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

[Technical Field]

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

[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 a set of allowed quantum states. Also, for example, in a general aspect, there is a technique for selecting parameter values ​​for a quantum approximate optimization algorithm using a Bayesian optimizer. Also, for example, there is a technique for executing a quantum approximate optimization algorithm. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Special Publication No. 2022-509841 [Patent Document 2] Special Publication No. 2021-504805 [Patent Document 3] U.S. Patent No. 10,846,366 [Patent Document 4] US Patent Application Publication No. 2022 / 0245497 Summary of the Invention [Problem to be solved by the invention]

[0005] However, it is difficult to efficiently solve combinatorial optimization problems using conventional techniques. 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. [Means for solving the problem]

[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. [Effects of the Invention]

[0008] According to one aspect, combinatorial optimization problems can be made easier to solve. [Brief explanation of the drawings]

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

[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] (An example of an information processing method according to an embodiment) 1 is an explanatory diagram illustrating an example of an information processing method according to an embodiment. An 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 constraints. Conventional methods for solving combinatorial optimization problems include, for example, the simulated annealing (SA) method or a quantum approximation optimization algorithm. In the following explanation, the quantum approximation optimization algorithm may be referred to as "QAOA (Quantum Approximate Optimazation Algorithm)."

[0013] The SA method is a method for solving combinatorial optimization problems by repeatedly searching for solutions to combinations of variables while adjusting the range of search for solutions for combinations of variables, for example, by using thermal noise. The QAOA method is a method for solving combinatorial optimization problems by using, for example, quantum circuits that represent quantum states corresponding to combinations of variables. The SA method is also known as simulated annealing.

[0014] Specifically, QAOA solves combinatorial optimization problems by repeating the following 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, BFGS method, quadratic approximation method, Powell's method, or Bayesian estimation when changing the parameters of a 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, with SA, the farther the initial value is from the optimal solution, the longer it takes to solve the combinatorial optimization problem and find the optimal solution. A similar tendency exists with quantum annealing. 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 relationship between energy and the parameters of the quantum circuit may be non-convex, 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, the 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 QAOA quantum circuit 130 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 becomes 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 z1 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 z1 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] Here, the case where the information processing device 100 has a QPU has been described, but this is not limiting. 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] (An example of the 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 the combinatorial optimization problem based on, for example, the received information. The information processing device 100 identifies, for example, a QAOA quantum circuit 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, for example, calculates a second solution to the combinatorial optimization problem 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 device 100) Next, an example of the hardware configuration of the information processing device 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, CPU 301 is responsible for overall control of information processing device 100. 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 or ROM stores various programs, and RAM is used as a work area for CPU 301. The programs stored in memory 302 are loaded into CPU 301, causing CPU 301 to execute 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 running 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 above-described components, 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 the recording medium I / Fs 304 and recording media 305.

[0049] (Example of hardware configuration of client device 201) A specific example of the hardware configuration of the client device 201 is 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 device 100) Next, an example of the functional configuration of the information processing device 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 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, for example.

[0054] The storage unit 400 stores various types of information that are referenced or updated in the processing of 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 be set in advance by a user, for example.

[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 QAOA quantum circuit corresponding to a combinatorial optimization problem. The QAOA quantum circuit represents a quantum operation procedure. The QAOA quantum circuit has a function of outputting a quantum state corresponding to a solution to the combinatorial optimization problem. The QAOA quantum circuit is acquired, for example, by the acquisition unit 401. The QAOA quantum circuit 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 different from the information processing device 100.

[0058] The acquiring unit 401 acquires, for example, a processing request for solving 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 acquiring unit 401 acquires, for example, information indicating a combinatorial optimization problem. Specifically, the acquiring unit 401 acquires the information indicating the combinatorial optimization problem by accepting input of the information indicating the combinatorial optimization problem based on an operational input from a user. Specifically, the acquiring 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 acquiring 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 operational 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, the 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 acquiring unit 401 acquires, for example, a quantum circuit of QAOA. Specifically, the acquiring unit 401 acquires the quantum circuit of QAOA by accepting input of the quantum circuit of QAOA based on an operational input from a user. Specifically, the acquiring unit 401 may receive the quantum circuit of QAOA from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 401 may acquire the quantum circuit of QAOA by extracting it from a processing request.

[0063] The acquiring unit 401 may receive a start trigger to start 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 acquiring unit 401 receives, for example, acquisition of a processing request as a start trigger to start processing by the first calculating unit 402, the determining unit 403, and the second calculating unit 404.

[0064] The first calculation unit 402 calculates a first solution to the combinatorial optimization problem based on the Ising model. For example, in response to the acquisition unit 401 acquiring a processing request, the first calculation unit 402 calculates the first solution to the combinatorial optimization problem based on set initial values ​​and the Ising model. 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 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 parameter values ​​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 parameter values ​​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. 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 the 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 a 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 is, 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 result of at least one of the functional units. The output format is, 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. In this way, the output unit 405 can notify the user of the processing result 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 the present invention is not limited to this. 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] (An example of the operation of the information processing device 100) Next, an example of the 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 * ) is determined. Now, moving to the explanation of FIG. 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 using the QPU 307. The superposition state |s> is defined by, for example, the following formula (1).

[0080]

number

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

[0082] The information processing device 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(γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> The quantum circuit 700 for the swap test includes a Hadamard gate 701, and at a measurement point 710, p z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> Make it measurable.

[0083] Specifically, the information processing device 100 performs n-shot sampling of the quantum state at the measurement point 710 in accordance with 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=10, the information processing device 100 measures probability p z0 (γ,β)=10 / 1000.

[0084] The information processing device 100 uses the CPU 301 to calculate the measured probability p z0 The 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 * ) is repeatedly determined. The information processing device 100 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 * )> and obtain the optimal classical state z1 * Now, let us return to the explanation of Figure 6 and determine the optimal classical state z1 * An example of determining the above will be described.

[0087] Figure 6 shows the optimal classical state z1 * 6 shows an example of determining (γ * ,β * ) for n qubits, U c (γ1)U x (β1)…U c (γ p )U x (β p ), we 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 sampled n-shot to determine n classical states z1. For example, the information processing device 100 uses the QPU 307 to * ,β * ) is set, the quantum state |ψ(γ * ,β * )> is projected in the Z direction to obtain 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 tentative solution to the combinatorial optimization problem based on n classical states z1. * The information processing apparatus 100 determines, for example, min(E1) by the CPU 301. <min(E0,E1 *Here, the information processing device 100 determines whether min(E1) is satisfied. <min(E0,E1 * ), the CPU 301 * On the other hand, the information processing device 100 determines, for example, 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, by the CPU 301, whether or not a termination condition is satisfied. 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 to explain the effects of the information processing device 100.

[0092] Fig. 8 shows the effect of the information processing device 100. 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 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 a 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 Emin. 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 Emin increases. This enables the information processing device 100 to improve the efficiency of searching for an optimal solution through QAOA.

[0094] Then, the information processing device 100 increases the probability that the quantum state represents a classical state z that takes a value around Emin, and then calculates a solution to the combinatorial optimization problem using QAOA. Graph 820 in Fig. 8 shows 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 Emin that is closer to Emin.

[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 z1 * 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 z1 * Determine.

[0097] (Application example of 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)) by the CPU 301 (step S901). Next, the information processing device 100 calculates a state z0 that is a solution to C(z) by the Ising machine 306 based on an 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 * )> and obtain the optimal classical state z1 * is determined (step S904).

[0101] Next, the information processing device 100 calculates the optimal classical state z1 * It is determined 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 z1 * (step S906). Then, the information processing device 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] (First decision processing procedure) Next, an example of a first determination process procedure executed by the information processing device 100 will be described with reference to Fig. 10. 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. 3.

[0105] FIG. 10 is a flowchart showing an example of the 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)|z0><z0|ψ(γ,β)> (Step S1003). Then, the information processing device 100 measures the probability p z0 The hyperparameter (γ * ,β * ) is determined (step S1004).

[0107] Next, the information processing device 100 calculates the hyperparameter (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] (Second decision processing procedure) Next, an example of a procedure of the second determination process executed by the information processing device 100 will be described with reference to Fig. 11. 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. 3.

[0109] 11 is a flowchart illustrating an example of the procedure of the second determination process. 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 * ) for n qubits, U c (γ1)U x (β1)…U c (γ p )U x (β p ), we obtain the quantum state |ψ(γ * ,β * )> (step S1102). Then, the information processing device 100 identifies the quantum state |ψ(γ * ,β * )> is sampled n shots to determine n classical states z1 (step S1103).

[0111] Next, the information processing device 100 calculates the energy E1 corresponding to each classical state z1, and calculates min(E1) <min(E0,E1 * ) (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] where min(E1) <min(E0,E1 * ) (step S1104: Yes), the information processing apparatus 100 proceeds to the process of step S1105. <min(E0,E1 *) (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 device 100 calculates z1 based on E1 and the Hamming Distance. * (Step S1106). E1, Hamming Distance is determined as, 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 processes in the steps of the flowcharts in FIGS. 9 to 11. For example, the processes in steps S905 and S906 can be omitted. For example, the process in 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 enabling the information processing device 100 to improve the accuracy of calculating 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] The following additional notes are provided regarding the above-described embodiment.

[0123] (Supplementary Note 1) 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 that the probability that a quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution is maximized; calculating 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; An information processing program that causes a computer to execute a process.

[0124] (Supplementary Note 2) A first solution to the combinatorial optimization problem is newly calculated based on the Ising model in which the calculated second solution is set as an initial value; determining new values ​​of the parameters so that the probability that the quantum state of the quantum circuit of the quantum approximate optimization algorithm will become the newly calculated first solution is maximized; calculating a new second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximate optimization algorithm to which the newly determined parameter values ​​have been set; 2. The information processing program according to claim 1, wherein the program causes the computer to repeatedly execute the process until a predetermined condition is satisfied.

[0125] (Supplementary Note 3) The information processing program according to Supplementary Note 2, wherein the predetermined condition is that the second solution is calculated a predetermined number of times.

[0126] (Appendix 4) Outputting the calculated second solution. 4. The information processing program according to any one of claims 1 to 3, which causes the computer to execute the process.

[0127] (Supplementary Note 5) The process of calculating the first solution includes: calculating the first solution to the combinatorial optimization problem based on the Ising model using an Ising machine that solves the combinatorial optimization problem; The process of calculating the second solution includes: 2. The information processing program according to claim 1, further comprising: calculating the 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, using a quantum processing device that processes the quantum circuit of the quantum approximate optimization algorithm.

[0128] (Appendix 6) Calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining parameter values ​​of the quantum approximation optimization algorithm so that the probability that a quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution is maximized; calculating 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; An information processing method characterized in that the processing is executed by a computer.

[0129] (Supplementary Note 7) Calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining parameter values ​​of the quantum approximation optimization algorithm so that the probability that a quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution is maximized; calculating 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; An information processing device comprising a control unit. [Explanation of symbols]

[0130] 100 Information processing device 101 First Solution 102 Second Solution 110 Ising model 120 parameters 130,600,700 quantum circuit 200 Information Processing Systems 201 Client device 210 Network 300 Bus 301 CPU 302 memory 303 Network I / F 304 Recording Media I / F 305 Recording Media 306 Ising Machine 307 QPUs 400 Storage section 401 Acquisition Department 402 First Calculation Unit 403 Decision Section 404 Second Calculation Unit 405 Output Section 601,701 Hadamard Gate 610 QAOA Ansatz 611,612,613,614 gates 710 measurement points 800,810,820 graph

Claims

1. calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining parameter values ​​of the quantum approximation optimization algorithm so that the probability that a quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution is maximized; calculating 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; An information processing program that causes a computer to execute a process.

2. a new first solution to the combinatorial optimization problem is calculated based on the Ising model in which the calculated second solution is set as an initial value; determining new values ​​of the parameters so that the probability that the quantum state of the quantum circuit of the quantum approximate optimization algorithm will become the newly calculated first solution is maximized; calculating a new second solution to the combinatorial optimization problem based on the quantum circuit of the quantum approximate optimization algorithm to which the newly determined parameter values ​​have been set; 2. The information processing program according to claim 1, wherein the program causes the computer to repeatedly execute the process until a predetermined condition is satisfied.

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

4. calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining parameter values ​​of the quantum approximation optimization algorithm so that the probability that a quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution is maximized; calculating 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; An information processing method characterized in that the processing is executed by a computer.

5. calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining parameter values ​​of the quantum approximation optimization algorithm so that the probability that a quantum state of a quantum circuit of the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will become the calculated first solution is maximized; calculating 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; An information processing device comprising a control unit.

Images