Non-transitory computer-readable storage medium, information processing method

Abstract

To shorten the calculation time of variational quantum eigenvalue calculation.SOLUTION: An information processing device 10 executes a plurality of times update processing of a value of a first parameter which is a variable included in a cost function and is applied to a variational quantum circuit 1 used for variational quantum eigenvalue calculation. The information processing apparatus 10 uses a ratio between a first value of a cost function calculated by a variational quantum eigenvalue calculation using a value of a first parameter obtained in a kth update process and a second value of the cost function calculated by a variational quantum eigenvalue calculation using a value of the first parameter obtained in a (k-1) th update process to determine a value of a second parameter representing a weight of an amount of change in the value of the first parameter for each update process. Then, the information processing apparatus 10 performs the (k + 1) - th update processing using the amount of change weighted by the determined value of the second parameter.SELECTED DRAWING: Figure 1

Description

[Technical Field]

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

[0002] The variational quantum eigenvalue algorithm is a method for performing quantum chemical calculations using quantum computers or simulators. The VQE (Variational Quantum Eigensolver) algorithm is also known, which uses this algorithm. The VQE algorithm is used, for example, to calculate the ground-state energy value of a substance.

[0003] In quantum chemistry calculations using the VQE algorithm, for example, a quantum computer measures the expectation value of a quantum state based on a variational quantum circuit parameterized by multiple parameters. From the expectation value of the quantum state, the value of a cost function representing energy is obtained. One parameter is the rotation angle of a rotation gate, which is one of the quantum gates included in the variational quantum circuit. The value of the cost function represents the sum of the energies calculated for each quantum bit (total energy value). Hereinafter, unless otherwise specified, when we refer to the energy value, we mean the total energy value.

[0004] The classical computer updates the parameter values ​​based on the expectation value of the quantum state so that the energy becomes lower. The quantum computer generates a quantum state using the adjusted parameter values ​​and measures the expectation value again. The quantum and classical computers optimize the parameters by repeating the measurement of the expectation value of the quantum state and the update of the parameter values ​​until the energy converges.

[0005] One parameter optimization method is the gradient method, which optimizes parameters based on the gradient of a cost function when the parameter value is changed. As a technique related to VQE, for example, a method has been proposed in which parameter values ​​are updated using an optimization method called the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, which is a type of gradient method. Furthermore, a method has been proposed for simulating quantum systems, using quantum imaginary time evolution to find the wave function of a quantum system. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Publication No. 2023-113956 [Patent Document 2] Special Publication No. 2022-529187 [Patent Document 3] US Patent Application Publication No. 2023 / 0289639 [Patent Document 4] US Patent Application Publication No. 2023 / 0141618 Summary of the Invention [Problem to be solved by the invention]

[0007] In conventional gradient methods, a fixed parameter (sometimes called a step size or learning rate) is used to represent the weight of the change in the parameter value for each update process. If this fixed parameter is not an appropriate value, the number of iterations required to converge the energy increases, which may result in a long calculation time for the variational quantum eigenvalue calculation.

[0008] In one aspect, the present invention aims to reduce the computation time of variational quantum eigenvalue calculations. [Means for solving the problem]

[0009] In one proposal, an information processing program is provided that causes a computer to perform multiple updates to the value of a first parameter, which is a variable included in a cost function, applied to a variational quantum circuit used in variational quantum eigenvalue calculation.

[0010] The computer determines a value of a second parameter representing a weight of a change in the value of the first parameter for each update process, using a ratio between a first value of the cost function calculated by variational quantum eigenvalue calculation using the value of the first parameter obtained in the k-th update process (k is a natural number) and a second value of the cost function calculated by variational quantum eigenvalue calculation using the value of the first parameter obtained in the k-1-th update process.The computer then performs the (k+1)-th update process using the change weighted by the determined value of the second parameter. [Effects of the Invention]

[0011] According to one aspect, the computation time for variational quantum eigenvalue calculations is reduced. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 2 illustrates an example of an information processing method according to the first embodiment. [Figure 2] FIG. 10 illustrates an example of a system configuration according to a second embodiment. [Figure 3] FIG. 1 is a diagram illustrating an example of hardware of a classical computer. [Figure 4] FIG. 1 is a block diagram showing an example of the functionality of a classical computer for VQE calculations. [Figure 5] FIG. 1 is a diagram illustrating an example of a variational quantum circuit. [Figure 6] 10 is a flowchart illustrating an example of a procedure for VQE calculation processing. [Figure 7] FIG. 1 is a diagram showing an example of a VQE calculation of the energy of a hydrogen molecule. [Figure 8] FIG. 10 is a diagram showing an example of the change in step size during VQE calculation of the energy of hydrogen molecules. [Figure 9]FIG. 10 is a diagram showing an example of optimization of a parameter set θ when calculating the VQE of the energy of a hydrogen molecule. [Figure 10] FIG. 1 shows an example of a VQE calculation of the energy of a benzene molecule. [Figure 11] FIG. 10 is a diagram showing an example of the change in step size during VQE calculation of the energy of benzene. [Figure 12] FIG. 10 is a diagram showing the experimental results of the relationship between the value of the parameter m and the number of iterations until the convergence condition is satisfied. DETAILED DESCRIPTION OF THE INVENTION

[0013] The present embodiment will be described below with reference to the drawings. Note that each embodiment can be implemented in combination with a plurality of other embodiments within a range that does not contradict each other. [First embodiment] The first embodiment is an information processing method that reduces the number of iterations of processing by speeding up the convergence of energy in variational quantum eigenvalue calculations, thereby shortening the calculation time.

[0014] Fig. 1 is a diagram illustrating an example of an information processing method according to a first embodiment. Fig. 1 illustrates an information processing device 10 that implements the information processing method. The information processing device 10 can implement the information processing method by, for example, executing an information processing program.

[0015] 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.

[0016] The storage unit 11 stores a variational quantum circuit 1 corresponding to a quantum many-body system to be solved by variational quantum eigenvalue calculation. The variational quantum circuit 1 is parameterized by a first parameter θ, which is a variable included in a cost function f(θ). The first parameter θ includes, for example, a set of multiple parameters (θ1, θ2, ...).

[0017] The processing unit 12 performs variational quantum eigenvalue calculation. In the variational quantum eigenvalue calculation, the processing unit 12 measures the expectation value of the quantum state using, for example, the quantum computer 2, the variational quantum circuit 1 to which the value of the first parameter θ is applied. The processing unit 12 calculates the energy of the quantum many-body system based on the expectation value of the quantum state. The processing unit 12 determines whether the calculated energy satisfies a predetermined convergence condition, and if not, updates the value of the first parameter θ in a direction that reduces the energy. Such updating of the value of the first parameter θ is called parameter optimization. The processing unit 12 repeatedly performs expectation value measurement and parameter optimization using the quantum computer 2 multiple times until the energy satisfies the convergence condition.

[0018] Instead of using the quantum computer 2, the processing unit 12 may measure the expected value of the quantum state by using a simulator and the variational quantum circuit 1 to which the value of the first parameter θ is applied.

[0019] θ included in the first parameter θ i In the k+1th (k is a natural number) update process of the first parameter θ by the gradient method, the value of is updated, for example, according to the following equation (1).

[0020]

number

[0021] In equation (1), θ i,k+1 is the θ obtained in the k+1th update process. i θ i,k is the θ obtained in the kth update process. i where η is the second parameter that represents the weight of the change in the value of the first parameter θ for each update process. η can also be said to be a parameter that represents the degree to which the value of the first parameter θ is changed. Note that η is sometimes called the step size or learning rate of the gradient method. f(θ) is the cost function that represents energy. ∂f(θ) / ∂θ i is the parameter θi is the partial derivative of f(θ) relative to the change in the value of θ. More specifically, ∂f(θ) / ∂θ i is the parameter θ i represents the axial gradient of f(θ) at the point (θ 1,k ,θ 2,k , , ) parameter θ i is the partial derivative with respect to

[0022] If η is a fixed value, the following problems may occur. For example, if the value of η is too large in the early stages of optimization of the first parameter θ, the value of the first parameter θ will change too much in one update process. In this case, the optimization may deviate from the intended optimization path and not go well. Furthermore, if the value of η is too small, especially in the final stages of optimization, the amount of change in the value of the first parameter θ may be underestimated, increasing the number of iterations of the update process until the convergence condition is met. For these reasons, the time required for variational quantum eigenvalue calculation may become long.

[0023] Therefore, in the information processing method according to the first embodiment, the processing unit 12 uses a variable value η as shown below as the second parameter instead of the fixed value η. k Use η k represents the second parameter used in the k+1th update process of the first parameter θ. k The value of f(θ i,k ) and f(θ i,k-1 ) is determined using the ratio.

[0024] f(θ i,k ) is the θ obtained in the kth update process. i,k is the value of the cost function calculated by the variational quantum eigenvalue calculation using the value of f(θ i,k-1 ) is the θ obtained in the k-1th update process. i,k-1 is the value of the cost function calculated by variational quantum eigenvalue calculation using the value of

[0025] For example, η kis determined according to the following formula (2):

[0026]

number

[0027] In equation (2), η0 is a predetermined reference value. The value of the third parameter m, which is an exponent in equation (2), is set so as to reduce the number of update processes until the convergence condition is satisfied. The method for setting the value of the third parameter m will be described later (see FIG. 12).

[0028] f(θ i,k ) and f(θ i,k-1 ) is the ratio of f(θ i,k ) / f(θ i,k-1 ) is larger, η k The value of f(θ i,k ) / f(θ i,k-1 ) is smaller, η k The value of becomes smaller.

[0029] The processing unit 12 updates the second parameter η determined as described above in the update process repeatedly executed in the calculation process of the variational quantum eigenvalue. k The value of the first parameter θ is updated by a change amount weighted by the value of

[0030] In the (k+1)th update process, the processing unit 12 updates θ according to, for example, the following equation (3).

[0031]

number

[0032] Unlike equation (1), equation (3) uses f(θ i,k ) and f(θ i,k-1 ) and the second parameter, η k That is, the processing unit 12 uses η k and ∂f(θ) / ∂θ iThe product of these is the parameter θ obtained in the kth update process. i,k The value subtracted from the updated parameter θ i,k+1 The value is determined as follows.

[0033] As mentioned above, η k The value of this time (kth time) f(θ i,k ) and the previous (k-1) f(θ i,k-1 ) and the change in the value of the cost function obtained in the calculation process of the variational quantum eigenvalues ​​is determined by η k In the early stage when the optimization of the first parameter θ is not progressing (when the value of k is small), i,k ) and f(θ i,k-1 ) is not well-defined, and the difference between the two values ​​tends to be large. i,k ) and f(θ i,k-1 ) shows such a tendency, f(θ i,k ) and f(θ i,k-1 ) and η k The value of also shows a tendency to fluctuate greatly. k The value of the first parameter θ, whose change is weighted by , and the value (energy) of the cost function f(θ) also tend to increase or decrease by large amounts. This behavior corresponds to a quick, albeit somewhat rough, search of a wide area of ​​the search space.

[0034] Depending on the quantum many-body system being solved, this may lead to faster energy convergence by proceeding along an optimization path toward lower energy at an earlier stage than when a fixed value of the second parameter η is used. This reduces the number of iterations of the process for optimizing the first parameter θ, and is therefore expected to shorten the calculation time.

[0035] As will be shown in the second embodiment below, for example, when the value of the first parameter θ is optimized so that the energy of a hydrogen molecule (H2) or a benzene molecule (CH2) is reduced, the above-mentioned effect of shortening the calculation time was confirmed. Obtaining the effect of shortening the calculation time at least for these molecules is sufficiently beneficial in the field of quantum chemical calculations.

[0036] Second Embodiment The second embodiment shortens the time required for variational quantum eigenvalue calculation by accelerating the convergence of energy in variational quantum eigenvalue calculation using a quantum computer. In the second embodiment, variational quantum eigenvalues ​​are calculated by VQE. In the second embodiment, the process of updating the values ​​of a set of multiple parameters θ (the first parameter θ in the first embodiment) so as to reduce the energy of a quantum many-body system is called an optimization process. In addition, a parameter (the second parameter η in the first embodiment) representing the weight of the amount of change in the value of the set of multiple parameters θ for each optimization process is called an optimization process. k ) with step size η k It is called.

[0037] (System configuration and hardware example) FIG. 2 is a diagram illustrating an example of a system configuration according to the second embodiment. A classical computer 100 and a quantum computer 200 are connected via a network. The classical computer 100 is a von Neumann-type computer. The classical computer 100 performs processes such as parameter optimization calculations in VQE calculations. The quantum computer 200 is a quantum gate-type quantum computer that performs desired calculations by manipulating the state of quantum bits based on a quantum circuit. In VQE calculations, the quantum computer 200 obtains, based on the variational quantum circuit, the expected value of the quantum state represented by the variational quantum circuit in accordance with the values ​​of specified parameters.

[0038] FIG. 3 is a diagram illustrating an example of hardware for a classical computer. A classical computer 100 is entirely controlled by a processor 101. A memory 102 and multiple 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 some 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).

[0039] The memory 102 is used as a main storage device of the classical computer 100. The memory 102 temporarily stores at least a portion 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 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.

[0040] 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 a network interface 108.

[0041] 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 the OS program, application programs, and various data. Note that the storage device 103 may be, for example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive).

[0042] The GPU 104 is an arithmetic unit that performs image processing and is also called a graphics controller. The GPU 104 is connected to a monitor 21. 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 organic EL (Electro Luminescence) or a liquid crystal display device.

[0043] The input interface 105 is connected to a keyboard 22 and a mouse 23. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. 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.

[0044] The optical drive device 106 uses a laser beam or the like to read data recorded on an 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 reflected 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), and the like.

[0045] 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 function for communicating with the device connection interface 107. The memory reader / writer 26 is a device for writing data to the memory card 27 or reading data from the memory card 27. The memory card 27 is a card-type recording medium.

[0046] The network interface 108 is connected to the quantum computer 200 via a network. The network interface 108 transmits information such as a quantum computation request to the quantum computer 200 and receives information indicating the computation result from the quantum computer 200. The network interface 108 is a wired communication interface that is connected by a cable to a wired communication device such as a switch or a router.

[0047] The classical computer 100 can realize the processing functions of the second embodiment with the hardware described above. The device shown in the first embodiment can also be realized with hardware similar to the classical computer 100 shown in FIG.

[0048] The classical computer 100 realizes the processing functions of the second embodiment by executing a program recorded on, for example, a computer-readable recording medium. The program describing the processing to be executed by the classical computer 100 can be recorded on various recording media. For example, the program to be executed by the classical computer 100 can be stored in a storage device 103. The processor 101 loads at least a portion 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 on a portable recording medium such as an optical disk 24, a memory device 25, or a memory card 27. The program stored on the portable recording medium becomes executable after being installed on the storage device 103, for example, under the control of the processor 101. The processor 101 can also read and execute the program directly from the portable recording medium.

[0049] In such a system, a classical computer 100 and a quantum computer 200 cooperate to perform VQE calculations. (Example of function block) 4 is a block diagram showing an example of the functions of a classical computer for VQE calculation. The classical computer 100 includes a quantum calculation manager 110 and an optimization calculation unit 120.

[0050] The quantum computing manager 110 generates a variational quantum circuit for calculating the energy of a quantum many-body system such as a molecule, and instructs the quantum computer 200 to measure the expectation value of a quantum state based on the variational quantum circuit. For example, the quantum computing manager 110 generates a variational quantum circuit for quantum chemical calculations and sets a set of parameters θ related to gate operations at quantum gates in the variational quantum circuit. Before the first energy calculation based on the variational quantum circuit, the quantum computing manager 110 sets initial values ​​for the set of parameters θ. The initial values ​​of each parameter included in the set of parameters θ are, for example, values ​​specified in advance by the user. Alternatively, random values ​​may be used as the initial values ​​of each parameter.

[0051] The quantum computing manager 110 acquires from the quantum computer 200 the measurement results of the expected value of the quantum state based on the variational quantum circuit parameterized by the parameter set θ. The quantum computing manager 110 calculates the energy based on the measurement results of the expected value. The quantum computing manager 110 then determines whether the energy has converged. If the quantum computing manager 110 determines that the energy has not converged, it instructs the optimization calculation unit 120 to optimize the parameter set θ.

[0052] The optimization calculation unit 120 performs optimization of the parameter set θ for each optimization process. For example, the optimization calculation unit 120 calculates η k Then, the optimization calculation unit 120 determines the determined η k and updates the value of the parameter set θ according to the above-mentioned equation (3). When the optimization calculation is completed, the optimization calculation unit 120 notifies the quantum computation management unit 110 of the updated value of the parameter set θ.

[0053] The functions of the elements shown in FIG. 4 can be realized, for example, by causing a computer to execute a program module corresponding to the element. (Example of a variational quantum circuit) FIG. 5 is a diagram showing an example of a variational quantum circuit. FIG. 5 shows an example of a variational quantum circuit 30 that measures the expectation value of the quantum state of a hydrogen molecule. The variational quantum circuit 30 includes a plurality of quantum gates that perform gate operations on four quantum bits (qubits 0 to 3). The quantum gate that performs the gate operation on each quantum bit is shown on the horizontal line associated with that quantum bit. When the quantum computer 200 performs quantum computation, the gate operations set for each quantum bit are executed in order from left to right.

[0054] The one-qubit gates 31a to 31d are quantum gates that perform rotation operations around the y-axis of the Bloch sphere by a specified angle. The one-qubit gates 31a to 31d perform rotation operations by a rotation angle of θ0 for qubit 0, θ2 for qubit 1, θ4 for qubit 2, and θ6 for qubit 3.

[0055] The one-qubit gates 31e to 31h are quantum gates that perform a rotation operation around the z-axis of the Bloch sphere by a specified angle. The one-qubit gates 31e to 31h perform a rotation operation with a rotation angle of θ1 for qubit 0, θ3 for qubit 1, θ5 for qubit 2, and θ7 for qubit 3.

[0056] The two-qubit gates 32a to 32c are controlled Z (CZ) gates that perform an operation (CZ operation) to invert the sign of a state when the first bit (control bit) and the second bit (target bit) of two qubits are both "1". The two-qubit gate 32a performs a CZ operation between qubit 0 and qubit 1. The two-qubit gate 32b performs a CZ operation between qubit 2 and qubit 3. The two-qubit gate 32c performs a CZ operation between qubit 1 and qubit 2.

[0057] The gate operation by the one-qubit gates 31a to 31h and the two-qubit gates 32a to 32c as described above is repeated four times (i.e., depth (circuit depth) = 4). In the second to fourth rotation operations, the rotation angles θ8 to θ 31 is used.

[0058] Then, gate operations are again applied by the one-qubit gates 31i to 31p. The one-qubit gates 31i to 31l are quantum gates that perform rotation operations around the y-axis of the Bloch sphere by a specified angle. The one-qubit gates 31i to 31l apply θ 32 , qubit 1 has θ 34 , qubit 2 has θ 36 , qubit 3 has θ 38The rotation operation is performed by the rotation angle of θ. The one-qubit gates 31m to 31p are quantum gates that perform a rotation operation around the z-axis of the Bloch sphere by a specified angle. The one-qubit gates 31m to 31p rotate qubit 0 by the rotation angle of θ. 33 , qubit 1 has θ 35 , qubit 2 has θ 37 , qubit 3 has θ 39 The rotation operation is performed with a rotation angle of .

[0059] Then, the quantum state of each quantum bit is measured. The quantum state measurement operation is indicated by symbols 33a to 33d at the right end of the line corresponding to each quantum bit. In VQE calculations, when determining the basis value of the energy of hydrogen molecules, for example, the variational quantum circuit 30 as described above is used.

[0060] (Example of VQE calculation process) 6 is a flowchart showing an example of the VQE calculation process. The process shown in FIG. 6 will be explained below in order of step number.

[0061] [Step S101] The quantum computation manager 110 generates a variational quantum circuit parameterized by a set of parameters θ. The quantum computation manager 110 uses, for example, a pre-specified value as the initial value of the set of parameters θ.

[0062] [Step S102] The quantum computing manager 110 calculates the step size η s The quantum computing manager 110 also acquires the value of a third parameter m (hereinafter simply referred to as parameter m), which is the exponent of equation (2). For example, the quantum computing manager 110 accepts input of the reference value η0 and the value of the parameter m by a user. The quantum computing manager 110 transmits the acquired reference value η0 and the value of the parameter m to the optimization calculator 120. The optimization calculator 120 stores the reference value η0 and the value of the parameter m.

[0063] [Step S103] The quantum computing manager 110 instructs the quantum computer 200 to measure the expected value. For example, the quantum computing manager 110 transmits the generated variational quantum circuit and the value of the set of parameters θ to the quantum computer 200, and instructs it to calculate the expected value of the quantum state (the value of each quantum bit) based on the variational quantum circuit. The quantum computer 200 measures the expected value of the quantum state based on the variational quantum circuit parameterized by the set of parameters θ.

[0064] [Step S104] The quantum computation manager 110 calculates the value of the cost function f(θ) (corresponding to the total energy value) from the expected value of the quantum state. [Step S105] The quantum computing manager 110 determines whether the value of the cost function f(θ) has converged. If the value of the cost function f(θ) satisfies a predetermined convergence condition, the quantum computing manager 110 determines that the value of the cost function f(θ) has converged. For example, if the value of the cost function f(θ) has reached a known value as the energy value of the ground state, the quantum computing manager 110 determines that the value of the cost function f(θ) has converged. In addition, the quantum computing manager 110 compares the value of the cost function f(θ) calculated this time with the value of the cost function f(θ) calculated previously (f(θ) old ) is equal to or smaller than a predetermined threshold, it may be determined that the value of the cost function f(θ) has converged.

[0065] If the quantum computing manager 110 determines that the value of the cost function f(θ) has converged, it outputs a solution corresponding to the quantum state at that time and terminates the VQE computation process. If the quantum computing manager 110 determines that the value of the cost function f(θ) has not converged, it proceeds to step S106.

[0066] [Step S106] The quantum computing manager 110 determines whether the current optimization process is the first time (first optimization step). If the quantum computing manager 110 determines that it is the first optimization step, it proceeds to step S107. If the quantum computing manager 110 determines that it is not the first optimization step, it proceeds to step S108.

[0067] [Step S107] The optimization calculation unit 120 calculates the step size η k The value of the set of multiple parameters θ is updated by performing the calculation (optimization calculation) shown in equation (3) using the reference value η0 as θ. After that, the process of step S110 is performed.

[0068] [Step S108] The optimization calculation unit 120 calculates the value of the cost function f(θ) and old Using this, the new step size η is calculated according to equation (2). k The value of the cost function f(θ) is calculated by f(θ i,k ) and f(θ) old is f(θ i,k-1 ) corresponds to

[0069] [Step S109] The optimization calculation unit 120 calculates the step size η k The value of the set of multiple parameters θ is updated by performing the calculation (optimization calculation) shown in equation (3) using the above equations. After that, the process of step S110 is performed.

[0070] [Step S110] The quantum computing manager 110 calculates the value of f(θ) as old and stores it in the memory 102. After that, the optimization calculation unit 120 advances the process to step S103.

[0071] By performing such VQE calculation processing, the classical computer 100 changes the value of f(θ) obtained during the VQE calculation in a step size η k In the early stages of optimization, the values ​​of f(θ) and f(θ) old The magnitude relationship between f(θ) and f(θ) is not fixed, and the difference between the two values ​​tends to become large. old If f(θ) and f(θ) show this tendency, old The step size η is determined using the ratio k The value of also shows a tendency to increase or decrease significantly. kThe value of the set of parameters θ, whose change amount is weighted by θ, and the value (energy) of f(θ) also tend to increase or decrease by a large amount.

[0072] Depending on the quantum many-body system being solved, this may lead to faster energy convergence by proceeding along an optimization path toward lower energy at an earlier stage than when a fixed step size η is used. This reduces the number of iterations of the process for optimizing multiple parameter sets θ, which is expected to shorten the calculation time.

[0073] The VQE calculation process procedure shown in FIG. 6 is an example, and the order of the processes may be changed as appropriate. (Example of VQE calculation application) Next, an example of VQE calculation of the energy of a hydrogen molecule and the energy of a benzene molecule will be described according to the procedure shown in FIG.

[0074] FIG. 7 shows an example of a VQE calculation of the energy of a hydrogen molecule. In FIG. 7(A), graph 41 shows the results of a VQE calculation of the energy of a hydrogen molecule when the interatomic distance is 0.74 Å. FIG. 7(B) shows graph 41a, which is an enlarged view of the energy range of graph 41 from -1.15 to -0.95. The horizontal axis of graphs 41 and 41a represents the number of iterations of the optimization process, and the vertical axis represents energy. The VQE calculation of the energy of a hydrogen molecule used the variational quantum circuit 30 shown in FIG. 5, which measures the expectation value of the quantum state of a hydrogen molecule.

[0075] The polygonal line 42a represents the change in energy when a fixed step size η is applied, and the polygonal line 42b represents the change in energy when the step size η is varied according to equation (2). k In the calculation example of Fig. 7, the value of parameter m in equation (2) is set to 2.0. Also, the value of the fixed step size η and the value of the step size η k The initial values ​​of both are the reference value η0.

[0076] When a fixed step size η is used, as shown by the polygonal line 42a, the energy decreases significantly at first, and then continues to decrease gradually. k When the above formula is applied, as shown by the broken line 42b, when the number of repetitions is small (for example, 50 or less), the energy repeatedly increases and decreases by a large amount.

[0077] However, the step size η k When a step size η is applied, the convergence condition is met and the calculation is completed sooner than when a fixed value of the step size η is applied. In the example of Figure 7, when a step size η is applied, the number of iterations until the convergence condition is met is 359, while when a step size η is applied, the number of iterations until the convergence condition is met is 100. k When step size η was applied, the number of iterations until the convergence condition was met was 174. In other words, when step size η was applied, k When this method was applied, the reduction in calculation time was approximately 52%.

[0078] Fig. 8 is a diagram showing an example of the change in step size when calculating the VQE of the energy of a hydrogen molecule. The horizontal axis of the graph 43 shown in Fig. 8 represents the number of iterations of the optimization process, and the vertical axis represents the value of the step size. A straight line 43a represents a fixed value of the step size η (=η0). A broken line 43b represents a variable value of the step size η k Shows the change in

[0079] As shown by the broken line 43b, in the early stage when optimization is not progressing (when the number of iterations is small), the step size η k As the optimization progresses, the step size η k The value of is approximately equal to the value of the fixed step size η.

[0080] Fig. 9 is a diagram showing an example of optimization of the parameter set θ when calculating the VQE of the energy of a hydrogen molecule. The horizontal axis of graph 44 shown in Fig. 9 represents the number of iterations of the optimization process, and the vertical axis represents the values ​​of θ5 and θ7 of the parameter set θ. Line 44a shows the change in θ5, and line 44b shows the change in θ7.

[0081] When the number of iterations is small, the step size η shown in Fig. 8 k Due to the fluctuation of the value of θ5, θ7 also fluctuates greatly as shown by broken lines 44a and 44b. k When the fluctuation of the value of θ decreases, the fluctuation of the values ​​of θ5 and θ7 also decreases as shown by the broken lines 44a and 44b, and the values ​​become almost constant. i also shows a similar trend of change.

[0082] As described above, in the initial stage of optimization, the parameter set θ is optimized so that the value fluctuates greatly, and as a result, the energy also repeatedly increases and decreases by large amounts, as shown in Figure 7. As a result, the optimization proceeds along an optimization path that leads to lower energy at an earlier stage than when a fixed step size η is used, and the energy converges more quickly.

[0083] Next, we will explain an example of VQE calculation of the energy of a benzene molecule. For the VQE calculation of the energy of a benzene molecule, a variational quantum circuit (not shown) was used to measure the expectation value of the quantum state of the benzene molecule.

[0084] Figure 10 shows an example of a VQE calculation of the energy of a benzene molecule. In Figure 10, the results of calculating the energy of a benzene molecule using VQE are shown in graph 45. The interatomic distance between carbon atoms in the benzene molecule is 1.39 Å, and the interatomic distance between a carbon atom and a hydrogen atom is 1.07 Å. The horizontal axis of graph 45 represents the number of iterations of the optimization process, and the vertical axis represents energy.

[0085] The polygonal line 45a represents the change in energy when a fixed step size η is applied, and the polygonal line 45b represents the change in energy when the step size η is varied according to equation (2). k In the calculation example of Fig. 10, the value of parameter m in equation (2) is set to 2.0. Also, the value of the fixed step size η and the value of the step size η k The initial values ​​of both are the reference value η0.

[0086] When a fixed step size η is used, as shown by the broken line 45a, the energy initially decreases significantly, and after a period of almost no change, it decreases again and reaches convergence. During this period of almost no change in the energy, the energy is constrained to a valley (local minimum) of the energy potential that is greater than the minimum value.

[0087] On the other hand, the step size η k When the step size η is applied, the energy repeatedly increases and decreases by a large amount in the initial stage, and then decreases significantly and reaches convergence, as shown by the broken line 45b. In the example of Figure 10, when the step size η is applied, the number of iterations until the convergence condition is satisfied is 170, while when the step size η is applied, the number of iterations until the convergence condition is satisfied is 170. k When the step size η was applied, the number of iterations until the convergence condition was met was 68. In other words, when the step size η was applied, k When this method was applied, the reduction in calculation time was 60%.

[0088] Fig. 11 is a diagram showing an example of the change in step size during VQE calculation of the energy of benzene. The horizontal axis of a graph 46 shown in Fig. 11 represents the number of iterations of the optimization process, and the vertical axis represents the value of the step size. A straight line 46a represents a fixed value of the step size η. A broken line 46b represents a variable value of the step size η s Shows the change in

[0089] As shown by line 46b, in the early stage when optimization is not progressing (when the number of iterations is small), the step size η kAs the optimization progresses, the step size η k The value of is approximately equal to the value of the fixed step size η.

[0090] Although not shown, the value of the parameter set θ is set to a value of η when the number of iterations is small. k Due to the magnitude of the change in , the value fluctuates greatly when optimized. Due to the change in the value of the parameter set θ, the energy also repeatedly increases and decreases by large amounts, as shown in Figure 10. This allows the energy potential valley (minimum) to be overcome at an earlier stage than when a fixed step size η is used. As a result, optimization proceeds along an optimization path that leads to lower energy at an earlier stage, and energy convergence is accelerated.

[0091] (Example of setting the value of parameter m) The value of the parameter m is set, for example, taking into consideration the following points so as to reduce the number of iterations of the optimization process until the convergence condition is satisfied.

[0092] In equation (2), |f(θ i,k ) / f(θ i,k-1 ) |>1 and m>0, or |f(θ i,k ) / f(θ i,k-1 )|<1 and m<0, as the absolute value of parameter m increases, |f(θ i,k ) / f(θ i,k-1 )| m When the absolute value of parameter m becomes extremely large, |f(θ i,k ) / f(θ i,k-1 )| m The value of η also becomes extremely large. k The value of also becomes extremely large, and the value of the parameter set θ changes too much, which may cause the energy to not converge (the calculation to fail).

[0093] On the other hand, in equation (2), |f(θ i,k ) / f(θ i,k-1 )|>1 and m<0, or |f(θi,k ) / f(θ i,k-1 )|<1 and m>0, as the absolute value of parameter m increases, |f(θ i,k ) / f(θ i,k-1 )| m When the absolute value of parameter m becomes extremely large, |f(θ i,k ) / f(θ i,k-1 )| m The value of η also becomes extremely small. k The value of θ may also become extremely small, and the value of the parameter set θ may hardly change.

[0094] Taking the above into consideration, the inventors of the present application have found that it is preferable to set the value of the parameter m so that the absolute value of the parameter m is a real number greater than 0 and equal to or less than 5.0. Fig. 12 shows the experimental results of the relationship between the value of the parameter m and the number of iterations until the convergence condition is satisfied. In Fig. 12, the step size η k The number of iterations obtained when VQE calculations of the energy of the hydrogen molecule using the formula (2) are performed for different values ​​of the parameter m is shown.

[0095] As shown in Figure 12, when the value of parameter m was negative, the number of iterations was almost the same in the range up to -6.0. When the value of parameter m was positive, the smallest number of iterations (174) was obtained when m = 2.0, and the convergence condition was not met when m = 6.0.

[0096] From the above, it was found that it is preferable to set the value of m to approximately 0 < |m| ≦ 5.0. Also, as mentioned above, the number of iterations is smallest when the value of parameter m is 2.0, so m = 2.0 was used in the calculation shown in Figure 7 above.

[0097] Although not shown in the figure, when calculating the VQE of the energy of a benzene molecule, the number of iterations was smallest when the value of the parameter m was 2.0. As described above, in each step of optimizing the parameter set θ in the VQE calculation, the dynamically changing step size η k By using this method, energy convergence is accelerated and the number of optimization iterations can be reduced. As a result, the calculation time required for optimization is also reduced. The number of iterations until energy convergence can be reduced by approximately 52% for hydrogen molecules and approximately 60% for benzene molecules, and the calculation time for optimization can also be reduced by the same amount.

[0098] The effect of reducing the calculation time, at least for these molecules, is of great benefit in the field of quantum chemical calculations. The foregoing merely illustrates the principles of the present invention. Further, since numerous modifications and changes will be apparent to those skilled in the art, the present invention is not limited to the exact construction and application shown and described above, and all corresponding modifications and equivalents are deemed to be within the scope of the present invention as defined by the appended claims and their equivalents. [Explanation of symbols]

[0099] 1 Variational quantum circuits 2. Quantum Computers 10. Information processing equipment 11 Storage section 12 Processing section

Claims

1. An information processing program that causes a computer to execute a process of updating a value of a first parameter, which is a variable included in a cost function, multiple times, to be applied to a variational quantum circuit used for variational quantum eigenvalue calculation, the program comprising: determining a value of a second parameter representing a weight of a change in the value of the first parameter for each update process, using a ratio between a first value of the cost function calculated by the variational quantum eigenvalue calculation using the value of the first parameter obtained in a k-th update process (k is a natural number) and a second value of the cost function calculated by the variational quantum eigenvalue calculation using the value of the first parameter obtained in a k-1th update process; performing the (k+1)th update process using the amount of change weighted by the determined value of the second parameter; An information processing program that causes a computer to execute a process.

2. 2. The information processing program according to claim 1, wherein in the process of determining the value of the second parameter, the absolute value of the ratio is raised to the power of the value of a third parameter, and the product of the result of the exponentiation and a reference value of the second parameter is determined as the value of the second parameter.

3. 2. The information processing program according to claim 1, wherein in the (k+1)th update process, the product of the value of the second parameter determined in the process of determining the value of the second parameter and a partial differential coefficient representing the gradient of the cost function with respect to a change in the value of the first parameter is subtracted from the value of the first parameter obtained in the kth update process to determine the value of the first parameter after update.

4. 3. The information processing program according to claim 2, wherein the absolute value of the third parameter is a real number greater than 0 and less than or equal to 5.

5. 3. The information processing program according to claim 2, wherein when the variational quantum circuit measures the expectation value of the quantum state of a hydrogen molecule or a benzene molecule, the value of the third parameter is 2.

0.

6. 1. An information processing method in which a computer executes a process of updating a value of a first parameter, which is a variable included in a cost function, multiple times, the process being applied to a variational quantum circuit used in variational quantum eigenvalue calculation, the method comprising: determining a value of a second parameter representing a weight of a change in the value of the first parameter for each update process, using a ratio between a first value of the cost function calculated by the variational quantum eigenvalue calculation using the value of the first parameter obtained in a k-th update process (k is a natural number) and a second value of the cost function calculated by the variational quantum eigenvalue calculation using the value of the first parameter obtained in a k-1th update process; performing the (k+1)th update process using the amount of change weighted by the determined value of the second parameter; An information processing method in which the computer executes the processing.

7. An information processing device that executes a process of updating a value of a first parameter, which is a variable included in a cost function, multiple times, and is applied to a variational quantum circuit used for variational quantum eigenvalue calculation, a processing unit that determines a value of a second parameter representing a weight of a change in the value of the first parameter for each update process, using a ratio between a first value of the cost function calculated by the variational quantum eigenvalue calculation using the value of the first parameter obtained in the k-th update process (k is a natural number) and a second value of the cost function calculated by the variational quantum eigenvalue calculation using the value of the first parameter obtained in the k-1th update process, and performs the k+1th update process using the change weighted by the determined value of the second parameter; An information processing device having the above.

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