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

Abstract

To easily solve a combination optimization problem.SOLUTION: The information processing apparatus 100 calculates a first solution 101 of the combinatorial optimization problem based on the Ising model 110. The information processing apparatus 100 determines a value of the parameter 120 of the first quantum circuit 111 such that a probability that a quantum state of the first quantum circuit 111 becomes the calculated first solution 101 is maximized. At this time, the information processing device 100 determines the value of the parameter 120 by, for example, repeating processing of updating the value of the parameter 120 of the first quantum circuit 111 by QPU using the second quantum circuit 112 by QAE. The information processing apparatus 100 calculates the second solution 102 of the combinatorial optimization problem based on the first quantum circuit 111 in which the determined value of the parameter 120 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, mapping a cost function associated with a combinatorial optimization problem to an optimization problem over a set of allowed quantum states. Other examples include using machine learning models to process optimization problems for radiation therapy planning to estimate one or more optimization variables. Other examples include using perturbations such as noise to improve the speed and accuracy of quantum annealing. Other examples include using virtualization to facilitate network routing. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Special Publication No. 2021-504805 [Patent Document 2] Special Publication No. 2022-542826 [Patent Document 3] U.S. Patent Application Publication No. 2020 / 0090071 [Patent Document 4] US Patent Application Publication No. 2012 / 0020352 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.

[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, and determine parameter values ​​of the quantum approximation optimization algorithm so as to maximize the probability that the quantum state of a first quantum circuit by the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will be the calculated first solution, by using a second quantum circuit by quantum amplitude estimation, which has an auxiliary quantum bit and includes a partial circuit whose quantum state is 1 when the quantum state of the first quantum circuit is the first solution, and by repeatedly updating the value of the parameter according to a result of measuring the probability based on a phase that specifies the amplitude that specifies the probability, and calculate a second solution to the combinatorial optimization problem based on the first quantum circuit 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. [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 according to the first embodiment. [Figure 5] FIG. 5 is an explanatory diagram showing an example of the operation of the information processing device 100 in the first embodiment. [Figure 6] FIG. 6 is an explanatory diagram showing an example of a first quantum circuit 600. [Figure 7] FIG. 7 is an explanatory diagram showing an example of determining the hyperparameters (γ*, β*). [Figure 8] FIG. 8 is an explanatory diagram showing an example of the state preparation circuit 720. As shown in FIG. [Figure 9] FIG. 9 is an explanatory diagram showing the effect of the information processing device 100. [Figure 10] FIG. 10 is a flowchart illustrating an example of an overall processing procedure according to the first embodiment. [Figure 11] FIG. 11 is a flowchart illustrating an example of a procedure of the first determination process according to the first embodiment. [Figure 12] FIG. 12 is a flowchart illustrating an example of a measurement processing procedure. [Figure 13] FIG. 13 is a flowchart illustrating an example of a procedure of the second determination process according to the first embodiment. [Figure 14] FIG. 14 is an explanatory diagram showing the flow of operations of the information processing device 100 in the second embodiment. [Figure 15] FIG. 15 is a block diagram showing an example of the functional configuration of an information processing device 100 according to the second embodiment. [Figure 16] FIG. 16 is an explanatory diagram showing an example of the operation of the information processing device 100 in the second embodiment. [Figure 17] FIG. 17 is a flowchart illustrating an example of an overall processing procedure according to the second embodiment. [Figure 18] FIG. 18 is a flowchart illustrating an example of a procedure of the first determination process according to the second embodiment. [Figure 19] FIG. 19 is a flowchart illustrating an example of a procedure of the second determination process according to the second embodiment. [Figure 20] FIG. 20 is a flowchart illustrating an example of the third determination process procedure in the second embodiment. 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 facilitating the solution of 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 technique for solving combinatorial optimization problems by repeatedly searching for solutions to combinations of variables while adjusting the range in which solutions for combinations of variables are searched, for example, using thermal noise. The SA method is also known as simulated annealing. The QAOA is a technique based on the variational quantum algorithm, for example. The variational quantum algorithm is a technique that applies the Rayleigh-Ritz variation method, which uses the Schrödinger equation, to quantum circuits.

[0014] QAOA is a method for solving combinatorial optimization problems using, for example, quantum circuits that represent quantum states corresponding to combinations of variables. Specifically, QAOA solves combinatorial optimization problems by repeating a series of processes: "identify the quantum state of the 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 (Broyden-Fletcher-Goldfarb-Shanno) method, quadratic approximation method, Powell's algorithm, or Bayesian estimation when changing the parameters of the quantum circuit.

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

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

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

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

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

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

[0021] However, conventionally, it has been difficult to efficiently solve combinatorial optimization problems. For example, the time required to solve a combinatorial optimization problem tends to increase. Specifically, 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] In response to this, a method can be considered that shortens the time required to solve combinatorial optimization problems by extending QAOA using an Ising machine. This method repeats a series of processes: "Calculate a first solution to the combinatorial optimization problem using an Ising machine, determine the parameter values ​​of the quantum circuit so that the probability that the quantum state of the quantum circuit will be the first solution is maximized, and calculate a second solution to the combinatorial optimization problem." In this method, for example, when determining the parameter values ​​of the quantum circuit, the probability that the quantum state of the quantum circuit will be the first solution is measured. This measurement is realized, for example, by a Hadamard test. In the Hadamard test, the measurement is performed, for example, by sampling with the number of shots = n.

[0025] Even with this method, it can be difficult to efficiently solve combinatorial optimization problems. For example, the time required to solve a combinatorial optimization problem tends to increase. Here, when measuring the probability that the quantum state of a quantum circuit will be the first solution, the measurement error is thought to be on the order of 1 / n. For this reason, in order to suppress measurement error, it is desirable to increase the number of shots. On the other hand, the time required for measurement tends to increase as the number of shots increases. Therefore, when suppressing measurement error, the time required for measurement tends to increase, and it is thought that the time required for solving a combinatorial optimization problem also tends to increase.

[0026] Therefore, in this embodiment, an information processing method that can make combinatorial optimization problems easier to solve will be described. Specifically, this information processing method makes combinatorial optimization problems easier to solve by utilizing quantum amplitude estimation to extend QAOA. In the following description, quantum amplitude estimation may be referred to as "QAE (Quantum Amplitude Estimation)." This information processing method can reduce the time required to solve combinatorial optimization problems.

[0027] 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.

[0028] The information processing device 100 includes, for example, a QPU (Quantum Processing Unit). The information processing device 100 includes, for example, an Ising machine. The information processing device 100 sets, for example, an Ising model 110 corresponding to the acquired combinatorial optimization problem. The information processing device 100 sets, for example, a first quantum circuit 111 by QAOA corresponding to the combinatorial optimization problem, which represents a quantum state corresponding to a state z. The first quantum circuit 111 is, for example, a QAOA Anzatz. The quantum state, for example, probabilistically represents each value that the state z can take.

[0029] (1-1) The information processing device 100 calculates a first solution 101 of the combinatorial optimization problem based on the set Ising model 110. The information processing device 100 uses, for example, a digital annealer Ising machine to calculate a state z0 that becomes the first solution 101 of the combinatorial optimization problem based on the Ising model 110 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] (1-2) The information processing device 100 determines the value of the parameter 120 of the first quantum circuit 111 so as to maximize the probability that the quantum state of the set first quantum circuit 111 becomes the calculated first solution 101. The information processing device 100 sets a second quantum circuit 112 using, for example, a QAE. The second quantum circuit 112 includes, for example, a partial circuit. The partial circuit has, for example, an ancillary quantum bit. When the quantum state of the first quantum circuit 111 becomes the first solution 101, the quantum state of the ancillary quantum bit becomes 1. The information processing device 100 determines the value of the parameter 120 by, for example, using the second quantum circuit 112 with a QPU, repeating a process of updating the value of the parameter 120 of the first quantum circuit 111.

[0031] In this case, in the updating process, specifically, the information processing device 100 first measures the probability that the quantum state of the first quantum circuit 111 will become the first solution 101 based on the phase that defines the amplitude that specifies the probability that the quantum state of the first quantum circuit 111 will become the first solution 101. Next, in the updating process, specifically, the information processing device 100 updates the value of the parameter 120 of the first quantum circuit 111 according to the result of measuring the probability.

[0032] (1-3) The information processing device 100 calculates a second solution 102 of the combinatorial optimization problem based on the first quantum circuit 111 in which the determined values ​​of the parameters 120 are set. The information processing device 100 performs n-shot sampling of the quantum state using, for example, a QPU, 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 first quantum circuit 111 in 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.

[0033] 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 first quantum circuit 111 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.

[0034] Furthermore, the information processing device 100 can measure the probability that the quantum state of the first quantum circuit 111 becomes the first solution 101 by utilizing the QAE without relying on the Hadamard test. Here, according to the QAE, the measurement error is 1 / n 2 It is considered that the order of n is the number of shots. Therefore, the information processing device 100 can, for example, reduce the time required for measurement while suppressing measurement errors, and can reduce the time required for performing QAOA.

[0035] (1-4) 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), and (1-3) 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.

[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 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 from the other computer.

[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 control another computer having a QPU to calculate a second solution 102 of a combinatorial optimization problem, and may acquire the second solution 102 from the other computer.

[0039] Here, the case where the information processing device 100 solves a combinatorial optimization problem by the first method that performs the above-described series of processes has been described, but the present invention is not limited to this. For example, the information processing device 100 may solve a combinatorial optimization problem by a second method that is an improvement of the above-described first method. Specifically, the second method is a method that combines the first method with a process of determining a first value of the parameter 120 so that the energy corresponding to the quantum state of the first quantum circuit 111 is minimized.

[0040] Specifically, the second method calculates a first solution 101 and determines a first value of a parameter 120, and then determines a second value of the parameter 120 from the determined first value so as to maximize the probability that the quantum state of the first quantum circuit 111 becomes the first solution 101. Here, it is preferable that the second method does not rely on the Hadamard test but utilizes a QAE, as in the first method, to measure the probability that the quantum state of the first quantum circuit 111 becomes the first solution 101. Specifically, the second method calculates a second solution 102 to the combinatorial optimization problem based on the first quantum circuit 111 in which the determined second value of the parameter 120 is set.

[0041] A first embodiment in which the information processing device 100 solves a combinatorial optimization problem by a first method will be described later with reference to Figures 4 to 13. A second embodiment in which the information processing device 100 solves a combinatorial optimization problem by a second method will be described later with reference to Figures 14 to 20.

[0042] (An example of an information processing system) Next, an example of an information processing system to which the information processing device 100 shown in FIG. 1 is applied will be described with reference to FIG.

[0043] 2 is an explanatory diagram illustrating an example of an information processing system. In FIG. 2, the information processing system includes an information processing device 100 and a client device 201.

[0044] In the information processing system, an information processing device 100 and a 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.

[0045] 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 obtains, for example, a solution to the identified combinatorial optimization problem. The information processing device 100 transmits the obtained solution to the combinatorial optimization problem to the client device 201. The information processing device 100 is, for example, a server or a PC.

[0046] 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.

[0047] 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.

[0048] (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.

[0049] 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.

[0050] 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.

[0051] 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.

[0052] 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.

[0053] The Ising machine 306 has an Ising model. The Ising machine 306 is a computing device that uses the Ising model to run a digital annealer to solve a combinatorial optimization problem. The QPU 307 is a computing device that executes quantum operations defined in a quantum circuit. The QPU 307 solves a combinatorial optimization problem by executing, for example, QAOA.

[0054] 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.

[0055] (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 description thereof will be omitted. The client device 201 does not need to include the Ising machine 306, the QPU 307, or the like.

[0056] (First Example) Next, a first embodiment corresponding to the case where the information processing device 100 solves a combinatorial optimization problem by the above-described first technique will be described with reference to FIGS.

[0057] (Example of functional configuration of information processing device 100 in the first embodiment) First, an example of the functional configuration of the information processing device 100 in the first embodiment will be described with reference to FIG.

[0058] 4 is a block diagram showing an example of the functional configuration of the information processing device 100 according to the first embodiment. 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] The storage unit 400 stores, for example, a first quantum circuit based on QAOA that corresponds to a combinatorial optimization problem. The first quantum circuit represents a quantum operation procedure. The first quantum circuit realizes a function of outputting a quantum state that corresponds to a solution to the combinatorial optimization problem. The first quantum circuit is acquired, for example, by the acquisition unit 401. The first quantum circuit may be set in advance by a user, for example.

[0064] The storage unit 400 stores, for example, a second quantum circuit using a QAE. The second quantum circuit includes, for example, a partial circuit. The partial circuit has, for example, an ancillary quantum bit. When the quantum state of the first quantum circuit is a first solution, the quantum state of the ancillary quantum bit becomes 1. The second quantum circuit is acquired, for example, by the acquisition unit 401. The second quantum circuit may be set in advance by a user, for example.

[0065] 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.

[0066] 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, an initial value of the Ising model, a first quantum circuit, and a second quantum circuit. 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.

[0067] 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 the information indicating the combinatorial optimization problem from a processing request.

[0068] The acquisition unit 401 acquires, for example, an Ising model. Specifically, the acquisition unit 401 acquires the Ising model by accepting input of the Ising model based on an operation input from a user. Specifically, the acquisition unit 401 may receive the Ising model from another computer. The other computer is, for example, the client device 201. Specifically, the acquisition unit 401 may acquire the Ising model by extracting the Ising model from a processing request.

[0069] The acquiring unit 401 acquires, for example, an initial value of the Ising model. Specifically, the acquiring 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 acquiring 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 acquiring unit 401 may acquire the initial value of the Ising model by extracting the initial value of the Ising model from a processing request.

[0070] The acquiring unit 401 acquires, for example, a first quantum circuit. Specifically, the acquiring unit 401 acquires the first quantum circuit by accepting input of the first quantum circuit based on an operational input from a user. Specifically, the acquiring unit 401 may receive the first quantum circuit from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 401 may acquire the first quantum circuit by extracting the first quantum circuit from a processing request.

[0071] The acquiring unit 401 acquires, for example, a second quantum circuit. Specifically, the acquiring unit 401 acquires the second quantum circuit by accepting input of the second quantum circuit based on an operational input from a user. Specifically, the acquiring unit 401 may receive the second quantum circuit from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 401 may acquire the second quantum circuit by extracting the second quantum circuit from a processing request.

[0072] 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.

[0073] 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 parameter values ​​of the QAOA, making it easier to determine the parameter values ​​of the QAOA.

[0074] 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 guidelines for determining parameter values ​​of the QAOA, making it easier to determine the parameter values ​​of the QAOA. The first calculation unit 402 corresponds to, for example, the Ising machine 306 that follows Digital Annealer.

[0075] The determination unit 403 determines the parameter values ​​of the QAOA so as to maximize the probability that the quantum state of the first quantum circuit becomes 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 first quantum circuit becomes the first solution. Specifically, the determination unit 403 uses a second quantum circuit based on a QAE to repeat the process of "updating the parameter values ​​of the QAOA in accordance with the result of measuring the probability that the quantum state of the first quantum circuit becomes the first solution based on the phase." The phase specifies an amplitude that specifies the probability that the quantum state of the first quantum circuit becomes the first solution. More specifically, the determination unit 403 repeats the process of "updating the parameter values ​​of the QAOA in accordance with the result of measuring the probability that the quantum state of the first quantum circuit becomes the first solution based on the phase" based on the distribution of quantum states represented by the second quantum circuit.

[0076] This allows the determination unit 403 to appropriately determine the parameter values ​​of the QAOA. Then, the determination unit 403 can easily calculate the second solution to the combinatorial optimization problem based on the first quantum circuit. The determination unit 403 can utilize the QAE to reduce the time required to determine the parameter values ​​of the QAOA. The determination unit 403 corresponds to, for example, the QPU 307.

[0077] The second calculation unit 404 calculates a second solution to the combinatorial optimization problem based on the first quantum circuit in which the parameter values ​​determined by the determination unit 403 are set. The second calculation unit 404 calculates the second solution to the combinatorial optimization problem based on, for example, the distribution of quantum states represented by the first quantum circuit. Specifically, each time the determination unit 403 determines a parameter value, the second calculation unit 404 sets the parameter value in the first quantum circuit. Specifically, the second calculation unit 404 calculates the second solution to the combinatorial optimization problem based on the first quantum circuit in which the parameter values ​​are 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, for example, the QPU 307.

[0078] 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 may be, for example, executing the series of processes a predetermined number of times. The predetermined condition may be, for example, calculating the second solution a predetermined number of times. The predetermined condition may be, for example, the difference between the second solution calculated this time and the second solution calculated previously being equal to or less than a threshold. This allows the information processing device 100 to bring the second solution calculated by the second calculation unit 404 closer to an optimal solution to the combinatorial optimization problem.

[0079] 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.

[0080] 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.

[0081] 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.

[0082] (Example of operation of the information processing device 100 in the first embodiment) Next, an example of the operation of the information processing device 100 in the first embodiment will be described with reference to FIG.

[0083] Fig. 5 is an explanatory diagram showing an example of the operation of the information processing device 100 in the first embodiment. 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.

[0084] 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 first quantum circuit 600 by QAOA that corresponds to the combinatorial optimization problem. Now, moving on to the description of FIG. 6, an example of the first quantum circuit 600 will be described.

[0085] Fig. 6 is an explanatory diagram showing an example of a first quantum circuit 600. In Fig. 6, the first quantum circuit 600 includes a Hadamard gate 601 that represents an operation on the quantum state of each of the n quantum bits, and a QAOA Ansatz 610 that represents an operation on the quantum state of each of the n quantum bits, where n is the number of quantum bits.

[0086] 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 of the QAOA Ansatz 610.

[0087] 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.

[0088] (5-2) The information processing device 100, by using the CPU 301 and the QPU 307, calculates the hyperparameter (γ * ,β * Next, referring to FIG. 7, the information processing device 100 determines the hyperparameter (γ * ,β * An example of determining the .times. ...

[0089] Figure 7 shows the hyperparameter (γ * ,β * 7 is an explanatory diagram showing an example of determining |s>. In FIG. 7, (7-1) the information processing device 100 applies a superposition state |s> to n quantum bits by the QPU 307. Here, the superposition state |s> is defined by, for example, the following formula (1).

[0090]

number

[0091] (7-2) 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), where i=1, 2, . . . , p. The information processing device 100 uses the QAE by the QPU 307 to determine the probability p that the quantum state |ψ(γ, β)> of the first quantum circuit 600 becomes z0. z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> =<ψ(γ,β)|z0> 2 Measure.

[0092] QAE is a method that utilizes the property that the square of the absolute value of the amplitude corresponding to a quantum state is the probability of that quantum state. For example, if |ψ>=α|0>+β|1>, α corresponds to the amplitude of quantum state 0, and |α| 2 corresponds to the probability of the quantum state 0. Specifically, when the following formula (2) holds, the amplitude sinθ value of |ψ1> can be specified according to the QAE, and |sinθ| 2 Based on this, the probability p z0 (γ, β) can be measured.

[0093]

number

[0094] Therefore, |ψ> in the above formula (2) n+1 It is desirable to prepare a second quantum circuit 700 using a QAE, which includes a state preparation circuit representing the following. For information on QAEs, see, for example, Reference 7, Reference 8, and Reference 9 below.

[0095] Reference 7: Brassard, Gilles, et al. “Quantum amplitude amplification and estimation.” Contemporary Mathematics 305 (2002): 53-74.

[0096] Reference 8: Kitaev, A. Yu. “Quantum measurements and the Abelian stabilizer problem.” arXiv preprint quant-ph / 9511026 (1995).

[0097] Reference 9: Suzuki, Yohichi, et al. “Amplitude estimation without phase estimation.” Quantum Information Processing 19 (2020): 1-17.

[0098] The information processing device 100 prepares a second quantum circuit 700 using a QAE, as shown in Fig. 7, for example. The second quantum circuit 700 relates to m+2n+1 quantum bits. Line segments 701 in Fig. 7 correspond to each quantum bit of the m quantum bits. Line segments 702 in Fig. 7 correspond to each quantum bit of the 2n+1 quantum bits.

[0099] The m quantum bits correspond to the amplitude to be measured. Of the 2n+1 quantum bits, n quantum bits correspond to the quantum state |ψ(γ,β)> of the first quantum circuit 600. Of the remaining n+1 quantum bits, n quantum bits correspond to the solution state z0. The remaining one quantum bit is an ancillary quantum bit. The quantum state of the ancillary quantum bit becomes 1 when the quantum state |ψ(γ,β)> of the first quantum circuit 600 becomes z0.

[0100] The second quantum circuit 700 includes a gate 711 corresponding to a Fourier transform of m quantum bits and a gate 712 corresponding to an inverse Fourier transform of m quantum bits. The second quantum circuit 700 includes a measurement unit 713 for each quantum bit of the m quantum bits. The second quantum circuit 700 includes a state preparation circuit 720 for 2n+1 quantum bits. The second quantum circuit 700 includes quantum amplitude amplification circuits 721-723 for 2n+1 quantum bits.

[0101] Q=-SψS f Sψ=2|ψ> n <ψ| n -I. Sψ represents the operation of inverting around |ψ>. S f =|ψ0> n <ψ0| n -|ψ1> n <ψ1| n S f is the quantum state of the ancillary qubit, |ψ> n Here, the phase of Q is e± j2 Therefore, it is considered that if the phase θ is found by QPE (Quantum Phase Estimate) in the second quantum circuit 700, the amplitude sin θ can be specified.

[0102] The information processing device 100 calculates, for example, a probability p z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> Turning now to FIG. 8, an example of a state preparation circuit 720 will be described.

[0103] FIG. 8 is an explanatory diagram showing an example of the state preparation circuit 720. Line segment 801 in FIG. 8 corresponds to each of the n quantum bits. The n line segments 801 correspond to the quantum state |ψ(γ,β)> of the first quantum circuit 600. Line segment 802 in FIG. 8 corresponds to each of the n quantum bits. The n line segments 802 correspond to the solution state z0. Line segment 803 in FIG. 8 corresponds to one ancillary quantum bit.

[0104] 8, the state preparation circuit 720 includes a rotation gate 811 around the X axis and a QAOA Ansatz 812. The QAOA Ansatz 812 prepares the quantum state |ψ(γ,β)> of the first quantum circuit 600. The QAOA Ansatz 812 is similar to, for example, the QAOA Ansatz 610.

[0105] Furthermore, state preparation circuit 720 includes a CNOT (Controlled-NOT) gate 813 and a CNOT gate 814. The combination of CNOT gates 813 and 814 acts to set the quantum state of the ancillary quantum bit to 1 when the quantum state |ψ(γ, β)> of first quantum circuit 600 matches the solution state z0.

[0106] The state preparation circuit 720 also includes a CNOT gate 815 and a rotation gate 816 around the X axis. The combination of the CNOT gate 815 and the rotation gate 816 around the X axis acts to undo the action of the combination of the rotation gate 811 around the X axis and the CNOT gate 813. In the state preparation circuit 720, θ 0,1 depends on Z0. For example, Z 0i If =0, then θ 0,1 = π. For example, Z 0i = 1, then θ 0,1 =0.

[0107] Returning to the explanation of FIG. 7, (7-3) 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 determined by calculating

[0108] 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 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.

[0109] 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.

[0110] 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 * )>.

[0111] 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 * 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.

[0112] 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.

[0113] 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.

[0114] 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.

[0115] 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.

[0116] As described with reference to FIGS. 7 and 8, the information processing device 100 utilizes QAE to calculate the probability p z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> Therefore, the information processing device 100 can measure the measurement error by 1 / n 2 Therefore, when suppressing measurement errors, the information processing device 100 can suppress an increase in the number of shots, thereby reducing the time required for measurement and the time required for calculating a solution to a combinatorial optimization problem. Next, we will move on to the explanation of FIG. 9 to explain the effects of the information processing device 100.

[0117] Fig. 9 is an explanatory diagram showing the effect of the information processing device 100. Graph 900 in Fig. 9 shows the distribution of the probability that the 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 the quantum state initially represents a classical state z that takes on each value of energy E is uniform.

[0118] In response to this, the information processing device 100 performs a calculation for a combinatorial optimization problem in accordance with the calculation result of the Ising machine 306, and then performs a calculation for a combinatorial optimization problem in accordance with the calculation result of the Ising machine 306, in which the quantum state is E min The hyperparameters (γ, β) are determined so that the probability of representing a classical state z taking a value in the vicinity is high. Graph 910 in FIG. 9 shows the distribution of the probability that the quantum state will represent a classical state z taking each value of energy E after the hyperparameters (γ, β) are determined. As shown in graph 910 in FIG. 9, the probability that the quantum state will represent E min The probability of representing the classical state z taking a surrounding value increases. This enables the information processing device 100 to improve the efficiency of searching for an optimal solution by QAOA.

[0119] Then, the information processing device 100 detects that the quantum state is E min After increasing the probability of representing a classical state z that takes a value in the vicinity, a solution to the combinatorial optimization problem is calculated using QAOA. Graph 920 in FIG. 9 shows the distribution of probabilities that a quantum state will represent a classical state z that takes each value of energy E when a solution to the combinatorial optimization problem is calculated using QAOA. As shown in graph 920 in FIG. 9, when a quantum state is min Among the surrounding areas, E min The probability of representing a classical state z that takes on a narrow range of values ​​closer to

[0120] 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.

[0121] Furthermore, when calculating a solution to a combinatorial optimization problem by QAOA, the information processing device 100 utilizes QAE to calculate a probability p z0 The time required to measure (γ, β) can be reduced. Therefore, the information processing device 100 can more easily reduce the time required to calculate a solution to a combinatorial optimization problem by using QAOA.

[0122] 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.

[0123] (Overall processing procedure in the first embodiment) Next, an example of an overall processing procedure in the first embodiment 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.

[0124] 10 is a flowchart showing an example of an overall processing procedure in the first embodiment. In FIG. 10, the information processing device 100 acquires a combinatorial optimization problem min(E=C(z)) using the CPU 301 (step S1001). Next, the information processing device 100 calculates a state z0 that is a solution to C(z) using the Ising machine 306 based on the initial value (step S1002).

[0125] Next, the information processing device 100 executes a first determination process, which will be described later with reference to FIG. 11, using the QPU 307 to determine the hyperparameter (γ * ,β * ) (step S1003). Then, the information processing device 100 determines the quantum state |ψ(γ * ,β * )> and obtain the optimal classical state z1 * is determined (step S1004).

[0126] 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 S1005). 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 S1005: No), the information processing device 100 proceeds to the processing of step S1006. On the other hand, if the predetermined number of times has been determined (step S1005: Yes), the information processing device 100 proceeds to the processing of step S1007.

[0127] In step S1006, the information processing device 100 sets the initial value of the Ising machine 306 to the optimal classical state z1 * (step S1006). Then, the information processing device 100 returns to the process of step S1002.

[0128] In step S1007, the information processing device 100 calculates min(C(z0),C(z1 * )) (step S1007). The information processing device 100 may output argmin(C(z)). Then, the information processing device 100 ends the overall processing.

[0129] (First decision processing procedure in the first embodiment) Next, an example of a first determination process procedure in the first embodiment 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.

[0130] 11 is a flowchart showing an example of a first determination process procedure in the first embodiment. 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 identifies the quantum state |ψ(γ,β)> by performing a measurement process described later with reference to FIG. 12 (step S1102).

[0131] Next, the information processing device 100 performs a measurement process, which will be described later with reference to FIG. 12, to obtain a probability p z0(γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> (step S1103). Then, the information processing device 100 measures the probability p z0 The hyperparameter (γ * ,β * ) is determined (step S1104).

[0132] Next, the information processing device 100 calculates the hyperparameter (γ * ,β * ) has 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 predetermined number of times has not been determined (step S1105: No), the information processing device 100 returns to the processing of step S1101. On the other hand, if the predetermined number of times has been determined (step S1105: Yes), the information processing device 100 ends the first determination processing.

[0133] (Measurement procedure) Next, an example of a measurement processing procedure executed by the information processing device 100 will be described with reference to Fig. 12. The measurement 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, and the QPU 307 shown in Fig. 3.

[0134] 12 is a flowchart showing an example of a measurement procedure. In FIG. 12, the information processing device 100 sets a state preparation circuit based on z0, γ, and β (step S1201). Then, the information processing device 100 sets a QAE quantum circuit including the set state preparation circuit (step S1202).

[0135] Next, the information processing device 100 measures the phase θ by executing the set QAE quantum circuit n-shot (step S1203). Then, the information processing device 100 calculates the probability p z0 (γ,β)=sinθ 2 (step S1204). After that, the information processing device 100 ends the measurement process.

[0136] (Second determination process procedure in the first embodiment) Next, an example of the second determination process procedure in the first embodiment executed by the information processing device 100 will be described with reference to Fig. 13. 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.

[0137] Fig. 13 is a flowchart showing an example of the procedure of the second determination process in the first embodiment. In Fig. 13, the information processing device 100 applies the superposition state |s> to n quantum bits (step S1301).

[0138] 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).

[0139] 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.

[0140] 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.

[0141] 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 second determination process.

[0142] 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)) -1 Then, the information processing device 100 ends the second determination process.

[0143] Here, the information processing device 100 may omit some of the processes in the steps of the flowcharts of Figures 10 to 13. For example, the processes of steps S1005 and S1006 can be omitted. For example, the process of step S1105 can be omitted.

[0144] (Second Example) Next, a second embodiment will be described with reference to FIGS. 14 to 20, in which the information processing device 100 solves a combinatorial optimization problem using the second method described above.

[0145] (Operation flow of information processing device 100) First, the flow of operations of the information processing device 100 in the second embodiment will be described with reference to FIG.

[0146] FIG. 14 is an explanatory diagram showing the flow of operations of the information processing device 100 in the second embodiment. In FIG. 14, 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.

[0147] The information processing device 100 includes, for example, an Ising machine. The information processing device 100 sets, for example, an Ising model 1410 corresponding to the acquired combinatorial optimization problem. The information processing device 100 sets, for example, a first quantum circuit 1411 by QAOA corresponding to the combinatorial optimization problem, which represents a quantum state corresponding to a state z. The first quantum circuit 1411 is, for example, a QAOA Anzatz. The quantum state probabilistically represents, for example, each value that the state z can take.

[0148] (14-1) The information processing device 100 determines the first value 1401 of the parameter of the first quantum circuit 1411 so that the energy corresponding to the quantum state of the first quantum circuit 1411 is minimized. The energy corresponds to, for example, the measured value of <ψ(γ,β)|C(z)|ψ(γ,β)>. This allows the information processing device 100 to approximate the first quantum circuit 1411 to an eigenvalue problem. For details on approximating the first quantum circuit 1411 to an eigenvalue problem, see, for example, Reference 10 below.

[0149] Reference 10: Peruzzo, Alberto, et al. “A variational eigenvalue solver on a photonic quantum processor.” Nature communications 5.1 (2014): 4213.

[0150] (14-2) The information processing device 100 calculates a first solution 1403 of the combinatorial optimization problem based on the set Ising model 1410. The information processing device 100 uses, for example, a digital annealer Ising machine to calculate a state z0 that becomes the first solution 1403 of the combinatorial optimization problem based on the Ising model 1410 and the 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.

[0151] (14-3) The information processing device 100 determines the second value 1402 of the parameter of the first quantum circuit 1411 so as to maximize the probability that the quantum state of the set first quantum circuit 1411 will become the calculated first solution 1403. For example, the information processing device 100 determines the second value 1402 of the parameter of the first quantum circuit 1411 from the first value 1401 of the parameter of the first quantum circuit 1411 so as to maximize the probability that the quantum state of the first quantum circuit 1411 will become the first solution 1403.

[0152] Specifically, the information processing device 100 sets a second quantum circuit 1412 using a QAE. The second quantum circuit 1412 includes, for example, a partial circuit. The partial circuit has, for example, an ancillary quantum bit. When the quantum state of the first quantum circuit 1411 becomes a first solution 1403, the quantum state of the ancillary quantum bit becomes 1. The information processing device 100, for example, uses a QPU to repeatedly update the value of the parameter of the first quantum circuit 1411 from a first value 1401 of the parameter of the first quantum circuit 1411 using the second quantum circuit 1412. In this way, the information processing device 100 determines a second value 1402 of the parameter of the first quantum circuit 1411.

[0153] In this case, in the updating process, the information processing device 100 first measures, specifically, the probability that the quantum state of the first quantum circuit 1411 will become the first solution 1403 based on the phase. The phase defines an amplitude that specifies the probability that the quantum state of the first quantum circuit 1411 will become the first solution 1403. In the updating process, the information processing device 100 then updates the parameter values ​​of the first quantum circuit 1411 according to the result of measuring the probability.

[0154] (14-4) The information processing device 100 calculates a second solution 1404 of the combinatorial optimization problem based on the first quantum circuit 1411 to which the determined second parameter value 1402 is set. The information processing device 100 performs n-shot sampling of the quantum state using the QPU 307, for example, and calculates a state z1 that is the second solution 1404.

[0155] Specifically, the information processing device 100 repeatedly performs Z-direction projection measurement of the quantum state represented by the first quantum circuit 1411 to which the determined second parameter value 1402 is set, to obtain a state z n times. Specifically, the information processing device 100 calculates a state z1 that is a second solution 1404 based on the distribution of the obtained states z.

[0156] 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 of the first quantum circuit 1411 based on the first solution 1403 calculated using the Ising model 1410, 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.

[0157] Furthermore, the information processing device 100 can measure the probability that the quantum state of the first quantum circuit 1411 becomes the first solution 1403 by utilizing the QAE without relying on the Hadamard test. Here, according to the QAE, the measurement error is 1 / n 2It is considered that the order of n is the number of shots. Therefore, the information processing device 100 can, for example, reduce the time required for measurement while suppressing measurement errors, and can reduce the time required for performing QAOA.

[0158] (14-5) The information processing device 100 may set the calculated state z1 as a new initial value and repeat the series of processes shown in (14-1), (14-2), (14-3), and (14-4) 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. 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.

[0159] Here, for example, suppose the combinatorial optimization problem is a MaxCut problem, and the first quantum circuit 1411 solves the combinatorial optimization problem without approximating it to an eigenvalue problem. In this case, if the depth p of the first quantum circuit 1411 is relatively small, the first quantum circuit 1411 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 first quantum circuit 1411 is relatively small.

[0160] (Example of functional configuration of information processing device 100 in the second embodiment) Next, an example of the functional configuration of the information processing device 100 according to the second embodiment will be described with reference to FIG.

[0161] 15 is a block diagram showing an example of the functional configuration of an information processing device 100 according to the second embodiment. The information processing device 100 includes a storage unit 1500, an acquisition unit 1501, a first determination unit 1502, a first calculation unit 1503, a second determination unit 1504, a second calculation unit 1505, and an output unit 1506.

[0162] The storage unit 1500 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 1500 is included in the information processing device 100 will be described, but this is not limiting. For example, the storage unit 1500 may be included in a device different from the information processing device 100, and the stored contents of the storage unit 1500 may be accessible from the information processing device 100.

[0163] The acquiring unit 1501 to the output unit 1506 function as an example of a control unit. Specifically, the acquiring unit 1501 to the output unit 1506 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.

[0164] The storage unit 1500 stores various information that is referenced or updated during processing by each functional unit. The storage unit 1500 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 1501. The information that indicates a combinatorial optimization problem may be set in advance by a user, for example.

[0165] The storage unit 1500 stores, for example, an Ising model corresponding to a combinatorial optimization problem. The Ising model is acquired, for example, by the acquisition unit 1501. The Ising model may be set in advance by a user. The storage unit 1500 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 1501. The initial values ​​may be set in advance by a user.

[0166] The storage unit 1500 stores, for example, a first quantum circuit based on QAOA that corresponds to a combinatorial optimization problem. The first quantum circuit represents a quantum operation procedure. The first quantum circuit has a function of outputting a quantum state that corresponds to a solution to the combinatorial optimization problem. The first quantum circuit is acquired, for example, by the acquisition unit 1501. The first quantum circuit may be set in advance by a user, for example.

[0167] The storage unit 1500 stores, for example, a second quantum circuit using a QAE. The second quantum circuit includes, for example, a partial circuit. The partial circuit has, for example, an ancillary quantum bit. When the quantum state of the first quantum circuit is a first solution, the quantum state of the ancillary quantum bit becomes 1. The second quantum circuit is acquired, for example, by the acquisition unit 1501. The second quantum circuit may be set in advance by a user, for example.

[0168] The acquisition unit 1501 acquires various types of information used in processing by each functional unit. The acquisition unit 1501 stores the acquired various types of information in the storage unit 1500 or outputs the acquired various types of information to each functional unit. The acquisition unit 1501 may also output the various types of information stored in the storage unit 1500 to each functional unit. The acquisition unit 1501 acquires various types of information based on, for example, a user's operation input. The acquisition unit 1501 may receive various types of information from, for example, a device different from the information processing device 100.

[0169] The acquiring unit 1501 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, an initial value of the Ising model, a first quantum circuit, and a second quantum circuit. Specifically, the acquiring unit 1501 acquires the processing request by accepting input of the processing request based on an operation input by a user. Specifically, the acquiring unit 1501 may receive the processing request from another computer. The other computer is, for example, the client device 201.

[0170] The acquiring unit 1501 acquires, for example, information indicating a combinatorial optimization problem. Specifically, the acquiring unit 1501 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 1501 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 1501 may acquire the information indicating the combinatorial optimization problem by extracting the information indicating the combinatorial optimization problem from a processing request.

[0171] The acquiring unit 1501 acquires, for example, an Ising model. Specifically, the acquiring unit 1501 acquires the Ising model by accepting input of the Ising model based on an operational input from a user. Specifically, the acquiring unit 1501 may receive the Ising model from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 1501 may acquire the Ising model by extracting the Ising model from a processing request.

[0172] The acquiring unit 1501 acquires, for example, an initial value of the Ising model. Specifically, the acquiring unit 1501 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 acquiring unit 1501 may receive the initial value of the Ising model from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 1501 may acquire the initial value of the Ising model by extracting the initial value of the Ising model from a processing request.

[0173] The acquiring unit 1501 acquires, for example, a first quantum circuit. Specifically, the acquiring unit 1501 acquires the first quantum circuit by accepting input of the first quantum circuit based on an operational input from a user. Specifically, the acquiring unit 1501 may receive the first quantum circuit from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 1501 may acquire the first quantum circuit by extracting the first quantum circuit from a processing request.

[0174] The acquiring unit 1501 acquires, for example, a second quantum circuit. Specifically, the acquiring unit 1501 acquires the second quantum circuit by accepting input of the second quantum circuit based on an operational input from a user. Specifically, the acquiring unit 1501 may receive the second quantum circuit from another computer. The other computer is, for example, the client device 201. Specifically, the acquiring unit 1501 may acquire the second quantum circuit by extracting the second quantum circuit from a processing request.

[0175] The acquiring unit 1501 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 1501 receives, for example, acquisition of a processing request as a start trigger to start processing by the first determining unit 1502, the first calculating unit 1503, the second determining unit 1504, and the second calculating unit 1505.

[0176] The first determination unit 1502 determines first values ​​of parameters of the QAOA so that the energy corresponding to the quantum state of the first quantum circuit is minimized. For example, the first determination unit 1502 determines first values ​​of parameters of the QAOA so that the energy corresponding to the quantum state of the first quantum circuit is minimized in response to the acquisition of a processing request by the acquisition unit 1501. This allows the first determination unit 1502 to appropriately determine the parameters of the QAOA, and allows the first quantum circuit to approximate an eigenvalue problem.

[0177] For example, each time the second calculation unit 1505 calculates a second solution, the first determination unit 1502 determines a new first value of the parameter of the QAOA so that the energy corresponding to the quantum state of the first quantum circuit is minimized. This allows the first determination unit 1502 to appropriately determine the parameter of the QAOA and approximate the first quantum circuit to an eigenvalue problem. The first determination unit 1502 corresponds to the QPU 307.

[0178] The first calculation unit 1503 calculates a first solution to the combinatorial optimization problem based on the Ising model. For example, the first calculation unit 1503 calculates the first solution to the combinatorial optimization problem based on set initial values ​​and the Ising model in response to the acquisition of a processing request by the acquisition unit 1501. This allows the first calculation unit 1503 to obtain guidelines for determining parameters of the QAOA, making it easier to determine the parameters of the QAOA.

[0179] For example, each time the second calculation unit 1505 calculates a second solution, the first calculation unit 1503 sets the second solution as an initial value. For example, each time the second calculation unit 1505 calculates a second solution, the first calculation unit 1503 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 1503 to obtain a guideline for determining parameters of the QAOA, making it easier to determine the parameters of the QAOA. The first calculation unit 1503 corresponds to, for example, the Ising machine 306.

[0180] The second determination unit 1504 determines a second value of a parameter of the QAOA from the first value of the parameter of the QAOA so as to maximize the probability that the quantum state of the first quantum circuit will be the first solution calculated by the first calculation unit 1503. For example, each time the first calculation unit 1503 calculates a first solution, the second determination unit 1504 determines a second value of a parameter of the QAOA from the first value of the parameter of the QAOA so as to maximize the probability that the quantum state of the first quantum circuit will be the first solution. Specifically, the second determination unit 1504 uses the second quantum circuit based on the QAE to repeat the process of "updating the value of the parameter according to the result of measuring the probability that the quantum state of the first quantum circuit will be the first solution based on the phase" from the first value of the parameter of the QAOA. The phase, for example, specifies an amplitude that specifies the probability that the quantum state of the first quantum circuit will be the first solution.

[0181] This allows the second determination unit 1504 to determine the second value of the parameter of the QAOA. The second determination unit 1504 can appropriately determine the value of the parameter of the QAOA. Then, the second determination unit 1504 can make it easier to calculate the second solution to the combinatorial optimization problem based on the first quantum circuit. The second determination unit 1504 can utilize the QAE to reduce the time required to determine the second value of the parameter of the QAOA. The determination unit 403 corresponds to, for example, the QPU 307.

[0182] The second calculation unit 1505 calculates a second solution to the combinatorial optimization problem based on the first quantum circuit in which the second value of the parameter determined by the second determination unit 1504 is set. For example, each time the second determination unit 1504 determines the second value of the parameter, the second calculation unit 1505 sets the second value of the parameter in the first quantum circuit. For example, the second calculation unit 1505 calculates the second solution to the combinatorial optimization problem based on the first quantum circuit in which the second value of the parameter is set. This allows the second calculation unit 1505 to calculate an appropriate solution to the combinatorial optimization problem. The second calculation unit 1505 corresponds to the QPU 307.

[0183] The information processing device 100 repeatedly executes a series of processes by the first determination unit 1502, the first calculation unit 1503, the second determination unit 1504, and the second calculation unit 1505 until a predetermined condition is met. The predetermined condition may be, for example, executing the series of processes a predetermined number of times. The predetermined condition may be, for example, calculating the second solution a predetermined number of times. The predetermined condition may be, for example, the difference between the second solution calculated this time and the second solution calculated previously being equal to or less than a threshold. This allows the information processing device 100 to bring the second solution calculated by the second calculation unit 1505 closer to an optimal solution to the combinatorial optimization problem.

[0184] The output unit 1506 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 1506 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.

[0185] The output unit 1506 outputs the second solution calculated by the second calculation unit 1505. The output unit 1506 outputs, for example, the second solution last calculated by the second calculation unit 1505. Specifically, the output unit 1506 outputs the second solution last calculated by the second calculation unit 1505 so that it can be referenced by a user. Specifically, the output unit 1506 may transmit the second solution last calculated by the second calculation unit 1505 to another computer. In this way, the output unit 1506 can make the solution to the combinatorial optimization problem available externally.

[0186] Here, the case where the information processing device 100 includes the first calculation unit 1503 and the second calculation unit 1505 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 1503 by communicating with another computer having the first calculation unit 1503. For example, the information processing device 100 may use the second calculation unit 1505 by communicating with another computer having the second calculation unit 1505.

[0187] (Example of operation of information processing device 100 in the second embodiment) Next, an example of the operation of the information processing device 100 in the second embodiment will be described with reference to FIG.

[0188] FIG. 16 is an explanatory diagram showing an example of the operation of the information processing device 100 in the second example. In FIG. 16, the information processing device 100 acquires information indicating a combinatorial optimization problem min(E=C(z)), similar to FIG. 5. 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. Similar to FIG. 5, 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. Similar to FIG. 5, the information processing device 100 sets a quantum circuit 600 by QAOA corresponding to the combinatorial optimization problem.

[0189] (16-1) 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 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.

[0190] (16-1a) 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 above formula (1). (16-1b) Specifically, the information processing device 100 applies 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.

[0191] (16-1c) Specifically, 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. More specifically, the information processing device 100 sets an objective function that minimizes the energy E(γ,β) using the Grid method, the BFGS method, the quadratic approximation method, the Powell method, or Bayesian estimation, and calculates the hyperparameters (γ',β').

[0192] (16-1d) The information processing device 100, specifically, repeatedly determines the hyperparameters (γ′, β′) by the CPU 301. The information processing device 100, specifically, returns to the process of (16-1a) until the hyperparameters (γ′, β′) are determined a predetermined number of times by the CPU 301.

[0193] When the information processing device 100 determines the hyperparameters (γ', β') a predetermined number of times using the CPU 301, the hyperparameters (γ', β') are statistically determined. The predetermined number of times is, for example, set in advance. The predetermined number of times is, for example, a third number. Here, the reason for approximating the QAOA Ansatz 610 to a combinatorial optimization problem will be described.

[0194] Graph 1600 in Figure 16 represents the MaxCut problem. Nodes in graph 1600 correspond to quantum bits. Among the nodes in graph 1600, nodes with dotted hatching represent the range represented by QAOA Ansatz 1610 for p=1. QAOA Ansatz 1610 includes Hadamard gate 1611. QAOA Ansatz 1610 includes, for example, gates 1612 and 1613.

[0195] Here, the energy is defined by, for example, the following formula (3): As shown in the following formula (3), the other quantum bits other than the quantum bits subscripted with j and k are cancelled out by U shown in the following formula (4).

[0196]

number

[0197]

number

[0198] Therefore, the QAOA Ansatz 1610 for p=1 has the problem of being unable to represent the entire graph 1600. Similarly, graph 1620 represents the MaxCut problem. The nodes of graph 1620 correspond to quantum bits. Among the nodes of graph 1620, the nodes with dotted hatching represent the range represented by QAOA Ansatz 1630 for p=2. QAOA Ansatz 1630 includes Hadamard gate 1631. QAOA Ansatz 1630 includes gates 1632 to 1635. Like the QAOA Ansatz 1610 for p=1, the QAOA Ansatz 1630 for p=2 has the problem of being unable to represent the entire graph 1620.

[0199] Therefore, it is preferable that the information processing device 100 determines the hyperparameters (γ', β') so that the representation range 1641 of the QAOA Ansatz 610 approximates the combinatorial optimization problem 1640. For details about approximating the representation range 1641 of the QAOA Ansatz 610 to the combinatorial optimization problem 1640, the above-mentioned Reference 10 can be referred to.

[0200] (16-2) 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.

[0201] (16-3) 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 becomes z0 is maximized. * ,β * ) to determine

[0202] (16-3a) Specifically, the information processing device 100 sets the hyperparameters (γ', β') as the hyperparameters (γ, β). (16-3b) Specifically, the information processing device 100 applies a superposition state |s> to n quantum bits by the QPU 307, as in Figures 7 and 8. Here, the superposition state |s> is defined by, for example, the above formula (1).

[0203] (16-3c) Specifically, the information processing device 100 prepares a second quantum circuit 700 using QAE, similar to FIGS. 7 and 8. Specifically, the information processing device 100 calculates a probability p z0(γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> Measure.

[0204] (16-3d) 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 determined by calculating

[0205] 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 (16-3b). * ,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 fourth number.

[0206] (16-4) 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 *The information processing device 100 applies the superposition state |s> to n quantum bits by, for example, the QPU 307. The information processing device 100 determines (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 * )>.

[0207] The information processing device 100, for example, calculates the quantum state |ψ(γ * ,β * )> is sampled n-shot to determine n classical states z1. Specifically, 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.

[0208] 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.

[0209] (16-5) The information processing device 100 determines, via the CPU 301, whether or not a termination condition is satisfied. The termination condition is, for example, that the series of processes (16-1), (16-2), (16-3), and (16-4) 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, the fifth number. The termination condition may be defined, for example, by a threshold value for the energy E or the state z.

[0210] 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 (16-1), (16-2), (16-3), and (16-4) are executed again.

[0211] 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.

[0212] The information processing device 100 utilizes QAE to calculate the probability p z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> Therefore, the information processing device 100 can measure the measurement error by 1 / n 2 Therefore, when suppressing measurement errors, the information processing device 100 can suppress an increase in the number of shots, reduce the time required for measurement, and reduce the time required for calculating a solution to a combinatorial optimization problem.

[0213] 9, the information processing device 100 can use QAOA to efficiently and accurately approximate a solution to a combinatorial optimization problem to an optimal solution. For example, by using QAOA, the information processing device 100 can consider all states represented by quantum states that could be solutions to the combinatorial optimization problem, and can accurately calculate a solution to the combinatorial optimization problem. Therefore, by using QAOA, the information processing device 100 can reduce the time required to calculate a solution to the combinatorial optimization problem.

[0214] 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.

[0215] 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.

[0216] (Overall processing procedure in the second embodiment) Next, an example of an overall processing procedure in the second embodiment executed by the information processing device 100 will be described with reference to Fig. 17. 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.

[0217] Fig. 17 is a flowchart showing an example of the overall processing procedure in the second embodiment. In Fig. 17, the information processing device 100 acquires a combinatorial optimization problem min(E=C(z)) by the CPU 301 (step S1701).

[0218] Next, the information processing device 100 executes a first determination process, which will be described later with reference to Fig. 18, using the QPU 307 (step S1702). 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.

[0219] 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 S1703).

[0220] Next, the information processing device 100 executes a second determination process, which will be described later with reference to FIG. 19, 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 S1704). 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

[0221] Then, the information processing device 100 executes a third determination process, which will be described later with reference to FIG. 20, using the QPU 307 (step S1705). 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.

[0222] 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 S1706). 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 S1706: No), the information processing device 100 proceeds to the processing of step S1707. On the other hand, if the predetermined number of times has been determined (step S1706: Yes), the information processing device 100 proceeds to the processing of step S1708.

[0223] In step S1707, the information processing device 100 sets the initial value of the Ising machine 306 to the optimal classical state z1 * (step S1707). Then, the information processing apparatus 100 returns to the process of step S1702.

[0224] In step S1708, the information processing device 100 calculates min(C(z0),C(z1 * )) (step S1708). Here, the information processing device 100 may output argmin(C(z)). Then, the information processing device 100 ends the overall processing.

[0225] (First determination process procedure in the second embodiment) Next, an example of a first determination process procedure in the second embodiment executed by the information processing device 100 will be described with reference to Fig. 18. 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.

[0226] FIG. 18 is a flowchart showing an example of the first determination process procedure in the second embodiment. In FIG. 18, the information processing device 100 applies a superposition state |s> to n quantum bits (step S1801). 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 S1802).

[0227] Next, the information processing device 100 measures the energy E(γ,β)=<ψ(γ,β)|C(z)|ψ(γ,β)> (step S1803). Then, the information processing device 100 determines the hyperparameters (γ',β') of the QAOA so that the energy E(γ,β) is minimized (step S1804).

[0228] Next, the information processing device 100 determines whether the hyperparameters (γ', β') of QAOA have been determined a predetermined number of times (step S1805). 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 S1805: No), the information processing device 100 returns to the processing of step S1801. On the other hand, if the hyperparameters have been determined the predetermined number of times (step S1805: Yes), the information processing device 100 ends the first determination processing.

[0229] (Second decision processing procedure in the second embodiment) Next, an example of a procedure of a second determination process in the second embodiment executed by the information processing device 100 will be described with reference to Fig. 19. 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.

[0230] 19 is a flowchart showing an example of the second determination process procedure in the second embodiment. In FIG. 19, the information processing device 100 determines whether or not it is the first loop (step S1901). If it is the first loop (step S1901: Yes), the information processing device 100 sets γ=γ' and β=β' (step S1902) and proceeds to the process of step S1904. On the other hand, if it is not the first loop (step S1901: No), the information processing device 100 sets γ=γ * ,β=β * (step S1903), and the process proceeds to step S1904.

[0231] In step S1904, the information processing device 100 applies the superposition state |s> to n quantum bits (step S1904). Next, the information processing device 100 identifies the quantum state |ψ(γ, β)> by performing the measurement process shown in FIG. 12 (step S1905). Next, the information processing device 100 identifies the quantum state |ψ(γ, β)> with a probability p z0 (γ,β)=<ψ(γ,β)|z0><z0|ψ(γ,β)> (step S1906). Then, the information processing device 100 measures the probability p z0 The hyperparameter (γ * ,β * ) is determined (step S1907).

[0232] Next, the information processing device 100 calculates the hyperparameter (γ * ,β * ) has been determined a predetermined number of times (step S1908). 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 S1908: No), the information processing device 100 returns to the processing of step S1901. On the other hand, if the predetermined number of times has been determined (step S1908: Yes), the information processing device 100 ends the second determination processing.

[0233] (Third decision processing procedure in the second embodiment) Next, an example of a third determination process procedure in the second embodiment executed by the information processing device 100 will be described with reference to Fig. 20. 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.

[0234] Fig. 20 is a flowchart showing an example of the third determination process procedure in Example 2. In Fig. 20, the information processing device 100 applies the superposition state |s> to n quantum bits (step S2001).

[0235] 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 S2002). Then, the information processing device 100 identifies the quantum state |ψ(γ * ,β * )> is sampled n shots to determine n classical states z1 (step S2003).

[0236] Next, the information processing device 100 calculates the energy E1 corresponding to each classical state z1, and calculates min(E1) <min(E0,E1 * ) (step S2004). 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.

[0237] where min(E1) <min(E0,E1 * ) (step S2004: Yes), the information processing apparatus 100 proceeds to the process of step S2005. <min(E0,E1 * ) (step S2004: No), the information processing device 100 proceeds to the process of step S2006.

[0238] In step S2005, the information processing device 100 * is determined to be argmin(E1) (step S2005). 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.

[0239] In step S2006, the information processing device 100 calculates z1 based on E1 and the Hamming Distance. * (Step S2006). E1, Hamming Distance is determined, for example, as ((E1-E0) x Hamming Distance(z1, z0)) -1 Then, the information processing device 100 ends the third determination process.

[0240] Here, the information processing device 100 may interchange the processes of some steps in the flowcharts of Figures 17 to 20. For example, the processes of steps S1702 and S1703 can be interchanged. The information processing device 100 may omit the processes of some steps in the flowcharts of Figures 17 to 20. For example, the processes of steps S1706 and S1707 can be omitted.

[0241] (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.

[0242] 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 approximation optimization algorithm to maximize the probability that the quantum state of a first quantum circuit calculated by the quantum approximation optimization algorithm corresponding to the combinatorial optimization problem will be the calculated first solution. The information processing device 100 can prepare a second quantum circuit using quantum amplitude estimation, for example, including an auxiliary quantum bit and a partial circuit in which the quantum state of the auxiliary quantum bit becomes 1 when the quantum state of the first quantum circuit is the first solution. The information processing device 100 can determine parameter values ​​by, for example, repeatedly updating the parameter values ​​using the second quantum circuit based on the results of measuring the probability based on a phase that defines the amplitude that specifies the probability. The information processing device 100 can calculate a second solution to the combinatorial optimization problem based on the determined parameter values. This allows the information processing device 100 to reduce the time required to accurately calculate a solution to a combinatorial optimization problem.

[0243] The information processing device 100 can determine a first value of a parameter for a first quantum circuit so that the energy corresponding to the quantum state of the first quantum circuit is minimized. The information processing device 100 can calculate a first solution based on an Ising model. 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 is maximized. The information processing device 100 can determine the second value of the parameter by, for example, repeatedly updating the value of the parameter according to the result of measuring the probability based on the phase using a second quantum circuit. The information processing device 100 can calculate a second solution based on the first quantum circuit in 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. Furthermore, the information processing device 100 can improve the accuracy of calculating a solution to a combinatorial optimization problem.

[0244] 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.

[0245] According to the information processing device 100, a series of processes of calculating a first value of a parameter, calculating a first solution, determining a second value of the parameter, and calculating the 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.

[0246] 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.

[0247] 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.

[0248] According to the information processing device 100, the process of calculating the first solution can be executed using an Ising machine that solves combinatorial optimization problems in accordance with a digital annealer. According to the information processing device 100, the process of determining parameter values ​​and the process of calculating the second solution can be executed using a quantum processing device that processes a quantum circuit. This allows the information processing device 100 to efficiently calculate the first solution and efficiently calculate the second solution.

[0249] According to the information processing device 100, the process of calculating a first solution can be executed using an Ising machine that solves combinatorial optimization problems in accordance with a digital annealer. According to the information processing device 100, the process of determining a first value of a parameter, the process of determining a second value of a parameter, and the process of calculating a second solution can be executed using a quantum processing device that processes a quantum circuit. This enables the information processing device 100 to efficiently calculate the first solution and efficiently calculate the second solution.

[0250] 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.

[0251] The following additional notes are provided regarding the above-described embodiment.

[0252] (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 the quantum state of a first quantum circuit obtained by 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 first quantum circuit to which the determined parameter values ​​have been set; Have the computer execute the process, The determining process includes: 1. An information processing program comprising: a second quantum circuit using quantum amplitude estimation, the second quantum circuit including a partial circuit having an auxiliary quantum bit, the quantum state of the auxiliary quantum bit being 1 when the quantum state of the first quantum circuit is the first solution; and a process of updating the value of the parameter according to a result of measuring the probability based on a phase that defines an amplitude that specifies the probability, thereby determining the value of the parameter.

[0253] (Supplementary Note 2) Regarding the first quantum circuit, determining a first value of the parameter so that energy corresponding to a quantum state of the first quantum circuit is minimized; calculating the first solution based on the Ising model; determining a second value of the parameter from the determined first value of the parameter such that the probability is maximized; calculating the second solution based on the first quantum circuit to which the determined second value of the parameter has been set; Have the computer execute the process, The process of determining the second value includes: 2. The information processing program according to claim 1, further comprising: determining a second value of the parameter by repeating a process of updating the value of the parameter according to a result of measuring the probability based on the phase using the second quantum circuit.

[0254] (Supplementary Note 3) The first solution 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 first quantum circuit will become the newly calculated first solution is maximized; calculating a new second solution based on the first quantum circuit 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.

[0255] (Supplementary Note 4) Based on the calculated second solution, a first value of the parameter is newly determined so that the energy corresponding to the quantum state of the first quantum circuit is minimized; a new first solution is calculated based on the Ising model in which the calculated second solution is 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 first quantum circuit will become the newly calculated first solution is maximized; calculating a new second solution based on the first quantum circuit to which the newly determined second value of the parameter has been set; 3. The information processing program according to claim 2, wherein the computer repeatedly executes the process until a predetermined condition is satisfied.

[0256] (Supplementary Note 5) The information processing program according to Supplementary Note 3 or 4, wherein the predetermined condition is that the second solution is calculated a predetermined number of times.

[0257] (Appendix 6) Output the calculated second solution. 6. The information processing program according to any one of claims 1 to 5, which causes the computer to execute processing.

[0258] (Supplementary Note 7) The process of calculating the first solution is performed using an Ising machine that solves the combinatorial optimization problem in accordance with Digital Annealer; The information processing program according to claim 1, wherein the process of determining the parameter value and the process of calculating the second solution are executed using a quantum processing device that processes a quantum circuit.

[0259] (Supplementary Note 8) The process of calculating the first solution is performed using an Ising machine that solves the combinatorial optimization problem in accordance with Digital Annealer; The information processing program according to claim 2, 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 processes a quantum circuit.

[0260] (Appendix 9) The information processing program according to Appendix 1, characterized in that the process of calculating the second solution to the combinatorial optimization problem calculates the second solution to the combinatorial optimization problem based on a distribution of quantum states represented by the first quantum circuit.

[0261] (Appendix 10) The information processing program described in Appendix 1, characterized in that the determining process determines the value of the parameter by repeating a process of updating the value of the parameter in accordance with the result of measuring the probability based on the distribution of quantum states represented by the second quantum circuit.

[0262] (Supplementary Note 11) 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 the quantum state of a first quantum circuit obtained by 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 first quantum circuit to which the determined parameter values ​​have been set; The computer executes the processing, The determining process includes: 1. An information processing method comprising: determining a value of the parameter by repeating a process of updating the value of the parameter in accordance with a result of measuring the probability based on a phase that defines an amplitude that specifies the probability, using a second quantum circuit using quantum amplitude estimation, the second quantum circuit including a partial circuit having an auxiliary quantum bit, the quantum state of the auxiliary quantum bit being 1 when the quantum state of the first quantum circuit becomes the first solution.

[0263] (Supplementary Note 12) 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 the quantum state of a first quantum circuit obtained by 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 first quantum circuit to which the determined parameter values ​​have been set; A control unit is provided. The control unit an information processing device, characterized in that, when determining the value of the parameter, the information processing device determines the value of the parameter by repeating a process of updating the value of the parameter according to a result of measuring the probability based on a phase that defines an amplitude that specifies the probability, using a second quantum circuit using quantum amplitude estimation, the second quantum circuit including a partial circuit having an auxiliary quantum bit and whose quantum state is 1 when the quantum state of the first quantum circuit becomes the first solution. [Explanation of symbols]

[0264] 100 Information processing device 101,1403 First solution 102,1404 Second solution 110,1410 Ising model 111,600,1411 The first quantum circuit 112,700,1412 Second quantum circuit 120 parameters 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 400,1500 storage unit 401,1501 Acquisition Department 402,1503 First Calculation Section 403 Decision Section 404,1505 Second calculation unit 405,1506 Output section 601,1611,1631 Hadamard Gate 610,812,1610,1630 QAOA Ansatz Gates 611-614, 711, 712, 1612, 1613, 1632-1635 701, 702, 801~803 lines 713 Measuring part 720 State Preparation Circuit 811,816 revolving gate 813~815 CNOT Gate 900,910,920,1600,1620 graph 1401 First Value 1402 Second Value 1502 First Decision Section 1504 Second Decision Section 1640 Optimization Problems 1641 Expression Range

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 the quantum state of a first quantum circuit obtained by 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 first quantum circuit to which the determined parameter values ​​have been set; Have the computer execute the process, The determining process includes:

1. An information processing program comprising: a second quantum circuit using quantum amplitude estimation, the second quantum circuit including a partial circuit having an auxiliary quantum bit, the quantum state of the auxiliary quantum bit being 1 when the quantum state of the first quantum circuit is the first solution; and a process of updating the value of the parameter according to a result of measuring the probability based on a phase that defines an amplitude that specifies the probability, thereby determining the value of the parameter.

2. determining a first value of the parameter for the first quantum circuit such that an energy corresponding to a quantum state of the first quantum circuit is minimized; calculating the first solution based on the Ising model; determining a second value of the parameter from the determined first value of the parameter such that the probability is maximized; calculating the second solution based on the first quantum circuit to which the determined second value of the parameter has been set; Have the computer execute the process, The process of determining the second value includes:

2. The information processing program according to claim 1, wherein the second value of the parameter is determined by repeating a process of updating the value of the parameter according to a result of measuring the probability based on the phase using the second quantum circuit.

3. a new first solution 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 first quantum circuit will become the newly calculated first solution is maximized; calculating a new second solution based on the first quantum circuit 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.

4. determining a new first value of the parameter based on the calculated second solution so that the energy corresponding to the quantum state of the first quantum circuit is minimized; a new first solution is calculated based on the Ising model in which the calculated second solution is 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 first quantum circuit will become the newly calculated first solution is maximized; calculating a new second solution based on the first quantum circuit to which the newly determined second value of the parameter has been set; 3. The information processing program according to claim 2, wherein the program causes the computer to repeatedly execute the process until a predetermined condition is satisfied.

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

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 the quantum state of a first quantum circuit obtained by 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 first quantum circuit to which the determined parameter values ​​have been set; The computer executes the processing, The determining process includes:

1. An information processing method comprising: determining a value of the parameter by repeating a process of updating the value of the parameter in accordance with a result of measuring the probability based on a phase that defines an amplitude that specifies the probability, using a second quantum circuit using quantum amplitude estimation, the second quantum circuit including a partial circuit having an auxiliary quantum bit, the quantum state of the auxiliary quantum bit being 1 when the quantum state of the first quantum circuit is the first solution.

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 the quantum state of a first quantum circuit obtained by 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 first quantum circuit to which the determined parameter values ​​have been set; A control unit is provided. The control unit an information processing device, characterized in that, when determining the value of the parameter, the information processing device determines the value of the parameter by repeating a process of updating the value of the parameter according to a result of measuring the probability based on a phase that defines an amplitude that specifies the probability, using a second quantum circuit using quantum amplitude estimation, the second quantum circuit including a partial circuit having an auxiliary quantum bit and whose quantum state becomes 1 when the quantum state of the first quantum circuit becomes the first solution.

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