Quantum calculation support program, quantum calculation support method, and information processing device

Abstract

To reduce impacts of noise in quantum calculations.SOLUTION: An information processing device 10 learns a regression model 5 based on a correspondence relationship between calculation results for each of multiple quantum calculations for each parameter value according to a quantum circuit 2 including parameters and parameter values set in the quantum calculations. The regression model 5 uses the parameter values as explanatory variables and the calculation results of the quantum calculations as objective variables. The information processing device 10 then identifies an answer 7 of the quantum calculations by using the regression model 5.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a quantum computing assistance program, a quantum computing assistance method, and an information processing device. [Background technology]

[0002] Quantum chemical calculations can be used to investigate the properties of unknown substances. In quantum chemical calculations, the energy of a substance is calculated with high precision. The ground state energy of a quantum many-body system can be calculated, for example, by VQE (Variational Quantum Eigensolver). VQE is an algorithm that uses a non-error-correcting medium-scale quantum computer (NISQ: Noisy Intermediate-Scale Quantum Computer). VQE is expected to be applied to drug discovery and the discovery of new substances.

[0003] In VQE, parameters are optimized based on the evaluation results of quantum circuits in NISQ. For example, methods such as SPSA (Simultaneous Perturbation Stochastic Approximation) are used for parameter optimization. VQE can also be used as a subroutine in DMET (Density Matrix Embedding Theory). DMET is a quantum embedding theory for calculating frequency-independent quantities such as the ground state properties of infinite systems. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] "SPSA(Simultaneous Perturbation Stochastic Approximation) - A Method for System Optimization", [online], The Johns Hopkins University Applied Physics Laboratory, [searched on September 19, 2023], Internet <URL:https(scheme name): / / www.jhuapl.edu / SPSA / (host name + path name)> [Non-Patent Document 2] Knizia, Gerald, and Garnet Kin-Lic Chan, "Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory", Physical review letters, 2 November 2012, Vol. 109, Iss. 18 [Summary of the Invention] [Problems to be Solved by the Invention]

[0005] In the search for solutions in optimization using noisy quantum devices such as NISQ, the solutions obtained may be affected by noise and deviate from the true optimal solution. Such errors in the solutions due to the influence of noise are problems that occur similarly in many quantum computations using NISQ, not only in VQE, but also in quantum computations such as QAOA (Quantum Approximate Optimization Algorithm), an algorithm for combinatorial optimization, and DMET that uses VQE as a subroutine.

[0006] In one aspect, the present invention aims to reduce the influence of noise in quantum computing. [Means for Solving the Problems]

[0007] In one proposal, a quantum computing support program is provided that causes a computer to execute the following processing. The computer learns a regression model in which the parameter values ​​are explanatory variables and the quantum computation results are objective variables based on the correspondence between the computation results of multiple quantum computations for each parameter value according to a quantum circuit including the parameters and the parameter values ​​set in the quantum computation.The computer then identifies a solution to the quantum computation using the regression model. Effect of the Invention

[0008] According to one embodiment, the influence of noise in quantum computing can be reduced. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 illustrates an example of a quantum computing assistance method according to a first embodiment. [Diagram 2] FIG. 1 illustrates an example of a system configuration according to a second embodiment; [Diagram 3] FIG. 1 is a diagram illustrating an example of hardware of a device constituting a quantum computing system. [Figure 4] FIG. 1 is a diagram showing an example of quantum chemical calculation by VQE. [Diagram 5] FIG. 13 is a diagram showing an example of estimation using a Gaussian process or kernel method with an optimization history. [Figure 6] FIG. 2 is a block diagram showing an example of the functionality of a quantum computer system. [Figure 7] FIG. 13 is a diagram illustrating an example of a basis energy calculation process. [Figure 8] 13 is a flowchart illustrating an example of a procedure for a regression model learning process. [Figure 9] FIG. 1 illustrates an example of a Gaussian process or kernel method regression model. [Figure 10] FIG. 1 illustrates an example of a solution based on a Gaussian process or kernel method regression model. [Figure 11] 11 is a flowchart illustrating an example of a procedure for a regression model learning process including adjustment of a regularization parameter. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, the present embodiment will be described with reference to the drawings. Note that each embodiment can be implemented in combination with a plurality of other embodiments as long as no contradiction occurs. First Embodiment The first embodiment is a quantum computing assistance method for suppressing the influence of noise in quantum computing.

[0011] Fig. 1 is a diagram showing an example of a quantum assisted computing method according to a first embodiment. Fig. 1 shows an information processing device 10 for implementing the quantum assisted computing method. The information processing device 10 can implement the quantum assisted computing method by, for example, executing a quantum assisted computing program.

[0012] The information processing device 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the information processing device 10. The processing unit 12 is, for example, a processor or an arithmetic circuit included in the information processing device 10.

[0013] The storage unit 11 stores the quantum circuit 2 including the parameters. For example, the quantum circuit 2 includes a quantum gate that indicates a gate operation according to the parameters. An example of the quantum circuit 2 including the parameters is a quantum circuit for obtaining a ground state of a quantum many-body system. For example, when obtaining a ground state of a quantum many-body system by VQE, a quantum circuit 2 including a quantum gate that performs a gate operation of rotation specified by an angle parameter is used.

[0014] The processing unit 12 calculates a solution 7 with reduced noise effects based on the calculation result of the quantum computation using the quantum circuit 2. For example, the processing unit 12 first obtains history information 3 indicating the correspondence between the calculation result and the parameter value.

[0015] Specifically, the processing unit 12 repeatedly executes a process of updating (optimization) parameter values ​​in a direction that brings the calculation result closer to the ground state, and a process of calculating the calculation result based on a gate operation according to the quantum circuit 2 in which the updated parameter values ​​are set. The processing unit 12 can, for example, cause the quantum computer 1 to execute a gate operation according to the quantum circuit 2 in which the updated parameter values ​​are set, and calculate the calculation result based on the measurement result by the quantum computer 1.

[0016] When quantum computer 1 is NISQ, the gate operations and measurements performed by quantum computer 1 according to quantum circuit 2 contain noise. Therefore, when points showing the relationship between the parameter values ​​shown in history information 3 and the calculation results are plotted on graph 4, the plotted points will have variations due to noise. In the optimization process, for example, the parameter value at the point where the calculation result value showing the ground state energy is the smallest becomes optimization solution 6. However, the accuracy of the calculation results may be reduced due to the effects of noise, and there is no guarantee that optimization solution 6 is the true solution showing the ground state.

[0017] Therefore, the processing unit 12 learns (trains) the regression model 5 based on the correspondence between the calculation results for each of multiple calculations (quantum calculations) for each parameter value according to the quantum circuit 2 and the parameter values ​​set in the quantum calculations. The regression model 5 is a model in which the parameter values ​​are explanatory variables and the calculation results are objective variables.

[0018] For example, the processing unit 12 uses a Gaussian process (GP) or a kernel method to train the regression model 5. Note that, as a method for generating the regression model 5, there are also methods such as linear regression or polynomial regression using a feature vector, but these linear regression and polynomial regression can also be regarded as special cases of the Gaussian process or kernel method.

[0019] Then, the regression model 5 identifies a solution 7 of the quantum computation using the regression model 5. For example, the processing unit 12 identifies a value of the explanatory variable in the regression model 5 at which the value of the objective variable takes an extreme value (for example, a minimum value) as the solution 7 of the quantum computation.

[0020] In this way, by learning the regression model 5 based on the history information 3 and identifying the solution 7 using the regression model 5, it is possible to obtain the solution 7 with reduced effects of noise contained in the calculation based on the quantum circuit 2. In other words, it is possible to obtain the solution 7 with a small error from the true optimal solution.

[0021] Moreover, since the history information 3 is allowed to include the influence of noise, the processing unit 12 can acquire the history information 3 by using an optimization method with a low processing load, such as SPSA. Therefore, the processing load required to identify the solution 7 with reduced influence of noise is small.

[0022] Furthermore, the processing unit 12 may specify a solution taking into consideration the uncertainty of the estimation of the value of the objective function in the regression model 5. For example, the processing unit 12 calculates the uncertainty of the estimation of the objective variable according to the explanatory variables of the regression model 5 by a Gaussian process or a kernel method. Then, the processing unit 12 specifies the solution 7 of the quantum computation from the range of explanatory variable values ​​(where the reliability of the estimated value is high) where the uncertainty of the estimation of the objective variable is equal to or greater than a predetermined value. This makes it possible to obtain the solution 7 with a small error from the true optimal solution.

[0023] Gaussian processes or kernel methods are effective for learning smooth functions from a relatively small amount of data. In the current NISQ, the number of optimization iterations is not very large, and there is not a large amount of data. Therefore, by using Gaussian processes or kernel methods, it is possible to generate a highly accurate regression model5 even with a small number of optimization iterations.

[0024] The processing unit 12 may learn regression model candidates to which a plurality of regularization parameters are applied, based on the correspondence between the calculation results and the parameter values. In this case, the processing unit 12 determines a regression model from among the regression model candidates for each of the plurality of regularization parameters, based on a predetermined condition.

[0025] For example, the calculation result using a quantum circuit 2 having a parameter will be a smooth function with respect to the parameter if there is no noise. In the case of a simple quantum circuit 2 having one parameter, the function will be a trigonometric function. More generally, even in the case of a quantum circuit 2 having multiple parameters, if one parameter is focused on, the corresponding function of a representative quantum circuit 2 will be a trigonometric function. Therefore, the processing unit 12 may determine the regression model 5 from among the regression model candidates for each of the multiple regularization parameters based on the consistency with the trigonometric function.

[0026] By determining a regression model based on a predetermined condition from among the regression model candidates for each of the multiple regularization parameters, it is possible to obtain a regression model 5 using an appropriate regularization parameter even when the appropriate regularization parameter is unknown. Moreover, in optimization, it may be known that the regression model 5 is expressed by a trigonometric function if there is no influence of noise. In such a case, by identifying the regression model 5 that is highly consistent with the trigonometric function among the multiple regression model candidates, the regression model candidate to which the appropriate regularization parameter is applied can be correctly identified as the regression model 5.

[0027] Second Embodiment The second embodiment suppresses the influence of noise in quantum chemical calculations using VQE and improves the accuracy of the solution. Quantum chemical calculations are used to obtain the energy of a quantum many-body system (types of molecules + basis functions). Basis functions are functions that are the basis of which molecular orbitals are constructed. By obtaining the energy of a quantum many-body system, the characteristics of the molecule can be grasped. The energies to be obtained include ground energy and excitation energy. Ground energy is the energy in a state in which the molecular structure is stable. Excitation energy is the energy in a state in which the molecular structure is unstable. The energy of the state in which the energy is the smallest among the possible states of the molecule is the ground energy.

[0028] 2 is a diagram showing an example of a system configuration of the second embodiment. In the second embodiment, a quantum computer system 300 and a terminal device 400 are connected via a network 20. The terminal device 400 transmits a quantum computation request to the quantum computer system 300 in response to an operation from a user.

[0029] The quantum computer system 300 includes a classical computer 100 and a quantum computer 200. The classical computer 100 and the quantum computer 200 are connected via a communication interface. The classical computer 100 is a von Neumann-type computer, and performs processes such as generating quantum circuits and optimizing parameters used in quantum circuit calculations. The quantum computer 200 is a computer that performs quantum chemical calculations by performing operations based on quantum gates on quantum bits. The quantum computer 200 performs quantum chemical calculations using the VQE algorithm according to the quantum circuits and parameters generated by the classical computer 100.

[0030] 3 is a diagram showing an example of hardware of a device constituting a quantum computing system. A classical computer 100 is entirely controlled by a processor 101. A memory 102 and a plurality of peripheral devices are connected to the processor 101 via a bus 109. The processor 101 may be a multiprocessor. The processor 101 is, for example, a central processing unit (CPU), a micro processing unit (MPU), or a digital signal processor (DSP). At least a part of the functions realized by the processor 101 executing a program may be realized by an electronic circuit such as an application specific integrated circuit (ASIC) or a programmable logic device (PLD).

[0031] The memory 102 is used as a main storage device of the classical computer 100. The memory 102 temporarily stores at least a part of the OS (Operating System) program and application programs to be executed by the processor 101. The memory 102 also stores various data used in the processing by the processor 101. As the memory 102, for example, a volatile semiconductor storage device such as a RAM (Random Access Memory) is used.

[0032] The peripheral devices connected to the bus 109 include a storage device 103, a GPU (Graphics Processing Unit) 104, an input interface 105, an optical drive device 106, a device connection interface 107, and network interfaces 108a and 108b.

[0033] The storage device 103 writes and reads data electrically or magnetically to and from a built-in recording medium. The storage device 103 is used as an auxiliary storage device for the classical computer 100. The storage device 103 stores an OS program, application programs, and various data. Note that, for example, a hard disk drive (HDD) or a solid state drive (SSD) can be used as the storage device 103.

[0034] The GPU 104 is an arithmetic device that performs image processing. The GPU 104 is an example of a graphic controller. The monitor 21 is connected to the GPU 104. The GPU 104 displays an image on the screen of the monitor 21 in accordance with an instruction from the processor 101. The monitor 21 may be a display device using an organic EL (Electro Luminescence) display device or a liquid crystal display device.

[0035] The input interface 105 is connected to the keyboard 22 and the mouse 23. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. Note that the mouse 23 is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

[0036] The optical drive device 106 uses a laser beam or the like to read data recorded on the optical disc 24 or write data to the optical disc 24. The optical disc 24 is a portable recording medium on which data is recorded so that it can be read by reflection of light. The optical disc 24 includes a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Recordable) / RW (ReWritable), etc.

[0037] The device connection interface 107 is a communication interface for connecting peripheral devices to the classical computer 100. For example, a memory device 25 or a memory reader / writer 26 can be connected to the device connection interface 107. The memory device 25 is a recording medium equipped with a communication function with the device connection interface 107. The memory reader / writer 26 is a device that writes data to the memory card 27 or reads data from the memory card 27. The memory card 27 is a card-type recording medium.

[0038] The network interface 108a is connected to the network 20. The network interface 108a transmits and receives data to and from other computers or communication devices via the network 20. The network interface 108a is a wired communication interface connected by a cable to a wired communication device such as a switch or a router. The network interface 108a may also be a wireless communication interface communicatively connected by radio waves to a wireless communication device such as a base station or an access point.

[0039] The network interface 108b is an interface for connecting to the quantum computer 200. The processor 101 transmits a quantum circuit to the quantum computer 200 via the network interface 108b, and causes the quantum computer 200 to execute a quantum calculation. The processor 101 also obtains a result of the quantum calculation via the network interface 108b.

[0040] The classical computer 100 can realize the processing function of the second embodiment by the above-mentioned hardware. The information processing device 10 shown in the first embodiment can also be realized by the same hardware as the classical computer 100 shown in FIG.

[0041] The classical computer 100 realizes the processing function of the second embodiment by executing a program recorded in, for example, a computer-readable recording medium. The program describing the processing content to be executed by the classical computer 100 can be recorded in various recording media. For example, the program to be executed by the classical computer 100 can be stored in the storage device 103. The processor 101 loads at least a part of the program in the storage device 103 into the memory 102 and executes the program. The program to be executed by the classical computer 100 can also be recorded in a portable recording medium such as the optical disk 24, the memory device 25, or the memory card 27. The program stored in the portable recording medium becomes executable after being installed in the storage device 103 under the control of, for example, the processor 101. The processor 101 can also read and execute the program directly from the portable recording medium.

[0042] The quantum computer 200 includes a control device 210 and a quantum device 220. The control device 210 executes a gate operation on a quantum bit in the quantum device according to a quantum circuit. The quantum device 220 includes a plurality of quantum bits. The quantum device 220 is, for example, a quantum processing unit (QPU).

[0043] In the quantum computer system 300, the classical computer 100 and the quantum computer 200 work in conjunction with each other to perform quantum chemical calculations using VQE. At this time, since the quantum computer 200 is a NISQ, the accuracy of the optimization solution obtained by VQE decreases due to the influence of noise.

[0044] FIG. 4 is a diagram showing an example of quantum chemical calculation by VQE. In quantum chemical calculation by VQE, a quantum computer 200 performs quantum measurement based on the initial value of a parameter θ (a set of variables of a circuit corresponding to electronic excitation). That is, the quantum computer 200 performs a quantum measurement based on a plurality of divided Hamiltonians (H1, H2, . . . , H N) (N is a natural number).

[0045] The quantum circuit 30 used for quantum measurement includes an Ansatz circuit. The quantum circuit 30 is a quantum computation model described by combining multiple quantum gates. The quantum gates include an Amadhal gate 31, an X gate 32, a Y gate 33, a Z gate 34, an S gate 35, a T gate 36, and a rotation gate 37 to a rotation gate 39.

[0046] The gate operation of the Amadal gate 31 is expressed by the formula (1).

[0047]

number

[0048] The gate operation of the X gate 32 is expressed by equation (2).

[0049]

number

[0050] The gate operation of the Y gate 33 is expressed by equation (3).

[0051]

number

[0052] The gate operation of the Z gate 34 is expressed by equation (4).

[0053]

number

[0054] The gate operation of the S gate 35 is expressed by equation (5).

[0055]

number

[0056] The gate operation of the T-gate 36 is expressed by equation (6).

[0057]

number

[0058] The gate operation of the rotation gate 37 that rotates the state around the X-axis by an angle indicated by the parameter θ is expressed by equation (7).

[0059]

number

[0060] The gate operation of the rotation gate 38, which rotates the state around the Y axis by an angle indicated by the parameter θ, is expressed by equation (8).

[0061]

number

[0062] The gate operation of the rotation gate 39 that rotates the state around the Z axis by an angle indicated by the parameter θ is expressed by equation (9).

[0063]

number

[0064] Although all of the quantum gates shown in FIG. 4 are one-qubit gates, quantum circuit 30 also uses quantum gates that operate on multiple quantum bits (for example, two-qubit gates). The quantum gates used in the quantum circuit 30 include those whose rotation angle is specified by a parameter θ, such as rotation gates 37 to 39. When the quantum circuit 30 includes multiple rotation gates, the value of the parameter θ is specified for each rotation gate. The quantum computer 200 applies the specified value of the parameter θ and performs a gate operation on the quantum bit in accordance with the quantum circuit 30, thereby executing a quantum computation. As a result, multiple divided Hamiltonians are calculated.

[0065] The calculated multiple Hamiltonians are added up by the classical computer 100 to obtain the expected value of the energy of the entire system. The classical computer 100 then optimizes one or more parameters θ based on the expected value of the energy. For example, the classical computer 100 updates the parameter θ in a direction that reduces the expected value of the energy. When the parameter θ is updated, the quantum computer 200 again calculates the expected value of the energy based on the updated parameter θ.

[0066] This calculation of the energy expectation value and parameter update are repeated until the basis energy is obtained. One example of a parameter optimization technique is SPSA. SPSA is an algorithm that takes into account the presence of noise in function evaluation. It has been shown that SPSA can produce a good solution by averaging the results of multiple optimization trials, but in a single trial, which is random, the returned solution is easily affected by noise. When affected by noise, an error occurs between the solution output by optimization and the true optimal solution.

[0067] Therefore, it is possible to perform estimation using a Gaussian process or kernel method to reduce the influence of noise. In this case, if learning of the Gaussian process or kernel method is performed during optimization, the estimation calculation using the Gaussian process or kernel method will be performed multiple times, resulting in an excessive amount of calculation. In addition, it is not obvious how to combine estimation using the Gaussian process or kernel method with an optimization method such as SPSA that has a proven track record in NISQ, and there is a possibility that the influence of noise cannot be sufficiently suppressed.

[0068] Methods for optimizing while removing the effects of noise include IMFIL (IMplicit Filtering algorithm) and Bayesian optimization. IMFIL is a method that uses discrete Fourier transform to remove high-frequency oscillations from a function, but does not remove random noise. Specifically, IMFIL is a method that uses discrete Fourier transform to estimate a smoothed function while optimizing. Because IMFIL is an optimization method, there is a possibility that post-processing using a regression model, which will be described later, can reduce noise that could not be reduced by discrete Fourier transform.

[0069] Bayesian optimization is an optimization method that uses Gaussian processes or kernel methods to estimate a model of a function. Bayesian optimization is computationally intensive compared to other methods such as stochastic gradient descent, since it performs estimations at each optimization iteration.

[0070] There are also techniques that use Gaussian process or kernel methods to reduce noise in NISQ optimization. For example, "GP+Imfil" uses Gaussian process or kernel methods for the initial point of Imfil (a local search method). It may be possible to get a better initial point, but the effects of noise may remain in the solution returned by the local search method.

[0071] Therefore, the quantum computer system 300 uses the history of optimization performed during the VQE calculation process to estimate the true optimal solution using a Gaussian process or kernel method. Fig. 5 is a diagram showing an example of estimation by a Gaussian process or kernel method using an optimization history. Graph 40 shows the relationship between the value of a parameter (one-dimensional) included in the energy calculation formula and the energy value. The horizontal axis of graph 40 is the parameter value, and the vertical axis is the energy value.

[0072] The points in graph 40 indicate the parameter values ​​obtained in the optimization process performed during the VQE calculation, and the energy values ​​obtained from the calculation results of the quantum circuit when those parameter values ​​are input. Point 41, where the energy value is the minimum, is the solution of the quantum calculation by the VQE calculation. As shown in graph 40, the energy values ​​obtained by quantum calculation for each parameter include errors due to the influence of noise.

[0073] Here, a regression model 42 showing the relationship between the parameter values ​​and the energy values ​​can be generated based on the history of optimization performed in the VQE calculation process. The regression model 42 is a function with the parameter values ​​as explanatory variables and the energy values ​​as objective variables. The regression model 42 is obtained as a result of estimation using, for example, a Gaussian process or a kernel method. The regression model 42 is a curve connecting the expected values ​​of the energy values ​​according to the parameter values.

[0074] The parameter values ​​at point 43 where the energy value is minimum in regression model 42 are shifted from the parameter values ​​at point 41 where the energy is minimum in quantum computation. By using the parameter values ​​and energy value corresponding to point 43 as the solution of the optimization computation, a solution in which the effects of noise are suppressed can be obtained.

[0075] 6 is a block diagram showing an example of the functions of a quantum computer system. The classical computer 100 includes a quantum computation manager 110, a parameter updater 120, and a regression model trainer .

[0076] The quantum computing manager 110 acquires a quantum circuit for calculating the energy of a quantum many-body system such as a molecule. For example, the quantum computing manager 110 acquires a quantum circuit for performing an optimization calculation using a VQE algorithm from the terminal device 400. The quantum computing manager 110 instructs the quantum computer 200 to perform a quantum calculation based on the acquired quantum circuit.

[0077] For example, before the first quantum computation, the quantum computation management unit 110 sets initial values ​​to the values ​​of multiple parameters. The quantum computation management unit 110 acquires a computation result based on a quantum circuit parameterized by multiple parameters from the quantum computer 200. Then, the quantum computation management unit 110 acquires updated parameter values ​​from the parameter update unit 120. Then, the quantum computation management unit 110 instructs the quantum computer 200 to perform computation based on a quantum circuit in which the updated parameter values ​​have been set.

[0078] The quantum computing management unit 110 calculates an energy value according to the set parameter value based on the measurement result by the quantum computer 200. For example, the quantum computing management unit 110 sets the sum of the divided Hamiltonian values ​​as the energy. When the energy value converges, the quantum computing management unit 110 sets the energy value at that time as the basis energy. When the energy value does not converge, the quantum computing management unit 110 instructs the parameter update unit 120 to update the parameters.

[0079] Furthermore, when the quantum computing management unit 110 acquires an optimal solution of parameters when the influence of noise is reduced from the regression model learning unit 130, it instructs the quantum computing based on the optimal solution to the quantum computer 200. Then, the quantum computing management unit 110 calculates an energy value according to the optimal solution based on the measurement result by the quantum computer 200.

[0080] The parameter update unit 120 updates all or part of the values ​​of the multiple parameters for each quantum computation so that the energy value decreases. The parameter update unit 120 notifies the quantum computation management unit 110 of the updated values ​​of the multiple parameters.

[0081] The regression model learning unit 130 learns a regression model that indicates the relationship between the parameter values ​​and the energy values ​​based on the values ​​of multiple parameters for each quantum computation and the energy values ​​obtained by the quantum computation. For example, the regression model learning unit 130 generates a regression model by a Gaussian process or a kernel method. The regression model learning unit 130 calculates an optimal solution of the parameter values ​​with reduced influence of noise based on the regression model obtained by the learning. Then, the regression model learning unit 130 instructs the quantum computation management unit 110 to perform quantum computation based on the optimal solution of the parameter values.

[0082] The functions of each element in the classical computer 100 shown in FIG. 6 can be realized, for example, by causing the computer to execute a program module corresponding to that element. Such a quantum computer system 300 performs basis energy calculations with reduced effects of noise.

[0083] 7 is a diagram showing an example of a basis energy calculation process. The basis energy calculation process by the quantum computer system 300 is roughly divided into an optimization process by VQE (step S10) and an expected value measurement process by an optimal solution in which the influence of noise is reduced (step S20).

[0084] In the optimization process (step S10), first, a quantum state preparation process (step S11) is performed. For example, the quantum computation manager 110 instructs the quantum computer 200 to perform a gate operation to set the quantum bit to a predetermined initial state. The quantum computer 200 sets the quantum bit to the instructed initial state.

[0085] When the quantum state preparation process (step S11) is completed, an expected value measurement process (step S12) is performed. For example, the quantum computing manager 110 instructs the quantum computer 200 to execute a quantum gate operation based on a quantum circuit for implementing VQE. The quantum computer 200 performs the quantum gate operation according to the instruction. After the quantum gate operation according to the quantum circuit, the quantum computer 200 measures the state of the designated quantum bit. For example, the quantum computer 200 repeats the quantum gate operation based on the quantum circuit and the measurement a predetermined number of times, and transmits the expected value of the state of the quantum bit to be measured to the quantum computing manager 110.

[0086] The quantum computing management unit 110 calculates the energy based on the expected value of the quantum bit state. Then, the parameter update unit 120 performs a parameter update process (step S13). In the parameter update process (step S13), the parameter update unit 120 updates at least some values ​​of a plurality of parameters so as to reduce the energy. For example, the parameter update unit 120 updates the parameter values ​​by SPSA.

[0087] When the parameter values ​​are updated, quantum state preparation processing (step S11), expectation value measurement processing (step S12), and parameter update processing (step S13) are performed based on the quantum circuit parameterized with the updated parameters. The quantum state preparation processing (step S11), expectation value measurement processing (step S12), and parameter update processing (step S13) are repeated until the calculated energy value is determined to be the basis energy.

[0088] Through the optimization process (step S10), a pair of a parameter value and an energy value when the parameter value is applied is recorded as history information in the memory 102 or the storage device 103. By acquiring the recorded history information, an expected value measurement process (step S20) is executed using an optimal solution in which the effects of noise are reduced.

[0089] In the expected value measurement process (step S20) using the optimal solution with reduced noise effects, a regression model learning process (step S21), a quantum state preparation process (step S22), and an expected value measurement process (step S23) are executed.

[0090] In the regression model learning process (step S21), the regression model learning unit 130 learns a regression model, for example, by a Gaussian process or a kernel method. The regression model learning unit 130 calculates an optimal solution that reduces the influence of noise based on the learned regression model. The optimal solution is a parameter value that minimizes the energy value.

[0091] When the optimal solution is obtained, a quantum state preparation process (step S22) is performed based on the optimal solution. For example, the quantum computing manager 110 instructs the quantum computer 200 to perform a gate operation to set the quantum bit to a predetermined initial state. The quantum computer 200 sets the quantum bit to the instructed initial state.

[0092] When the quantum state preparation process (step S22) is completed, an expected value measurement process (step S23) is performed. For example, the quantum computing management unit 110 instructs the quantum computer 200 to execute a quantum gate operation based on a quantum circuit for implementing VQE. The quantum computer 200 performs the quantum gate operation according to the instruction. After the quantum gate operation according to the quantum circuit, the quantum computer 200 measures the state of the designated quantum bit. For example, the quantum computer 200 repeats the quantum gate operation based on the quantum circuit and the measurement a predetermined number of times, and transmits the expected value of the state of the quantum bit to be measured to the quantum computing management unit 110. The quantum computing management unit 110 then calculates the energy according to the optimal solution based on the expected value of the state of the quantum bit.

[0093] In the expected value measurement process (step S20) using the optimal solution with reduced noise effects, energy calculation may be performed using a quantum simulator or the like. In this case, quantum simulation is performed using quantum simulator software instead of the quantum state preparation process (step S22) and the expected value measurement process (step S23). The quantum simulation is a process of calculating the change in the state of a quantum bit according to the quantum gate operation shown in the quantum circuit by calculation using a classical computer 100. By performing the energy calculation using the quantum simulator, an energy value with the effects of noise removed can be obtained.

[0094] Next, the regression model learning process based on the optimization history information (step S21) will be described in detail. 8 is a flowchart showing an example of a procedure for a regression model learning process. The process shown in FIG. 8 will be described below in order of step numbers.

[0095] [Step S101] The regression model learning unit 130 acquires optimization history information. The optimization history information is a history of pairs of parameters and observed values ​​(for example, energy values). Here, the parameters of the quantum circuit are x n Let x n is R d is a vector of (R d is a real space with dimensionality d (a natural number). n = {1, 2, . . . , N} (N is the number of iterations of the optimization process). x N is the solution obtained by the optimization process.

[0096] Also, x n The measurement result when the quantum circuit with the parameter y is executed on the quantum computer 200 is n In this case, the history information is {(x1, y1), (x2, y2), . . . , (x N ,y N )}.

[0097] [Step S102] The regression model learning unit 130 learns a regression model by a Gaussian process or kernel method based on the acquired history information. The regression model is expressed as a function with parameters as explanatory variables and observed values ​​as response variables.

[0098] [Step S103] The regression model learning unit 130 identifies the parameter values ​​that minimize the function estimated by the Gaussian process or the kernel method as an optimal solution with reduced noise. For example, the regression model learning unit 130 identifies the parameter values ​​that minimize the function estimated by the Gaussian process or the kernel method as an optimal solution with reduced noise. N The function estimate is minimized near x * is identified as the optimal solution with reduced noise effects.

[0099] The regression model learning unit 130 can also identify an optimal solution with reduced noise effects from among parameter values ​​for which the reliability of the energy value estimated by the regression model is at least a certain level. For example, when the number of samples (pairs of parameter values ​​and energy values) of history information is small, the reliability of the estimation by the Gaussian process or kernel method is low. In this case, the regression model learning unit 130 identifies an optimal solution with reduced noise effects from among parameter values ​​for which the reliability is at least a certain level, thereby preventing an erroneous optimal solution from being identified due to a small number of samples.

[0100] [Step S104] The regression model learning unit 130 outputs an optimal solution in which the effects of noise have been reduced. In this way, by learning the regression model based on the optimization history information, it is possible to obtain an optimal solution with reduced influence of noise. The regression model learning unit 130 can determine the optimal solution taking into account the uncertainty of the estimation by using a Gaussian process or a kernel method as the regression model.

[0101] Gaussian process or kernel methods are described in detail below. In Gaussian processes or kernel methods, X is the space of parameters, and k:X×X→R (R is the real number space) is the kernel. The kernel represents the similarity between two parameters, and examples of kernels that are used include the Matern kernel and the Squared Exponential kernel.

[0102] The history information, which is a pair of parameters and measurements for each expected value measurement in the optimization process, is {(x1, y1), (x2, y2), . . . , (x N ,y N )}, where K n The (i,j) component is k(x i ,x j ) (i, j are natural numbers). Then, when x is a parameter, the i component is k(x,x i ) column vector k n Let's call it (x).

[0103] Let λ be the regularization parameter (λ>0). The regularization parameter is a value that is multiplied by the regularization term included in the equation that represents the regression model. The regularization term is a term for smoothing noise. The regularization parameter adjusts the degree to which noise is smoothed. The estimated μ in Gaussian process or kernel method n (x) is given by the following equation (10).

[0104]

number

[0105] In addition, the uncertainty of the estimation σ n (x) is given by the following equation (11).

[0106]

number

[0107] The uncertainty of the estimation is the estimated μ n This indicates the likelihood that the value of (x) is correct. Due to the uncertainty of the estimation, the estimated μn The width of the confidence interval for (x) is determined. The narrower the confidence interval, the lower the estimated μ n The value of (x) is likely to be correct (high confidence).

[0108] When such a Gaussian process or kernel method is applied to the history information of VQE, the angle parameter θ in VQE is used as the parameter x in equations (10) and (11). The value obtained by estimation is an energy value. By estimating the energy value according to the parameter using the Gaussian process or kernel method, the uncertainty of the energy value can also be calculated.

[0109] FIG. 9 is a diagram showing an example of a regression model using a Gaussian process or a kernel method. In a graph 50, the horizontal axis represents the parameter value, and the vertical axis represents the energy value. The points in the graph 50 represent samples included in the history information. Based on the parameter values ​​and energy values ​​represented in the samples, a Gaussian process or a kernel method is trained to obtain a regression model 51. The regression model 51 is a function represented by equation (10). The width of a confidence interval 52 in the energy value direction is represented by equation (11). That is, the confidence interval 52 is [μ n (x)-σ n (x),μ n (x)+σ n (x)].

[0110] FIG. 10 is a diagram showing an example of a solution based on a regression model using a Gaussian process or a kernel method. When identifying an optimal solution that reduces the influence of noise from among parameter values ​​with a certain degree of reliability or higher, for example, "σ n The constraint is set as follows: (x)≦c (c is a positive real number). In the example of graph 50, the region surrounded by the dashed line satisfies the constraint. Outside the region surrounded by the dashed line, the estimated μ n The confidence in (x) is low (uncertainty σ n (x) is large). Therefore, the regression model learning unit 130 performs optimization "min μ n Calculate "(x)".

[0111] In this way, when the number of samples is small, the regression model learning unit 130 estimates μ n Instead of searching for (x) in the entire region, we focus on the region with low uncertainty and search μ n Find the point 53 that minimizes (x), and set the parameter value of the point 53 to the optimal solution x with reduced noise. * This is expressed as the following formula.

[0112]

number

[0113] This allows the optimum solution to be identified within an interval with high reliability, resulting in a highly reliable optimum solution. The regression model learning unit 130 minimizes the function by taking into account the uncertainty σ n (x) is small, and the estimated μ n For example, the regression model learning unit 130 may set the parameter x with a small value of μ n (x)+a×σ n The parameter x that minimizes "(x)" (a is a real number greater than 0) is defined as the optimal solution.

[0114] In this way, a regression model is learned using a Gaussian process or kernel method based on optimization history information, and the parameter value that minimizes the energy value in the regression model is set as the optimal solution, thereby making it possible to obtain an optimal solution with reduced effects of noise.

[0115] Moreover, since the Gaussian process or kernel method is trained as a post-processing of the optimization method, the amount of calculation required is smaller than that of a method in which the Gaussian process or kernel method is trained multiple times during optimization. Furthermore, since it is a post-processing of the optimization method, it can be used in combination with any optimization method.

[0116] Moreover, by identifying the optimal solution from within a region with high reliability, a highly reliable optimal solution can be obtained. Third embodiment The third embodiment is configured to be able to calculate an optimal solution by calculation using an appropriate regularization parameter when the appropriate regularization parameter is unknown.

[0117] The regularization parameter is a parameter that indicates how much noise is smoothed when training a Gaussian process or kernel method. Since the strength of the noise is unknown in NISQ, it is difficult to know in advance what the regularization parameter should be set to.

[0118] Here, many of the functions used to minimize energy using quantum circuits such as VQE are trigonometric functions when one dimension of the parameters is considered. Therefore, in the quantum computer system 300, the regularization parameters are adjusted so that the trigonometric functions are well represented (high consistency is achieved). When the parameter to be optimized is x, the trigonometric function that represents the energy is, for example, "a sin(x+x0)+b" or "a sin(2(x+x0))+b" (a, b, and x0 are real numbers).

[0119] 11 is a flowchart showing an example of a procedure for a regression model learning process including adjustment of a regularization parameter. The process shown in FIG. 11 will be described below in order of step numbers. [Step S201] The regression model learning unit 130 acquires optimization history information. The optimization history information is a history of pairs of parameters and observed values ​​(for example, energy values).

[0120] Here, the parameters of the quantum circuit are x n Let x n is R d is a vector of (R d is a real space with dimensionality d (a natural number). n = {1, 2, . . . , N} (N is the number of iterations of the optimization process). x N is the solution obtained by the optimization process.

[0121] Also, x n The measurement result when the quantum circuit with the parameter y is executed on the quantum computer 200 is nIn this case, the history information is {(x1, y1), (x2, y2), . . . , (x N ,y N )}.

[0122] [Step S202] The regression model training unit 130 acquires a list L of regularization parameters. For example, the regression model training unit 130 reads out a list L prepared in advance from a memory. The list L is, for example, [10 -4 ,10 -3 ,10 -2 ].

[0123] [Step S203] The regression model learning unit 130 selects one of the unselected regularization parameters from the list L. The selected regularization parameter is defined as λ (λ∈L). [Step S204] The regression model learning unit 130 applies the selected regularization parameter λ, and uses the history information to learn a regression model (regression model candidate) by a Gaussian process or kernel method.

[0124] [Step S205] The regression model learning unit 130 generates sample data for trigonometric function learning. For example, the regression model learning unit 130 generates sample data for learning trigonometric functions using “z1, z2, . . . , z r ;z r+1 ,z r+2 ,...,z r+s ∈R d Among them, "z1,z2,...,z r " is used to generate models expressed as trigonometric functions. "z r+1 ,z r+2 ,...,z r+s " is used to calculate the error of the generated model.

[0125] For example, the regression model learning unit 130 may use the optimization solution x N It is generated by changing any one component of (d-dimensional vector) to a nearby value. In other words, the i-th component (1≦i≦d) of the sample data is the optimization solution x NThe jth component (1≦j≦d, j≠i) other than the i-th component of the sample data is x N It is the same value as the j-th component of

[0126] [Step S206] The regression model learning unit 130 calculates an estimate of each sample data based on the regression model obtained by the Gaussian process or the kernel method. r ;z r+1 ,z r+2 ,...,z r+s Let each estimate be "y1',y2',...,y r ';y r+1 ',y r+2 ',...,y r+s '".

[0127] [Step S207] The regression model learning unit 130 calculates a set of r pieces of sample data and estimated values ​​“(z1, y1′), (z2, y2′), . . . , (z r ,y r The regression model learning unit 130 uses the training data to learn the trigonometric function "f(x)=a sin(x+x0)+b)". For example, the regression model learning unit 130 uses the training data "x=z k " (1≦k≦r) f(x) and y k Learn the values ​​of the constants "a, b, x0" so that the difference with "x0" is small.

[0128] [Step S208] The regression model learning unit 130 calculates the error of the learned trigonometric function. For example, the regression model learning unit 130 uses s sample data “z r+1 ,z r+2 ,...,z r+s The regression model learning unit 130 calculates the value of the trigonometric function by using y r+1 ",y r+2 ",y r+s Then, the regression model learning unit 130 sets "y r+1 ',y r+2 ',...,y r+s ' and 'y r+1 ",yr+2 ",y r+s For example, the regression model learning unit 130 calculates the error between y m '-y" m The maximum value of "(r+1≦m≦r+s)" is taken as the error. The error is expressed by the following formula (13).

[0129]

number

[0130] It can be determined that the smaller the error of a regression model candidate is, the higher the consistency with the trigonometric function is. [Step S209] The regression model training unit 130 determines whether or not there are any unselected regularization parameters. If there are any unselected regularization parameters, the regression model training unit 130 proceeds to step S203. If all regularization parameters have been selected, the regression model training unit 130 proceeds to step S210.

[0131] [Step S210] The regression model training unit 130 identifies the regularization parameter with the smallest error as the optimal regularization parameter. Then, the regression model training unit 130 identifies the regression model candidate generated using the identified regularization parameter as the regression model for estimating the optimal solution with reduced influence of noise.

[0132] [Step S211] The regression model training unit 130 identifies, as an optimal solution, a parameter value that minimizes the energy in the regression model corresponding to the identified regularization parameter. For example, the regression model training unit 130 may identify, as an optimal solution, a parameter value that minimizes the energy in the regression model corresponding to the identified regularization parameter. N The parameter values ​​that minimize the function estimate in the vicinity of x are called the optimal solution. * Identify as:

[0133] [Step S212] The regression model learning unit 130 outputs the optimal solution. In this way, an appropriate regularization parameter is specified, and an optimal solution based on a regression model generated using history information of the optimization process using the regularization parameter is output. This makes it possible to obtain an optimal solution using an appropriate regularization parameter even when the appropriate regularization parameter is unknown.

[0134] Other embodiments In the second and third embodiments, the optimization process is performed by VQE. However, the method of identifying the optimal solution shown in the second and third embodiments can also be applied to the calculation results obtained by using a method other than VQE.

[0135] Although the embodiments have been described above, the configurations of the parts shown in the embodiments can be replaced with other parts having similar functions. Any other components or steps may be added. Furthermore, any two or more configurations (features) of the above-mentioned embodiments may be combined. [Explanation of symbols]

[0136] 1. Quantum Computer 2 Quantum circuit 3. Historical information 4. Graphs 5 Regression models 6 Optimization Solutions 7 solution 10. Information processing device 11 Storage section 12 Processing section

Claims

1. Based on a correspondence between a calculation result for each of a plurality of quantum computations for each value of the parameter according to a quantum circuit including the parameter and a value of the parameter set in the quantum computation, a regression model is learned in which the value of the parameter is an explanatory variable and the calculation result of the quantum computation is an objective variable; identifying a solution to the quantum computation using the regression model; A quantum computing support program that causes a computer to carry out processing.

2. In the process of learning the regression model, the regression model is learned using a Gaussian process or a kernel method. The quantum computing support program according to claim 1.

3. In the process of learning the regression model, an uncertainty of an estimation of the objective variable according to the explanatory variables of the regression model is calculated by the Gaussian process or the kernel method; In the process of identifying a solution of the quantum computation, the solution of the quantum computation is identified from a range of values ​​of the explanatory variables in which the uncertainty of the estimation of the objective variable is equal to or greater than a predetermined value. The quantum computing support program according to claim 2.

4. In the process of learning the regression model, the regression model is learned based on a correspondence relationship between the values ​​of the parameters for each of a plurality of quantum calculations for obtaining a ground state of a quantum many-body system and the calculation results of the quantum calculations. The quantum computing support program according to claim 1.

5. and further causing the computer to execute a process of acquiring a correspondence between the result of the quantum computation and the value of the parameter by repeatedly executing a process of updating the value of the parameter in a direction that brings the result of the quantum computation closer to the ground state, and a process of causing the quantum computer to execute a gate operation according to the quantum circuit in which the updated value of the parameter is set, and calculating the result of the computation based on a measurement result by the quantum computer. The quantum computing support program according to claim 4.

6. In the process of identifying a solution of the quantum computation, a value of the explanatory variable at which the value of the objective variable in the regression model takes an extreme value is identified as the solution of the quantum computation. The quantum computing support program according to claim 1.

7. In the process of learning the regression model, regression model candidates to which a plurality of regularization parameters are applied are learned based on a correspondence relationship between the calculation result of the quantum computing and the parameter values, and the regression model is determined based on a predetermined condition from among the regression model candidates for each of the plurality of regularization parameters. The quantum computing support program according to claim 1.

8. In the process of learning the regression model, the regression model is determined from among the regression model candidates to which the plurality of regularization parameters are respectively applied, based on consistency with a trigonometric function. The quantum computing support program according to claim 7.

9. Based on a correspondence between a calculation result for each of a plurality of quantum computations for each value of the parameter according to a quantum circuit including the parameter and a value of the parameter set in the quantum computation, a regression model is learned in which the value of the parameter is an explanatory variable and the calculation result of the quantum computation is an objective variable; identifying a solution to the quantum computation using the regression model; A quantum computing assisted method in which the processing is performed by a computer.

10. a processing unit that learns a regression model in which the value of the parameter is an explanatory variable and the calculation result of the quantum computation is an objective variable based on a correspondence relationship between each calculation result of a plurality of quantum computations for each value of the parameter according to a quantum circuit including the parameter, and the value of the parameter set in the quantum computation, and identifies a solution of the quantum computation using the regression model; An information processing device having the above configuration.

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