JP2018180084A - Quantum gate device - Google Patents

Abstract

A technique capable of performing quantum computation other than a SWAP gate is provided. A quantum gate device includes a superconducting qubit 4 coupled to a resonator 3, a first waveguide 1 coupled to the resonator 3 and into which microwave photons are incident, and a superconducting quantum The second waveguide 2 coupled to the bit 4 and into which the microwave driving light is incident, the frequency of the microwave driving light, the intensity of the microwave driving light, the frequency of the resonator, the frequency of the superconducting qubit and the superconducting qubit. and an operation unit 5 capable of controlling at least one of the coupling strength between the conduction qubit and the resonator. [Selection drawing] Fig. 1

Description

  The present invention relates to quantum computing technology.

  In recent years, it has been studied to perform quantum information processing by using an artificial atomic structure composed of a superconducting circuit as a qubit. Non-Patent Document 1 has proposed a quantum gate device between a superconducting qubit and a propagating microwave photon.

  Non-Patent Document 1 shows a method of performing SWAP gate between microwave photon and superconducting qubit by constructing a lambda type three-level system.

Koshino, K., Inomata, K., Yamamoto, T., & Nakamura, Y. "Implementation of an Impedance-Matched Dr System by Dressed-State Engineering", Physical Review Letters, 111, 153601, (2013).

  In the method of Non-Patent Document 1, only SWAP gates between microwave photons and superconducting qubits were possible, and quantum calculations other than SWAP gates were not possible between microwave photons and superconducting qubits.

  The present invention has been made in view of such problems, and an object thereof is to provide a quantum gate device capable of performing quantum calculations other than SWAP gates between microwave photons and superconducting qubits. It is.

  A quantum gate device according to one aspect of the present invention comprises a superconducting qubit coupled to a resonator, a first waveguide coupled to the resonator, on which microwave photons are incident, and a superconducting qubit. A second waveguide coupled with the microwave drive light, the frequency of the microwave drive light, the intensity of the microwave drive light, the frequency of the resonator, the frequency of the superconducting qubit, and the superconducting qubit And a control unit capable of controlling at least one of the coupling strengths of the resonators.

  Quantum calculations other than SWAP gates can be performed.

FIG. 2 is a block diagram for explaining an example of a quantum gate device.

[Embodiment]
Hereinafter, a quantum gate device according to an embodiment of the present invention will be described with reference to the drawings.

  As shown in FIG. 1, the quantum gate device includes a first waveguide 1, a second waveguide 2, a resonator 3, a superconducting qubit 4, an operation unit 5, an input unit 6, a circulator 7, an output unit 8, and a determination. For example, the unit 9 is provided. The operation unit 5 includes, for example, a first operation unit 51, a second operation unit 52, a third operation unit 53, and a fourth operation unit 54.

  The superconducting qubit 4 has a two-level system and is coupled to the resonator 3 (see, for example, reference 1). In many cases, the superconducting qubit 4 actually has an upper level, but in such a case, the lowest two levels will be used.

  [Reference 1] K. Koshino, K. Inomata, Z. R. Lin, Y. Tokunaga, T. Yamamoto, Y. Nakamura, "Tunable quantum gate between a superconducting atom and a propagating microwave photon", (2016)

  The resonator 3 and the superconducting qubit 4 are coupled to the first waveguide 1 and the second waveguide 2 respectively.

  The first operation unit 51 can emit microwave drive light. Further, the first operation unit 51 can control the frequency and the intensity of the microwave drive light to be emitted. The first operation unit 51 controls, for example, the frequency and the intensity of the microwave drive light so that the value determined by the determination unit 9 is obtained. See, for example, reference 2 for control of the frequency and intensity of microwave drive light.

  [Reference 2] K. Inomata, ZR Lin, K. Koshino, WD Oliver, JS Tsai, T. Yamamoto and Y. Nakamura, "Single microwave-photon detector using an artificial Λ-type three-level system", Nature Communications 7 (2016) 12303

  The microwave drive light emitted by the first operation unit 51 is incident on the second waveguide 2. Depending on the frequency and intensity of the microwave drive light incident on the second waveguide 2, the action of the quantum gate between the superconducting qubit 4 and the microwave photon changes. In other words, the microwave drive light affects the coated state consisting of the superconducting qubit 4 and the resonator 3.

  The microwave photons emitted from the input unit 6 are incident on the first waveguide 1 through the circulator 7. The microwave photons incident on the first waveguide 1 act on the superconducting qubit 4 in accordance with the above-mentioned wearing state, and return to the first waveguide 1. The microwave photons returned to the first waveguide 1 are output to the output unit 8 through the circulator 7.

  The second operation unit 52, the third operation unit 53, and the fourth operation unit 54 can control the frequency of the resonator 3, the frequency of the superconducting qubit 4 and the coupling strength of the superconducting qubit 4 and the resonator 3, respectively. is there. The second operating unit 52, the third operating unit 53, and the fourth operating unit 54 each have, for example, the frequency of the resonator 3, the frequency of the superconducting qubit 4, and the frequency of the superconducting qubit 4 so as to have values determined by the determining unit 9. The coupling strength between the conduction qubit 4 and the resonator 3 is controlled. The frequency of the superconducting qubit 4 is more precisely the frequency between two levels of the superconducting qubit 4.

  The second operation unit 52, the third operation unit 53, and the fourth operation unit 54 are, for example, the intensity of direct current connected to the resonator 3 and the superconducting qubit 4, the resonator 3 and the superconducting qubit 4 The frequency of the resonator 3, the frequency of the superconducting qubit 4 and the superconducting qubit 4 and the resonator are controlled by controlling the intensity of the external magnetic field applied to the connected superconducting quantum interferometer (SQUID) (not shown). The bond strength of 3 can be controlled.

  For details of the control of the frequency of the resonator 3 by the second operation unit 52, see, for example, reference document 3.

  [Reference 3] Martin Sandberg, CM Wilson, Fredrik Persson, Thilo Bauch, Goran Johansson, Vitaly Shumeiko, Tim Duty, Per Delsing, "Tuning the field in a microwave resonator faster than the photon lifetime", Appl. Phys. Lett. 92, 203501 (2008)

  For details of the control of the frequency of the superconducting qubit 4 by the third operation unit 53, see, for example, reference document 4.

  [Reference 4] R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O'Malley , P. Roushan, J. Wenner, TC White, AN Cleland, John M. Martinis, "Coherent Josephson qubit suitable for scalable quantum integrated circuits", Pysical Review Letters 111, 080502 (2013)

  For details of the control of the coupling strength of the superconducting qubit 4 and the resonator 3 by the fourth operation unit 54, refer to, for example, reference document 5.

  [Reference 5] Yu Chen, C. Neill, P. Roushan, N. Leung, M. Fang, R. Barends, J. Kelly, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, A. Megrant, JY Mutus, PJJ O'Malley, CM Quintana, D. Sank, A. Vainsencher, J. Wenner, TC White, Michael R. Geller, AN Cleland, John M. Martinis, "Qubit Architecture with High Coherence and Fast Tunable Coupling ", Pysical R eview Letters 113, 220502 (2014)

As will be described later, the determination unit 9 gives the coefficients ξ ₁₁ (ω), ξ ₁₂ (ω), ξ ₂₁ (ω), and ξ ₂₂ (ω) corresponding to the desired quantum gate, and the equation (12) With the frequency of microwave drive light ω _d , the intensity of microwave drive light Ω _d , the frequency ω _r of the resonator 3, the frequency ω _a of the superconducting qubit 4 and the superconducting qubit 4 At least one value of the coupling strength g of the resonator 3 is determined.

At this time, the determination unit 9 determines the frequency of the microwave drive light as ω _d , the intensity of the microwave drive light Ω _d , the frequency of the resonator 3 ω _r , the frequency ω _a of the superconducting qubit 4 and the superconducting qubit 4 And a part of the coupling strength g of the resonator 3 are further given, the frequency ω _{d of} the microwave drive light, the intensity Ω _d of the microwave drive light, the frequency ω _r of the resonator 3 and the frequency of the superconducting qubit 4 The other part of ω _a and the coupling strength g of the superconducting qubit 4 and the resonator 3 may be determined.

[Technical background]
The Hamiltonian _Har of a system composed of the superconducting qubit 4 and the resonator 3 is expressed by the equation (1) in the rotational coordinate system according to the amplitude Ω _d and the frequency ω _d of the microwave drive light.

Here, χ = g ² / (ω _r −ω _a ) is a dispersion shift. ω _r is the frequency of the resonator 3, ω _a is the frequency of the superconducting qubit 4, and is the coupling strength g of the superconducting qubit 4 and the resonator 3. Here, ω _r , ω _a and g are assumed to be predetermined fixed values. a is the annihilation operator of the superconducting qubit 4, σ is the annihilation operator of the resonator 3, and † means transpose conjugate.

The four energy levels from the bottom of the system consisting of superconducting qubit 4 and resonator 3 are | g, 0>, | e, 0>, | g, 1>, | e, 1> and these are This is an eigenstate when the drive field is off, in other words, when there is no microwave drive light. If ω _d is defined as ω _a −2χ <ω _d <ω _a , in the rotational coordinate system of ω _d , the energy level structure is ω _{| g, 0>} <ω _{| e, 0>} <ω _{| e, 1 >} It becomes a nested type that becomes <ω _{| g, 1>} .

  On the other hand, when the drive field is on, in other words, when there is microwave drive light, these states become clothes states and can be written as Expression (2)-(5).

Here, θ ₁ and θ _h are defined by formulas (5 ′) and (5 ′ ′).

Then, the eigen energies ~ ₁ , ~ ₂ , ~ ₃ and ~ ₄ of the above-mentioned dressing state become the equations (6)-(7 ').

In this four-level system, energy relaxation is performed from | ̃3>, | ̃4> to | ̃1>, | ̃2>, and a photon is emitted to the first waveguide 1 at that time. Relaxation rate ^~ kappa ₃₁ clothed state where the resonator 3 consisting of a superconducting qubit _{^{4, ~ κ 32, ~ κ}} 41, is ^~ kappa ₄₂ Equation (8) and (9). As i = 3, 4, j = 1, 2, ^{~ ~} _ij means the relaxation rate from | ~ i> to | ~ j>. θ _t = θ ₁ + θ _h κ is the relaxation rate of the resonator 3 itself, which is a predetermined constant.

The system of propagating microwave photons and this dressed state perform conversion as shown in equations (10) and (11). ω is the frequency of the microwave photons, ω = ω ₁ , ω _h . It is Δω = ω _h −ω _l . The definitions of ω _l and ω _h will be described later.

This corresponds to a quantum gate. | ~ 1>, | ~ 2> are two-state systems of superconducting qubits 4, in other words, the energy quasiquarries in the coated state formed by the superconducting qubits 4 and the resonator 3 affected by the microwave drive light The basis of the microwave photons corresponds to the two low-dressed clothing states, | ω _l >, | ω _h >, and (ω _l , ω _h ) = (̃ω ₃₂ , ̃ω ₃₁ ) or ( ω ₄₂ , ̃ω ₄₁ ). Here, for _{example, ~ ω 32 = ~ ω 3} - a _{~ ω 2, ~ ω 31 =} ~ ω 3 - a _{~ ω 1, ~ ω 42 =} ~ ω 4 - a ~ ω _2, ~ ω ₄₁ = ~ ω ₄ - is ~ ω _1.

Here, when the relaxation rate is ~ _{31 31} = ~ _{32 32} (ie, when θ _t = π / 4, the conditions of ω _d and ω _d become equation (17)), the equation (12) - _{(15), (ω l, ω h)} = (~ ω 32, ~ ω 31) when _{ξ 11 (ω l) = ξ} 21 (ω l) = 1, ξ 12 (ω l) = ξ ₂₂ (ω _l ) = 0, ξ ₁₁ (ω _h ) = ξ ₂₁ (ω _h ) = 0, ξ ₁₂ (ω _h ) = ξ ₂₂ (ω _h ) = 1. This is the same as when the relaxation rate is ̃ = ₄₁ = ̃κ ₄₂ and (ω ₁ , ω _h ) = (̃ω ₄₂ , ̃ω ₄₁ ). That is, the conversion formula of microwave photons to atoms is a SWAP gate as shown in equation (16).

Further, in order to fix the frequency base of the input and output photons, it is necessary that Δω = ω _h −ω ₁ = Expression (18) be a constant.

A omega _d and Omega _d when subsequent When constant SWAP gates [Delta] [omega omega _d ^sw and Omega _d ^sw is the formula (19) and (20).

  At this time, the frequency bases of the microwave photons become the equations (21) and (22).

  Hereinafter, this frequency base is used. Next, √ SWAP gate will be described.

In order to configure the S SWAP gate, the determination unit 9 sets ξ ₁₁ (ω _l ) = 1, ξ ₁₂ (ω _l ) = 0, ξ ₂₁ (ω _l ) = (1 + i) / 2, ξ ₂₂ ( ω _l ) = (1-i) / 2, ξ ₁₁ (ω _h ) = (1-i) / 2, ξ ₁₂ (ω _h ) = (1 + i) / 2, ξ ₂₁ (ω _h ) = 0 , ξ ₂₂ (ω _h ) = 1 or ξ ₁₁ (ω _l ) = 1, ξ ₁₂ (ω _l ) = 0, ξ ₂₁ (ω _l ) = (1-i) / 2, ξ ₂₂ (ω _l ) = (1 + i) / 2, ξ ₁₁ (ω _h ) = (1 + i) / 2, ξ ₁₂ (ω _h ) = (1-i) / 2, ξ ₂₁ (ω _h ) = 0, ξ ₂₂ ( Choose ω _d and Ω _d such that ω _h ) = 1. At this time, the value of the allowable error range may be deviated. At this time, if the frequency bases of the microwave photons are selected to be equations (21) and (22), the bases of the SWAP gate and the √SWAP gate become equal.

In the above description, the determination unit 9 fixes ω _r , ω _a and g to predetermined values, and sets ξ ₁₁ (ω _l ) and ξ ₁₂ (ω _l ) corresponding to the desired quantum gate. , ξ ₂₁ (ω _l ), ξ ₂₂ (ω _l ), ξ ₁₁ (ω _h ), ξ ₁₂ (ω _h ), ξ ₂₁ (ω _h ), ξ ₂₂ (ω _h ), Ω _d , ω _d have been determined, but this is only an example.

The determination unit 9 fixes a part of ω _r , ω _a , g, Ω _d , and ω _{d and} sets ξ ₁₁ (ω ₁ ), ξ ₁₂ (ω ₁ ), ξ ₂₁ () corresponding to a desired quantum gate. ω _l ), ξ ₂₂ (ω _l ), ξ ₁₁ (ω _h ), ξ ₁₂ (ω _h ), ξ ₂₁ (ω _h ), ξ ₂₂ (ω _h ) so that ω _r , ω _a , The other part of g, Ω _d and ω _d may be determined. For example, the determination unit 9 fixes Ω _d and ω _d and sets ξ ₁₁ (ω _l ), ξ ₁₂ (ω _l ), ξ ₂₁ (ω _l ), ξ ₂₂ (ω _l ) corresponding to the desired quantum gate. ω _r , ω _a and g may be determined such that) ₁₁ (ω _h ), 得₁₂ (ω _h ), ξ ₂₁ (ω _h ) and ξ ₂₂ (ω _h ) are obtained.

Incidentally, so far in the description of, because it was a predetermined value a frequency omega _a frequency omega _r and superconducting quantum bit 4 of the resonator 3, the frequency of the frequency omega _r and superconducting quantum bit 4 of the resonator 3 the shift of the omega _a did not mention, when moving the frequency omega _a frequency omega _r and superconducting quantum bit 4 of the resonator 3, it is necessary to consider the shift. In consideration of the shift, in the above description, the frequency of the resonator 3 ^- and omega _r, the frequency of the superconducting qubit 4 ^- and ^{_{ω a, χ = g 2 /}} (- ω r - - ω a And ω _r = ⁻ ω _r + χ and ω _a = ⁻ ω _a −χ.

The determination unit 9 corresponds to the desired quantum gate by ξ ₁₁ (ω _l ), ξ ₁₂ (ω _l ), ξ ₂₁ (ω _l ), ξ ₂₂ (ω _l ), ξ ₁₁ (ω _h ), ξ ₁₂ ( The values of ω _r , ω _a , g, Ω _d and ω _d corresponding to ω _h ), ξ ₂₁ (ω _h ), ξ ₂₂ (ω _h ) are determined, and the operation unit 5 has the determined values. By controlling ω _r , ω _a , g, Ω _d and ω _d , it is possible to configure a quantum gate device capable of performing quantum calculation other than SWAP gate.

  Also, quantum entanglement can be generated by the above-described quantum gate device.

[Modification]
It is needless to say that the above embodiment is merely an example, and that changes can be made as appropriate without departing from the spirit of the present invention.

  For example, the quantum gate device may not include the circulator 7. In this case, for example, in the quantum gate device, microwave photons emitted from the input unit 6 are incident on the first waveguide 1 and microwave photons returned from the resonator 3 to the first waveguide 1 are output to the output unit 8 An incident switch may be provided instead of the circulator 7.

  In the above description, although the frequency bases defined by Equations (21) and (22) are used as the frequency bases of microwave photons, the frequency bases of microwave photons are defined by Equations (21) and (22) It is not limited to the frequency base to be As the frequency base of microwave photons, frequency bases other than the frequency bases defined by the equations (21) and (22) may be used.

Reference Signs List 1 first waveguide 2 second waveguide 3 resonator 4 superconducting qubit 5 operation unit 6 input unit 7 circulator 8 output unit 9 determination unit

Claims (3)

A superconducting qubit coupled to the resonator,
A first waveguide coupled to the resonator to which microwave photons are incident;
A second waveguide coupled to the superconducting qubit and into which microwave drive light is incident;
The frequency of the microwave driving light, the intensity of the microwave driving light, the frequency of the resonator, the frequency of the superconducting qubit, and the coupling strength of the superconducting qubit and the resonator can be controlled. Operation unit,
A quantum gate device including: In the quantum gate device of claim 1,
The operation unit is a first operation unit capable of controlling the frequency of the microwave drive light and the intensity of the microwave drive light.
Quantum gate device. In the quantum gate device of claim 1,
The frequency of the microwave drive light is omega _d, the intensity of the microwave drive light is Omega _d, the frequency of the resonator ^- and omega _r, the frequency of the superconducting qubits ^- and ω _a, χ = g ² / a ^{_{(- - ω r - ω a}} ), ω r = - ω r + χ, ω a = - and ω _a -χ, the bond strength of the superconducting qubit and the resonator 3 and g, The two coated states with low energy levels in the coated state formed by the superconducting qubit and resonator affected by the microwave drive light are denoted by | 1> and | ̃2>, where ω is the above It is assumed that the frequency of the microwave photon is ω = ω ₁ , ω _h, and (ω ₁ , ω _h ) = (̃ω ₃₂ , ̃ω ₃₁ ) or (̃ω ₄₂ , ̃ω ₄₁ ), ̃ω ₃₂ = Let ω _3- ̃ω ₂ , ̃ω ₃₁ = ̃ω ₃ − ̃ω ₁ , ̃ω ₄₂ = ̃ω ₄ − ̃ω ₂ , ̃ω ₄₁ = ̃ω ₄ − ̃ω ₁ and Δω = ω and _{h -ω l, ~ ω 1,} ~ ω 2, is ~ ω _3, ~ ω ₄ (6) - as defined by (7 '), the quantum gate has the formula (10), (11) Do conversion And the coefficients ξ ₁₁ (ω), ξ ₁₂ (ω), ξ ₂₁ (ω), ξ ₂₂ (ω) corresponding to the quantum gate are defined by the equations (12)-(15), and κ is predetermined With θ _t = θ ₁ + θ _h , where θ _l and θ _h are defined by equations (5 ′) and (5 ′ ′),

The microwave drive satisfying the equations (12) to (15) given the coefficients ξ ₁₁ (ω), ξ ₁₂ (ω), ξ ₂₁ (ω), and ξ ₂₂ (ω) corresponding to the quantum gate The frequency ω _{d of} light, the intensity Ω _d of the microwave drive light, the frequency ⁻ ω _{r of} the resonator, the frequency ⁻ ω _a of the superconducting qubit, and the coupling intensity g of the superconducting qubit and the resonator 3 Further comprising a determining unit for determining at least one value of
The operation unit is configured to adjust the frequency ω _{d of} the microwave drive light, the intensity Ω _d of the microwave drive light, the frequency ⁻ ω _{r of} the resonator, and the superconducting qubit so as to obtain the determined values. Controlling at least one of the frequency ^- ω _a and the coupling strength g of the superconducting qubit and the resonator 3;
Quantum gate device.

Images