Information processing program, information processing method, and information processing apparatus

Abstract

To facilitate solving a combination optimization problem.SOLUTION: An information processing apparatus 100 determines a first value 101 of a parameter of a quantum circuit 130 of a QAOA so that energy corresponding to a quantum state of the quantum circuit 130 is minimal. On the basis of an ising model 110 corresponding to an acquired combination optimization problem, the information processing apparatus 100 calculates a first solution 121 of the combination optimization problem. The information processing apparatus 100 determines a second value 102 of the parameter of the quantum circuit 130 from the determined first value 101 of the parameter of the quantum circuit 130 so that the probability that a set quantum state of the quantum circuit 130 is the calculated first solution 121 is maximal. The information processing apparatus 100 calculates a second solution 122 of the combination optimization problem on the basis of the quantum circuit 130 to which the determined second value 102 of the parameter is set.SELECTED DRAWING: Figure 1

Description

[Technical Field]

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

[0002] Conventionally, there are quantum approximate optimization algorithms that solve combinatorial optimization problems. For example, quantum approximate optimization algorithms solve combinatorial optimization problems 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."

[0003] Prior art includes, for example, a technique for mapping a cost function associated with a combinatorial optimization problem to an optimization problem on a permissible quantum state. Another example is a technique in which an AI (artificial intelligence) control unit determines one or more adjustable parameters corresponding to a calculation. Another example is a technique for calculating an objective function of a combinatorial optimization problem from second information extracted from first information and used in a process formulated as a combinatorial optimization problem. Another example is a technique for approximating unitary quantum dynamics. Another example is a technique for searching for a configuration of shapes subject to boundary distance constraints between shapes. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Special Publication No. 2021-504805 [Patent Document 2] Special Publication No. 2022-509841 [Patent Document 3] International Publication No. 2022 / 113720 [Patent Document 4] US Patent Application Publication No. 2014 / 0297247 [Patent Document 5] US Patent Application Publication No. 2011 / 0035194 Summary of the Invention [Problem to be solved by the invention]

[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. Specifically, in quantum approximate optimization algorithms, the energy and the parameters of a 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 optimal parameters.

[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, with respect to a quantum circuit of a quantum approximation optimization algorithm corresponding to a combinatorial optimization problem, determine first values ​​of parameters of the quantum approximation optimization algorithm so that energy corresponding to the quantum state of the quantum circuit is minimized, calculate a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem, determine second values ​​of the parameters from the determined first values ​​of the parameters so that the probability that the quantum state of the quantum circuit will become the calculated first solution is maximized, and set the determined second values ​​of the parameters, and calculate a second solution to the combinatorial optimization problem based on the quantum circuit. [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 an explanatory diagram (part 5) showing an example of the operation of the information processing device 100. [Figure 10] FIG. 10 is a flowchart illustrating an example of the overall processing procedure. [Figure 11] FIG. 11 is a flowchart illustrating an example of a procedure of the first determination process. [Figure 12] FIG. 12 is a flowchart illustrating an example of a procedure of the second determination process. [Figure 13] FIG. 13 is a flowchart illustrating an example of a procedure of the third 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. Information processing device 100 is a computer for solving a combinatorial optimization problem. Information processing device 100 is a computer for solving a combinatorial optimization problem. 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 in which solutions for combinations of variables are searched, for example, by using thermal noise. The SA method is also known as simulated annealing. The QAOA is a method based on the Variational Quantum Algorithm. The QAOA is a method for solving combinatorial optimization problems by using, for example, a quantum circuit that represents a quantum state corresponding to a combination of variables.

[0014] Specifically, QAOA solves combinatorial optimization problems by repeating the following process: "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." QAOA considers the distribution of energies of all classical states, for example, using quantum superposition states. 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, 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. For this reason, even with QAOA, the time required to solve a combinatorial optimization problem tends to increase.

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

[0025] 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.

[0026] 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 circuit 130 is, for example, a QAOA Anzatz. The quantum state probabilistically represents, for example, each value that the state z can take.

[0027] (1-1) The information processing device 100 determines a first value 101 of a parameter of the quantum circuit 130 so that the energy corresponding to the quantum state of the quantum circuit 130 of QAOA is minimized. The energy corresponds to, for example, a measurement value of <ψ(γ,β)|C(z)|ψ(γ,β)>. This allows the information processing device 100 to approximate the quantum circuit 130 to an eigenvalue problem. For information on approximating the quantum circuit 130 to an eigenvalue problem, see, for example, Reference 7 below.

[0028] Reference 7: Peruzzo, Alberto, et al. “A variational eigenvalue solver on a photonic quantum processor.” Nature communications 5.1 (2014): 4213.

[0029] (1-2) The information processing device 100 calculates a first solution 121 of the combinatorial optimization problem based on the 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 121 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.

[0030] (1-3) The information processing device 100 determines a second value 102 of the parameter of the quantum circuit 130 from the determined first value 101 of the parameter 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 121.

[0031] This makes it easier for the information processing device 100 to solve combinatorial optimization problems. The information processing device 100 can appropriately set parameters of the quantum circuit 130 based on the first solution 121 calculated using the Ising model 110, and can reduce the time required to perform QAOA.

[0032] (1-4) The information processing device 100 calculates a second solution 122 of the combinatorial optimization problem based on the quantum circuit 130 to which the determined second parameter values ​​102 are set. The information processing device 100 performs n-shot sampling of the quantum state using, for example, a QPU (Quantum Processing Unit) to calculate a state z1 that is the second solution 122.

[0033] 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 second parameter value 102 is set to obtain a state z n times, and calculates a state z1 that is the second solution 122 based on the distribution of the obtained states z. This allows the information processing device 100 to obtain a state z1 that is relatively close to the optimal solution and is a preferable solution.

[0034] (1-5) 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), (1-2), (1-3), and (1-4) 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.

[0035] Here, for example, suppose the combinatorial optimization problem is a MaxCut problem, and the quantum circuit 130 solves the combinatorial optimization problem without approximating it to an eigenvalue problem. In this case, if the depth p of the quantum circuit 130 is relatively small, the quantum circuit 130 may not be able to represent the entire combinatorial optimization problem, making it difficult to solve the combinatorial optimization problem accurately. On the other hand, the information processing device 100 can make it easy to solve the combinatorial optimization problem accurately even if the depth p of the quantum circuit 130 is relatively small.

[0036] Here, the case where the functions of the information processing device 100 are realized by 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 cooperation of multiple computers. For example, the functions of the information processing device 100 may be realized on the cloud.

[0037] 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 acquire the first solution 121 by controlling another computer having an Ising machine to calculate the first solution 121 of the combinatorial optimization problem.

[0038] 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 acquire a first solution 121 by controlling another computer having a QPU to calculate a first solution 121 of a combinatorial optimization problem. Furthermore, for example, the information processing device 100 may acquire a second solution 122 by controlling another computer having a QPU to calculate a second solution 122 of the combinatorial optimization problem.

[0039] (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.

[0040] 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.

[0041] 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.

[0042] 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.

[0043] (2-2) The information processing device 100 determines first values ​​of parameters of the identified quantum circuit so that the energy corresponding to the quantum state of the identified quantum circuit is minimized. 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 determines second values ​​of parameters of the identified quantum circuit from the determined first values ​​of parameters of the quantum circuit, for example, so that the probability that the quantum state of the identified quantum circuit will become the calculated first solution is maximized. 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 second values ​​of parameters are set.

[0044] (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.

[0045] 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.

[0046] 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 function of the client device 201 and may also operate as the client device 201.

[0047] (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.

[0048] 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.

[0049] 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.

[0050] 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.

[0051] 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.

[0052] 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.

[0053] 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 the recording medium I / Fs 304 and recording media 305.

[0054] (Example of hardware configuration of client device 201) Specifically, an 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. The client device 201 does not necessarily have to include the QPU 307.

[0055] (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.

[0056] 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 determination unit 402, a first calculation unit 403, a second determination unit 404, a second calculation unit 405, and an output unit 406.

[0057] 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.

[0058] The acquiring unit 401 to the output unit 406 function as an example of a control unit. Specifically, the acquiring unit 401 to the output unit 406 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 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] 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 processing request by accepting input of the processing request based on an operation input by a user. Specifically, the acquiring unit 401 may receive the processing request from another computer. The other computer is, for example, the client device 201.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] 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.

[0068] 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 determining unit 402, the first calculating unit 403, the second determining unit 404, and the second calculating unit 405.

[0069] The first determination unit 402 determines first values ​​of parameters of the QAOA so that the energy corresponding to the quantum state of the quantum circuit of the QAOA is minimized. For example, the first determination unit 402 determines first values ​​of parameters of the QAOA so that the energy corresponding to the quantum state of the quantum circuit of the QAOA is minimized in response to acquisition of a processing request by the acquisition unit 401. This allows the first determination unit 402 to appropriately determine the parameters of the QAOA, and allows the quantum circuit of the QAOA to approximate an eigenvalue problem.

[0070] For example, each time the second calculation unit 405 calculates a second solution, the first determination unit 402 determines a new first value of the parameter of the QAOA so that the energy corresponding to the quantum state of the quantum circuit of the QAOA is minimized. This allows the first determination unit 402 to appropriately determine the parameter of the QAOA and to approximate the quantum circuit of the QAOA to an eigenvalue problem. The first determination unit 402 corresponds to the QPU 307.

[0071] The first calculation unit 403 calculates a first solution to the combinatorial optimization problem based on the Ising model. For example, in response to acquisition of a processing request by the acquisition unit 401, the first calculation unit 403 calculates the first solution to the combinatorial optimization problem based on set initial values ​​and the Ising model. This allows the first calculation unit 403 to obtain guidelines for determining parameters of the QAOA, making it easier to determine the parameters of the QAOA.

[0072] For example, each time the second calculation unit 405 calculates a second solution, the first calculation unit 403 sets the second solution as an initial value. For example, each time the second calculation unit 405 calculates a second solution, the first calculation unit 403 newly calculates a first solution to the combinatorial optimization problem based on the set initial value and the Ising model. This allows the first calculation unit 403 to obtain a guideline for determining parameters of the QAOA, making it easier to determine the parameters of the QAOA. The first calculation unit 403 corresponds to, for example, the Ising machine 306.

[0073] The second determination unit 404 determines second values ​​of the parameters of the QAOA from the first 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 403. For example, each time the first calculation unit 403 calculates a first solution, the second determination unit 404 determines second values ​​of the parameters of the QAOA from the first 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. This allows the second determination unit 404 to appropriately determine the parameters of the QAOA, making it easier to calculate a second solution to a combinatorial optimization problem based on the quantum circuit of the QAOA. The second determination unit 404 corresponds to the QPU 307.

[0074] The second calculation unit 405 calculates a second solution to the combinatorial optimization problem based on the quantum circuit of the QAOA in which the second value of the parameter determined by the second determination unit 404 is set. For example, each time the second value of the parameter is determined by the second determination unit 404, the second calculation unit 405 sets the second value of the parameter in the quantum circuit of the QAOA. For example, the second calculation unit 405 calculates the second solution to the combinatorial optimization problem based on the quantum circuit of the QAOA in which the second value of the parameter is set. This allows the second calculation unit 405 to calculate an appropriate solution to the combinatorial optimization problem. The second calculation unit 405 corresponds to the QPU 307.

[0075] The information processing device 100 repeatedly executes a series of processes by the first determination unit 402, the first calculation unit 403, the second determination unit 404, and the second calculation unit 405 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 405 closer to an optimal solution to the combinatorial optimization problem.

[0076] The output unit 406 outputs the processing results 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 406 can 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.

[0077] The output unit 406 outputs the second solution calculated by the second calculation unit 405. The output unit 406 outputs, for example, the second solution last calculated by the second calculation unit 405. Specifically, the output unit 406 outputs the second solution last calculated by the second calculation unit 405 so that it can be referenced by a user. Specifically, the output unit 406 may transmit the second solution last calculated by the second calculation unit 405 to another computer. In this way, the output unit 406 can make the solution to the combinatorial optimization problem available externally.

[0078] Here, the case where the information processing device 100 includes the first calculation unit 403 and the second calculation unit 405 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 403 by communicating with another computer having the first calculation unit 403. For example, the information processing device 100 may use the second calculation unit 405 by communicating with another computer having the second calculation unit 405.

[0079] (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.

[0080] 5 to 9 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.

[0081] 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.

[0082] 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.

[0083] The QAOA Ansatz 610 includes 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). The hyperparameters (γ, β) are, for example, p (γ i ,β i ) In the example of FIG. 6, the level p of the QAOA Ansatz 610 is 2. p corresponds to the depth.

[0084] 5, (5-1) the information processing device 100, using the CPU 301 and the QPU 307, determines the hyperparameters (γ', β') so that the energy of the quantum state |ψ(γ, β)> of the QAOA quantum circuit 600 is minimized. This allows the information processing device 100 to determine the hyperparameters (γ', β') so that the QAOA Ansatz 610 approximates a combinatorial optimization problem.

[0085] (5-1-1) Specifically, 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 equation (1).

[0086]

number

[0087] (5-1-2) The information processing device 100 calculates 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.

[0088] (5-1-3) The information processing device 100 measures the energy E(γ,β)=<ψ(γ,β)|C(z)|ψ(γ,β)> using the QPU 307. The information processing device 100 determines the hyperparameters (γ',β') so that the measured energy E(γ,β) is minimized using the CPU 301. The information processing device 100 sets an objective function that minimizes the energy E(γ,β) using, for example, the Grid method, the BFGS method, the quadratic approximation method, the Powell method, or Bayesian estimation, and calculates the hyperparameters (γ',β').

[0089] (5-1-4) The information processing device 100 repeatedly determines the hyperparameters (γ', β') using the CPU 301. The information processing device 100 returns to the process of (5-1-1) until the hyperparameters (γ', β') have been determined the predetermined number of times using the CPU 301. When the hyperparameters (γ', β') have been determined the predetermined number of times using the CPU 301, the information processing device 100 statistically determines the hyperparameters (γ', β'). The predetermined number of times is, for example, set in advance. The predetermined number of times is, for example, a first number. Now, moving on to the explanation of FIG. 7, the reason for approximating the QAOA Ansatz 610 to a combinatorial optimization problem will be explained.

[0090] Graph 700 in FIG. 7 represents the MaxCut problem. Nodes in graph 700 correspond to quantum bits. Among the nodes in graph 700, nodes with dotted hatching represent the range represented by QAOA Ansatz 710 for p=1. QAOA Ansatz 710 includes a Hadamard gate 711. QAOA Ansatz 710 includes, for example, gates 712 and 713. Here, energy is defined, for example, by the following formula (2). As shown in formula (2) below, quantum bits other than the quantum bits with subscripts j and k are canceled out by U shown in formula (3) below.

[0091]

number

[0092]

number

[0093] Therefore, the QAOA Ansatz 710 for p=1 has the problem of being unable to represent the entire graph 700. Similarly, graph 720 represents the MaxCut problem. The nodes of graph 720 correspond to quantum bits. Among the nodes of graph 720, the nodes with dotted hatching represent the range represented by the QAOA Ansatz 730 for p=2. The QAOA Ansatz 730 includes a Hadamard gate 731. The QAOA Ansatz 730 includes gates 732 to 735. The QAOA Ansatz 730 for p=2, like the QAOA Ansatz 710 for p=1, has the problem of being unable to represent the entire graph 720.

[0094] Therefore, it is preferable that the information processing device 100 determines the hyperparameters (γ', β') so that the representation range 741 of the QAOA Ansatz 610 approximates the combinatorial optimization problem 740. For details about approximating the representation range 741 of the QAOA Ansatz 610 to the combinatorial optimization problem 740, the above-mentioned Reference 7 can be referred to.

[0095] 5, (5-2) 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.

[0096] (5-3) The information processing device 100 calculates the hyperparameter (γ * ,β *The information processing device 100 determines the hyperparameter (γ', β') from the hyperparameters (γ', β') so that the probability that the quantum state |ψ(γ, β)> of the quantum circuit 600 of the QAOA becomes z0 is maximized. * ,β * ) is determined. Now, moving to the explanation of FIG. 8, the information processing device 100 determines the hyperparameter (γ * ,β * An example of determining the .times. ...

[0097] Figure 8 shows the hyperparameter (γ * ,β * 8 shows an example of determining the hyperparameters (γ', β') as the hyperparameters (γ, β). (8-1) 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 above formula (1).

[0098] (8-2) The information processing device 100 calculates 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.

[0099] (8-3) The information processing device 100 performs a swap test using the QPU 307 to obtain a 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 800 for the swap test includes a Hadamard gate 801, and at a measurement point 810, p z0(γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> Make it measurable.

[0100] Specifically, the information processing device 100 performs n-shot sampling of the quantum state at the measurement point 810 in accordance with the swap test quantum circuit 800 shown in FIG. 8, and calculates the probability p z0 More specifically, if n=1000, and the number of times the quantum state of the measurement point 810 is measured as 0=10, the information processing device 100 measures probability p z0 (γ,β)=10 / 1000.

[0101] (8-4) The information processing device 100 calculates 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.

[0102] (8-5) 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 determined a predetermined number of times, the last calculated hyperparameter (γ * ,β * ) as the hyperparameters (γ, β), and the process returns to (8-1). * ,β * ) is determined 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 second number.

[0103] Returning to the explanation of FIG. 5, (5-4) 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 * Here, again using Figure 6, the optimal classical state z1 * An example of determining the above will be described.

[0104] 6, the information processing device 100 applies a superposition state |s> to n quantum bits by the QPU 307. The information processing device 100 applies a superposition state |s> to n quantum bits by the QPU 307 by * ,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 * )>.

[0105] The information processing device 100 uses the QPU 307 to calculate 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.

[0106] 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.

[0107] Returning to the explanation of FIG. 5, (5-5) 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 a series of processes (5-1), (5-2), (5-3), and (5-4) 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 third number. The third number may be the same as the second number. The termination condition may be defined, for example, by a threshold value for the energy E or the state z.

[0108] 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), (5-2), (5-3), and (5-4) are performed again.

[0109] 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.

[0110] Fig. 9 shows the effect of the information processing device 100. Graph 900 in Fig. 9 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 900 in Fig. 9, 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.

[0111] In response to this, the information processing device 100 performs E min The hyperparameters (γ, β) are determined so that the probability that the quantum state represents the classical state z that takes on a value in the vicinity is increased. Graph 910 in FIG. 9 shows the distribution of the probability that the quantum state represents the classical state z that takes on each value of energy E after the hyperparameters (γ, β) are determined. As shown in graph 910 in FIG. 9, E min The probability that the quantum state represents the classical state z that takes a value in the vicinity increases. This enables the information processing device 100 to improve the efficiency of searching for an optimal solution by QAOA.

[0112] Then, the information processing device 100 min After increasing the probability that the quantum state represents the classical state z that takes on surrounding values, a solution to the combinatorial optimization problem is calculated using QAOA. Graph 920 in Figure 9 shows the distribution of probabilities that the quantum state represents the classical state z that takes on each value of energy E when the solution to the combinatorial optimization problem is calculated using QAOA. As shown in graph 920 in Figure 9, E min Among the surrounding areas, E min This increases the probability that the quantum state represents a classical state z that takes on a narrow range of values ​​closer to

[0113] 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.

[0114] Furthermore, the information processing device 100 can determine the hyperparameters (γ', β') so that the representation range of the QAOA Ansatz 610 approximates the combinatorial optimization problem. Therefore, even if the depth p of the QAOA Ansatz 610 is relatively small, the information processing device 100 can make the QAOA Ansatz 610 represent the entire picture of the combinatorial optimization problem, making it easier to solve the combinatorial optimization problem with high accuracy.

[0115] 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.

[0116] (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.

[0117] (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. 10. 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.

[0118] 10 is a flowchart showing an example of the overall processing procedure. In FIG. 10, the information processing device 100 acquires a combinatorial optimization problem min(E=C(z)) by the CPU 301 (step S1001).

[0119] Next, the information processing device 100 executes a first determination process (step S1002) using the QPU 307, which will be described later with reference to Fig. 11. By executing the first determination process, the information processing device 100 determines hyperparameters (γ', β') of the QAOA so that the energy E(γ, β) is minimized.

[0120] Next, the information processing device 100 calculates a state z0 that is a solution to C(z) based on the initial value using the Ising machine 306 (step S1003).

[0121] Next, the information processing device 100 executes a second determination process, which will be described later with reference to FIG. 12, using the QPU 307 based on the hyperparameters (γ', β') of the QAOA and the state z0 that is the solution of C(z) (step S1004). By executing the second determination process, the information processing device 100 determines the hyperparameters (γ', β') of the QAOA from the hyperparameters (γ', β') of the QAOA so that the probability that the quantum state |ψ(γ, β)> becomes z0 is maximized. * ,β * ) to determine

[0122] Then, the information processing device 100 executes a third determination process, which will be described later with reference to FIG. 13, using the QPU 307 (step S1005). By executing the third determination process, the information processing device 100 determines the quantum state |ψ(γ * ,β * )> and obtain the optimal classical state z1 * Determine.

[0123] 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 S1006). 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 S1006: No), the information processing device 100 proceeds to the processing of step S1007. On the other hand, if the predetermined number of times has been determined (step S1006: Yes), the information processing device 100 proceeds to the processing of step S1008.

[0124] In step S1007, the information processing device 100 sets the initial value of the Ising machine 306 to the optimal classical state z1 * (step S1007). Then, the information processing device 100 returns to the process of step S1002.

[0125] In step S1008, the information processing device 100 calculates min(C(z0),C(z1 *)) (step S1008). Here, the information processing device 100 may output argmin(C(z)). Then, the information processing device 100 ends the overall processing.

[0126] (First decision processing procedure) Next, an example of a procedure of the first determination process executed by the information processing device 100 will be described with reference to Fig. 11. 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.

[0127] FIG. 11 is a flowchart showing an example of the first determination process procedure. In FIG. 11, the information processing device 100 applies a superposition state |s> to n quantum bits (step S1101). 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 S1102).

[0128] Next, the information processing device 100 measures the energy E(γ,β)=<ψ(γ,β)|C(z)|ψ(γ,β)> (step S1103). Then, the information processing device 100 determines the hyperparameters (γ',β') of the QAOA so that the energy E(γ,β) is minimized (step S1104).

[0129] Next, the information processing device 100 determines whether the hyperparameters (γ', β') of the QAOA have been determined a predetermined number of times (step S1105). The predetermined number of times is set in advance by the user, for example. If the hyperparameters have not been determined the predetermined number of times (step S1105: No), the information processing device 100 returns to the processing of step S1101. On the other hand, if the hyperparameters have been determined the predetermined number of times (step S1105: Yes), the information processing device 100 ends the first determination processing.

[0130] (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. 12. 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.

[0131] 12 is a flowchart showing an example of the second determination process procedure. In FIG. 12, the information processing device 100 determines whether or not it is the first loop (step S1201). If it is the first loop (step S1201: Yes), the information processing device 100 sets γ=γ' and β=β' (step S1202) and proceeds to the process of step S1204. On the other hand, if it is not the first loop (step S1201: No), the information processing device 100 sets γ=γ * ,β=β * (step S1203), and the process proceeds to step S1204.

[0132] In step S1204, the information processing device 100 applies the superposition state |s> to n quantum bits (step S1204). Next, the information processing device 100 applies the superposition state |s> to n quantum bits (step S1204). 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 S1205).

[0133] Next, the information processing device 100 calculates the probability p z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> (step S1206). Then, the information processing device 100 measures the probability p z0 The hyperparameter (γ * ,β * ) is determined (step S1207).

[0134] Next, the information processing device 100 calculates the hyperparameter (γ * ,β * ) has been determined a predetermined number of times (step S1208). 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 S1208: No), the information processing device 100 returns to the processing of step S1201. On the other hand, if the predetermined number of times has been determined (step S1208: Yes), the information processing device 100 ends the second determination processing.

[0135] (Third decision-making procedure) Next, an example of a third determination process procedure executed by the information processing device 100 will be described with reference to Fig. 13. The third 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.

[0136] 13 is a flowchart illustrating an example of the third determination process procedure. In FIG. 13, the information processing device 100 applies a superposition state |s> to n quantum bits (step S1301).

[0137] 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 S1302). Then, the information processing device 100 identifies the quantum state |ψ(γ * ,β * )> is sampled n shots to determine n classical states z1 (step S1303).

[0138] Next, the information processing device 100 calculates the energy E1 corresponding to each classical state z1, and calculates min(E1) <min(E0,E1 * ) (step S1304). 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.

[0139] where min(E1) <min(E0,E1 * ) (step S1304: Yes), the information processing apparatus 100 proceeds to the process of step S1305. <min(E0,E1 * ) (step S1304: No), the information processing apparatus 100 proceeds to the process of step S1306.

[0140] In step S1305, the information processing device 100 * is determined to be argmin(E1) (step S1305). 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 third determination process.

[0141] In step S1306, the information processing device 100 calculates z1 based on E1 and the Hamming Distance. * (Step S1306). E1, Hamming Distance is determined, for example, as ((E1-E0) x Hamming Distance(z1, z0)) -1Then, the information processing device 100 ends the third determination process.

[0142] Here, the information processing device 100 may interchange the processes of some steps in the flowcharts of Figures 10 to 13. For example, the processes of steps S1002 and S1003 can be interchanged. The information processing device 100 may omit the processes of some steps in the flowcharts of Figures 10 to 13. For example, the processes of steps S1006 and S1007 can be omitted.

[0143] As described above, the information processing device 100 can determine a first value of a parameter of a quantum approximate optimization algorithm so that the energy corresponding to the quantum state of a quantum circuit of the quantum approximate optimization algorithm is minimized. 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 a second value of a parameter from the determined first value of the parameter so that the probability that the quantum state of the quantum circuit of the quantum approximate optimization algorithm will become the calculated first solution is maximized. The information processing device 100 can calculate a second solution to a combinatorial optimization problem based on a quantum circuit of the quantum approximate optimization algorithm to which the determined second value of the parameter is set. This allows the information processing device 100 to reduce the time required to accurately calculate a solution to a combinatorial optimization problem.

[0144] According to the information processing device 100, a series of processes of determining a first value, calculating a first solution, determining a second value, 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.

[0145] 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.

[0146] 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.

[0147] According to the information processing device 100, it is possible to execute a process of calculating a first solution by utilizing an Ising machine that solves a combinatorial optimization problem. According to the information processing device 100, it is possible to execute a process of determining a first value, a process of determining a second value, and a process of calculating a second solution by utilizing a quantum processing device that handles a quantum circuit of a quantum approximate optimization algorithm. In this way, the information processing device 100 can efficiently calculate the first solution and can efficiently calculate the second solution.

[0148] 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.

[0149] 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.

[0150] The following additional notes are provided regarding the above-described embodiment.

[0151] (Supplementary Note 1) Regarding a quantum circuit of a quantum approximate optimization algorithm corresponding to a combinatorial optimization problem, determining a first value of a parameter of the quantum approximate optimization algorithm so that the energy corresponding to the quantum state of the quantum circuit is minimized; calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining a second value of the parameter from the determined first value of the parameter so as to maximize the probability that the quantum state of the quantum circuit will be the calculated first solution; calculating a second solution to the combinatorial optimization problem based on the quantum circuit to which the determined second values ​​of the parameters have been set; An information processing program that causes a computer to execute a process.

[0152] (Supplementary Note 2) Based on the calculated second solution, a first value of the parameter is newly calculated so that the energy corresponding to the quantum state of the quantum circuit is minimized; calculating a new first solution to the combinatorial optimization problem based on the Ising model with the calculated second solution set as an initial value; determining a new second value of the parameter from the newly determined first value of the parameter so that the probability that the quantum state of the quantum circuit will become the newly calculated first solution is maximized; calculating a new second solution to the combinatorial optimization problem based on the quantum circuit to which the newly determined second values ​​of the parameters 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.

[0153] (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.

[0154] (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.

[0155] (Supplementary Note 5) The process of calculating the first solution is executed using an Ising machine that solves the combinatorial optimization problem, The information processing program according to claim 1, wherein the process of determining a first value of the parameter, the process of determining a second value of the parameter, and the process of calculating the second solution are executed using a quantum processing device that handles the quantum circuit.

[0156] (Supplementary Note 6) The process of calculating the first solution includes: 2. The information processing program according to claim 1, further comprising: calculating a first solution to the combinatorial optimization problem based on the Ising model in accordance with a Digital Annealer.

[0157] (Supplementary Note 7) With respect to a quantum circuit of a quantum approximate optimization algorithm corresponding to a combinatorial optimization problem, determining a first value of a parameter of the quantum approximate optimization algorithm so that the energy corresponding to the quantum state of the quantum circuit is minimized; calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining a second value of the parameter from the determined first value of the parameter so as to maximize the probability that the quantum state of the quantum circuit will be the calculated first solution; calculating a second solution to the combinatorial optimization problem based on the quantum circuit to which the determined second values ​​of the parameters have been set; An information processing method characterized in that the processing is executed by a computer.

[0158] (Supplementary Note 8) With respect to a quantum circuit of a quantum approximate optimization algorithm corresponding to a combinatorial optimization problem, determining a first value of a parameter of the quantum approximate optimization algorithm so that the energy corresponding to the quantum state of the quantum circuit is minimized; calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining a second value of the parameter from the determined first value of the parameter so as to maximize the probability that the quantum state of the quantum circuit will be the calculated first solution; calculating a second solution to the combinatorial optimization problem based on the quantum circuit to which the determined second values ​​of the parameters have been set; An information processing device comprising a control unit. [Explanation of symbols]

[0159] 100 Information processing device 101 First Value 102 Second Value 110 Ising model 121 First Solution 122 Second Solution 130,600,800 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 Decision Section 403 First Calculation Unit 404 Second Decision Section 405 Second Calculation Unit 406 Output section 601,711,731,801 Hadamard Gate 610,710,730 QAOA Ansatz Gates 611-614, 712, 713, 732-735 700,720,900,910,920 graph 740 Optimization Problems 741 Range of Expression 810 measurement points

Claims

1. determining a first value of a parameter of a quantum approximate optimization algorithm for a quantum circuit corresponding to a combinatorial optimization problem, such that energy corresponding to a quantum state of the quantum circuit is minimized; calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining a second value of the parameter from the determined first value of the parameter so as to maximize the probability that the quantum state of the quantum circuit will be the calculated first solution; calculating a second solution to the combinatorial optimization problem based on the quantum circuit to which the determined second values ​​of the parameters have been set; An information processing program that causes a computer to execute a process.

2. Based on the calculated second solution, a new first value of the parameter is calculated so that the energy corresponding to the quantum state of the quantum circuit is minimized; calculating a new first solution to the combinatorial optimization problem based on the Ising model with the calculated second solution set as an initial value; determining a new second value of the parameter from the newly determined first value of the parameter so that the probability that the quantum state of the quantum circuit will become the newly calculated first solution is maximized; calculating a new second solution to the combinatorial optimization problem based on the quantum circuit to which the newly determined second values ​​of the parameters 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. determining a first value of a parameter of a quantum approximate optimization algorithm for a quantum circuit corresponding to a combinatorial optimization problem, such that energy corresponding to a quantum state of the quantum circuit is minimized; calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining a second value of the parameter from the determined first value of the parameter so as to maximize the probability that the quantum state of the quantum circuit will be the calculated first solution; calculating a second solution to the combinatorial optimization problem based on the quantum circuit to which the determined second values ​​of the parameters have been set; An information processing method characterized in that the processing is executed by a computer.

5. determining a first value of a parameter of a quantum approximate optimization algorithm for a quantum circuit corresponding to a combinatorial optimization problem, such that energy corresponding to a quantum state of the quantum circuit is minimized; calculating a first solution to the combinatorial optimization problem based on an Ising model corresponding to the combinatorial optimization problem; determining a second value of the parameter from the determined first value of the parameter so as to maximize the probability that the quantum state of the quantum circuit will be the calculated first solution; calculating a second solution to the combinatorial optimization problem based on the quantum circuit to which the determined second values ​​of the parameters have been set; An information processing device comprising a control unit.

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