Information processing program, information processing method, and information processing device

Abstract

To create a quantum circuit that expresses a prescribed operation with fewer calculations.SOLUTION: An information processing device 100 obtains a first quantum circuit 101 expressing an operation of a time evolution operator, a second quantum circuit 102 having fewer quantum gates than the first quantum circuit 101 and having a plurality of parameters, and a third quantum circuit 103, wherein each of these circuits has a first size. The third quantum circuit 103 defines one or more quantum states which are part of a plurality of quantum states. The information processing device 100 downsizes the first quantum circuit 101, the second quantum circuit 102, and the third quantum circuit 103 to a second size, thereby creating a first local circuit 111, a second local circuit 112, and a third local circuit 113. The information processing device 100 calculates solutions of the plurality of parameters so as to be defined by the third local circuit 113 and to minimize the value of a cost function 130 representing a difference between the first local circuit 111 and the second local circuit 112.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 apparatus.

Background Art

[0002] Conventionally, in fields such as material development or drug discovery research, when performing quantum chemical calculations by quantum simulation, a quantum circuit representing a predetermined operation such as a time evolution operator is created. Here, in order to maintain the accuracy of quantum chemical calculations, it is desirable to reduce the number of operations in the quantum circuit. For example, when the number of quantum gates is large and the number of operations in the quantum circuit is large, errors generated in the quantum bits due to environmental noise, interference from other quantum bits, and noise during the operation of the quantum bits may accumulate for each quantum gate.

[0003] As prior art, for example, there is one that generates a second plurality of two-qubit quantum gates that are functionally equivalent to a first plurality of two-qubit quantum gates. Also, for example, there is a technique for generating a shortened quantum circuit such that the probability distribution obtained when performing quantum calculation by the shortened quantum circuit for a plurality of quantum bits approximates the probability distribution obtained when performing quantum calculation by the reference quantum circuit for the plurality of quantum bits. Also, for example, there is a technique that removes a quantum bit operated by a Pauli operator of a first single qubit and a quantum bit operated by a Pauli operator of a second single qubit. Also, for example, there is a technique for randomizing the terms of the Hamiltonian.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Patent Document 3

[0005] However, in the prior art, it is difficult to create a quantum circuit that represents a predetermined operation so as to reduce the number of operations. For example, when creating a quantum circuit that represents the operation of a time evolution operator by means of the Trotter decomposition method, the scale or depth of the quantum circuit tends to increase, and there are cases where a quantum circuit cannot be created so as to reduce the number of operations. The scale is, for example, the number of quantum gates. The depth is, for example, the number of groups of parallelizable quantum gates grouped together.

[0006] In one aspect, the present invention aims to create a quantum circuit that represents a predetermined operation so as to reduce the number of operations. [Means for Solving the Problems]

[0007] According to one embodiment, a first quantum circuit representing the action of a time evolution operator for a target problem, each having a first size, a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters, and a third quantum circuit defining one or more quantum states that are part of a plurality of quantum states for the target problem are obtained. By reducing the obtained first quantum circuit, second quantum circuit, and third quantum circuit to a second size smaller than the first size respectively, a first local circuit, a second local circuit, and a third local circuit, each having the second size, are created. Based on a cost function defined by the created third local circuit with the plurality of parameters as explanatory variables and representing the difference between the created first local circuit and the second local circuit, a solution of the plurality of parameters is calculated to minimize the value of the cost function for each of the one or more quantum states. An information processing program, an information processing method, and an information processing apparatus for setting a new quantum circuit representing the action of the time evolution operator based on the second quantum circuit and the calculated solution of the plurality of parameters are proposed.

[0008] Also, according to one embodiment, a first quantum circuit representing a predetermined action for a target problem, a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters, and a group of basis vectors defining two or more quantum states that are part of a plurality of quantum states for the target problem are obtained. Based on a cost function defined by the obtained group of basis vectors with the plurality of parameters as explanatory variables and representing the difference between the obtained first quantum circuit and the second quantum circuit, a solution of the plurality of parameters is calculated to minimize the value of the cost function for each of the two or more quantum states. An information processing program, an information processing method, and an information processing apparatus for setting a new quantum circuit representing the predetermined action based on the second quantum circuit and the calculated solution of the plurality of parameters are proposed.

Advantages of the Invention

[0009] According to one aspect, it becomes possible to create a quantum circuit that represents a predetermined operation so that the number of operations is reduced.

Brief Description of the Drawings

[0010]

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Embodiments for Carrying Out the Invention

[0011] Hereinafter, with reference to the drawings, embodiments of an information processing program, an information processing method, and an information processing apparatus according to the present invention will be described in detail.

[0012] (An Example of the Information Processing Method According to the Embodiment) FIG. 1 is an explanatory diagram showing an example of the information processing method according to the embodiment. The information processing apparatus 100 is a computer for creating a quantum circuit that represents a predetermined operation. The information processing apparatus 100 is, for example, a server or a PC (Personal Computer). The predetermined operation is, for example, the operation of a time evolution operator.

[0013] Conventionally, in fields such as material development or drug discovery research, when performing specific calculation processes such as quantum chemical calculations or material property calculations by quantum simulation, it is necessary to create a quantum circuit that represents a predetermined operation such as a time evolution operator. Here, in order to maintain the accuracy of the specific calculation process, it is desirable to reduce the number of operations in the quantum circuit. An operation is, for example, an operation on a quantum bit.

[0014] For example, the number of operations in a quantum circuit depends on factors such as the scale or depth of the quantum circuit. The scale is, for example, the number of quantum gates forming the quantum circuit. The depth is, for example, the number of groups of parallelizable quantum gates. For example, when the scale of the quantum circuit is large, the number of operations in the quantum circuit increases. For example, when the depth of the quantum circuit is large, the number of operations in the quantum circuit increases, and the calculation time in the quantum circuit becomes long.

[0015] For example, when the scale of the quantum circuit is large and the number of quantum gates is large, resulting in a large number of operations in the quantum circuit, errors occurring in the qubits may accumulate for each quantum gate, and it may not be possible to maintain the accuracy of a specific calculation process. The errors are caused by environmental noise, interference from other qubits, and noise during qubit operations. For example, when the depth of the quantum circuit is large, resulting in a large number of operations in the quantum circuit, the calculation time in the quantum circuit becomes long, and it may not be possible to meet the limitation of the coherence time, and it may not be possible to maintain the accuracy of a specific calculation process. The coherence time represents the limit time during which the quantum nature of the qubit can be maintained. Thus, the more operations there are in the quantum circuit, the more difficult it is to maintain the accuracy of a specific calculation process. Therefore, it is desirable to reduce the number of operations in the quantum circuit to make it easier to maintain the accuracy of a specific calculation process.

[0016] In particular, in a quantum computer with a scale of several hundred qubits, since it is difficult to correct errors occurring in the qubits, it is desirable to reduce the number of operations in the quantum circuit to make it easier to maintain the accuracy of a specific calculation process. A quantum computer with a scale of several hundred qubits is, for example, a NISQ (Noisy Intermediate Scale Quantum Computer) or an Early-FTQC (Fault-Tolerant Quantum Computer).

[0017] However, conventionally, it has been difficult to create a quantum circuit that represents a predetermined operation so as to reduce the number of operations. For example, when creating a quantum circuit that represents the operation of a time evolution operator by means of the Trotter decomposition method, the scale or depth of the quantum circuit tends to increase. Therefore, there are cases where it is not possible to create a quantum circuit that represents the operation of a time evolution operator so as to reduce the number of operations.

[0018] Also, for example, as a method for creating a quantum circuit that represents the operation of a time evolution operator, there is LVQC (Local Variational Quantum Compilation). For example, for LVQC, reference can be made to the following Reference 1.

[0019] Reference 1: Mizuta, Kaoru, et al. “Local variational quantum compilation of large-scale hamiltonian dynamics.” PRX Quantum 3.4 (2022): 040302.

[0020] Here, in LVQC, there is a problem that it is difficult to reduce the computational cost required to create a quantum circuit that represents the operation of a time evolution operator. Also, in LVQC, when simulating the long-time dynamics of any quantum state using a quantum circuit that represents the operation of a time evolution operator, there is a problem that it is difficult to maintain the accuracy of the simulation as time elapses.

[0021] Therefore, in the present embodiment, an information processing method capable of creating a quantum circuit that represents a predetermined operation so as to reduce the number of operations will be described. According to this information processing method, specifically, it is possible to create a quantum circuit that represents a predetermined operation such as a time evolution operator so that the scale or depth of the quantum circuit is reduced.

[0022] In FIG. 1, the information processing apparatus 100 creates a quantum circuit that represents the action of a time evolution operator with a relatively small number of quantum gates and is used when solving a target problem. The target problem is a problem of performing specific computational processing such as quantum chemistry calculations or material property calculations. The target problem includes, for example, a plurality of qubits for representing a quantum state.

[0023] (1-1) The information processing apparatus 100 acquires a first quantum circuit 101, a second quantum circuit 102, and a third quantum circuit 103, each of which has a first size. The first size represents the magnitude of a range that includes the entirety of a plurality of qubits related to the target problem. The magnitude of the range is defined by the number of qubits.

[0024] The first quantum circuit 101 represents, for example, the action of a time evolution operator related to the target problem. The first quantum circuit 101 is created, for example, according to the Trotter decomposition method. The second quantum circuit 102 has, for example, fewer quantum gates than the first quantum circuit 101 and has a plurality of parameters. The parameters are, for example, coefficients set for the quantum gates. The second quantum circuit 102 is created in advance by the user, for example.

[0025] The third quantum circuit 103 defines, for example, one or more quantum states that are part of a plurality of quantum states related to the target problem. The plurality of quantum states correspond to the entire state space 120. The one or more quantum states correspond to a subspace 121 within the entire state space 120. The third quantum circuit 103 is created in advance by the user, for example.

[0026] The information processing apparatus 100 acquires the first quantum circuit 101 by creating the first quantum circuit 101 according to the Trotter decomposition method, for example. The information processing apparatus 100 acquires the second quantum circuit 102 by receiving the input of the second quantum circuit 102 based on a user's operation input, for example. The information processing apparatus 100 acquires the third quantum circuit 103 by receiving the input of the third quantum circuit 103 based on a user's operation input, for example.

[0027] (1-2) The information processing apparatus 100 reduces the acquired first quantum circuit 101, second quantum circuit 102, and third quantum circuit 103 to the second size respectively. Thereby, the information processing apparatus 100 creates a first local circuit 111, a second local circuit 112, and a third local circuit 113, each of which is of the second size.

[0028] The second size is smaller than the first size. The second size represents the magnitude of a range including one or more qubits that are part of a plurality of qubits related to the target problem. The magnitude of the range is defined by the number of qubits. The first local circuit 111 corresponds to the first quantum circuit 101. The second local circuit 112 corresponds to the second quantum circuit 102. The third local circuit 113 corresponds to the third quantum circuit 103.

[0029] The information processing apparatus 100 acquires the second size, for example. Specifically, the information processing apparatus 100 acquires the second size by receiving an input of the second size based on a user's operation input. The second size may be set by the user in advance, for example. The information processing apparatus 100 identifies, for example, for each of the plurality of qubits, one or more qubits included in the range of the second size with respect to the qubit as a reference.

[0030] The information processing apparatus 100 creates the first local circuit 111, for example, by extracting quantum gates related to the identified one or more qubits from the first quantum circuit 101 for each qubit. Also, the information processing apparatus 100 creates the second local circuit 112, for example, by extracting quantum gates related to the identified one or more qubits from the second quantum circuit 102 for each qubit.

[0031] Further, the information processing apparatus 100 creates, for example, a third local circuit 113 for each qubit by extracting quantum gates related to one or more specified qubits among the third quantum circuits 103. In this way, the information processing apparatus 100 creates, for example, a combination of the first local circuit 111, the second local circuit 112, and the third local circuit 113 for each qubit.

[0032] (1-3) The information processing apparatus 100 sets a cost function 130 that is defined by the created third local circuit 113, uses a plurality of parameters as explanatory variables, and represents the difference between the created first local circuit 111 and the second local circuit 112. The information processing apparatus 100 sets, for example, a cost function 130 that represents the difference between the first local circuit 111 and the second local circuit 112 in all of the created combinations.

[0033] The information processing apparatus 100 calculates solutions for the plurality of parameters so as to minimize the value of the set cost function 130 for each of the one or more quantum states defined by the third quantum circuit 103. The information processing apparatus 100 calculates solutions for the plurality of parameters, for example, by solving an optimization problem of minimizing the value of the set cost function 130 according to a predetermined optimization algorithm.

[0034] (1-4) The information processing apparatus 100 sets a new quantum circuit that represents the action of the time evolution operator based on the second quantum circuit 102 and the solutions for the plurality of calculated parameters. The information processing apparatus 100 sets, for example, the second quantum circuit 102 as a new quantum circuit that represents the action of the time evolution operator by setting the solutions for the plurality of calculated parameters to the quantum gates of the second quantum circuit 102.

[0035] As a result, the information processing apparatus 100 can set a quantum circuit that represents the action of the time evolution operator so that the number of quantum gates is reduced and the number of operations is reduced. For example, the information processing apparatus 100 can set a second quantum circuit 102 that represents the action of the time evolution operator so that the number of quantum gates is less and the number of operations is less than those of the first quantum circuit 101 created according to the Trotter decomposition method. Therefore, when the information processing apparatus 100 executes specific calculation processing such as quantum chemistry calculation or material physical property calculation by quantum simulation using a quantum circuit that represents the action of the time evolution operator, it can maintain the accuracy of the specific calculation processing.

[0036] For example, the information processing apparatus 100 can reduce the scale of the quantum circuit that represents the action of the time evolution operator, and can make it difficult for errors generated in the qubits to accumulate. For example, the information processing apparatus 100 can reduce the depth of the quantum circuit that represents the action of the time evolution operator, can reduce the calculation time in the quantum circuit, and can easily satisfy the coherence time limit. In this way, the information processing apparatus 100 can reduce the number of operations in the quantum circuit and can easily maintain the accuracy of specific calculation processing. Therefore, the information processing apparatus 100 can easily execute specific calculation processing even with a quantum computer on the order of several hundred qubits.

[0037] In addition, the information processing apparatus 100 can reduce the calculation cost required to create a quantum circuit that represents the action of the time evolution operator compared to LVQC. When simulating the long-time dynamics for any quantum state using a quantum circuit that represents the action of the time evolution operator, the information processing apparatus 100 can more easily maintain the simulation accuracy as time elapses compared to LVQC. A specific example of comparing the method for creating a quantum circuit that represents the action of the time evolution operator by the information processing apparatus 100 with LVQC will be described later with reference to FIG. 10.

[0038] Here, although the case where the functions of the information processing apparatus 100 are realized by a single computer has been described, it is not limited to this. For example, the functions of the information processing apparatus 100 may be realized by the cooperation of a plurality of computers. For example, the functions of the information processing apparatus 100 may be realized on the cloud.

[0039] In the following description, the method of creating a quantum circuit that represents the action of the time evolution operator by the information processing apparatus 100 may be denoted as "LSVQC (Local Subspace Variational Quantum Compilation)".

[0040] (An example of the information processing system 200) Next, an example of the information processing system 200 to which the information processing apparatus 100 shown in FIG. 1 is applied will be described with reference to FIG. 2.

[0041] FIG. 2 is an explanatory diagram showing an example of the information processing system 200. In FIG. 2, the information processing system 200 includes an information processing apparatus 100, a computing apparatus 201, and a client apparatus 202.

[0042] In the information processing system 200, the information processing apparatus 100 and the computing apparatus 201 are connected via a wired or wireless network 210. The network 210 is, for example, a LAN (Local Area Network), a WAN (Wide Area Network), the Internet, or the like. Also, in the information processing system 200, the information processing apparatus 100 and the client apparatus 202 are connected via a wired or wireless network 210.

[0043] The information processing apparatus 100 is a computer for creating a quantum circuit that represents a predetermined operation such as a time evolution operator so that the number of operations is reduced. The information processing apparatus 100 acquires, for example, a processing request that requests solving a target problem. The processing request includes, for example, information regarding the target problem. The processing request includes, for example, a definition of a plurality of qubits for representing a quantum state. Specifically, the information processing apparatus 100 acquires the processing request by receiving the processing request from another computer. The other computer is, for example, a client device 202 or the like. Specifically, the information processing apparatus 100 acquires the processing request by accepting an input of the processing request based on a user's operation input. In response to the processing request, the information processing apparatus 100 creates a quantum circuit that represents the action of the time evolution operator and is used when solving the target problem so that the number of operations is small and the number of quantum gates is small.

[0044] Specifically, the information processing apparatus 100 acquires a first quantum circuit, a second quantum circuit, and a third quantum circuit, each having a first size. Specifically, the information processing apparatus 100 creates a first local circuit, a second local circuit, and a third local circuit, each having a second size, by reducing the acquired first quantum circuit, second quantum circuit, and third quantum circuit to the second size, respectively. The information processing apparatus 100 calculates a solution of a plurality of parameters so as to minimize the value of a cost function that is defined by the created third local circuit, uses the plurality of parameters as explanatory variables, and represents the difference between the created first local circuit and the second local circuit. The information processing apparatus 100 sets a new quantum circuit that represents the action of the time evolution operator based on the second quantum circuit and the solution of the plurality of calculated parameters.

[0045] The information processing apparatus 100 cooperates with the computing device 201 and executes specific computational processing to solve a target problem based on a new quantum circuit that represents the action of a time-evolution operator. The information processing apparatus 100 controls the computing device 201, for example, so as to share all or part of the specific computational processing. Specifically, the information processing apparatus 100 controls the computing device 201 so as to share the quantum computation in the specific computational processing. Thereby, the information processing apparatus 100 can cooperate with the computing device 201, execute the specific computational processing, and solve the target problem.

[0046] The information processing apparatus 100 may output the result of solving the target problem. The information processing apparatus 100 transmits, for example, the result of solving the target problem to another computer. The other computer is, for example, the client device 202 or the like. The information processing apparatus 100 outputs, for example, the result of solving the target problem so that the user can refer to it. Thereby, the information processing apparatus 100 can make the result of solving the target problem available for external use. The information processing apparatus 100 is, for example, a server or a PC or the like.

[0047] The computing device 201 is a computer for executing quantum computation. The computing device 201 shares all or part of the specific computational processing according to the control of the information processing apparatus 100. The computing device 201 may be, for example, a classical computer that activates a quantum simulator. In this case, the computing device 201 is, for example, a server or a PC or the like. Also, the computing device 201 may be, for example, a physical quantum computer.

[0048] The client device 202 is a computer used by a user who desires to execute specific calculation processing. Based on the user's operation input, the client device 202 generates a processing request that requests to solve a target problem and transmits it to the information processing device 100. The client device 202 receives the result of solving the target problem from the information processing device 100. The client device 202 outputs the result of solving the target problem in a manner that can be referred to by the user. The client device 202 is, for example, a PC, a tablet terminal, or a smartphone, etc.

[0049] Here, the case where the information processing device 100 and the computing device 201 are different devices has been described, but it is not limited to this. For example, the information processing device 100 may have the function of the computing device 201 and may also operate as the computing device 201. Also, the case where the information processing device 100 and the client device 202 are different devices has been described, but it is not limited to this. For example, the information processing device 100 may have the function of the client device 202 and may also operate as the client device 202.

[0050] (Example of the hardware configuration of the information processing device 100) Next, with reference to FIG. 3, an example of the hardware configuration of the information processing device 100 will be described.

[0051] FIG. 3 is a block diagram showing an example of the hardware configuration of the information processing device 100. In FIG. 3, the information processing device 100 includes a CPU (Central Processing Unit) 301, a memory 302, a network I / F (Interface) 303, a recording medium I / F 304, and a recording medium 305. Also, each component is connected by a bus 300.

[0052] Here, the CPU 301 controls the entire information processing apparatus 100. The memory 302 has, for example, a ROM (Read Only Memory), a RAM (Random Access Memory), and a flash ROM. Specifically, for example, the flash ROM and the ROM store various programs, and the RAM is used as the work area of the CPU 301. The programs stored in the memory 302 are loaded into the CPU 301 to cause the CPU 301 to execute the coded processing.

[0053] The network I / F 303 is connected to the network 210 through a communication line and is connected to other computers via the network 210. Then, the network I / F 303 controls the interface between the network 210 and the inside and controls the input / output of data from other computers. The network I / F 303 is, for example, a modem or a LAN adapter.

[0054] The recording medium I / F 304 controls the read / write of data with respect to the recording medium 305 according to the control of the CPU 301. The recording medium I / F 304 is, for example, a disk drive, an SSD (Solid State Drive), a USB (Universal Serial Bus) port, or the like. The recording medium 305 is a non-volatile memory that stores the data written under the control of the recording medium I / F 304. The recording medium 305 is, for example, a disk, a semiconductor memory, a USB memory, or the like. The recording medium 305 may be detachable from the information processing apparatus 100.

[0055] In addition to the above-described components, the information processing apparatus 100 may have, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, or the like. Also, the information processing apparatus 100 may have a plurality of recording medium I / Fs 304 and recording media 305. Further, the information processing apparatus 100 may not have the recording medium I / F 304 and the recording medium 305.

[0056] (Hardware Configuration Example of the Computing Device 201) When the computing device 201 is a classical computer that activates a quantum simulator, the hardware configuration example of the computing device 201 is the same as the hardware configuration example of the information processing device 100 shown in FIG. 3, and thus the description thereof is omitted.

[0057] On the other hand, it is conceivable that the computing device 201 is an actual quantum computer. Here, with reference to FIG. 4, a hardware configuration example of the computing device 201 when the computing device 201 is an actual quantum computer will be described.

[0058] FIG. 4 is a block diagram showing a hardware configuration example of the computing device 201. In FIG. 4, the computing device 201 includes a CPU 401, a memory 402, a network I / F 403, a recording medium I / F 404, and a recording medium 405. The computing device 201 further includes an arithmetic unit I / F 406 and an arithmetic unit 407. Also, each component is connected by a bus 400.

[0059] Here, the CPU 401 controls the overall operation of the computing device 201. The memory 402 includes, for example, a ROM, a RAM, and a flash ROM. Specifically, for example, the flash ROM and the ROM store various programs, and the RAM is used as a work area for the CPU 401. The programs stored in the memory 402 are loaded into the CPU 401 to cause the CPU 401 to execute the coded processing.

[0060] The network I / F 403 is connected to the network 210 through a communication line and is connected to other computers via the network 210. Then, the network I / F 403 manages the interface with the network 210 and controls the input / output of data from / to other computers. The network I / F 403 is, for example, a modem or a LAN adapter.

[0061] The recording medium I / F 404 controls the read / write of data to / from the recording medium 405 according to the control of the CPU 401. The recording medium I / F 404 is, for example, a disk drive, an SSD, a USB port, etc. The recording medium 405 is a non-volatile memory that stores the data written under the control of the recording medium I / F 404. The recording medium 405 is, for example, a disk, a semiconductor memory, a USB memory, etc. The recording medium 405 may be detachable from the computing device 201.

[0062] The arithmetic unit I / F 406 controls the access to the arithmetic unit 407 according to the control of the CPU 401. The arithmetic unit I / F 406 uses a microwave pulse generator to convert the output signal from the CPU 401 into an input signal for the arithmetic unit 407 and transmits it to the arithmetic unit 407. The arithmetic unit I / F 406 uses a microwave pulse demodulator to convert the output signal from the arithmetic unit 407 into an input signal for the CPU 401 and transmits it to the CPU 401. The arithmetic unit 407 is an arithmetic device equipped with one or more quantum bit chips cooled to an extremely low temperature of 10 mK. The quantum bit chips represent, for example, logical quantum bits. The arithmetic unit 407 uses one or more quantum bit chips to perform a predetermined operation according to the input signal and outputs an output signal corresponding to the result of the predetermined operation.

[0063] In addition to the components described above, the computing device 201 may have, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, etc. Also, the computing device 201 may have a plurality of recording medium I / Fs 404 and recording media 405. Also, the computing device 201 may not have the recording medium I / F 404 and the recording medium 405. Also, the quantum bit chips in the arithmetic unit 407 may be controlled by a method other than microwaves. The quantum bit chips in the arithmetic unit 407 may realize, for example, optical quantum bits.

[0064] (Example of the hardware configuration of the client device 202) The hardware configuration example of the client device 202 is the same as the hardware configuration example of the information processing device 100 shown in FIG. 3, and thus the description thereof is omitted.

[0065] (Functional configuration example of the information processing device 100) Next, a functional configuration example of the information processing device 100 will be described with reference to FIG. 5.

[0066] FIG. 5 is a block diagram showing a functional configuration example of the information processing device 100. The information processing device 100 includes a storage unit 500, an acquisition unit 501, a creation unit 502, a reduction unit 503, a calculation unit 504, a setting unit 505, an arithmetic unit 506, and an output unit 507.

[0067] The storage unit 500 is realized by a storage area such as the memory 302 and the recording medium 305 shown in FIG. 3, for example. Hereinafter, the case where the storage unit 500 is included in the information processing device 100 will be described, but it is not limited thereto. For example, the storage unit 500 may be included in a device different from the information processing device 100, and the stored content of the storage unit 500 may be referable from the information processing device 100.

[0068] The acquisition unit 501 to the output unit 507 function as an example of a control unit. Specifically, the acquisition unit 501 to the output unit 507 realize their functions by causing the CPU 301 to execute a program stored in a storage area such as the memory 302 and the recording medium 305 shown in FIG. 3, or by the network I / F 303. The processing results of each functional unit are stored in a storage area such as the memory 302 and the recording medium 305 shown in FIG. 3, for example.

[0069] The storage unit 500 stores various information that is referred to or updated in the processing of each functional unit. The storage unit 500 stores, for example, information regarding a target problem. The target problem is a problem for performing a specific calculation process such as quantum chemical calculation or material physical property calculation, for example. The target problem includes, for example, a plurality of quantum bits for expressing a quantum state. The information regarding the target problem includes, for example, definitions of a plurality of quantum states regarding the target problem.

[0070] The memory unit 500 specifically includes the definitions of a plurality of qubits related to the target problem. The definitions include, for example, the indices of the qubits. The definitions include, for example, a first size. The first size represents the magnitude of the range including the entirety of the plurality of qubits. The magnitude of the range is defined by the number of qubits. Information related to the target problem is acquired, for example, by the acquisition unit 501 and stored by the memory unit 500.

[0071] The memory unit 500 stores, for example, a quantum circuit having a first size. A quantum circuit having a first size means a quantum circuit that performs operations on a plurality of qubits included in a range of the first size.

[0072] The memory unit 500 specifically stores a first quantum circuit having a first size. The first quantum circuit represents, for example, the action of the time evolution operator related to the target problem. The first quantum circuit is created, for example, by the creation unit 502 according to the Trotter decomposition method and stored by the memory unit 500. The first quantum circuit may be acquired, for example, by the acquisition unit 501 and stored by the memory unit 500. The first quantum circuit may be created in advance by the user and stored by the memory unit 500.

[0073] The memory unit 500 specifically stores a second quantum circuit having a first size. The second quantum circuit has, for example, fewer quantum gates than the first quantum circuit and has a plurality of parameters. The parameters are, for example, coefficients set for the quantum gates. The second quantum circuit is acquired, for example, by the acquisition unit 501 and stored by the memory unit 500. The second quantum circuit may be created in advance by the user and stored by the memory unit 500.

[0074] Specifically, the memory unit 500 stores a third quantum circuit having a first size. The third quantum circuit defines, for example, one or more quantum states that are part of a plurality of quantum states related to a target problem. The one or more quantum states are linearly independent and non-orthogonal to each other. The third quantum circuit is, for example, created in advance by a user. The third quantum circuit is, for example, acquired by the acquisition unit 501 and stored by the memory unit 500. The third quantum circuit may be, for example, created in advance by a user and stored by the memory unit 500.

[0075] The memory unit 500 stores, for example, a second size that is smaller than the first size. The second size is, for example, acquired by the acquisition unit 501 and stored by the memory unit 500. The second size may be, for example, specified in advance by a user and stored by the memory unit 500.

[0076] The memory unit 500 stores, for example, a quantum circuit having a second size. The second size represents the magnitude of a range that includes a part of a plurality of qubits related to a target problem. The magnitude of the range is defined by the number of qubits. The quantum circuit having a second size means a quantum circuit that performs operations on one or more qubits included in the range of the second size.

[0077] Specifically, the memory unit 500 stores a first local circuit having a second size. The first local circuit corresponds to the first quantum circuit. The first local circuit is created, for example, by reducing the first quantum circuit to the second size. The first local circuit is created, for example, by the reduction unit 503 and stored by the memory unit 500.

[0078] Specifically, the memory unit 500 stores a second local circuit having a second size. The second local circuit corresponds to the second quantum circuit. The second local circuit is created, for example, by reducing the second quantum circuit to the second size. The second local circuit is created, for example, by the reduction unit 503 and stored by the memory unit 500.

[0079] Specifically, the memory unit 500 stores a third local circuit that is of the second size. The third local circuit corresponds to a third quantum circuit. The third local circuit is created, for example, by reducing the third quantum circuit to the second size. The third local circuit is created, for example, by the reduction unit 503 and stored by the memory unit 500.

[0080] The acquisition unit 501 acquires various information used for the processing of each functional unit. The acquisition unit 501 stores the acquired various information in the memory unit 500 or outputs it to each functional unit. Further, the acquisition unit 501 may output the various information stored in the memory unit 500 to each functional unit. The acquisition unit 501 acquires various information, for example, based on a user's operation input. The acquisition unit 501 may receive various information from a device different from the information processing apparatus 100, for example.

[0081] The acquisition unit 501 acquires, for example, a processing request. The processing request requests to create a quantum circuit that represents the action of a time-evolution operator used when solving a target problem. The processing request may further request to solve the target problem, for example. The processing request includes information about the target problem, for example.

[0082] Specifically, the acquisition unit 501 acquires a processing request by receiving an input of the processing request. Specifically, the acquisition unit 501 may acquire it by receiving a processing request from another computer. The other computer is, for example, the client device 202 or the like. The acquisition unit 501 acquires it by extracting information about the target problem from the processing request.

[0083] The acquisition unit 501 acquires, for example, a first quantum circuit. Specifically, the acquisition unit 501 acquires the first quantum circuit by receiving an input of the first quantum circuit based on a user's operation input. Specifically, the acquisition unit 501 may acquire it by receiving the first quantum circuit from another computer. The other computer is, for example, the client device 202 or the like.

[0084] The acquisition unit 501 acquires, for example, a second quantum circuit. Specifically, the acquisition unit 501 acquires the second quantum circuit by receiving the input of the second quantum circuit based on the user's operation input. Specifically, the acquisition unit 501 may also acquire the second quantum circuit by receiving it from another computer. The other computer is, for example, the client device 202 or the like.

[0085] The acquisition unit 501 acquires, for example, a third quantum circuit. Specifically, the acquisition unit 501 acquires the third quantum circuit by receiving the input of the third quantum circuit based on the user's operation input. Specifically, the acquisition unit 501 may also acquire the third quantum circuit by receiving it from another computer. The other computer is, for example, the client device 202 or the like.

[0086] The acquisition unit 501 acquires, for example, a second size. Specifically, the acquisition unit 501 acquires the second size by receiving the input of the second size based on the user's operation input. Specifically, the acquisition unit 501 may also acquire the second size by receiving it from another computer. The other computer is, for example, the client device 202 or the like.

[0087] The acquisition unit 501 may receive a start trigger for starting the processing of any functional unit. The start trigger is, for example, that there has been a predetermined operation input by the user. The start trigger may be, for example, that predetermined information has been received from another computer. The start trigger may be, for example, that any functional unit has output predetermined information. The acquisition unit 501 may receive, for example, the fact that a processing request has been acquired as a start trigger for starting the processing of the creation unit 502, the reduction unit 503, the calculation unit 504, and the setting unit 505.

[0088] The creation unit 502 creates the first quantum circuit, for example, according to the Trotter decomposition method. The creation unit 502 creates the first quantum circuit, for example, when the acquisition unit 501 does not acquire the first quantum circuit, according to the Trotter decomposition method. Thereby, the creation unit 502 can create the first quantum circuit as a sample representing the action of the time evolution operator. The creation unit 502 can obtain the first quantum circuit that serves as a guideline for determining how to set a plurality of parameters so that the second quantum circuit represents the action of the time evolution operator.

[0089] The reduction unit 503 creates the first local circuit, the second local circuit, and the third local circuit, each of which has the second size, by reducing the first quantum circuit, the second quantum circuit, and the third quantum circuit to the second size, respectively. The reduction unit 503 reduces the first quantum circuit, the second quantum circuit, and the third quantum circuit to the second size, which is a predetermined range based on each quantum bit, for each quantum bit of the plurality of quantum bits, for example.

[0090] Specifically, the reduction unit 503 identifies one or more quantum bits included in the range of the second size based on each quantum bit for each quantum bit of the plurality of quantum bits. Specifically, the reduction unit 503 creates the first local circuit by extracting the quantum gates related to the identified one or more quantum bits from the first quantum circuit for each quantum bit. Specifically, the reduction unit 503 creates the second local circuit by extracting the quantum gates related to the identified one or more quantum bits from the second quantum circuit for each quantum bit.

[0091] Specifically, the reduction unit 503 creates a third local circuit by extracting quantum gates related to one or more specified qubits from the third quantum circuit for each qubit. In this way, specifically, the reduction unit 503 creates a combination of the first local circuit, the second local circuit, and the third local circuit for each qubit. Thereby, the reduction unit 503 can obtain information for defining a subsystem cost function in order to substantially optimize a total system cost function representing the difference between the first quantum circuit and the second quantum circuit.

[0092] Moreover, it is conceivable that the first quantum circuit, the second quantum circuit, and the third quantum circuit each have translational symmetry. In this case, the reduction unit 503 may, for example, reduce the first quantum circuit, the second quantum circuit, and the third quantum circuit to a second size that is a predetermined range based on any one of the plurality of qubits. Any one qubit is one qubit selected as a representative in consideration of translational symmetry.

[0093] In this way, specifically, the reduction unit 503 creates a combination of the first local circuit, the second local circuit, and the third local circuit for one qubit selected as a representative. Thereby, the reduction unit 503 can obtain information for defining a subsystem cost function in order to substantially optimize a total system cost function representing the difference between the first quantum circuit and the second quantum circuit. Also, the reduction unit 503 can reduce the processing load involved in reduction by utilizing translational symmetry.

[0094] The calculation unit 504 defines a subsystem cost function that is defined by the third local circuit created by the reduction unit 503, uses a plurality of parameters as explanatory variables, and represents the difference between the first local circuit and the second local circuit created by the reduction unit 503. Specifically, the subsystem cost function is defined by the local fidelity measured for the third local circuit. The calculation unit 504 sets, for example, a subsystem cost function that represents the difference between the first local circuit and the second local circuit in all combinations created by the reduction unit 503. Thereby, the calculation unit 504 can obtain a guideline for calculating the solutions of a plurality of parameters so that the second quantum circuit represents the action of the time evolution operator in the same manner as the first quantum circuit.

[0095] The calculation unit 504 calculates the solutions of a plurality of parameters so as to minimize the value of the set subsystem cost function for each quantum state of one or more quantum states defined by the third quantum circuit. The calculation unit 504 calculates the solutions of a plurality of parameters, for example, by solving an optimization problem of minimizing the value of the set subsystem cost function according to a predetermined optimization algorithm. Thereby, the calculation unit 504 can calculate the solutions of a plurality of parameters so that the second quantum circuit represents the action of the time evolution operator in the same manner as the first quantum circuit.

[0096] The setting unit 505 sets a new quantum circuit that represents the action of the time evolution operator based on the second quantum circuit and the solutions of a plurality of parameters calculated by the calculation unit 504. The setting unit 505 sets, for example, the second quantum circuit as a new quantum circuit that represents the action of the time evolution operator by setting the solutions of a plurality of parameters calculated by the calculation unit 504 to the quantum gates of the second quantum circuit. Thereby, the setting unit 505 can obtain a new quantum circuit that has fewer quantum gates than the first quantum circuit and represents the action of the time evolution operator so that the number of operation times is reduced.

[0097] The calculation unit 506 may obtain the solution to the target problem by solving the target problem using the new quantum circuit that expresses the action of the time evolution operator set by the setting unit 505. Thereby, the calculation unit 506 can solve the target problem and execute specific calculation processes such as quantum chemistry calculations or material property calculations.

[0098] The output unit 507 outputs the processing results of at least any one of the functional units. The output format is, for example, display on a display, print output to a printer, transmission to an external device via the network I / F 303, or storage in a storage area such as the memory 302 or the recording medium 305. Thereby, the output unit 507 can notify the user of the processing results of at least any one of the functional units and improve the convenience of the information processing apparatus 100.

[0099] The output unit 507 outputs, for example, the new quantum circuit that expresses the action of the time evolution operator set by the setting unit 505. Specifically, the output unit 507 transmits the new quantum circuit to another computer. The other computer is, for example, the computing device 201 or the client device 202. Specifically, the output unit 507 outputs the new quantum circuit so that the user can refer to it. Thereby, the output unit 507 can enable the solution of the target problem externally and enable the execution of specific calculation processes such as quantum chemistry calculations or material property calculations.

[0100] The output unit 507 may output, for example, the result of solving the target problem by the calculation unit 506. Specifically, the output unit 507 transmits the result of solving the target problem to another computer. The other computer is, for example, the client device 202. Specifically, the output unit 507 outputs the result of solving the target problem so that the user can refer to it. Thereby, the output unit 507 can make the result of solving the target problem available externally.

[0101] Here, the case where the information processing apparatus 100 sets a quantum circuit that represents the action of the time evolution operator so as to reduce the number of operations has been described, but it is not limited to this. For example, there may be a case where the information processing apparatus 100 sets a quantum circuit that represents a predetermined action not limited to the time evolution operator so as to reduce the number of operations. The processing contents of each functional unit in the case where the information processing apparatus 100 sets a quantum circuit that represents a predetermined action are shown below.

[0102] The acquisition unit 501 acquires, for example, a processing request for creating a quantum circuit that represents a predetermined action. The predetermined action is, for example, related to the target problem. The predetermined action may be the action of the time evolution operator. The processing request may, for example, further request to solve the target problem. The processing request includes, for example, information related to the target problem.

[0103] Specifically, the storage unit 500 stores a fourth quantum circuit having a first size. The fourth quantum circuit represents, for example, a predetermined action. The fourth quantum circuit is created by, for example, the creation unit 502 and stored by the storage unit 500. The fourth quantum circuit may be acquired by the acquisition unit 501 and stored by the storage unit 500. The fourth quantum circuit may be created by the user in advance and stored by the storage unit 500.

[0104] Specifically, the storage unit 500 stores a fifth quantum circuit having a first size. The fifth quantum circuit has, for example, fewer quantum gates than the fourth quantum circuit and has a plurality of parameters. The fifth quantum circuit is acquired by the acquisition unit 501 and stored by the storage unit 500. The fifth quantum circuit may be created by the user in advance and stored by the storage unit 500.

[0105] The memory unit 500 stores, for example, a group of basis vectors. The group of basis vectors is a collection of basis vectors that define each of two or more quantum states, which are part of a plurality of quantum states related to a target problem. The two or more quantum states are linearly independent and non-orthogonal to each other. The group of basis vectors is obtained, for example, by the acquisition unit 501 and stored by the memory unit 500. The group of basis vectors may be created in advance by the user and stored by the memory unit 500.

[0106] The acquisition unit 501 acquires, for example, a fourth quantum circuit. Specifically, the acquisition unit 501 acquires the fourth quantum circuit by receiving the input of the fourth quantum circuit based on the user's operation input. Specifically, the acquisition unit 501 may also acquire the fourth quantum circuit by receiving it from another computer. The other computer is, for example, the client device 202 or the like.

[0107] The acquisition unit 501 acquires, for example, a fifth quantum circuit. Specifically, the acquisition unit 501 acquires the fifth quantum circuit by receiving the input of the fifth quantum circuit based on the user's operation input. Specifically, the acquisition unit 501 may also acquire the fifth quantum circuit by receiving it from another computer. The other computer is, for example, the client device 202 or the like.

[0108] The acquisition unit 501 acquires, for example, a group of basis vectors. Specifically, the acquisition unit 501 acquires the group of basis vectors by receiving the input of the group of basis vectors based on the user's operation input. Specifically, the acquisition unit 501 may also acquire the group of basis vectors by receiving it from another computer. The other computer is, for example, the client device 202 or the like.

[0109] The calculation unit 504 defines a total system cost function that is defined by the basis vector group acquired by the acquisition unit 501, uses a plurality of parameters as explanatory variables, and represents the difference between the fourth quantum circuit and the fifth quantum circuit acquired by the acquisition unit 501. Specifically, the total system cost function is defined by the fidelity with respect to two or more quantum states calculated based on the basis vector group. Thereby, the calculation unit 504 can obtain a guideline for calculating the solutions of a plurality of parameters so that the fifth quantum circuit expresses a predetermined operation in the same manner as the fourth quantum circuit.

[0110] The calculation unit 504 calculates the solutions of a plurality of parameters so as to minimize the value of the set total system cost function for each quantum state of two or more quantum states defined by the basis vector group. The calculation unit 504 calculates the solutions of a plurality of parameters, for example, by solving an optimization problem of minimizing the value of the set total system cost function according to a predetermined optimization algorithm. Thereby, the calculation unit 504 can calculate the solutions of a plurality of parameters so that the fifth quantum circuit expresses a predetermined operation in the same manner as the fourth quantum circuit.

[0111] The setting unit 505 sets a new quantum circuit that expresses a predetermined operation based on the fifth quantum circuit and the solutions of a plurality of parameters calculated by the calculation unit 504. For example, the setting unit 505 sets the fifth quantum circuit as a new quantum circuit that expresses a predetermined operation by setting the solutions of a plurality of parameters calculated by the calculation unit 504 in the quantum gates of the fifth quantum circuit. Thereby, the setting unit 505 can obtain a new quantum circuit that has fewer quantum gates than the fourth quantum circuit and expresses a predetermined operation so that the number of calculation operations is reduced.

[0112] The operation unit 506 may obtain the solution of the target problem by solving the target problem using the new quantum circuit that expresses the predetermined operation set by the setting unit 505. Thereby, the operation unit 506 can solve the target problem and execute specific calculation processes such as quantum chemistry calculations or material property calculations.

[0113] The output unit 507 outputs, for example, a new quantum circuit that represents a predetermined operation set by the setting unit 505. Specifically, the output unit 507 transmits the new quantum circuit to another computer. The other computer is, for example, the computing device 201 or the client device 202. Specifically, the output unit 507 outputs the new quantum circuit so that the user can refer to it. Thereby, the output unit 507 can make the quantum circuit representing the predetermined operation available externally.

[0114] The output unit 507 may output, for example, the result of solving the target problem by the operation unit 506. Specifically, the output unit 507 transmits the result of solving the target problem to another computer. The other computer is, for example, the client device 202. Specifically, the output unit 507 outputs the result of solving the target problem so that the user can refer to it. Thereby, the output unit 507 can make the result of solving the target problem available externally.

[0115] Hereinafter, a specific example in which the information processing apparatus 100 sets a quantum circuit that represents the action of the time evolution operator so that the number of operations is reduced will be described as Example 1 with reference to FIGS. 6 to 13. Further, a specific example in which the information processing apparatus 100 sets a quantum circuit that represents a predetermined operation not limited to the time evolution operator so that the number of operations is reduced will be described as Example 2 with reference to FIGS. 14 to 22.

[0116] (Example 1) Next, Example 1 will be described with reference to FIGS. 6 to 10. Example 1 represents a specific example in which the information processing apparatus 100 sets a quantum circuit that represents the action of the time evolution operator so that the number of operations is reduced. FIGS. 6 to 10 are explanatory diagrams showing Example 1.

[0117] Specifically, first, with reference to FIG. 6, an example of the operation in Example 1 performed by the information processing apparatus 100 will be described. In FIG. 6, there exists an entire quantum system 600 of size L regarding the target problem. In the following description, a symbol with a tilde (~) above a character may be denoted as "(character)~". For example, a symbol with a tilde (~) above L may be denoted as "L~". In the following description, any character with a superscript may be denoted as "any character^superscript". In the following description, any character with a subscript may be denoted as "any character_subscript".

[0118] The information processing apparatus 100 acquires a compilation size L~ (≦L). The information processing apparatus 100 identifies a subspace 631 including one or more quantum states among all state spaces 630 regarding the target problem. The information processing apparatus 100 performs an optimization calculation on a quantum circuit 610 that represents the action of the time evolution operator on the subspace 631 in a partial quantum system 601 of size L~. As a result, the information processing apparatus 100 can implement a quantum circuit 620 that represents the action of the time evolution operator on the subspace 631 in the entire quantum system 600.

[0119] Here, considering the physical properties of molecules, etc., in some cases, the accuracy of specific calculation processes such as quantum chemical calculations or material property calculations can be maintained by examining at least some of the quantum states without examining all of them. Specifically, in some cases, the accuracy of quantum chemical calculations or material property calculations can be maintained by examining quantum states with relatively low energy without examining quantum states with relatively high energy. Therefore, if the information processing apparatus 100 implements a quantum circuit 620 that represents the action of the time evolution operator on the subspace 631 in the entire quantum system 600, the accuracy of quantum chemical calculations or material property calculations can be maintained.

[0120] In the following description, it is specifically shown how the information processing apparatus 100 implements a quantum circuit 620 that represents the action of the time evolution operator on the subspace 631 in the overall quantum system 600. In the following description, the D_S - dimensional subspace 631 may be denoted as "subspace S".

[0121] Here, it is assumed that there exists an approximate quantum circuit U^(L) for the D_S - dimensional subspace S = span(|ψ_1〉, ···, |ψ_(D_S)〉) in the overall quantum system 600 of size L. U^(L) is an approximation of the time evolution operator e^(-itH).

[0122] Also, it is assumed that there exists a variational quantum circuit V^(L)(θ) with parameter θ for the D_S - dimensional subspace S = span(|ψ_1〉, ···, |ψ_(D_S)〉) in the overall quantum system 600 of size L. The total - system cost function C_S^(L)(θ) representing the difference between the approximate quantum circuit U^(L) and the variational quantum circuit V^(L)(θ) is defined by the following formula (1) and the following formula (2). The following formula (1) includes the projection measurement operator for the j - th qubit. tr[] represents the trace operation. The basis {|ψ_s〉} spanning the subspace S is a set of linearly independent and non - orthogonal quantum states. Each element |ψ_s〉 is defined by the following formula (3) using the state preparation circuit W_s^(L).

[0123]

Number

[0124]

Number

[0125]

Number

[0126] The fact that the overall system cost function \(C_S^{(L)}(\theta)\) is 0 is a necessary and sufficient condition for the actions of \(U^{(L)}\) and \(V^{(L)}(\theta)\) to coincide for any state belonging to the subspace \(S\). In other words, the following equation (4) is a necessary and sufficient condition for the following equation (5).

[0127]

Number

[0128]

Number

[0129] Therefore, it is desirable for the information processing apparatus 100 to calculate the parameter \(\theta\) that defines \(V^{(L)}(\theta)\) whose action of the time-evolution operator coincides with \(U^{(L)}\) by minimizing the overall system cost function \(C_S^{(L)}(\theta)\). Here, as \(L\) increases, it tends to be more difficult to solve the optimization problem of directly minimizing the overall system cost function \(C_S^{(L)}(\theta)\). For this reason, in order to substantially minimize the overall system cost function \(C_S^{(L)}(\theta)\), it is conceivable to minimize the subsystem cost function \(\widetilde{C}_S^{(\widetilde{L})}(\theta)\) for the partial quantum system 601 of size \(\widetilde{L}(\leq L)\). The subsystem cost function \(\widetilde{C}_S^{(\widetilde{L})}(\theta)\) is defined by the following equations (6) and (7).

[0130]

Number

[0131]

Number

[0132] By the local compilation theorem, minimizing the subsystem cost function \(C_{\widetilde{S}}^{(\widetilde{L})}(\theta)\) can indirectly minimize the overall system cost function \(C_{S}^{(L)}(\theta)\). \(U^{(\widetilde{L},j)}, V^{(\widetilde{L},j)}(\theta), \{W_s^{(\widetilde{L},j)}\}\) are quantum circuits obtained by performing localization processing on \(U^{(L)}, V^{(L)}(\theta), \{W_s^{(L)}\}\) centered around site \(j\), respectively. An example of the localization processing will be described later with reference to Fig. 7.

[0133] Here, the local compilation theorem will be explained. For example, when implementing the time-evolution operator \(e^{-itH}\) of the overall quantum system Hamiltonian \(H\) of size \(L\) on a quantum circuit, if the Lieb-Robinson bound exists, the interaction of \(H\) is local, and the variational quantum circuit \(V^{(L)}(\theta)\) and the state preparation circuit \(\{W_s^{(L)}\}\) have a local quantum circuit structure, the following equation (8) holds. \(\varepsilon\) and \(\varepsilon_{LR}\) represent values close to 0. Also, the lower bound of \(\widetilde{L}\) is defined by the following equation (9).

[0134]

Equation

[0135]

Equation

[0136] Here, \(c\) is a constant of \(O(1)\). \(d_V\) is the depth of the variational quantum circuit \(V^{(L)}(\theta)\). \(d_W\) is the maximum depth of the state preparation circuit \(\{W_s^{(L)}\}\). Also, \(\varepsilon_{LR}\) is the error derived from the Lieb-Robinson bound. If \(\widetilde{L}\) is sufficiently large, \(\varepsilon_{LR}=\exp[-O(\widetilde{L})]\) and asymptotically approaches 0. Equation (8) above shows that minimizing the subsystem cost function \(C_{\widetilde{S}}^{(\widetilde{L})}(\theta)\) of size \(\widetilde{L}\) can indirectly minimize the overall system cost function \(C_{S}^{(L)}(\theta)\) of size \(L\).

[0137] Next, localization processing will be described with reference to FIG. 7. U^(L~,j), V^(L~,j)(θ), {W_s^(L~.j)} are obtained by performing localization processing on U^(L), V^(L)(θ), {W_s^(L)} centered around site j, respectively. Specifically, the localization processing is to create a local quantum circuit of size L~ by leaving only the quantum gates that operate on the qubits existing in the range 701 of size L~ centered around site j among the quantum circuits 700 of size L. Site j is the j-th qubit.

[0138] Next, a measurement method for measuring the value of the subsystem cost function C~_S^(L~)(θ) will be described with reference to FIG. 8. Specifically, the value of the subsystem cost function C~_S^(L~)(θ) is defined by the following formula (10) based on the local fidelity. The local fidelity is the term of tr[].

[0139]

Equation

[0140] Specifically, the local fidelity is obtained by measuring the quantum circuit 800 of size L~ by performing the LLET (Local Loschmidt Echo Test). The quantum circuit 800 includes the quantum gate 801 corresponding to {W_s^(L~.j)}. The quantum circuit 800 includes the quantum gate 802 corresponding to U^(L~,j). The quantum circuit 800 includes the quantum gate 803 corresponding to V^(L~,j). The quantum circuit 800 includes the quantum gate 804 corresponding to {W_s^((L~.j)†)}. The quantum circuit 800 includes the measurement unit 805. Specifically, since there are L×D_S independent components of the local fidelity, L×D_S LLETs will be performed per shot.

[0141] On the other hand, when each of U^(L), V^(L)(θ), and {W_s^(L)} has translational symmetry, there is no dependence of the local fidelity on site j. Therefore, in this case, the subsystem cost function C~_S^(L~)(θ) may be defined by the following equation (11).

[0142]

Number

[0143] Also, if the subsystem cost function C~_S^(L~)(θ) is defined by the above equation (11), the value of the subsystem cost function C~_S^(L~)(θ) can be measured by performing D_S times of LLET per shot. Therefore, if the subsystem cost function C~_S^(L~)(θ) is defined by the above equation (11), it is possible to reduce the processing burden involved in measuring the value of the subsystem cost function C~_S^(L~)(θ).

[0144] Next, with reference to FIG. 9, an example of applying LSVQC by the information processing apparatus 100 to the quantum simulation of the one-dimensional Fermi-Hubbard model 900 will be described. The Hamiltonian H corresponding to the one-dimensional Fermi-Hubbard model 900 is defined by the following equation (12) and the following equation (13). The following equation (12) represents, for example, electron hopping or electron repulsion. Here, c_iσ (c_iσ^†) is the annihilation (creation) operator for the electron at site i and spin σ. U is the electron correlation parameter. t is the hopping parameter.

[0145]

Number

[0146]

Number

[0147] In the following description, it is assumed that the information processing apparatus 100 calculates the dynamics of the spin density of the one-dimensional Fermi-Hubbard model 900. The expected value of the spin density at site j and time τ is defined by the following equations (14) and (15).

[0148]

Number

[0149]

Number

[0150] When calculating the spin density, it is sufficient to be able to represent the action of the time evolution operator on the subspace S spanned by the input state |ψ_0〉 and e^(-iHτ)|ψ_0〉 obtained by time-evolving the input state |ψ_0〉. Therefore, the information processing apparatus 100 will execute LSVQC on the Krylov subspace S defined by the following equation (16). The dimension N_k is preferably the maximum dimension for which linear independence is maintained. W is an approximate quantum circuit of the time evolution operator at time τ_K, defined by the following equation (17).

[0151]

Number

[0152]

Number

[0153] For the input state |ψ_0〉, for example, a Gaussian-type localized state is selected. The Gaussian-type localized state |ψ_0〉 can be efficiently prepared on a quantum computer by a local quantum circuit. The local quantum circuit is, for example, a Givens network circuit. Therefore, the application condition of LSVQC that the state preparation circuit {W_s^(L)} is a local quantum circuit is satisfied.

[0154] Specifically, the information processing apparatus 100 sets the time evolution operator \(e^{-iH\tau}\) of the \(L\)-site Fermi-Hubbard model 900 as the target quantum circuit \(U^{(L)}\) according to the Trotter decomposition method with a depth of 100. Specifically, the information processing apparatus 100 sets the VHA (Variational Hamiltonian Ansatz) as the variational quantum circuit \(V^{(L)}(\theta)\). The VHA is defined by the following equation (18). The Hamiltonian \(H\) is defined by the following equation (19).

[0155]

Number

[0156]

Number

[0157] Based on the set target quantum circuit \(U^{(L)}\) and the set variational quantum circuit \(V^{(L)}(\theta)\), the information processing apparatus 100 calculates the parameter \(\theta\) that represents the action of the time evolution operator. For example, the information processing apparatus 100 performs a localization process on the target quantum circuit \(U^{(L)}\), the variational quantum circuit \(V^{(L)}(\theta)\), and the state preparation circuit \(\{W_s^{(L)}\}(s = 1\sim D_S)\) with respect to sites \(j = 1\sim L\) as a reference. Thereby, the information processing apparatus 100 generates local quantum circuits \(U^{(L\sim,j)},V^{(L\sim,j)}(\theta),\{W_s^{(L\sim,j)}\}(j = 1\sim L)\).

[0158] The information processing apparatus 100 measures the local fidelity of the subsystem state set \(\{W_s^{(L\sim,j)}|0\rangle\}\) for \(j = 1\sim L\) and \(s = 1\sim D_S\) by LLET. Based on the measurement result, the information processing apparatus 100 calculates the value of the subsystem cost function \(C_S^{(L\sim)}(\theta)\). If the value of the subsystem cost function \(C_S^{(L\sim)}(\theta)\) has not converged, the information processing apparatus 100 updates the parameter \(\theta\), measures the local fidelity by LLET again, and calculates the value of the subsystem cost function \(C_S^{(L\sim)}(\theta)\).

[0159] If the value of the partial system cost function \(C_S^{(L)}(\theta)\) has converged, the information processing apparatus 100 sets the parameter \(\theta\) to the optimal parameter \(\theta_{opt}\). The information processing apparatus 100 implements the variational quantum circuit \(V^{(L)}(\theta)\) with the set optimal parameter \(\theta_{opt}\) as a quantum circuit representing the action of the time evolution operator on the entire system of size \(L\). Thereby, the information processing apparatus 100 can implement the VHA, which is a quantum circuit representing the action of the time evolution operator on the entire system of size \(L\) so that the number of operations is reduced.

[0160] Next, an example of the effect by the information processing apparatus 100 will be described with reference to FIG. 10. Assume that the information processing apparatus 100 implements the VHA by LSVQC. Here, the results of simulating the dynamics of the input state \(|\psi_0\rangle\) are compared for each of the VHA implemented by LSVQC, the VHA implemented by LVQC, and the quantum circuit implemented by the Trotter decomposition method. Assume that the lattice size is \(L = 4\) corresponding to 8 qubits. Assume that the time parameter is \(\tau=0.1\). Assume that the compilation sizes of LVQC and LSVQC are \(L' = 2\) corresponding to 4 qubits. Assume that the VHA has a depth of 5.

[0161] Graph 1000 shows the change in the cumulative absolute value error of the spin density expectation value with respect to the time step. The cumulative absolute value error is defined, for example, by the following formula (20).

[0162]

Equation

[0163] As shown in Graph 1000, LSVQC can ensure simulation accuracy comparable to that of LVQC. Also, LSVQC can ensure simulation accuracy comparable to that of the Trotter decomposition method with a depth of 100. Further, LSVQC can reduce the depth of the quantum circuit to 5 / 100 = 1 / 20 compared to the Trotter decomposition method with a depth of 100.

[0164] Also, when the number of time steps increases, the simulation accuracy of LVQC deteriorates more than that of the Trotter decomposition method with a depth of 5. On the other hand, even when the number of time steps increases, LSVQC can suppress the deterioration of simulation accuracy more than LVQC. Also, even when the number of time steps increases, LSVQC can ensure simulation accuracy comparable to that of the Trotter decomposition method with a depth of 30. LSVQC can reduce the depth of the quantum circuit to 5 / 30 = 1 / 6 compared to the Trotter decomposition method with a depth of 30.

[0165] As a result, LSVQC can maintain the simulation accuracy of the long-time dynamics of the input state |ψ_0〉 while reducing the depth of the quantum circuit compared to the Trotter decomposition method. Since LSVQC can make the cost function measurable by local gate operations compared to LVQC, it can be easily implemented.

[0166] In this way, the information processing apparatus 100 can obtain a quantum circuit that represents the action of the time-evolution operator and enables efficient execution of quantum simulation by LSVQC. The information processing apparatus 100 can reduce the number of quantum gates and the depth of the quantum circuit prepared for quantum simulation by LSVQC. For example, the information processing apparatus 100 can reduce the depth of the quantum circuit prepared for executing the dynamics calculation of the Fermi-Hubbard model 900 to about 1 / 20 compared to the Trotter decomposition method. Also, the information processing apparatus 100 can simulate dynamics with high accuracy over a longer time range than LVQC.

[0167] (Overall processing procedure in Example 1) Next, an example of the overall processing procedure in Example 1 executed by the information processing apparatus 100 will be described with reference to FIG. 11. The overall processing is realized, for example, by the CPU 301 shown in FIG. 3, a storage area such as the memory 302 and the recording medium 305, and the network I / F 303.

[0168] Figure 11 is a flowchart showing an example of the overall processing procedure in Example 1. In Figure 11, the information processing apparatus 100 acquires a target quantum circuit U^(L), a variational quantum circuit V^(L)(θ), a state preparation circuit {W_s^(L)}(s = 1 to D_S), and a compilation size L~(≦L) (step S1101).

[0169] The information processing apparatus 100 sets 1 to j (step S1102).

[0170] The information processing apparatus 100 performs a localization process on the target quantum circuit U^(L), the variational quantum circuit V^(L)(θ), and the state preparation circuit {W_s^(L)}(s = 1 to D_S) with respect to site j (step S1103). As a result, the information processing apparatus 100 can generate local quantum circuits U^(L~,j), V^(L~,j)(θ), {W_s^(L~,j)}(j = 1 to L).

[0171] The information processing apparatus 100 determines whether j≥L (step S1104). Here, if j≥L is not satisfied (step S1104: No), the information processing apparatus 100 proceeds to the process of step S1105. On the other hand, if j≥L is satisfied (step S1104: Yes), the information processing apparatus 100 proceeds to the process of step S1106.

[0172] In step S1105, the information processing apparatus 100 increments j (step S1105). The information processing apparatus 100 returns to the process of step S1103.

[0173] In step S1106, the information processing apparatus 100 selects any combination from all combinations of j = 1 to L and s = 1 to D_S (step S1106).

[0174] For the selected combination, the information processing apparatus 100 measures the local fidelity for the subsystem state set {|W_s^(L~,j)〉} by means of LLET (step S1107).

[0175] The information processing apparatus 100 determines whether all combinations have been selected (step S1108). Here, if any combination has not been selected (step S1108: No), the information processing apparatus 100 proceeds to the process of step S1109. On the other hand, if all combinations have been selected (step S1108: Yes), the information processing apparatus 100 proceeds to the process of step S1110.

[0176] In step S1109, the information processing apparatus 100 selects another combination (step S1109). The information processing apparatus 100 returns to the process of step S1107.

[0177] In step S1110, the information processing apparatus 100 calculates the value of the subsystem cost function C~_S^(L~)(θ) based on the measurement results (step S1110).

[0178] The information processing apparatus 100 determines whether the value of the subsystem cost function C~_S^(L~)(θ) has converged (step S1111). Here, if the value of the subsystem cost function C~_S^(L~)(θ) has not converged (step S1111: No), the information processing apparatus 100 proceeds to the process of step S1112. On the other hand, if the value of the subsystem cost function C~_S^(L~)(θ) has converged (step S1111: Yes), the information processing apparatus 100 sets the parameter θ to the optimal parameter θ_opt and proceeds to the process of step S1113.

[0179] In step S1112, the information processing apparatus 100 updates the parameter θ (step S1112). The information processing apparatus 100 returns to the process of step S1106.

[0180] In step S1113, the information processing apparatus 100 implements a quantum circuit that represents the action of the time evolution operator for the entire system of size L based on the optimal parameter θ_opt (step S1113). The information processing apparatus 100 ends the overall processing.

[0181] (Localization processing procedure in Example 1) Next, with reference to FIG. 12, an example of the localization processing procedure in Example 1 executed by the information processing apparatus 100 will be described. The localization processing is realized, for example, by the CPU 301 shown in FIG. 3, a storage area such as the memory 302 and the recording medium 305, and the network I / F 303.

[0182] FIG. 12 is a flowchart showing an example of the localization processing procedure in Example 1. In FIG. 12, the information processing apparatus 100 acquires a quantum circuit Q^(L) of size L and a compilation size L~(≦L) (step S1201).

[0183] The information processing apparatus 100 determines whether Q^(L) is local (step S1202). Here, when Q^(L) is not local (step S1202: No), the information processing apparatus 100 proceeds to the process of step S1203. On the other hand, when Q^(L) is local (step S1202: Yes), the information processing apparatus 100 proceeds to the process of step S1204.

[0184] In step S1203, the information processing apparatus 100 reselects Q^(L) (step S1203). The information processing apparatus 100 returns to the process of step S1202.

[0185] In step S1204, the information processing apparatus 100 sets 1 to j (step S1204).

[0186] The information processing apparatus 100 identifies quantum gates applied to one or more qubits existing in the range of size L~ centered on the j-th qubit among the quantum circuits Q^(L) of size L (step S1205). The information processing apparatus 100 creates a quantum circuit Q^(L~,j) of size L~ including the identified quantum gates (step S1206).

[0187] The information processing apparatus 100 determines whether j≥L (step S1207). Here, if j≥L is not satisfied (step S1207: No), the information processing apparatus 100 proceeds to the process of step S1208. On the other hand, if j≥L is satisfied (step S1207: Yes), the information processing apparatus 100 proceeds to the process of step S1209.

[0188] In step S1208, the information processing apparatus 100 increments j (step S1208). The information processing apparatus 100 returns to the process of step S1205.

[0189] In step S1209, the information processing apparatus 100 implements the quantum circuit Q^(L~,j) of size L~ (step S1209). The information processing apparatus 100 terminates the localization process.

[0190] (Example 2) Next, Example 2 will be described with reference to FIGS. 13 to 20. Example 2 represents a specific example in which the information processing apparatus 100 sets a quantum circuit that represents a predetermined operation so as to reduce the number of operations. FIGS. 13 to 20 are explanatory diagrams showing Example 2.

[0191] Conventionally, as a method for creating a quantum circuit that represents a predetermined operation, there is VQC (Variational Quantum Compiling). Specifically, for VQC, there are the FUMC (Full Unitary Matrix Compiling) method and the FISC (Fixed Input State Compiling) method.

[0192] The FUMC method is a method that minimizes the cost function so that the actions of the target quantum circuit U and the variational quantum circuit V(θ) are the same for all quantum states belonging to the entire state space. The FISC method is a method that minimizes the cost function so that the actions of the target quantum circuit U and the variational quantum circuit V(θ) are the same for a specific quantum state. For example, for FISC, reference 2 below can be referred to.

[0193] Reference 2: Gibbs, Joe, et al. “Long-time simulations for fixed input states on quantum hardware.” npj Quantum Information 8.1 (2022): 135.

[0194] Here, considering the physical properties of molecules, etc., it may be possible to maintain the accuracy of a specific calculation process by examining at least two or more quantum states that are part of the entire state space without examining all quantum states. Therefore, a new method is desired that minimizes the cost function so that the actions of the target quantum circuit U and the variational quantum circuit V(θ) are the same for at least two or more quantum states that are part of the entire state space. Here, we move on to the explanation of FIG. 13.

[0195] In FIG. 13, the information processing device 100 specifically minimizes the cost function so that the actions of the target quantum circuit 1310(U) and the variational quantum circuit 1320(V(θ)) are the same for a partial space 1301 that includes two or more quantum states in the entire state space 1300. The target quantum circuit U represents, for example, a predetermined action.

[0196] Specifically, for the quantum state |ψ〉 belonging to the subspace 1301, the variational quantum circuit V(θ) approximates the target quantum circuit U. On the other hand, for the quantum state |φ〉 not belonging to the subspace 1301, the variational quantum circuit V(θ) does not approximate the target quantum circuit U. Thereby, the information processing apparatus 100 can update the variational quantum circuit V(θ) to become a quantum circuit representing a predetermined operation, and can create a quantum circuit representing a predetermined operation.

[0197] In the following description, the method for creating a quantum circuit representing a predetermined operation by the information processing apparatus 100 may be denoted as "SC (Subspace Compiling)". Here, for the subspace S spanned by the basis B_S, the cost function representing the difference between the target quantum circuit U and the variational quantum circuit V(θ) is defined by the following formula (21). S is defined by the following formula (22). B_S is defined by the following formula (23).

[0198]

Number

[0199]

Number

[0200]

Number

[0201] The above-described cost function represents the result of subtracting from 1 the value obtained by taking the square mean of the fidelity between the two states U|ψ_s〉 and V(θ)|ψ_s〉 for the D_S basis vectors |ψ_s〉. Different from the FISC method, the above-described cost function does not use only the fidelity for a specific quantum state, but averages the fidelities for D_S different quantum states. Also, the above-described cost function is applicable to the subspace S spanned by the basis B_S.

[0202] The fact that the above cost function is zero is a necessary and sufficient condition for the actions of U and V(θ) to be identical for any quantum state belonging to the subspace S. In other words, the following equation (24) is a necessary and sufficient condition for the following equation (25). The subspace S and the basis B_S are preferably set according to the nature of the problem. For example, in quantum chemistry calculations and material property calculations, it is conceivable to set a subspace S corresponding to the symmetry of molecules or solid materials.

[0203] As the basis B_S that spans the subspace S, a combination of non-orthogonal state vectors to each other is set as a combination of the basis vectors |ψ_s〉. When a combination of orthogonal state vectors is set as the basis B_S that spans the subspace S, as shown in the following equation (24) and the following equation (25), a problem occurs that the global phases do not match.

[0204]

Number

[0205]

Number

[0206] The total number D_S of the basis vectors |ψ_s〉 that span the subspace S is preferably relatively small with respect to the dimension 2^L of the entire state space 1300. Therefore, in the following description, SC will be applied to the subspace S up to D_S = poly(L).

[0207] Specifically, the information processing apparatus 100 acquires a target quantum circuit U that represents a predetermined action, a variational quantum circuit V(θ), a basis {|ψ_s〉} of the subspace, and a parameter α of the cost function. Specifically, the information processing apparatus 100 prepares a quantum circuit for measuring the cost function. The quantum circuit for measuring the cost function will be described later with reference to FIG. 14.

[0208] Specifically, the information processing apparatus 100 performs a Loschmidt echo test on the basis |ψ_s〉 (s = 1 to D_S) using the prepared quantum circuit and obtains the measurement result. Specifically, the information processing apparatus 100 calculates the value of the cost function C_S(θ) based on the measurement result. Specifically, if the value of the cost function C_S(θ) has not converged, the information processing apparatus 100 updates the parameter θ, performs the Loschmidt echo test again, and calculates the value of the cost function C_S(θ).

[0209] Specifically, if the value of the cost function C_S(θ) has converged, the information processing apparatus 100 sets the parameter θ to the optimal parameter θ_opt. The information processing apparatus 100 implements the variational quantum circuit V(θ) with the set optimal parameter θ_opt as a quantum circuit representing a predetermined operation. Thereby, the information processing apparatus 100 can implement a quantum circuit representing a predetermined operation so that the number of operations is reduced.

[0210] Next, with reference to FIG. 14, the quantum circuit 1400 for measuring the cost function will be described. The quantum circuit 1400 includes a quantum gate 1401 corresponding to W_s. The quantum circuit 1400 includes a quantum gate 1402 corresponding to U. The quantum circuit 1400 includes a quantum gate 1403 corresponding to V^†. The quantum circuit 1400 includes a quantum gate 1404 corresponding to W_s^†. The quantum circuit 1400 includes a measurement unit 1405.

[0211] The information processing apparatus 100 performs a Loschmidt echo test on D_S basis vectors {|ψ_s〉} by the quantum circuit 1400 and obtains the measurement result. The information processing apparatus 100 measures the value of the cost function C_S(θ) by averaging the measurement results. The basis vector |ψ_s〉 can be obtained by the following formula (26).

[0212]

Equation

[0213] Next, with reference to FIG. 15, a specific example in which the information processing apparatus 100 minimizes the value of the cost function C_S(θ) will be described. Here, when the system size is relatively large, in the global cost function C_S^global(θ), the gradient becomes exponentially small, resulting in a phenomenon where the efficiency of minimization deteriorates. This phenomenon is called barren plateau. Therefore, when the system size is relatively large, the information processing apparatus 100 may preferably use the local cost function C_S^local(θ). The local cost function C_S^local(θ) is defined by the following equations (27) and (28).

[0214] [Number]

[0215] [Number]

[0216] Next, the quantum circuit 1500 for measuring the local cost function C_S^local(θ) will be described. The quantum circuit 1500 includes a quantum gate 1501 corresponding to W_s. The quantum circuit 1500 includes a quantum gate 1502 corresponding to U. The quantum circuit 1500 includes a quantum gate 1503 corresponding to V^†. The quantum circuit 1500 includes a quantum gate 1504 corresponding to W_s^†. The quantum circuit 1500 includes a measurement unit 1505.

[0217] The information processing apparatus 100 performs a Loschmidt echo test on D_S basis vectors {|ψ_s〉} using the quantum circuit 1500 and acquires measurement results. The information processing apparatus 100 measures the value of the local cost function C_S^local(θ) by averaging the measurement results. The fact that the above-described local cost function C_S^local(θ) is 0 is a necessary and sufficient condition for the actions of U and V(θ) to be identical for any quantum state belonging to the subspace S.

[0218] From the above, it is conceivable that the information processing apparatus 100 uses the cost function C_s(θ) so as to be adapted to the size of the system. The cost function C_s(θ) is defined by the following formula (29). For example, when the system size is relatively small, the information processing apparatus 100 uses the global cost function C_S^global(θ) with α = 1. For example, when the system size becomes relatively large, the information processing apparatus 100 approaches α to 0 so that the properties of the local cost function C_S^local(θ) become stronger.

[0219]

Number

[0220] The partial space S may be spanned, for example, by a quantum state obtained by applying the Pauli gate defined by the following formula (30) to the reference state |Ψ〉 as a basis. The orthogonality of the basis depends on the relationship between the reference state |Ψ〉 and the Pauli gate. On the other hand, if the basis is replaced with a basis of Pauli rotation gates, it is guaranteed that all bases have a finite overlap with the reference state |Ψ〉. Therefore, it is conceivable that the information processing apparatus 100 non-orthogonalizes the basis according to the following formula (31) and the following formula (32).

[0221]

Number

[0222]

Number

[0223]

Number

[0224] Next, an example of applying SC by the information processing apparatus 100 to the simulation of physical quantities of the Fermi-Hubbard model 1600 will be described with reference to FIG. 16. The Hamiltonian H corresponding to the Fermi-Hubbard model 1600 is defined by the following formula (33) and the following formula (34). Here, c_iσ (c_iσ^†) is the annihilation (creation) operator for the electron at site i and spin σ. U is the electron correlation parameter. t is the hopping parameter.

[0225]

Number

[0226]

Number

[0227] The physical quantity is defined by, for example, the Green's function. The Green's function is defined by, for example, the following formula (35). |Ψ〉 is the lowest energy state. a and b are the labels of the electrons. τ is the time parameter. If the time evolution operator U = e^(-iHτ) can be implemented as a quantum circuit, the Green's function can be calculated using a quantum computer.

[0228]

Number

[0229] Next, an example of the quantum circuit 1700 for calculating the Green's function will be described with reference to FIG. 17. The quantum circuit 1700 includes a Hadamard gate 1701. The quantum circuit 1700 includes a Pauli gate 1702. The quantum circuit 1700 includes a quantum circuit 1703 that represents the time evolution operator U = e^(-iHτ). The quantum circuit 1700 includes a Pauli gate 1704. The quantum circuit 1700 includes a Hadamard gate 1705. The quantum circuit 1700 includes a measurement unit 1706.

[0230] Hereinafter, it is assumed that the information processing apparatus 100 implements a quantum circuit that represents the time evolution operator U = e^(-iHτ) by means of SC. In order to calculate the Green's function, the information processing apparatus 100 sets a subspace spanned by the lowest energy state and the energy states in which one electron is generated / annihilated in the lowest energy state. Specifically, the information processing apparatus 100 sets the subspace according to Expression (38) obtained by non-orthogonalizing Expression (37) obtained by expressing the following Expression (36) in terms of qubits. The basis shown in Expression (38) becomes non-orthogonal due to the symmetry of the Fermi-Hubbard model 1600.

[0231] [Number]

[0232] [Number]

[0233] [Number]

[0234] Specifically, the information processing apparatus 100 sets the time evolution operator e^(-iHτ) of the Fermi-Hubbard model 1600 as the target quantum circuit U^(L) according to the Trotter decomposition method with a depth of 100. Specifically, the information processing apparatus 100 sets the VHA as the variational quantum circuit V^(L)(θ). The VHA is defined by the following Expression (39) and Expression (40).

[0235] [Number]

[0236] [Number]

[0237] The information processing apparatus 100 calculates a parameter θ that represents the action of the time evolution operator based on the set target quantum circuit U^(L) and the set variational quantum circuit V^(L)(θ). The information processing apparatus 100 implements the variational quantum circuit V^(L)(θ) with the set parameter θ as a quantum circuit that represents the action of the time evolution operator. Thereby, the information processing apparatus 100 can implement the VHA, which is a quantum circuit that represents the action of the time evolution operator, with fewer operation counts.

[0238] Next, an example of the effect by the information processing apparatus 100 will be described with reference to FIGS. 18 and 19. Assume that the information processing apparatus 100 implements the VHA by the SC. Here, the convergence speed in the case of minimizing the cost function will be described for the SC, the FUMC method, and the FISC method. The graph 1800 represents the change in the value of the cost function with respect to the number of iterations in the case of minimizing the cost function. As shown in the graph 1800, the SC can increase the convergence speed compared to the FUMC method. Next, the description will shift to FIG. 19.

[0239] The graph 1900 in FIG. 19 represents the results of calculating the time dependence of the Green's function and evaluating the absolute value error with respect to the exact solution for the SC, the FUMC method, and the FISC method. The vertical axis of the graph 1900 is the absolute value error. The horizontal axis of the graph 1900 is the time step. As shown in the graph 1900, at all times, the SC can calculate the Green's function with higher accuracy than the FUMC method and the FISC method.

[0240] Thereby, the SC can obtain a quantum circuit suitable for the purpose of calculating the Green's function without increasing the number of quantum gates of the quantum circuit that represents the action of the time evolution operator compared to the FUMC method and the FISC method.

[0241] In this way, the information processing apparatus 100 can obtain, by means of the SC, a quantum circuit that represents a predetermined operation and enables efficient execution of quantum computation by a quantum computer. The information processing apparatus 100 can, by means of the SC, reduce the number of quantum gates and the depth of the quantum circuit prepared for quantum computation regarding a specific problem. The information processing apparatus 100 can efficiently execute quantum computation related to specific computational processes such as quantum chemical computation or material physical property computation.

[0242] For example, the information processing apparatus 100 can improve the approximation accuracy of the Green's function of the Fermi-Hubbard model 1600 by a factor of 10 compared to the FUMC method. Therefore, when the information processing apparatus 100 guarantees an approximation accuracy comparable to that of the FUMC method by means of the SC, it can reduce the number of quantum gates forming the quantum circuit representing a predetermined operation compared to the FUMC method.

[0243] Next, differences among the SC, the FUMC method, and the FISC method will be described with reference to FIG. 20. As shown in FIG. 20, the SC realizes compilation for a subspace 2001 within the entire state space 2000. On the other hand, the FUMC method realizes compilation for the entire state space 2000. Also, the FISC method realizes compilation only for a specific quantum state |ψ〉 within the entire state space 2000.

[0244] Compared to the FISC method, the SC can create a quantum circuit that accurately represents a predetermined operation for a wide range of subspaces 2001. Compared to the FUMC method, the SC can reduce the number of qubits of the quantum circuit used for measuring the cost function.

[0245] (Overall processing procedure in Example 2) Next, an example of the overall processing procedure in Example 2 executed by the information processing apparatus 100 will be described with reference to FIG. 21. The overall processing is realized, for example, by the CPU 301 shown in FIG. 3, a storage area such as the memory 302 and the recording medium 305, and the network I / F 303.

[0246] Figure 21 is a flowchart showing an example of the overall processing procedure in the second embodiment. In Figure 21, the information processing apparatus 100 acquires a target quantum circuit U, a variational quantum circuit V(θ), a basis {|ψ_s〉} of a subspace, and a parameter α of a cost function (step S2101).

[0247] The information processing apparatus 100 prepares a quantum circuit for measuring the cost function (step S2102). The information processing apparatus 100 sets 1 to s (step S2103). The information processing apparatus 100 performs a Loschmidt echo test on the basis |ψ_s〉 using the prepared quantum circuit (step S2104).

[0248] The information processing apparatus 100 determines whether s≥D_S (step S2105). Here, when s<D_S (step S2105: No), the information processing apparatus 100 proceeds to the process of step S2106. On the other hand, when s≥D_S (step S2105: Yes), the information processing apparatus 100 proceeds to the process of step S2107.

[0249] In step S2106, the information processing apparatus 100 increments s (step S2106). The information processing apparatus 100 returns to the process of step S2104.

[0250] In step S2107, the information processing apparatus 100 calculates the value of the cost function C_S(θ) based on the measurement result (step S2107).

[0251] The information processing apparatus 100 determines whether the value of the cost function C_S(θ) has converged (step S2108). Here, when the value of the cost function C_S(θ) has not converged (step S2108: No), the information processing apparatus 100 proceeds to the process of step S2109.

[0252] In step S2109, the information processing apparatus 100 updates the parameter θ (step S2109) and returns to the process of step S2103. On the other hand, when the value of the cost function C_S(θ) has converged (step S2108: Yes), the information processing apparatus 100 implements a quantum circuit representing a predetermined operation based on the parameter θ (step S2110) and ends the overall process.

[0253] As described above, according to the information processing apparatus 100, it is possible to obtain a first quantum circuit that represents the action of the time evolution operator for the target problem and has a first size. According to the information processing apparatus 100, it is possible to obtain a second quantum circuit that has a smaller number of quantum gates than the first quantum circuit and has a first size and has a plurality of parameters. According to the information processing apparatus 100, it is possible to obtain a third quantum circuit that defines one or more quantum states that are part of a plurality of quantum states related to the target problem and has a first size. According to the information processing apparatus 100, by reducing the first quantum circuit, the second quantum circuit, and the third quantum circuit to a second size smaller than the first size, respectively, a first local circuit, a second local circuit, and a third local circuit, each having a second size, can be created. According to the information processing apparatus 100, it is possible to set a cost function that is defined by the created third local circuit, uses a plurality of parameters as explanatory variables, and represents the difference between the created first local circuit and the second local circuit. According to the information processing apparatus 100, based on the cost function, it is possible to calculate a solution of a plurality of parameters so as to minimize the value of the cost function for each quantum state of one or more quantum states. According to the information processing apparatus 100, based on the second quantum circuit and the calculated solution of the plurality of parameters, a new quantum circuit representing the action of the time evolution operator can be set. Thereby, the information processing apparatus 100 can set a quantum circuit that represents the action of the time evolution operator with fewer operation times and fewer quantum gates. The information processing apparatus 100 can suppress the deterioration of the accuracy of quantum calculation using the quantum circuit that represents the action of the time evolution operator. The information processing apparatus 100 can reduce the processing time required for quantum calculation using the quantum circuit that represents the action of the time evolution operator.

[0254] According to the information processing apparatus 100, by creating a first quantum circuit according to the Trotter decomposition method, the first quantum circuit can be obtained. Thereby, the information processing apparatus 100 can set a quantum circuit representing the action of the time evolution operator without acquiring the first quantum circuit from the outside. The information processing apparatus 100 can create a first quantum circuit appropriate as a sample, and can easily set a quantum circuit that accurately represents the action of the time evolution operator.

[0255] According to the information processing apparatus 100, a cost function defined by the local fidelity measured for the third local circuit can be set. Thereby, the information processing apparatus 100 can appropriately set the cost function, and can easily set a quantum circuit that accurately represents the action of the time evolution operator.

[0256] According to the information processing apparatus 100, for each of the plurality of qubits, the acquired first quantum circuit, the second quantum circuit, and the third quantum circuit can be reduced to a second size that is a predetermined range based on the corresponding qubit. According to the information processing apparatus 100, a plurality of combinations of the first local circuit, the second local circuit, and the third local circuit can be created. According to the information processing apparatus 100, based on the cost functions corresponding to the plurality of combinations, the solutions of the plurality of parameters can be calculated so as to minimize the values of the cost functions for each of the one or more quantum states. Thereby, the information processing apparatus 100 can consider the second size that is a predetermined range based on each qubit, can appropriately set the cost function, and can easily set a quantum circuit that accurately represents the action of the time evolution operator.

[0257] According to the information processing apparatus 100, the acquired first quantum circuit, second quantum circuit, and third quantum circuit can each be reduced to a second size that is a predetermined range based on any one of the qubits. Thereby, when the information processing apparatus 100 sets a quantum circuit that represents the action of the time evolution operator when the first quantum circuit, second quantum circuit, and third quantum circuit each have translational symmetry, it is possible to reduce the processing amount required.

[0258] According to the information processing apparatus 100, it is possible to acquire a third quantum circuit that defines one or more quantum states that are linearly independent and non-orthogonal to each other. Thereby, the information processing apparatus 100 can acquire a third quantum circuit that represents an appropriate subspace.

[0259] According to the information processing apparatus 100, it is possible to acquire a first quantum circuit that represents a predetermined action related to the target problem. According to the information processing apparatus 100, it is possible to acquire a second quantum circuit that has fewer quantum gates than the first quantum circuit and has a plurality of parameters. According to the information processing apparatus 100, it is possible to acquire a group of basis vectors that define two or more quantum states that are part of a plurality of quantum states related to the target problem. According to the information processing apparatus 100, based on the acquired group of basis vectors, a cost function can be set with the plurality of parameters as explanatory variables and representing the difference between the acquired first quantum circuit and the second quantum circuit. According to the information processing apparatus 100, based on the cost function, solutions for the plurality of parameters can be calculated so as to minimize the value of the cost function for each of the two or more quantum states. According to the information processing apparatus 100, based on the second quantum circuit and the solutions for the plurality of calculated parameters, a new quantum circuit that represents a predetermined action can be set. Thereby, the information processing apparatus 100 can set a quantum circuit that represents a predetermined action with fewer calculation times and fewer quantum gates. The information processing apparatus 100 can suppress deterioration in the accuracy of quantum calculation using the quantum circuit that represents a predetermined action. The information processing apparatus 100 can reduce the processing time required for quantum calculation using the quantum circuit that represents a predetermined action.

[0260] Note that the information processing method described in this embodiment can be realized by executing a pre-prepared program on a computer such as a PC or a workstation. The information processing program described in this embodiment is recorded on a computer-readable recording medium and executed by being read from the recording medium by a computer. The recording medium is a hard disk, a flexible disk, a CD (Compact Disc)-ROM, an MO (Magneto Optical disc), a DVD (Digital Versatile Disc), or the like. Further, the information processing program described in this embodiment may be distributed via a network such as the Internet.

[0261] Regarding the above-described embodiment, the following additional remarks are disclosed.

[0262] (Supplementary Note 1) A first quantum circuit representing the action of a time evolution operator for a target problem, each of which is of a first size, a second quantum circuit having a smaller number of quantum gates than the first quantum circuit and having a plurality of parameters, and a third quantum circuit defining one or more quantum states that are part of a plurality of quantum states related to the target problem are obtained. By reducing the obtained first quantum circuit, second quantum circuit, and third quantum circuit to a second size smaller than the first size, a first local circuit, a second local circuit, and a third local circuit, each of which is of the second size, are created. Based on a cost function defined by the created third local circuit, with the plurality of parameters as explanatory variables and representing the difference between the created first local circuit and the second local circuit, a solution of the plurality of parameters is calculated so as to minimize the value of the cost function for each of the one or more quantum states. Based on the second quantum circuit and the calculated solution of the plurality of parameters, a new quantum circuit representing the action of the time evolution operator is set. An information processing program characterized by causing a computer to execute the processing.

[0263] (Appendix 2) The obtaining process is obtaining the first quantum circuit by creating the first quantum circuit according to the Trotter decomposition method, the information processing program according to Appendix 1, characterized in that.

[0264] (Appendix 3) The cost function is defined by the local fidelity measured for the third local circuit, the information processing program according to Appendix 1, characterized in that.

[0265] (Appendix 4) The first size is a range including the whole of a plurality of qubits related to the target problem, The second size is a range including a part of the plurality of qubits, The creating process is for each of the plurality of qubits, reducing the obtained first quantum circuit, the second quantum circuit, and the third quantum circuit to the second size which is a predetermined range based on each qubit, to create a plurality of combinations of the first local circuit, the second local circuit, and the third local circuit, The calculating process is calculating the solution of the plurality of parameters so as to minimize the value of the cost function for each of the one or more quantum states based on the cost function corresponding to the plurality of combinations, the information processing program according to Appendix 1, characterized in that.

[0266] (Appendix 5) The creating process is When the first quantum circuit, the second quantum circuit, and the third quantum circuit each have translational symmetry, for any one of the plurality of qubits related to the target problem, the acquired first quantum circuit, the second quantum circuit, and the third quantum circuit are each reduced to the second size, which is a predetermined range based on the any one of the qubits, thereby creating a first local circuit, a second local circuit, and a third local circuit, each having the second size. The information processing program according to Appendix 1, characterized in that.

[0267] (Appendix 6) The one or more quantum states are linearly independent and non-orthogonal to each other. The information processing program according to any one of Appendices 1 to 5, characterized in that.

[0268] (Appendix 7) A first quantum circuit that represents the action of the time evolution operator related to the target problem, each having a first size, a second quantum circuit that has fewer quantum gates than the first quantum circuit and has a plurality of parameters, and a third quantum circuit that defines one or more quantum states that are part of the plurality of quantum states related to the target problem are acquired. The acquired first quantum circuit, the second quantum circuit, and the third quantum circuit are each reduced to a second size smaller than the first size, thereby creating a first local circuit, a second local circuit, and a third local circuit, each having the second size. Based on the cost function defined by the created third local circuit, with the plurality of parameters as explanatory variables and representing the difference between the created first local circuit and the second local circuit, the solution of the plurality of parameters is calculated so as to minimize the value of the cost function for each of the one or more quantum states. Based on the second quantum circuit and the calculated solution of the plurality of parameters, a new quantum circuit that represents the action of the time evolution operator is set. An information processing method characterized in that a computer executes the processing.

[0269] (Appendix 8) A first quantum circuit that represents the action of the time evolution operator for a target problem, each of which is of a first size, a second quantum circuit that has fewer quantum gates than the first quantum circuit and has a plurality of parameters, and a third quantum circuit that defines one or more quantum states that are part of a plurality of quantum states related to the target problem are obtained. By reducing the obtained first quantum circuit, the second quantum circuit, and the third quantum circuit to a second size that is smaller than the first size, respectively, a first local circuit, a second local circuit, and a third local circuit, each of which is of the second size, are created. Based on the cost function that is defined by the created third local circuit, uses the plurality of parameters as explanatory variables, and represents the difference between the created first local circuit and the second local circuit, the solution of the plurality of parameters is calculated so as to minimize the value of the cost function for each of the one or more quantum states. Based on the second quantum circuit and the solution of the calculated plurality of parameters, a new quantum circuit that represents the action of the time evolution operator is set. An information processing apparatus characterized by having a control unit.

[0270] (Appendix 9) A first quantum circuit that represents a predetermined action for a target problem, a second quantum circuit that has fewer quantum gates than the first quantum circuit and has a plurality of parameters, and a group of basis vectors that defines two or more quantum states that are part of a plurality of quantum states related to the target problem are obtained. Based on the cost function that is defined by the obtained group of basis vectors, uses the plurality of parameters as explanatory variables, and represents the difference between the obtained first quantum circuit and the second quantum circuit, the solution of the plurality of parameters is calculated so as to minimize the value of the cost function for each of the two or more quantum states. Based on the second quantum circuit and the solution of the calculated plurality of parameters, a new quantum circuit that represents the predetermined action is set. An information processing program characterized by causing a computer to execute processing.

[0271] (Appendix 10) Obtain a first quantum circuit that represents a predetermined operation related to the target problem, a second quantum circuit that has fewer quantum gates than the first quantum circuit and has a plurality of parameters, and a group of basis vectors that define two or more quantum states that are part of the plurality of quantum states related to the target problem. Based on the cost function defined by the obtained group of basis vectors, with the plurality of parameters as explanatory variables and representing the difference between the obtained first quantum circuit and the second quantum circuit, calculate the solution of the plurality of parameters so as to minimize the value of the cost function for each of the two or more quantum states. Set a new quantum circuit that represents the predetermined operation based on the second quantum circuit and the calculated solution of the plurality of parameters. An information processing method characterized in that a computer executes the process.

[0272] (Appendix 11) Obtain a first quantum circuit that represents a predetermined operation related to the target problem, a second quantum circuit that has fewer quantum gates than the first quantum circuit and has a plurality of parameters, and a group of basis vectors that define two or more quantum states that are part of the plurality of quantum states related to the target problem. Based on the cost function defined by the obtained group of basis vectors, with the plurality of parameters as explanatory variables and representing the difference between the obtained first quantum circuit and the second quantum circuit, calculate the solution of the plurality of parameters so as to minimize the value of the cost function for each of the two or more quantum states. Set a new quantum circuit that represents the predetermined operation based on the second quantum circuit and the calculated solution of the plurality of parameters. An information processing apparatus characterized by having a control unit.

Explanation of Signs

[0273] 100 Information processing apparatus 101 First quantum circuit 102 Second quantum circuit 103 Third quantum circuit 111 First local circuit 112 Second local circuit 113 Third local circuit 120, 630, 1300, 2000 Entire state space 121, 631, 1301, 2001 Subspace 130 Cost function 200 Information processing system 201 Computing device 202 Client device 210 Network 300, 400 Bus 301, 401 CPU 302, 402 Memory 303, 403 Network I / F 304, 404 Recording medium I / F 305, 405 Recording medium 406 Arithmetic unit I / F 407 Arithmetic unit 500 Memory section 501 Acquisition section 502 Creation section 503 Reduction section 504 Calculation section 505 Setting section 506 Arithmetic section 507 Output section 600 Entire quantum system 601 Sub - quantum system 610, 620, 700, 800, 1400, 1500, 1700, 1703 Quantum circuit 701 Range 801 - 804, 1401 - 1404, 1501 - 1504 Quantum gate 805, 1405, 1505, 1706 Measurement unit 900, 1600 Hubbard model 1000, 1800, 1900 Graph 1310 Target quantum circuit 1320 Variational quantum circuit 1701, 1705 Hadamard gate 1702, 1704 Pauli gate

Claims

1. A first quantum circuit representing the action of a time evolution operator for a target problem, each having a first size; a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters; and a third quantum circuit defining one or more quantum states that are part of a plurality of quantum states related to the target problem are obtained, By reducing the obtained first quantum circuit, second quantum circuit, and third quantum circuit to a second size smaller than the first size respectively, a first local circuit, a second local circuit, and a third local circuit, each having the second size, are created, Based on a cost function defined by the third local circuit created, with the plurality of parameters as explanatory variables and representing the difference between the created first local circuit and the second local circuit, a solution of the plurality of parameters is calculated to minimize the value of the cost function for each of the one or more quantum states, Based on the second quantum circuit and the calculated solution of the plurality of parameters, a new quantum circuit representing the action of the time evolution operator is set, An information processing program characterized by causing a computer to execute the process.

2. The obtaining process obtains the first quantum circuit by creating the first quantum circuit according to the Trotter decomposition method. The information processing program according to claim 1.

3. The cost function is defined by the local fidelity measured for the third local circuit. The information processing program according to claim 1.

4. The first size is a range including the entirety of a plurality of qubits related to the target problem, The second size is a range including a part of the plurality of qubits, The creating process creates a plurality of combinations of the first local circuit, the second local circuit, and the third local circuit by reducing the obtained first quantum circuit, second quantum circuit, and third quantum circuit to the second size, which is a predetermined range based on each qubit, for each qubit of the plurality of qubits respectively, The calculating process Based on the cost function corresponding to the plurality of combinations, calculating a solution of the plurality of parameters so as to minimize the value of the cost function for each quantum state of the one or more quantum states, the information processing program according to claim 1, characterized in that.

5. The process of creating is When the first quantum circuit, the second quantum circuit, and the third quantum circuit each have translational symmetry, for any one of the plurality of qubits related to the target problem, the acquired first quantum circuit, the second quantum circuit, and the third quantum circuit are each reduced to the second size within a predetermined range based on any one of the qubits, thereby creating a first local circuit, a second local circuit, and a third local circuit that are each of the second size, the information processing program according to claim 1, characterized in that.

6. Obtaining a first quantum circuit representing the action of the time evolution operator related to the target problem, which is each of the first sizes, a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters, and a third quantum circuit defining one or more quantum states that are part of the plurality of quantum states related to the target problem, Reducing the acquired first quantum circuit, second quantum circuit, and third quantum circuit to a second size smaller than the first size respectively, thereby creating a first local circuit, a second local circuit, and a third local circuit that are each of the second size, Based on the cost function defined by the created third local circuit, with the plurality of parameters as explanatory variables and representing the difference between the created first local circuit and the second local circuit, calculating a solution of the plurality of parameters so as to minimize the value of the cost function for each quantum state of the one or more quantum states, Setting a new quantum circuit representing the action of the time evolution operator based on the second quantum circuit and the calculated solution of the plurality of parameters, An information processing method characterized in that a computer executes the process.

7. Obtaining a first quantum circuit representing the action of the time evolution operator related to the target problem, which is each of the first sizes, a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters, and a third quantum circuit defining one or more quantum states that are part of the plurality of quantum states related to the target problem, By reducing the obtained first quantum circuit, the second quantum circuit, and the third quantum circuit to a second size smaller than the first size, respectively, a first local circuit, a second local circuit, and a third local circuit, each having the second size, are created. Based on a cost function defined by the created third local circuit, with the plurality of parameters as explanatory variables and representing the difference between the created first local circuit and the second local circuit, a solution of the plurality of parameters is calculated to minimize the value of the cost function for each of the one or more quantum states of the quantum states. Based on the second quantum circuit and the calculated solution of the plurality of parameters, a new quantum circuit representing the action of the time evolution operator is set. An information processing apparatus characterized by having a control unit.

8. A first quantum circuit representing a predetermined action regarding a target problem, a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters, and a group of basis vectors defining two or more quantum states that are part of a plurality of quantum states regarding the target problem are obtained. Based on a cost function defined by the obtained group of basis vectors, with the plurality of parameters as explanatory variables and representing the difference between the obtained first quantum circuit and the second quantum circuit, a solution of the plurality of parameters is calculated to minimize the value of the cost function for each of the two or more quantum states of the quantum states. Based on the second quantum circuit and the calculated solution of the plurality of parameters, a new quantum circuit representing the predetermined action is set. An information processing program characterized by causing a computer to execute processing.

9. A first quantum circuit representing a predetermined action regarding a target problem, a second quantum circuit having fewer quantum gates than the first quantum circuit and having a plurality of parameters, and a group of basis vectors defining two or more quantum states that are part of a plurality of quantum states regarding the target problem are obtained. Based on a cost function defined by the obtained group of basis vectors, with the plurality of parameters as explanatory variables and representing the difference between the obtained first quantum circuit and the second quantum circuit, a solution of the plurality of parameters is calculated to minimize the value of the cost function for each of the two or more quantum states of the quantum states. Based on the second quantum circuit and the solutions of the calculated plurality of parameters, a new quantum circuit representing the predetermined operation is set. An information processing method, characterized in that a computer executes the processing.

10. A first quantum circuit representing a predetermined operation related to a target problem, a second quantum circuit having a smaller number of quantum gates than the first quantum circuit and having a plurality of parameters, and a basis vector group defining two or more quantum states that are part of a plurality of quantum states related to the target problem are obtained. Based on the cost function defined by the obtained basis vector group, with the plurality of parameters as explanatory variables and representing the difference between the obtained first quantum circuit and the second quantum circuit, the solutions of the plurality of parameters are calculated so as to minimize the value of the cost function for each of the two or more quantum states. Based on the second quantum circuit and the solutions of the calculated plurality of parameters, a new quantum circuit representing the predetermined operation is set. An information processing apparatus, characterized by having a control unit.

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