy to be determined, determine the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix;

Based on the eigenvalues of the force constant matrix, the vibration frequency of the molecule to be determined is determined.

Optionally, the determining the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix according to the Hessian matrix of the ground state energy of the molecule to be determined includes:

Calculate the force constant matrix of the molecule to be determined by the following formula:

F=M×S×M

N为待确定分子所包含的原子体系个数，m_q为第q个原子的质量，q∈N。Among them, F is the force constant matrix of the molecule to be determined, M is the mass weight matrix, satisfying

N is the number of atomic systems contained in the molecule to be determined, m _q is the mass of the qth atom, q∈N.

Yet another embodiment of the present application provides a device for determining the vibrational frequency of a molecule, the device comprising:

An obtaining module, configured to obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state;

A judging module, configured to judge whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the molecular ground state energy to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets precision;

An update module, for if so, then based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the updated The energy expectation corresponding to the test state, continue to perform the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the molecule to be determined that meets the calculation termination condition is obtained The ground state energy of and the Hessian matrix of the molecular ground state energy to be determined;

A calculation module, configured to calculate the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined.

Optionally, the obtaining module includes:

The obtaining unit is used to obtain the test state of the molecule to be determined according to the pre-selected hypothetical mode and the determined Hartree Fock state of the molecule to be determined.

Optionally, the calculation module includes:

A first determining unit, configured to determine the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix according to the Hessian matrix of the ground state energy of the molecule to be determined;

The second determination unit is configured to determine the vibration frequency of the molecule to be determined based on the eigenvalues of the force constant matrix.

Yet another embodiment of the present application provides a storage medium, in which a computer program is stored, wherein the computer program is configured to implement the method described in any one of the above when running.

Yet another embodiment of the present application provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to realize any of the above-mentioned Methods.

Compared with the prior art, the present invention first obtains the test state of the molecule to be determined, and calculates the energy expectation corresponding to the current test state, and judges whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, and if so, then Based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, calculate the energy expectation corresponding to the updated test state, and continue to judge the energy expectation corresponding to the test state The step of whether the calculation termination condition of the molecular ground state energy to be determined is satisfied, until the ground state energy of the molecule to be determined meeting the calculation termination condition and the Hessian matrix of the molecular ground state energy to be determined are obtained, according to the Hessian matrix of the molecular ground state energy to be determined, calculate To determine the vibration frequency of the molecule, it accelerates the solution process of the molecular vibration frequency by using the quantum correlation characteristics, optimizes the solution method and improves the solution speed.

Description of drawings

Fig. 1 is a block diagram of the hardware structure of a computer terminal of a method for determining the molecular vibration frequency provided by an embodiment of the present invention;

Fig. 2 is a schematic flowchart of a method for determining molecular vibration frequency provided by an embodiment of the present invention;

Fig. 3 is a schematic structural diagram of a device for determining molecular vibration frequencies provided by an embodiment of the present invention.

Detailed ways

The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

Embodiments of the present invention firstly provide a method for determining the vibrational frequency of a molecule, which can be applied to electronic devices, such as computer terminals, specifically, ordinary computers, quantum computers, and the like.

The following will describe it in detail by taking it running on a computer terminal as an example. FIG. 1 is a block diagram of the hardware structure of a computer terminal for a method for determining the vibrational frequency of a molecule provided by an embodiment of the present invention. As shown in Figure 1, the computer terminal may include one or more (only one is shown in Figure 1) processors 102 (processors 102 may include but not limited to processing devices such as microprocessor MCU or programmable logic device FPGA, etc.) and a memory 104 for storing data. Optionally, the above-mentioned computer terminal may further include a transmission device 106 and an input and output device 108 for communication functions. Those skilled in the art can understand that the structure shown in FIG. 1 is only for illustration, and it does not limit the structure of the above computer terminal. For example, the computer terminal may also include more or fewer components than shown in FIG. 1 , or have a different configuration than that shown in FIG. 1 .

The memory 104 can be used to store software programs and modules of application software, such as the program instructions/modules corresponding to the method for determining the molecular vibration frequency in the embodiment of the present application, and the processor 102 runs the software programs and modules stored in the memory 104, thereby Executing various functional applications and data processing is to realize the above-mentioned method. The memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include a memory that is remotely located relative to the processor 102, and these remote memories may be connected to a computer terminal through a network. Examples of the aforementioned networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

The transmission device 106 is used to receive or transmit data via a network. The specific example of the above-mentioned network may include a wireless network provided by the communication provider of the computer terminal. In one example, the transmission device 106 includes a network interface controller (NIC), which can be connected to other network devices through a base station so as to communicate with the Internet. In one example, the transmission device 106 may be a radio frequency (Radio Frequency, RF) module, which is used to communicate with the Internet in a wireless manner.

It should be noted that a real quantum computer has a hybrid structure, which consists of two parts: one is a classical computer, which is responsible for performing classical calculation and control; the other is a quantum device, which is responsible for running quantum programs and realizing quantum computing. The quantum program is a series of instruction sequences written in a quantum language such as QRunes that can be run on a quantum computer, which supports the operation of quantum logic gates and finally realizes quantum computing. Specifically, a quantum program is a series of instruction sequences that operate quantum logic gates in a certain sequence.

In practical applications, due to the limitation of the development of quantum device hardware, quantum computing simulations are usually required to verify quantum algorithms, quantum applications, etc. Quantum computing simulation is the process of simulating the quantum program corresponding to a specific problem using a virtual architecture built with the resources of an ordinary computer (that is, a quantum virtual machine). Often, quantum programs corresponding to specific problems need to be constructed. The quantum program referred to in the embodiment of the present invention is a program written in a classical language to characterize qubits and their evolution, in which qubits, quantum logic gates, etc. related to quantum computing are represented by corresponding classical codes.

As an embodiment of quantum programs, quantum circuits are also called quantum logic circuits. They are the most commonly used general-purpose quantum computing models. They represent circuits that operate on qubits under an abstract concept. The components include qubits, circuits (timelines) , and various quantum logic gates, the results often need to be read out through quantum measurement operations.

Unlike traditional circuits, which are connected by metal wires to transmit voltage signals or current signals, in quantum circuits, the circuits can be regarded as connected by time, that is, the state of qubits evolves naturally with time, in the process according to The instruction of the Hamiltonian operator is operated until it encounters a logic gate.

A quantum program as a whole corresponds to a total quantum circuit, and the quantum program in the present invention refers to the total quantum circuit, wherein the total number of qubits in the total quantum circuit is the same as the total number of qubits in the quantum program. It can be understood as: a quantum program can be composed of quantum circuits, measurement operations for qubits in quantum circuits, registers for saving measurement results, and control flow nodes (jump instructions). A quantum circuit can contain tens, hundreds or even thousands of Tens of thousands of quantum logic gate operations. The execution process of a quantum program is the process of executing all quantum logic gates according to a certain time sequence. It should be noted that timing refers to the time sequence in which a single quantum logic gate is executed.

It should be noted that in classical computing, the most basic unit is a bit, and the most basic control mode is a logic gate. The purpose of controlling a circuit can be achieved through the combination of logic gates. Similarly, the way to handle qubits is quantum logic gates. The use of quantum logic gates can make the quantum state evolve. Quantum logic gates are the basis of quantum circuits. Quantum logic gates include single-bit quantum logic gates, such as Hadamard gates (H gates, Hadamard gates), Pauli-X gates (X gate), Pauli-Y gate (Y gate), Pauli-Z gate (Z gate), RX gate, RY gate, RZ gate, etc.; multi-bit quantum logic gates, such as CNOT gate, CR gate, iSWAP Doors, Toffoli doors and more. Quantum logic gates are generally represented by unitary matrices, and unitary matrices are not only in the form of matrices, but also a kind of operation and transformation. Generally, the effect of a quantum logic gate on a quantum state is calculated by multiplying the left side of the unitary matrix by the matrix corresponding to the right vector of the quantum state.

其中，a、b为表示|0>态、|1>态振幅(概率幅)的复数，这是经典比特不具备的。测量后，量子比特的状态会塌缩至一个确定的状态(本征态，此处为|0>态、|1>态)，其中，塌缩至|0>的概率是|a|²，塌缩至|1>的概率是|b|²，|a|²+|b|²＝1，|>为狄拉克符号。Those skilled in the art can understand that in a classical computer, the basic unit of information is a bit, and a bit has two states of 0 and 1, and the most common physical implementation method is to represent these two states through the level. In quantum computing, the basic unit of information is the qubit. A qubit also has two states of 0 and 1, denoted as |0> and |1>, but it can be in the superposition state of the two states of 0 and 1, which can be expressed for

Among them, a and b are complex numbers representing the amplitude (probability amplitude) of |0> state and |1> state, which is not available in classical bits. After measurement, the state of the qubit will collapse to a certain state (eigenstate, here is |0> state, |1> state), where the probability of collapsing to |0> is |a| ² , The probability of collapsing to |1> is |b| ² , |a| ² + |b| ² =1, and |> is the Dirac symbol.

The quantum state, that is, the state of the qubit, generally needs to be described by a set of orthogonal and complete basis vectors, and the calculation basis usually used is expressed in binary in the quantum algorithm (or quantum program). For example, a group of qubits is q0, q1, and q2, which represent the 0th, 1st, and 2nd qubits, and the order from high to low is q2q1q0, and the quantum state of this group of qubits is 2 ³ calculation bases Superposition state, 8 calculation bases refer to: |000>, |001>, |010>, |011>, |100>, |101>, |110>, |111>, each calculation base is related to qubit Correspondence is consistent, such as |000> state, 000 corresponds to q2q1q0 from high to low. In short, the quantum state is a superposition state composed of various basis vectors. When the probability amplitude of other basis is 0, it is in one of the certain basis vectors.

这样的矩阵通常称之为测量算符，非零算符都会有至少一个不为0的本征值λ以及与之对应的本征态|ψ>，满足H|ψ>＝λ|ψ>，如果算符H的本征值对应的是某一个体系的能级分布，那么这样的算符也可以称其为哈密顿量(Hamiltonian)。In quantum mechanics, all measurable mechanical quantities can be described by a Hermitian matrix. The definition of a Hermitian matrix is that the transposed conjugate of the matrix is the matrix itself, that is:

Such a matrix is usually called a measurement operator, and a non-zero operator will have at least one non-zero eigenvalue λ and the corresponding eigenstate |ψ>, satisfying H|ψ>=λ|ψ>, If the eigenvalue of the operator H corresponds to the energy level distribution of a certain system, then such an operator can also be called the Hamiltonian.

According to the time-dependent Schrödinger equation, the evolution from one state |ψ(t=0)> to another state |ψ(t=T)> is completed by using the unitary operator, that is, U(0,T)|ψ(t ＝0)>=|ψ(t=T)>, where the relationship between the Hamiltonian and the unitary operator is that if a quantum state evolves naturally under a certain system, the energy describing the system is the Hamiltonian, then The unitary operator can be written in terms of Hamiltonian:

一般来说，酉算符在量子计算中也称之为量子逻辑门。When the system starts from time 0 and the Hamiltonian does not change with time, the unitary operator is U=exp(-iHt). In the quantum calculation of a closed system, except for measurement, all quantum operations can be described by a unitary matrix. The definition of a unitary matrix is that the transpose conjugate of the matrix is the inverse of the matrix, that is:

In general, unitary operators are also called quantum logic gates in quantum computing.

Referring to Fig. 2, Fig. 2 is a schematic flowchart of a method for determining the molecular vibration frequency provided by an embodiment of the present invention, which may include the following steps:

S201: Obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state.

Specifically, the molecule to be determined can be regarded as a molecular structure model that the user wants to perform molecular property simulation and determine the molecular vibration frequency, for example, including the atom type, number of atoms, atomic coordinates, charge and spin multiplicity of the molecule to be determined wait.

Among them, obtaining the test state of the molecule to be determined may include:

According to the pre-selected hypothetical mode and the determined Hartree Fock state of the molecule to be determined, the test state of the molecule to be determined is obtained.

Exemplarily, according to the number of electrons and orbital information of the molecular system to be determined, the HartreeFock state of the molecule to be determined is obtained. That is, first of all, for the molecular system to be determined, the number of electrons is the number of electrons contained in the molecular system to be determined, generally refers to the number of electrons outside the nucleus of the molecular system to be determined; orbital information is a mathematical method to describe the molecular system to be determined in the nucleus The probability of finding an electron in a specific space outside, and indicate the possible position of the electron in three-dimensional space.

For example, for the molecular system to be determined, which contains four single-electron spin molecular orbitals and two electrons, according to the number of electrons and orbital information of the molecular system to be determined, if a qubit is used to represent a spin molecular orbital, that is, 0 means empty Orbital, 1 means occupied orbital, so the Hartree Fock (Hartley-Fock) state of the molecular system to be determined can be represented by the quantum state |0011>.

In an optional embodiment, according to the pre-selected design method, the Hartree Fock state of the molecular system to be determined is evolved, and the evolved quantum state is obtained as the test state of the molecular system to be determined. First, according to the pre-selected The proposed method is to calculate the cluster operator of the Fermion form of the molecular system to be determined; secondly, select the mapping method and transform the cluster operator of the Fermion form of the molecular system to be determined into a cluster operator of the Pauli operator form, where the mapping method It can be one of Jordan-Wigner transformation, Parity transformation, Bravyi-Kitaev transformation and SegmentParity transformation; finally, the cluster operator in the form of Pauli operator is decomposed into the corresponding unitary operator form and evolved to obtain the evolved quantum state As the experimental state of the molecular system to be determined.

It should be noted that, according to the experimental state of the molecule to be determined, the variable quantum eigenvalue solving algorithm can be used to calculate the energy expectation of the molecule to be determined.

Among them, the principle of the variable quantum eigenvalue solving algorithm is:

为待确定分子体系的哈密顿量，且满足：|Ψ> is the experimental state (assuming that |Ψ> is normalized), E is the energy expectation of the molecular system to be determined,

is the Hamiltonian of the molecular system to be determined, and satisfies:

Each item in the above formula is the kinetic energy item of the electron in the molecule to be determined, the repulsive energy item between the electrons, the potential energy item between the electron and the nucleus, and the repulsive energy item between the nucleus (atomic unit system), where r _i , R _i and Z _i represent the position of the electron, the position of the nucleus and the charge of the nucleus, respectively. Assuming that the system contains N atoms, the molecule can be represented by column vector R=[R ₁ ,R ₂ ,R ₃ ,...,R _i ...,R _3N-2 ,R _3N-1 ,R _3N ] ^T coordinate of.

转化为二次量子化的形式，并利用映射方法(如Jordan-Wigner变换、Parity变换等)将二次量子化形式的哈密顿量转化为泡利字符串的形式，即：Under the Born-Oppenheimer approximation, the Hamiltonian of the molecule to be determined can be

Transform into the form of double quantization, and use the mapping method (such as Jordan-Wigner transformation, Parity transformation, etc.) to convert the Hamiltonian in the form of double quantization into the form of Pauli string, namely:

为泡利字符串形式的算符，

I为单位矩阵，

为泡利算符，h_α(R)为电子积分相关的系数，一般在经典计算机上计算获得。in,

is an operator in Pauli string form,

I is the identity matrix,

is the Pauli operator, and h _α (R) is the coefficient related to electronic integration, which is usually calculated on a classical computer.

Exemplarily, the calculation of the energy expectation corresponding to the current test state may include:

The energy expectation corresponding to the test state is calculated by the following formula:

为待确定分子的哈密顿量，h_α为电子积分相关系数，

为泡利字符串形式的算符。Among them, n represents the number of cycles for calculating the energy expectation corresponding to the test state, E(n) is the energy expectation corresponding to the current test state |Ψ(n)>,

is the Hamiltonian of the molecule to be determined, h _α is the electron integral correlation coefficient,

is an operator in Pauli string form.

S202: Judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets the accuracy.

通过不断调节

来更新试验态，使根据更新后的试验态最终求解的能量期望非常接近待确定分子体系的基态能量。Specifically, if the obtained test state |Ψ(n)> is exactly the ground state of the system, the ground state energy E _min of the molecular system to be determined can be directly obtained; but more often than not, the obtained test state |Ψ(n )> Compared with the ground state of the molecular system to be determined, there is a certain gap, resulting in the calculated E(n) being much larger than E _min . At this time, a set of parameters needs to be introduced

by constantly adjusting

to update the test state, so that the energy expectation finally solved according to the updated test state is very close to the ground state energy of the molecular system to be determined.

并测量试验态

的能量期望E(n)，判断当前能量期望与前次确定的能量期望的差值是否符合精度，其中，精度可以由用户根据计算需求自行设定。或者通过判断实际迭代次数是否达到预设最大迭代次数作为计算终止条件均可，在此不再赘述。Specifically, by obtaining the experimental state of the molecular system to be determined

and measure the test state

The energy expectation E(n) is used to judge whether the difference between the current energy expectation and the previously determined energy expectation meets the accuracy. The accuracy can be set by the user according to the calculation requirements. Alternatively, judging whether the actual number of iterations reaches the preset maximum number of iterations can be used as the calculation termination condition, and details will not be described here.

S203: If yes, based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the updated test state corresponding to continue to perform the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the ground state energy of the molecule to be determined that meets the calculation termination condition is obtained And the Hessian matrix of the molecular ground state energy to be determined.

然后传给量子处理器，继续演化和测量，通过不断迭代参数

来更新试验态，使其最终获取满足计算终止条件的待确定分子体系的基态能量。Specifically, if the energy expectation corresponding to the test state of the molecular system to be determined satisfies the calculation termination condition, the obtained test state is just the ground state of the molecular system to be determined, and the ground state energy E _min of the molecular system to be determined is directly obtained; otherwise, use Optimization methods, such as Nelder-Mead algorithm or gradient descent method to optimize parameters

Then pass it to the quantum processor, continue to evolve and measure, by continuously iterating the parameters

to update the experimental state, so that it can finally obtain the ground state energy of the molecular system to be determined that meets the calculation termination conditions.

进行优化，更新优化后试验态，测量更新后的当前试验态的能量期望，返回执行S202的步骤，直到某次演化后的能量差值符合精度，并将该次演化后的试验态下的能量期望确定为满足计算终止条件的待确定分子的基态能量。For example, when obtaining the experimental state of the molecular system to be determined is the first evolution, the previous evolution does not exist, and the energy expectation of the experimental state measured after the previous evolution can be defaulted to 0, and the next iteration is directly entered; at the current energy When the difference between the expectation and the energy expectation after the previous measurement does not meet the accuracy, use the optimization method to adjust the adjustable parameters of the proposed medium quantum circuit

Carry out optimization, update the optimized test state, measure the energy expectation of the updated current test state, return to the step of executing S202, until the energy difference after a certain evolution meets the accuracy, and put the energy under the evolved test state It is desired to determine the ground state energy of the molecule to be determined that satisfies the calculation termination condition.

It should be noted that the calculation of the Hessian matrix of the molecular ground state energy to be determined may include:

Calculate the Hessian matrix of the molecular ground state energy to be determined by the following formula:

First, the first derivative of the ground state energy with respect to the coordinate R _i :

Right now:

Using the Hellmann-Feynman theorem and applying the central finite difference method, we get:

The second derivative of the ground state energy with respect to the coordinates R _i and R _j , we get:

Right now:

where R is the coordinates of the molecule.

Then, ignoring the effect of the wave function

make:

Applying the central finite difference method, we can get:

S _j,i ≈<Ψ(R)|X _j,i |Ψ(R)>

in:

所以可得：And because of

So you can get:

Among them, Δd is the difference step size, and e _i and e _j are unit vectors along the i and j directions, respectively.

S204: Calculate the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined.

Specifically, calculating the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined may include:

Step 1: Determine the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix according to the Hessian matrix of the ground state energy of the molecule to be determined.

In an optional embodiment, for a molecular system to be determined containing N atoms, the size of the Hessian matrix S of the ground state energy with respect to the coordinates is 3N×3N, where each element is the second derivative of the ground state energy with respect to the coordinates, Since the Hessian constant matrix is a symmetric matrix, we can get:

S _i,j =S _j,i

个S_j,i，但每个S_j,i均使用相同的基态波函数|Ψ(R)>，即整个海森矩阵S的计算基于相同的基态波函数，这表明待确定分子体系海森矩阵的量子计算量和待确定分子体系基态能量的量子计算量相同。将海森矩阵S转化为质量权重的海森矩阵，即通过以下算式计算所述待确定分子的力常数矩阵：So need to calculate

S _j,i , but each S _j,i uses the same ground state wave function |Ψ(R)>, that is, the calculation of the entire Hessian matrix S is based on the same ground state wave function, which shows that the molecular system to be determined Hessian The amount of quantum calculation of the matrix is the same as that of the ground state energy of the molecular system to be determined. The Hessian matrix S is converted into a Hessian matrix of mass weights, that is, the force constant matrix of the molecule to be determined is calculated by the following formula:

F=M×S×M

N为待确定分子所包含的原子体系个数，m_q为第q个原子的质量，q∈N。Among them, F is the force constant matrix of the molecule to be determined, M is the mass weight matrix, satisfying

N is the number of atomic systems contained in the molecule to be determined, m _q is the mass of the qth atom, q∈N.

Step 2: Determine the vibration frequency of the molecule to be determined based on the eigenvalues of the force constant matrix.

Through the force constant matrix of the molecule to be determined, the eigenvalues of the force constant matrix of the molecule to be determined are solved. For example, assuming that the force constant matrix F is a square matrix of order n, if there exists f and a non-zero n-dimensional column vector x such that Fx=fx holds true, then f is said to be a eigenvalue (characteristic value) or eigenvalue (eigenvalue) of F .

Exemplarily, the vibration frequency of the molecule to be determined can be obtained by judging the spatial structure of the molecule to be determined. If the molecule to be determined is a linear structure or a planar structure, the number of non-zero eigenvalues of the force constant matrix F is 3N-5 , otherwise it is 3N-6; if the eigenvalue is negative, you can first take the absolute value, then open the square root, and then multiply by -1, the vibration frequency of the molecule to be determined is called the imaginary frequency; if the eigenvalue is positive, Then directly extract the root sign to get the vibration frequency of the molecule to be determined.

It can be seen that the present invention first obtains the test state of the molecule to be determined, and calculates the energy expectation corresponding to the current test state, and judges whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, and if so, then based on the current energy expectation as The ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, calculate the energy expectation corresponding to the updated test state, and continue to judge whether the energy expectation corresponding to the test state satisfies the molecule to be determined The step of calculating the termination condition of the ground state energy, until the ground state energy of the molecule to be determined that satisfies the calculation termination condition and the Hessian matrix of the molecular ground state energy to be determined are obtained, and the vibration of the molecule to be determined is calculated according to the Hessian matrix of the ground state energy of the molecule to be determined Frequency, it accelerates the solution process of molecular vibration frequency by using quantum correlation characteristics, optimizes the solution method and improves the solution speed.

Referring to Fig. 3, Fig. 3 is a schematic structural diagram of a device for determining the molecular vibration frequency provided by an embodiment of the present invention, which corresponds to the process shown in Fig. 2 and may include:

Obtaining module 301, configured to obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state;

A judging module 302, configured to judge whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the molecular ground state energy to be determined, wherein the calculation termination condition is the difference between the current energy expectation and the previously determined energy expectation conform to the accuracy;

The updating module 303 is used to, if so, expect the ground state energy of the molecule to be determined based on the current energy, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the updated The energy expectation corresponding to the test state, continue to execute the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until obtaining the to-be-determined molecule that meets the calculation termination condition The ground state energy of the molecule and the Hessian matrix of the molecular ground state energy to be determined;

The calculation module 304 is configured to calculate the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined.

Specifically, the acquisition module includes:

The obtaining unit is used to obtain the test state of the molecule to be determined according to the pre-selected hypothetical mode and the determined Hartree Fock state of the molecule to be determined.

Specifically, the calculation module includes:

A first determining unit, configured to determine the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix according to the Hessian matrix of the ground state energy of the molecule to be determined;

The second determination unit is configured to determine the vibration frequency of the molecule to be determined based on the eigenvalues of the force constant matrix.

Compared with the prior art, the present invention first obtains the test state of the molecule to be determined, and calculates the energy expectation corresponding to the current test state, and judges whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, and if so, then Based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, calculate the energy expectation corresponding to the updated test state, and continue to judge the energy expectation corresponding to the test state The step of whether the calculation termination condition of the ground state energy of the molecule to be determined is satisfied, until the ground state energy of the molecule to be determined meeting the calculation termination condition and the Hessian matrix of the ground state energy of the molecule to be determined are obtained, according to the Hessian matrix of the ground state energy of the molecule to be determined, calculate To determine the vibration frequency of the molecule, it accelerates the solution process of the molecular vibration frequency by using the quantum correlation characteristics, optimizes the solution method and improves the solution speed.

An embodiment of the present invention also provides a storage medium, in which a computer program is stored, wherein the computer program is configured to implement the steps in any one of the above method embodiments when running.

Specifically, in this embodiment, the above-mentioned storage medium may be configured to store a computer program for implementing the following steps:

S201: Obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state;

S202: Judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets the accuracy;

S203: If yes, based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the updated test state corresponding to continue to perform the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the ground state energy of the molecule to be determined that meets the calculation termination condition is obtained and the Hessian matrix of the molecular ground state energy to be determined;

S204: Calculate the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined.

Specifically, in this embodiment, the above-mentioned storage medium may include but not limited to: U disk, read-only memory (Read-Only Memory, ROM for short), random access memory (Random Access Memory, RAM for short), mobile Various media that can store computer programs, such as hard disks, magnetic disks, or optical disks.

An embodiment of the present invention also provides an electronic device, including a memory and a processor, where a computer program is stored in the memory, and the processor is configured to run the computer program to implement any one of the method embodiments described above. A step of.

Specifically, the electronic device may further include a transmission device and an input and output device, wherein the transmission device is connected to the processor, and the input and output device is connected to the processor.

Specifically, in this embodiment, the above-mentioned processor may be configured to implement the following steps through a computer program:

S201: Obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state;

S202: Judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets the accuracy;

S203: If yes, based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the updated test state corresponding to continue to perform the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the ground state energy of the molecule to be determined that meets the calculation termination condition is obtained and the Hessian matrix of the molecular ground state energy to be determined;

S204: Calculate the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined.

The structure, features and effects of the present invention have been described in detail above based on the embodiments shown in the drawings. The above descriptions are only preferred embodiments of the present invention, but the present invention does not limit the scope of implementation as shown in the drawings. Changes made to the idea of the present invention, or modifications to equivalent embodiments that are equivalent changes, and still within the spirit covered by the description and illustrations, shall be within the protection scope of the present invention.

Claims (10)

1. A method for determining the molecular vibration frequency, characterized in that the method comprises: Obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state; Judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets the accuracy; If so, then based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the energy corresponding to the updated test state Expecting, continue to execute the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the ground state energy of the molecule to be determined that satisfies the calculation termination condition and the Describe the Hessian matrix of the molecular ground state energy to be determined; According to the Hessian matrix of the ground state energy of the molecule to be determined, the vibration frequency of the molecule to be determined is calculated. 2. The method according to claim 1, wherein said obtaining the test state of the molecule to be determined comprises: According to the pre-selected hypothetical mode and the determined Hartree Fock state of the molecule to be determined, the test state of the molecule to be determined is obtained. 3. The method according to claim 2, wherein the calculation of the energy expectation corresponding to the current test state comprises: The energy expectation corresponding to the test state is calculated by the following formula:

Among them, n represents the number of cycles for calculating the energy expectation corresponding to the test state, E(n) is the energy expectation corresponding to the current test state |Ψ(n)>,

is the Hamiltonian of the molecule to be determined, h _α is the electron integral correlation coefficient,

is an operator in Pauli string form. 4. The method according to claim 3, wherein said calculating the Hessian matrix of said molecular ground state energy to be determined comprises: Calculate the Hessian matrix of the molecular ground state energy to be determined by the following formula:

where R is the coordinates of the molecule. 5. method according to claim 4, is characterized in that, described according to the Hessian matrix of described molecular ground state energy to be determined, calculate the vibration frequency of described molecule to be determined, comprising: According to the Hessian matrix of the molecular ground state energy to be determined, determine the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix; Based on the eigenvalues of the force constant matrix, the vibration frequency of the molecule to be determined is determined. 6. The method according to claim 5, characterized in that, according to the Hessian matrix of the molecular ground state energy to be determined, determine the force constant matrix of the molecule to be determined and the eigenvalues of the force constant matrix, include: Calculate the force constant matrix of the molecule to be determined by the following formula: F=M×S×M Among them, F is the force constant matrix of the molecule to be determined, M is the mass weight matrix, satisfying

N is the number of atomic systems contained in the molecule to be determined, m _q is the mass of the qth atom, q∈N. 7. A device for determining the molecular vibration frequency, characterized in that the device comprises: An obtaining module, configured to obtain the test state of the molecule to be determined, and calculate the energy expectation corresponding to the current test state; A judging module, configured to judge whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the molecular ground state energy to be determined, wherein the calculation termination condition is that the difference between the current energy expectation and the previously determined energy expectation meets precision; An update module, for if so, then based on the current energy expectation as the ground state energy of the molecule to be determined, and calculate the Hessian matrix of the ground state energy of the molecule to be determined, otherwise, update the test state, and calculate the updated The energy expectation corresponding to the test state, continue to perform the step of judging whether the energy expectation corresponding to the test state satisfies the calculation termination condition of the ground state energy of the molecule to be determined, until the molecule to be determined that meets the calculation termination condition is obtained The ground state energy of and the Hessian matrix of the molecular ground state energy to be determined; A calculation module, configured to calculate the vibration frequency of the molecule to be determined according to the Hessian matrix of the ground state energy of the molecule to be determined. 8. The device according to claim 7, wherein the obtaining module comprises: The obtaining unit is used to obtain the test state of the molecule to be determined according to the pre-selected hypothetical mode and the determined Hartree Fock state of the molecule to be determined. 9. A storage medium, wherein a computer program is stored in the storage medium, wherein the computer program is configured to implement the method described in any one of claims 1 to 6 when running. 10. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to realize any one of claims 1 to 6 method described in .

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