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

Abstract

An information processing device (100) acquires a combinatorial optimization problem. The information processing device (100) sets, for example, a quantum circuit (130) of a QAOA corresponding to the combinatorial optimization problem, the quantum circuit (130) representing a quantum state corresponding to a state z. The information processing device (100) calculates a first solution (101) of the combinatorial optimization problem on the basis of an Ising model (110) corresponding to the acquired combinatorial optimization problem. The information processing device (100) determines the value of a parameter (120) of the quantum circuit (130) so as to maximize the probability that the quantum state of the set quantum circuit (130) is the calculated first solution (101). The information processing device (100) calculates a second solution (102) of the combinatorial optimization problem on the basis of the quantum circuit (130) in which the determined value of the parameter (120) is set.

Description

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

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

[0002] Conventionally, there are quantum approximate optimization algorithms that solve combinatorial optimization problems. For example, they solve combinatorial optimization problems by repeating a series of processes: identifying the quantum state of a quantum circuit, identifying the energy corresponding to the identified quantum state, and changing the parameters of the quantum circuit based on the identified energy.

[0003] In the prior art, for example, an AI (Artificial Intelligence) control unit determines one or more adjustable parameters corresponding to a calculation. Also, for example, the present technique includes a technique for mapping a cost function associated with a combinatorial optimization problem to an optimization problem over allowed quantum states. Also, for example, in a general aspect, there is a technique for selecting parameter values ​​of a quantum approximate optimization algorithm using a Bayesian optimizer. Also, for example, there is a technique for executing a quantum approximate optimization algorithm.

[0004] Japanese Patent Publication No. 2022-509841 Japanese Patent Publication No. 2021-504805 U.S. Patent No. 10,846,366 U.S. Patent Application Publication No. 2022 / 0245497

[0005] However, with conventional techniques, it is difficult to efficiently solve combinatorial optimization problems. For example, the time required to solve a combinatorial optimization problem tends to increase.

[0006] In one aspect, the present invention aims to make combinatorial optimization problems easier to solve.

[0007] According to one embodiment, an information processing program, an information processing method, and an information processing device are proposed that calculate a first solution to a combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem, determine parameter values ​​of the quantum approximation optimization algorithm so as to maximize the probability that the quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution, and calculate a second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximation optimization algorithm to which the determined parameter values ​​have been set.

[0008] According to one aspect, combinatorial optimization problems can be made easier to solve.

[0009] FIG. 1 is an explanatory diagram illustrating an example of an information processing method according to an embodiment. FIG. 2 is an explanatory diagram illustrating an example of an information processing system 200. FIG. 3 is a block diagram illustrating an example of a hardware configuration of an information processing device 100. FIG. 4 is a block diagram illustrating an example of a functional configuration of the information processing device 100. FIG. 5 is an explanatory diagram (part 1) illustrating an example of an operation of the information processing device 100. FIG. 6 is an explanatory diagram (part 2) illustrating an example of an operation of the information processing device 100. FIG. 7 is an explanatory diagram (part 3) illustrating an example of an operation of the information processing device 100. FIG. 8 is an explanatory diagram (part 4) illustrating an example of an operation of the information processing device 100. FIG. 9 is a flowchart illustrating an example of an overall processing procedure. FIG. 10 is a flowchart illustrating an example of a first determination processing procedure. FIG. 11 is a flowchart illustrating an example of a second determination processing procedure.

[0010] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an information processing program, an information processing method, and an information processing device according to embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[0011] (Example of Information Processing Method According to Embodiment) Fig. 1 is an explanatory diagram showing an example of an information processing method according to an embodiment. The information processing device 100 is a computer for solving combinatorial optimization problems. The information processing device 100 is, for example, a server or a PC (Personal Computer).

[0012] Here, a combinatorial optimization problem is a problem of finding a solution for a combination of variables that optimizes the value of an objective function under constraint conditions. Conventional methods for solving combinatorial optimization problems include, for example, the simulated annealing (SA) method or a quantum approximation optimization algorithm. In the following description, the quantum approximation optimization algorithm may be referred to as a "quantum approximation optimization algorithm (QAOA)."

[0013] The SA method is a technique for solving combinatorial optimization problems by repeatedly searching for solutions to combinations of variables while adjusting the range in which solutions for combinations of variables are searched, for example, using thermal noise. The QAOA method is a technique for solving combinatorial optimization problems by using, for example, a quantum circuit that represents a quantum state corresponding to a combination of variables. The SA method is also known as simulated annealing, for example.

[0014] Specifically, QAOA solves a combinatorial optimization problem by repeating a series of processes: "identify the quantum state of a quantum circuit, identify the energy corresponding to the identified quantum state, and change the parameters of the quantum circuit based on the identified energy." Specifically, QAOA uses the Grid method, the BFGS method, the quadratic approximation method, the Powell method, or Bayesian estimation when changing the parameters of the quantum circuit.

[0015] For the QAOA, see, for example, Reference 1 below. For the Grid method, see, for example, Reference 2 below. For the BFGS method, see, for example, Reference 3 below. For the quadratic approximation method, see, for example, Reference 4 below. For the Bayesian estimation, see, for example, Reference 5 below.

[0016] Reference 1: Farhi, Edward, Jeffrey Goldstone, and Sam Gutmann. “A quantum approximate optimization algorithm.” arXiv preprint arXiv:1411.4028 (2014).

[0017] Reference 2: Streif, Michael, and Martin Leib. "Forbidden subspaces for level-1 quantum approximate optimization algorithm and instantaneous quantum polynomial circuits." Physical Review A 102.4 (2020): 042416.

[0018] Reference 3: Streif, Michael, and Martin Leib. "Training the quantum approximate optimization algorithm without access to a quantum processing unit." Quantum Science and Technology 5.3 (2020): 034008.

[0019] Reference 4: Shaydulin, Ruslan, and Yuri Alexeev. "Evaluating quantum approximate optimization algorithm: A case study." 2019 tenth international green and sustainable computing conference (IGSC). IEEE, 2019.

[0020] Reference 5: Tibaldi, Simone, et al. "Bayesian Optimization for QAOA." arXiv preprint arXiv:2209.03824 (2022).

[0021] However, conventionally, it has been difficult to efficiently solve combinatorial optimization problems. For example, the time required to solve a combinatorial optimization problem tends to increase. Specifically, in the SA method, the further the initial value is from the optimal solution, the longer the time required to solve the combinatorial optimization problem and find the optimal solution tends to increase. The same tendency also exists in the quantum annealing method. For more information on this tendency, see, for example, Reference 6 below.

[0022] Reference 6: Katzgraber, Helmut G. , et al. “Seeking quantum speedup through spin glasses: The good, the bad, and the ugly.” Physical Review X 5.3 (2015): 031026.

[0023] Specifically, in QAOA, there is a problem that the energy and the parameters of the quantum circuit may have a non-convex relationship, which tends to increase the time required to appropriately change the parameters, making it difficult to find the optimal parameters.

[0024] Therefore, in this embodiment, an information processing method that can make it easier to solve combinatorial optimization problems will be described.

[0025] In FIG. 1 , an information processing device 100 acquires a combinatorial optimization problem. The information processing device 100 acquires, for example, an objective function min(E=C(z)) of the combinatorial optimization problem. z is, for example, a state and represents a combination of variables. E is, for example, energy. Here, it is desired to find a state z that minimizes E=C(z), which is a solution to the combinatorial optimization problem. The information processing device 100 sets, for example, a quantum circuit 130 of a QAOA corresponding to the combinatorial optimization problem, which represents a quantum state corresponding to the state z. The quantum state, for example, probabilistically represents each value that the state z can take.

[0026] (1-1) The information processing device 100 calculates a first solution 101 of the combinatorial optimization problem based on an Ising model 110 corresponding to the acquired combinatorial optimization problem. The information processing device 100, for example, uses an Ising machine of a digital annealer to calculate a state z0 that results in the first solution 101 of the combinatorial optimization problem based on the Ising model 110 of the digital annealer and a set initial value. The initial value is, for example, set in advance by a user. The initial value is, for example, the value of the state z.

[0027] (1-2) The information processing device 100 determines the values ​​of the parameters 120 of the quantum circuit 130 so as to maximize the probability that the quantum state of the set quantum circuit 130 will become the calculated first solution 101. The information processing device 100 calculates a second solution 102 to the combinatorial optimization problem based on the quantum circuit 130 to which the determined values ​​of the parameters 120 have been set.

[0028] The information processing device 100 uses, for example, a QPU (Quantum Processing Unit) to perform n-shot sampling of the quantum state and calculates a state z that is the second solution 102. Specifically, the information processing device 100 repeatedly performs Z-direction projection measurement of the quantum state represented by the quantum circuit 130 to which the determined values ​​of the parameters 120 are set to obtain a state z n times, and calculates a state z that is the second solution 102 based on the distribution of the obtained states z.

[0029] This makes it easier for the information processing device 100 to solve combinatorial optimization problems. The information processing device 100 can appropriately set the parameters 120 of the quantum circuit 130 based on the first solution 101 calculated using the Ising model 110, thereby reducing the time required to perform QAOA. The information processing device 100 can acquire a state z1 that is relatively close to the optimal solution and is a preferable solution.

[0030] (1-3) The information processing device 100 may set the calculated state z1 as a new initial value and repeat the series of processes shown in (1-1) and (1-2) until a convergence condition is met. The convergence condition may be, for example, that the series of processes has been performed a predetermined number of times. This allows the information processing device 100 to solve the combinatorial optimization problem with high accuracy. The information processing device 100 can obtain a state z1 that is closer to the optimal solution and is a preferable solution.

[0031] Here, the case where the information processing device 100 is a single computer has been described, but this is not limiting. For example, the functions of the information processing device 100 may be realized by multiple computers. Specifically, the functions of the information processing device 100 may be realized on a cloud.

[0032] Here, the case where the information processing device 100 has an Ising machine has been described, but this is not limiting. For example, the information processing device 100 may control another computer having an Ising machine to calculate a first solution 101 of a combinatorial optimization problem, and may acquire the first solution 101.

[0033] Although the case where the information processing device 100 has a QPU has been described here, the present invention is not limited to this. For example, the information processing device 100 may control another computer having a QPU to calculate a second solution 102 of a combinatorial optimization problem, and may acquire the second solution 102.

[0034] (Example of Information Processing System 200) Next, an example of an information processing system 200 to which the information processing device 100 shown in FIG. 1 is applied will be described with reference to FIG.

[0035] 2 is an explanatory diagram showing an example of an information processing system 200. In FIG. 2, the information processing system 200 includes an information processing device 100 and a client device 201.

[0036] In the information processing system 200, the information processing device 100 and the client device 201 are connected via a wired or wireless network 210. The network 210 is, for example, a local area network (LAN), a wide area network (WAN), or the Internet.

[0037] The information processing device 100 is a computer for solving combinatorial optimization problems. (2-1) The information processing device 100 receives, for example, information indicating a combinatorial optimization problem from the client device 201. The information processing device 100 identifies, for example, the combinatorial optimization problem based on the received information. The information processing device 100 identifies, for example, a quantum circuit of a QAOA corresponding to the identified combinatorial optimization problem. The information processing device 100 sets, for example, initial values ​​of an Ising model corresponding to the combinatorial optimization problem.

[0038] (2-2) The information processing device 100 calculates a first solution to the combinatorial optimization problem, for example, based on the set initial values ​​and an Ising model corresponding to the combinatorial optimization problem. The information processing device 100, for example, determines parameter values ​​of the identified quantum circuit so as to maximize the probability that the quantum state of the identified quantum circuit will become the calculated first solution. The information processing device 100 calculates a second solution to the combinatorial optimization problem, for example, based on the quantum circuit to which the determined parameter values ​​are set.

[0039] (2-3) The information processing device 100, for example, sets the calculated second solution as a new initial value of the Ising model, and repeats the series of processes shown in (2-2) until a convergence condition is satisfied. The convergence condition may be, for example, that the series of processes has been performed a predetermined number of times. When the convergence condition is satisfied, the information processing device 100 sets the last calculated second solution as the solution to the combinatorial optimization problem. The information processing device 100 transmits the solution to the combinatorial optimization problem to the client device 201. The information processing device 100 is, for example, a server or a PC.

[0040] The client device 201 is a computer used by a worker requesting a solution to a combinatorial optimization problem. The client device 201 generates information representing the combinatorial optimization problem based on, for example, operational input by the worker, and transmits the information to the information processing device 100. The information representing the combinatorial optimization problem includes, for example, an objective function of the combinatorial optimization problem. The information representing the combinatorial optimization problem may also include, for example, constraints of the combinatorial optimization problem. The client device 201 receives a solution to the combinatorial optimization problem from the information processing device 100. The client device 201 outputs the solution to the combinatorial optimization problem so that it can be referenced by the worker. The client device 201 is, for example, a PC, a tablet terminal, or a smartphone.

[0041] Here, the case where the information processing device 100 is a computer different from the client device 201 has been described, but this is not limiting. For example, the information processing device 100 may have the functions of the client device 201 and may also operate as the client device 201.

[0042] (Example of Hardware Configuration of Information Processing Apparatus 100) Next, an example of the hardware configuration of the information processing apparatus 100 will be described with reference to FIG.

[0043] 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. The information processing device 100 also includes an Ising machine 306 and a QPU 307. The components are connected to each other via a bus 300.

[0044] Here, the CPU 301 is responsible for overall control of the information processing device 100. The memory 302 includes, for example, a read-only memory (ROM), a random access memory (RAM), and a flash ROM. Specifically, for example, the flash ROM and ROM store various programs, and the RAM is used as a work area for the CPU 301. The programs stored in the memory 302 are loaded into the CPU 301, causing the CPU 301 to execute the coded processes.

[0045] The network I / F 303 is connected to the network 210 via a communication line, and is connected to other computers via the network 210. The network I / F 303 manages the internal interface with the network 210 and controls the input and output of data from other computers. The network I / F 303 is, for example, a modem or a LAN adapter.

[0046] The recording medium I / F 304 controls reading and writing of data from and to the recording medium 305 under the control of the CPU 301. The recording medium I / F 304 is, for example, a disk drive, a solid state drive (SSD), or a universal serial bus (USB) port. The recording medium 305 is a non-volatile memory that stores data written under the control of the recording medium I / F 304. The recording medium 305 is, for example, a disk, a semiconductor memory, or a USB memory. The recording medium 305 may be detachable from the information processing device 100.

[0047] The Ising machine 306 is a computing device that has an Ising model and solves combinatorial optimization problems by executing a digital annealer using the Ising model. The QPU 307 is a computing device that executes quantum operations defined in a quantum circuit. The QPU 307 solves combinatorial optimization problems by executing, for example, QAOA.

[0048] In addition to the components described above, the information processing device 100 may also include, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, etc. The information processing device 100 may also include a plurality of recording medium I / Fs 304 and recording media 305. The information processing device 100 may also not include a recording medium I / F 304 or a recording medium 305.

[0049] (Example of Hardware Configuration of Client Device 201) The example of the hardware configuration of the client device 201 is specifically similar to the example of the hardware configuration of the information processing device 100 shown in FIG. 3, and therefore a description thereof will be omitted.

[0050] (Example of Functional Configuration of Information Processing Apparatus 100) Next, an example of the functional configuration of the information processing apparatus 100 will be described with reference to FIG.

[0051] 4 is a block diagram showing an example of the functional configuration of the information processing device 100. The information processing device 100 includes a storage unit 400, an acquisition unit 401, a first calculation unit 402, a determination unit 403, a second calculation unit 404, and an output unit 405.

[0052] The storage unit 400 is realized by, for example, a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3. In the following, a case where the storage unit 400 is included in the information processing device 100 will be described, but this is not limiting. For example, the storage unit 400 may be included in a device different from the information processing device 100, and the stored contents of the storage unit 400 may be accessible from the information processing device 100.

[0053] The acquiring unit 401 to the output unit 405 function as an example of a control unit. Specifically, the acquiring unit 401 to the output unit 405 realize their functions by, for example, causing the CPU 301 to execute a program stored in a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3, or by using the network I / F 303. The processing results of each functional unit are stored in a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3.

[0054] The storage unit 400 stores various information that is referenced or updated during processing by each functional unit. The storage unit 400 stores, for example, information that indicates a combinatorial optimization problem. The information that indicates a combinatorial optimization problem includes, for example, an objective function of the combinatorial optimization problem. The information that indicates a combinatorial optimization problem may include, for example, constraints of the combinatorial optimization problem. The information that indicates a combinatorial optimization problem is acquired, for example, by the acquisition unit 401. The information that indicates a combinatorial optimization problem may, for example, be set in advance by a user.

[0055] The storage unit 400 stores, for example, an Ising model corresponding to a combinatorial optimization problem. The Ising model is acquired, for example, by the acquisition unit 401. The Ising model may be set in advance by a user. The storage unit 400 stores, for example, initial values ​​of the Ising model. The initial values ​​correspond to candidate solutions to the combinatorial optimization problem. The initial values ​​are acquired, for example, by the acquisition unit 401. The initial values ​​may be set in advance by a user.

[0056] The storage unit 400 stores, for example, a quantum circuit of a QAOA corresponding to a combinatorial optimization problem. The quantum circuit of the QAOA represents a procedure of quantum operations. The quantum circuit of the QAOA has a function of outputting a quantum state corresponding to a solution to the combinatorial optimization problem. The quantum circuit of the QAOA is acquired, for example, by the acquisition unit 401. The quantum circuit of the QAOA may be set in advance by a user, for example.

[0057] The acquisition unit 401 acquires various types of information used in processing by each functional unit. The acquisition unit 401 stores the acquired various types of information in the storage unit 400 or outputs it to each functional unit. The acquisition unit 401 may also output the various types of information stored in the storage unit 400 to each functional unit. The acquisition unit 401 acquires various types of information based on, for example, a user's operation input. The acquisition unit 401 may also receive various types of information from, for example, a device other than the information processing device 100.

[0058] The acquiring unit 401 acquires, for example, a processing request requesting the solution of a combinatorial optimization problem. The processing request may include information indicating the combinatorial optimization problem, an Ising model, initial values ​​of the Ising model, and a quantum circuit of the QAOA. Specifically, the acquiring unit 401 acquires the quantum circuit of the QAOA by accepting input of the quantum circuit of the QAOA based on an operational input from a user. Specifically, the acquiring unit 401 may receive the quantum circuit of the QAOA from another computer. The other computer is, for example, the client device 201.

[0059] The acquisition unit 401 acquires, for example, information indicating a combinatorial optimization problem. Specifically, the acquisition unit 401 acquires the information indicating the combinatorial optimization problem by accepting input of the information indicating the combinatorial optimization problem based on a user's operation input. Specifically, the acquisition unit 401 may receive the information indicating the combinatorial optimization problem from another computer. Specifically, the other computer is the client device 201. Specifically, the acquisition unit 401 may acquire the information indicating the combinatorial optimization problem by extracting it from a processing request.

[0060] The acquisition unit 401 acquires, for example, an Ising model. Specifically, the acquisition unit 401 acquires the Ising model by accepting input of the Ising model based on an operation input from a user. Specifically, the acquisition unit 401 may receive the Ising model from another computer. The other computer is, for example, the client device 201. Specifically, the acquisition unit 401 may acquire the Ising model by extracting it from a processing request.

[0061] The acquisition unit 401 acquires, for example, an initial value of the Ising model. Specifically, the acquisition unit 401 acquires the initial value of the Ising model by accepting input of the initial value of the Ising model based on an operation input by a user. Specifically, the acquisition unit 401 may receive the initial value of the Ising model from another computer. The other computer is, for example, the client device 201. Specifically, the acquisition unit 401 may acquire the initial value of the Ising model by extracting it from a processing request.

[0062] The acquisition unit 401 acquires, for example, the quantum circuit of the QAOA. Specifically, the acquisition unit 401 acquires the quantum circuit of the QAOA by accepting input of the quantum circuit of the QAOA based on operation input by a user. Specifically, the acquisition unit 401 may receive the quantum circuit of the QAOA from another computer. The other computer is, for example, the client device 201. Specifically, the acquisition unit 401 may acquire the quantum circuit of the QAOA by extracting it from a processing request.

[0063] The acquisition unit 401 may receive a start trigger for starting processing by any of the functional units. The start trigger may be, for example, a predetermined operational input by a user. The start trigger may be, for example, reception of predetermined information from another computer. The start trigger may be, for example, output of predetermined information by any of the functional units. The acquisition unit 401 receives, for example, acquisition of a processing request as a start trigger for starting processing by the first calculation unit 402, the determination unit 403, and the second calculation unit 404.

[0064] The first calculation unit 402 calculates a first solution to the combinatorial optimization problem based on the Ising model. For example, the first calculation unit 402 calculates the first solution to the combinatorial optimization problem based on set initial values ​​and the Ising model in response to the acquisition of a processing request by the acquisition unit 401. This allows the first calculation unit 402 to obtain guidelines for determining parameters of the QAOA, making it easier to determine the parameters of the QAOA.

[0065] For example, each time the second calculation unit 404 calculates a second solution, the first calculation unit 402 sets the second solution as an initial value. For example, each time the second calculation unit 404 calculates a second solution, the first calculation unit 402 calculates a new first solution to the combinatorial optimization problem based on the set initial value and the Ising model. This allows the first calculation unit 402 to obtain a guideline for determining the parameters of the QAOA, making it easier to determine the parameters of the QAOA. The first calculation unit 402 corresponds to, for example, the Ising machine 306.

[0066] The determination unit 403 determines the values ​​of the parameters of the QAOA so as to maximize the probability that the quantum state of the quantum circuit of the QAOA will be the first solution calculated by the first calculation unit 402. For example, each time the first calculation unit 402 calculates a first solution, the determination unit 403 determines the values ​​of the parameters of the QAOA so as to maximize the probability that the quantum state of the quantum circuit of the QAOA will be the solution of 1. This allows the determination unit 403 to appropriately determine the parameters of the QAOA, making it easier to calculate a second solution to the combinatorial optimization problem based on the quantum circuit of the QAOA.

[0067] The second calculation unit 404 calculates a second solution to the combinatorial optimization problem based on the quantum circuit of the QAOA in which the parameter values ​​determined by the determination unit 403 have been set. For example, each time the determination unit 403 determines a parameter value, the second calculation unit 404 sets the parameter value in the quantum circuit of the QAOA. For example, the second calculation unit 404 calculates a second solution to the combinatorial optimization problem based on the quantum circuit of the QAOA in which the parameter values ​​have been set. This allows the second calculation unit 404 to calculate an appropriate solution to the combinatorial optimization problem. The second calculation unit 404 corresponds to the QPU 307.

[0068] The information processing device 100 repeatedly executes the series of processes by the first calculation unit 402, the determination unit 403, and the second calculation unit 404 until a predetermined condition is met. The predetermined condition may be, for example, that the series of processes is calculated a predetermined number of times. This allows the information processing device 100 to bring the second solution calculated by the second calculation unit 404 closer to the optimal solution of the combinatorial optimization problem.

[0069] The output unit 405 outputs the processing results of at least one of the functional units. The output format may be, for example, display on a display, printout 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. This allows the output unit 405 to notify the user of the processing results of at least one of the functional units, thereby improving the convenience of the information processing device 100.

[0070] The output unit 405 outputs the second solution calculated by the second calculation unit 404. The output unit 405 outputs, for example, the second solution last calculated by the second calculation unit 404. Specifically, the output unit 405 outputs the second solution last calculated by the second calculation unit 404 so that it can be referenced by a user. Specifically, the output unit 405 may transmit the second solution last calculated by the second calculation unit 404 to another computer. In this way, the output unit 405 can make the solution to the combinatorial optimization problem available externally.

[0071] Here, the case where the information processing device 100 includes the first calculation unit 402 and the second calculation unit 404 has been described, but this is not limiting. For example, the information processing device 100 may use the first calculation unit 402 by communicating with another computer having the first calculation unit 402. For example, the information processing device 100 may use the second calculation unit 404 by communicating with another computer having the second calculation unit 404.

[0072] (Example of Operation of Information Processing Device 100) Next, an example of operation of the information processing device 100 will be described with reference to FIGS.

[0073] 5 to 8 are explanatory diagrams showing an example of the operation of the information processing device 100. In FIG. 5, the information processing device 100 acquires information indicating a combinatorial optimization problem min(E=C(z)). E is energy. E=C(z) is an objective function to be minimized. z is a state. The information processing device 100 identifies the combinatorial optimization problem min(E=C(z)) based on the information indicating the combinatorial optimization problem.

[0074] The information processing device 100 has an initial value for the Ising model. The initial value is, for example, the value of the state z. The information processing device 100 sets a QAOA quantum circuit 600 corresponding to the combinatorial optimization problem. Now, moving on to the description of FIG. 6 , an example of the QAOA quantum circuit 600 will be described.

[0075] Figure 6 shows an example of a QAOA quantum circuit 600. In Figure 6, the QAOA quantum circuit 600 includes a Hadamard gate 601 that represents an operation on the state of each of n qubits, and a QAOA Ansatz 610 that represents an operation on the state of the n qubits, where n is the number of qubits.

[0076] The QAOA Ansatz 610 represents gates 611 to 614. The gates 611 and 613 represent, for example, phase separation operators. The gates 612 and 614 represent, for example, mixing operators. The QAOA Ansatz 610 is defined by hyperparameters (γ, β). In the example of FIG. 6, the level of the QAOA Ansatz 610 is 2.

[0077] 5, (5-1) the information processing device 100 calculates a state z0 that is a solution to C(z) based on the Ising model and the initial value using the Ising machine 306. The information processing device 100 calculates a state z0 that is a solution to C(z) based on the Ising model and the initial value using the Ising machine 306 in accordance with, for example, a digital annealer.

[0078] (5-2) The information processing device 100, by using the CPU 301 and the QPU 307, calculates the hyperparameter (γ * , β * 7, the information processing device 100 determines the hyperparameter (γ * , β * An example of determining the .times. ...

[0079] Figure 7 shows the hyperparameter (γ * , β *7, (7-1) the information processing device 100 applies a superposition state |s> to n quantum bits by the QPU 307. The superposition state |s> is defined by, for example, the following formula (1).

[0080]

[0081] The information processing apparatus 100 uses the QPU 307 to calculate p (γ i , β i ) to n qubits. c (γ1)U x (β1)…U c (γ p ) U x (β p ), where i = 1, 2, ..., p, to identify the quantum state |ψ(γ, β)〉.

[0082] The information processing apparatus 100 performs a swap test using the QPU 307 to determine the probability p z0 (γ, β) = <ψ (γ, β) | z0> <z0 | ψ (γ, β)> = <ψ (γ, β) | z0> 2 The information processing device 100 measures the probability p z0 The quantum circuit 700 for the swap test includes a Hadamard gate 701, and measures p z0 (γ,β) = <ψ(γ,β)|z 0 ><z 0 |ψ(γ,β)> is measurable.

[0083] Specifically, the information processing device 100 performs n-shot sampling of the quantum state at the measurement point 710 according to the swap test quantum circuit 700 shown in FIG. 7, and calculates the probability p z0 More specifically, if n=1000, and the number of times the quantum state of the measurement point 710 is measured as 0 is 10, the information processing device 100 measures the probability p z0 (γ, β)=10 / 1000.

[0084] The information processing device 100 uses the CPU 301 to calculate the measured probability p z0The hyperparameter (γ * , β * The information processing device 100 determines the probability p z0 We set the objective function to maximize (γ, β) and the hyperparameter (γ * , β * ) is calculated.

[0085] As described above, the information processing device 100 uses the CPU 301 to calculate the hyperparameter (γ * , β * The information processing device 100 repeatedly determines the hyperparameter (γ * , β * ) is calculated a predetermined number of times, the hyperparameter (γ * , β * ) is statistically determined. The predetermined number of times is, for example, set in advance. The predetermined number of times is, for example, a first number.

[0086] Returning to the explanation of FIG. 5, (5-3) the information processing device 100, using the CPU 301 and the QPU 307, calculates (γ * , β * ), the quantum state |ψ(γ * , β * )> is shot-sampled to obtain the optimal classical state z * Now, we turn again to the explanation of FIG. 6 and determine the optimal classical state z * An example of determining the above will be described.

[0087] FIG. 6 shows the optimal classical state z * 6 shows an example of determining (γ * , β * ) to n qubits. c (γ1)U x (β1)…U c (γ p ) U x (βp ) to obtain the quantum state |ψ(γ * , β * The information processing device 100 uses the QPU 307 to identify the quantum state |ψ(γ * , β * )> is shot-sampled to determine n classical states z. For example, the information processing device 100 uses the QPU 307 to * , β * The quantum state |ψ(γ * , β * )> is projected in the Z direction to obtain the state z, and this is repeated n times to determine n classical states z1.

[0088] The information processing device 100 calculates, by the CPU 301, a classical state z1 that is a provisional solution to the combinatorial optimization problem based on n classical states z1. * The information processing apparatus 100 determines, for example, by the CPU 301, min(E1)<min(E0, E1 * Here, the information processing device 100 determines whether min(E1)<min(E0, E1) is satisfied. * ), the CPU 301 * On the other hand, the information processing device 100 determines that min(E1)<min(E0, E1) * ), the CPU 301 calculates z1 based on E1 and Hamming Distance. * Determine.

[0089] Returning to the explanation of FIG. 5 , (5-4) the information processing device 100 determines, via the CPU 301, whether or not a termination condition is met. The termination condition is, for example, that the series of processes (5-1) to (5-3) have been performed a predetermined number of times. The predetermined number of times is, for example, set in advance. The predetermined number of times is, for example, a second number. The second number may be the same as the first number. The termination condition may be defined, for example, by a threshold value for the energy E or the state z.

[0090] If the termination condition is not satisfied, the information processing device 100 causes the CPU 301 to * is set as the initial value of the Ising machine 306, and the series of processes (5-1) to (5-3) are performed again.

[0091] If the termination condition is satisfied, the information processing device 100 * ) and argmin(C(z)). argmin(C(z)) is, for example, z0 or z1 * As a result, the information processing device 100 can accurately calculate argmin(C(z)), which is the solution to the combinatorial optimization problem. The information processing device 100 can reduce the time required to calculate the solution to the combinatorial optimization problem. Next, we will move on to the explanation of FIG. 8 and describe the effects of the information processing device 100.

[0092] Fig. 8 shows the effect of the information processing device 100. A graph 800 in Fig. 8 represents the distribution of the probability that a quantum state initially represents a classical state z that takes on each value of energy E. As shown in the graph 800 in Fig. 8, the distribution of the probability that a quantum state initially represents a classical state z that takes on each value of energy E is uniform.

[0093] In response to this, the information processing device 100 determines the hyperparameters (γ, β) for the combinatorial optimization problem prior to QAOA in accordance with the calculation results of the Ising machine 306 so as to increase the probability that the quantum state will represent a classical state z that takes a value around E min. Graph 810 in FIG. 8 represents the distribution of probabilities that the quantum state will represent a classical state z that takes each value of energy E after the hyperparameters (γ, β) are determined. As shown in graph 810 in FIG. 8, the probability that the quantum state will represent a classical state z that takes a value around E min increases. This enables the information processing device 100 to improve the efficiency of searching for an optimal solution through QAOA.

[0094] The information processing device 100 then increases the probability that the quantum state represents a classical state z that takes a value around E min, and then calculates a solution to the combinatorial optimization problem using QAOA. Graph 820 in Fig. 8 represents the distribution of probabilities that the quantum state represents a classical state z that takes each value of energy E when the solution to the combinatorial optimization problem is calculated using QAOA. As shown in graph 820 in Fig. 8, there is an increased probability that the quantum state represents a classical state z that takes a value in a narrow range around E min that is closer to E min.

[0095] As a result, the information processing device 100 can use QAOA to efficiently and accurately approximate the optimal solution to the combinatorial optimization problem. For example, the information processing device 100 can use QAOA to consider all states represented by quantum states that could be solutions to the combinatorial optimization problem, and can accurately calculate the solution to the combinatorial optimization problem. Therefore, the information processing device 100 can use QAOA to reduce the time required to calculate the solution to the combinatorial optimization problem.

[0096] Here, the information processing device 100 uses the QPU 307 to calculate the hyperparameter (γ * , β * ) and determine the optimal classical state z * However, the present invention is not limited to this. For example, the information processing device 100 may have a quantum computer simulator. Specifically, the information processing device 100 uses the quantum computer simulator to determine the hyperparameter (γ * , β * ) and determine the optimal classical state z * Determine.

[0097] (Application Examples of the Information Processing Device 100) Next, application examples of the information processing device 100 will be described. The information processing device 100 can be applied, for example, to solving a combinatorial optimization problem of searching for a movement path for a moving object. The information processing device 100 can be applied, for example, to solving a combinatorial optimization problem of creating an employee work schedule. The information processing device 100 can be applied, for example, to solving a combinatorial optimization problem of creating a product manufacturing plan.

[0098] (Overall Processing Procedure) Next, an example of an overall processing procedure executed by the information processing device 100 will be described with reference to Fig. 9. The overall processing is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, the network I / F 303, the Ising machine 306, and the QPU 307 shown in Fig. 3.

[0099] 9 is a flowchart showing an example of an overall processing procedure. In FIG. 9, the information processing device 100 acquires a combinatorial optimization problem min(E=C(z)) using the CPU 301 (step S901). Next, the information processing device 100 calculates, using the Ising machine 306, a state z that is a solution to C(z) based on the initial value (step S902).

[0100] Next, the information processing device 100 executes a first determination process, which will be described later with reference to FIG. 10, using the QPU 307 to determine the hyperparameter (γ * , β * ) (step S903). Then, the information processing device 100 determines the quantum state |ψ(γ * , β * )> is shot-sampled to obtain the optimal classical state z * is determined (step S904).

[0101] Next, the information processing device 100 calculates the optimal classical state z *The information processing device 100 determines whether the predetermined number of times has been determined (step S905). The predetermined number of times is, for example, set in advance by the user. If the predetermined number of times has not been determined (step S905: No), the information processing device 100 proceeds to the processing of step S906. On the other hand, if the predetermined number of times has been determined (step S905: Yes), the information processing device 100 proceeds to the processing of step S907.

[0102] In step S906, the information processing device 100 sets the initial value of the Ising machine 306 to the optimal classical state z * (step S906). Then, the information processing apparatus 100 returns to the process of step S902.

[0103] In step S907, the information processing device 100 calculates min(C(z0), C(z1 * )) (step S907). The information processing device 100 may output argmin(C(z)). Then, the information processing device 100 ends the overall processing.

[0104] 10, an example of a procedure of the first determination process executed by the information processing device 100 will be described. The first determination process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, the network I / F 303, and the QPU 307 shown in FIG.

[0105] 10 is a flowchart illustrating an example of a first determination process. In FIG. 10, the information processing device 100 applies a superposition state |s> to n quantum bits (step S1001). Next, the information processing device 100 applies a superposition state |s> to n quantum bits (p number of (γ i , β i ) for n qubits, U c (γ1)U x (β1)…U c (γ p ) U x (β p ) to identify the quantum state |ψ(γ, β)> (step S1002).

[0106] Next, the information processing device 100 calculates the probability p z0(γ, β) = <ψ(γ, β) | z 0 ><z 0 | ψ(γ, β)> (step S1003). Then, the information processing device 100 measures the probability p z0 The hyperparameters (γ * , β * ) is determined (step S1004).

[0107] Next, the information processing device 100 calculates the hyperparameters (γ * , β * ) has been determined a predetermined number of times (step S1005). The predetermined number of times is set in advance by the user, for example. If the predetermined number of times has not been determined (step S1005: No), the information processing device 100 returns to the processing of step S1001. On the other hand, if the predetermined number of times has been determined (step S1005: Yes), the information processing device 100 ends the first determination processing.

[0108] 11, an example of a procedure of the second determination process executed by the information processing device 100 will be described. The second determination process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, the network I / F 303, and the QPU 307 shown in FIG.

[0109] 11 is a flowchart illustrating an example of the second determination process procedure. In FIG. 11, the information processing device 100 applies a superposition state |s> to n quantum bits (step S1101).

[0110] Next, the information processing device 100 calculates the latest (γ * , β * ) to n qubits. c (γ1)U x (β1)…U c (γ p ) U x (β p ) to obtain the quantum state |ψ(γ * , β * )> (step S1102). Then, the information processing device 100 identifies the quantum state |ψ(γ * , β *)> is sampled in n shots to determine n classical states z1 (step S1103).

[0111] Next, the information processing device 100 calculates the energy E corresponding to each classical state z, and satisfies min(E)<min(E, E). * ) (step S1104). E0 is the energy corresponding to z0. E1 * is z1 * is the energy corresponding to z1 * represents the classical state that is currently judged to be optimal.

[0112] Here, min(E1)<min(E0, E1 * If min(E1)<min(E0, E1) is satisfied (step S1104: Yes), the information processing apparatus 100 proceeds to the process of step S1105. * ) (step S1104: No), the information processing apparatus 100 proceeds to the process of step S1106.

[0113] In step S1105, the information processing device 100 * is determined to be argmin(E1) (step S1105). argmin(E1) represents any classical state z1 that takes min(E1) among E1 corresponding to each classical state z1. Then, the information processing device 100 ends the second determination process.

[0114] In step S1106, the information processing apparatus 100 calculates z based on E and the Hamming Distance. * (Step S1106). E1, Hamming Distance is, for example, ((E1-E0) x Hamming Distance (z1, z0)). -1 Then, the information processing device 100 ends the second determination process. Here, the information processing device 100 may omit some of the processing steps in the flowcharts of Figures 9 to 11. For example, the processing of steps S905 and S906 can be omitted. For example, the processing of step S1005 can be omitted.

[0115] As described above, the information processing device 100 can calculate a first solution to a combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem. The information processing device 100 can determine parameter values ​​for a quantum approximate optimization algorithm so as to maximize the probability that the quantum state of a quantum circuit of the quantum approximate optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution. The information processing device 100 can calculate a second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximate optimization algorithm to which the determined parameter values ​​have been set. This allows the information processing device 100 to reduce the time required to accurately calculate a solution to a combinatorial optimization problem.

[0116] According to the information processing device 100, a series of processes of calculating a first solution, determining parameter values, and calculating a second solution can be repeatedly executed until a predetermined condition is satisfied, thereby improving the accuracy with which the information processing device 100 calculates a solution to a combinatorial optimization problem.

[0117] According to the information processing device 100, it is possible to adopt a predetermined condition in which the second solution is calculated a predetermined number of times, thereby enabling the information processing device 100 to repeatedly execute a series of processes an appropriate number of times and to accurately calculate a solution to a combinatorial optimization problem.

[0118] The information processing device 100 can output the calculated second solution, thereby making the second solution available to the outside as a solution to the combinatorial optimization problem.

[0119] The information processing device 100 can use an Ising machine that solves combinatorial optimization problems to calculate a first solution to the combinatorial optimization problem based on an Ising model. The information processing device 100 can use a quantum processing device that handles quantum circuits of a quantum approximate optimization algorithm to calculate a second solution to the combinatorial optimization problem based on the quantum circuits of the quantum approximate optimization algorithm to which determined parameter values ​​are set. This allows the information processing device 100 to efficiently calculate the first solution and efficiently calculate the second solution.

[0120] According to the information processing device 100, a first solution to a combinatorial optimization problem can be calculated based on an Ising model in accordance with Digital Annealer. This allows the information processing device 100 to efficiently calculate the first solution.

[0121] The information processing method described in this embodiment can be realized by executing a 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 the computer. The recording medium may be a hard disk, a flexible disk, a CD (Compact Disc)-ROM, an MO (Magneto Optical Disc), a DVD (Digital Versatile Disc), or the like. The information processing program described in this embodiment may also be distributed via a network such as the Internet.

[0122] REFERENCE SIGNS LIST 100 Information processing device 101 First solution 102 Second solution 110 Ising model 120 Parameters 130, 600, 700 Quantum circuit 200 Information processing system 201 Client device 210 Network 300 Bus 301 CPU 302 Memory 303 Network I / F 304 Recording medium I / F 305 Recording medium 306 Ising machine 307 QPU 400 Storage unit 401 Acquisition unit 402 First calculation unit 403 Determination unit 404 Second calculation unit 405 Output unit 601, 701 Hadamard gate 610 QAOA Ansatz 611, 612, 613, 614 Gate 710 Measurement point 800, 810, 820 Graph

Claims

1. An information processing program that causes a computer to execute the following processes: calculate a first solution to a combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determine parameter values ​​of the quantum approximation optimization algorithm so as to maximize the probability that the quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution; and calculate a second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximation optimization algorithm in which the determined parameter values ​​are set.

2. The information processing program according to claim 1, further comprising: calculating a new first solution to the combinatorial optimization problem based on the Ising model with the calculated second solution set as its initial value; determining new parameter values ​​so as to maximize the probability that the quantum state of the quantum circuit of the quantum approximate optimization algorithm will become the newly calculated first solution; and calculating a new second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximate optimization algorithm with the newly determined parameter values ​​set thereto.

3. The information processing program according to claim 2, characterized in that the predetermined condition is that the second solution is calculated a predetermined number of times.

4. The information processing program according to any one of claims 1 to 3, characterized in that the information processing program causes the computer to execute a process of outputting the calculated second solution.

5. The information processing program according to claim 1, characterized in that the process of calculating the first solution uses an Ising machine that solves the combinatorial optimization problem to calculate the first solution to the combinatorial optimization problem based on the Ising model, and the process of calculating the second solution uses a quantum processing device that processes the quantum circuit of the quantum approximate optimization algorithm to calculate the second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximate optimization algorithm in which the determined parameter values ​​are set.

6. An information processing method, characterized in that a computer executes the following processes: calculating a first solution to a combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining parameter values ​​of the quantum approximation optimization algorithm so as to maximize the probability that the quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution; and calculating a second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximation optimization algorithm in which the determined parameter values ​​are set.

7. An information processing device having a control unit that calculates a first solution to a combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem, determines parameter values ​​of the quantum approximation optimization algorithm so as to maximize the probability that the quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution, and calculates a second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximation optimization algorithm in which the determined parameter values ​​are set.

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