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

Abstract

To improve the accuracy of solving combinatorial optimization problems. [Solution] The information processing device 100 sets a first function for the quantum circuit 110, which represents the first variational parameter 131 applied to the first subcircuit 121 representing the action of the mixer unitary operator. This function is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function. The information processing device 100 also sets a second function for the quantum circuit 110, which represents the second variational parameter 132 applied to the second subcircuit 122 representing the action of the cost unitary operator. This function is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function. The information processing device 100 uses the quantum circuit 110 to optimize the expected value of the energy represented by the cost function by updating the values ​​of the first transformation parameter 161 and the second transformation parameter 162, thereby calculating the solution to the combinatorial optimization problem.

Description

Technical Field

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

Background Art

[0002] Conventionally, there is a technique of QAOA (Quantum Approximate Optimization Algorithm) that solves a combinatorial optimization problem by using a multi-layer quantum circuit having two types of variational parameters per layer. QAOA solves a combinatorial optimization problem by, for example, searching for appropriate values of variational parameters so as to minimize the expected value of a cost function. The two types of variational parameters are a variational parameter related to a mixer unitary operator and a variational parameter related to a cost unitary operator.

[0003] As prior art, for example, there is one that selects values of QAOA parameters by a Bayesian optimizer. Also, for example, there is a technique of selectively arranging a plurality of qubits in a spatial structure. Also, for example, there is a technique of applying a sequence of resonance optical pulses having a non-constant duration and a non-constant optical phase to at least any one of a plurality of qubits.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, conventional techniques sometimes struggle to solve combinatorial optimization problems accurately. Specifically, increasing the number of layers in a quantum circuit increases the number of variational parameters, making it difficult to find appropriate values ​​for these parameters.

[0006] In one aspect, the present invention aims to improve the accuracy of solving combinatorial optimization problems. [Means for solving the problem]

[0007] According to one embodiment, an information processing program, information processing method, and information processing device are proposed for a quantum circuit that includes, layer by layer, a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator, used when solving a combinatorial optimization problem. The program sets a first function representing the first variational parameter of the first subcircuit, which is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function, and sets a second function representing the second variational parameter of the second subcircuit, which is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function. Using the quantum circuit after setting the first function and the second function, the program updates the values ​​of the first transformation parameter of the first function and the second transformation parameter of the second function to optimize the expected value of the cost function corresponding to the combinatorial optimization problem, thereby calculating the solution to the combinatorial optimization problem. [Effects of the Invention]

[0008] In one embodiment, it becomes possible to improve the accuracy of solving combinatorial optimization problems. [Brief explanation of the drawing]

[0009] [Figure 1] Figure 1 is an explanatory diagram showing one embodiment of the information processing method according to the embodiment. [Figure 2] Figure 2 is an explanatory diagram showing an example of the information processing system 200. [Figure 3]Figure 3 is a block diagram showing an example of the hardware configuration of the information processing device 100. [Figure 4] Figure 4 is a block diagram showing an example of the hardware configuration of the quantum computing device 201. [Figure 5] Figure 5 is a block diagram showing an example of the functional configuration of the information processing device 100. [Figure 6] Figure 6 is an explanatory diagram (part 1) showing an example of the operation of the information processing device 100. [Figure 7] Figure 7 is an explanatory diagram (part 2) showing an example of the operation of the information processing device 100. [Figure 8] Figure 8 is an explanatory diagram (part 1) showing one example of the effect. [Figure 9] Figure 9 is an explanatory diagram (part 2) showing an example of the effect. [Figure 10] Figure 10 is an explanatory diagram (part 3) showing an example of the effect. [Figure 11] Figure 11 is an explanatory diagram (part 4) showing an example of the effect. [Figure 12] Figure 12 is a flowchart showing an example of the overall processing procedure. [Figure 13] Figure 13 is a flowchart showing an example of the calculation process. [Modes for carrying out the invention]

[0010] Embodiments of the information processing program, information processing method, and information processing apparatus according to the present invention will be described in detail below with reference to the drawings.

[0011] (An embodiment of the information processing method according to the embodiment) Figure 1 is an explanatory diagram showing one embodiment of the information processing method according to the embodiment. The information processing device 100 is a computer for solving combinatorial optimization problems. The information processing device 100 is, for example, a server or a PC (Personal Computer).

[0012] 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. Traditionally, methods for solving combinatorial optimization problems have included, for example, QAOA (Quantum Approximation Optimization Algorithm), which utilizes gate-type quantum computers. QAOA is a method based on, for example, a variational quantum algorithm. QAOA is a method for solving combinatorial optimization problems using quantum circuits that contain multiple variational parameters.

[0013] The quantum circuits used in QAOA have one or more layers. Each layer has a pair of sub-circuits: a cost circuit that applies a cost unitary operator to a quantum state, and a mixer circuit that applies a mixer unitary operator. The cost circuit has a variational parameter γ. The cost unitary operator is expressed as an exponential function whose exponential part contains the cost Hamiltonian multiplied by the variational parameter γ. The mixer circuit has a variational parameter β. The mixer unitary operator is expressed as an exponential function whose exponential part contains the mixer Hamiltonian multiplied by the variational parameter β. The quantum circuit, with one or more layers, realizes the function of evolving an input quantum state to obtain an output quantum state. The input is also called, for example, the initial quantum state. The output is also called, for example, the trial quantum state.

[0014] QAOA sets up a quantum circuit by, for example, setting a cost Hamiltonian using an Ising model or the like based on the cost function of the combinatorial optimization problem which serves as the objective function. QAOA solves the combinatorial optimization problem by, for example, using the quantum circuit to minimize the expected value of the energy represented by the cost function, and by repeatedly updating a series of variations on multiple parameters until a predetermined termination condition is met. The predetermined termination condition is, for example, that the expected value of the energy falls below a predetermined threshold.

[0015] The sequence of operations includes, for example, setting an initial quantum state. The sequence of operations includes, for example, using a quantum circuit to evolve the set initial quantum state and obtain a trial quantum state. The sequence of operations includes, for example, calculating the expected value of the energy represented by the cost function corresponding to the obtained trial quantum state. The sequence of operations includes, for example, updating multiple variational parameters in a direction that minimizes the expected value of the energy represented by the cost function, based on the calculated expected value of the energy represented by the cost function. When QAOA performs the sequence of operations for the first time, for example, it is conceivable that QAOA sets the initial quantum state randomly. When QAOA performs the sequence of operations for the second time or later, for example, it is conceivable that the previous trial quantum state is set as the current initial quantum state.

[0016] Here, by repeatedly performing a series of processes until a predetermined termination condition is met, the optimization of multiple variational parameters will bring the trial quantum state closer to the optimal solution. Furthermore, optimizing multiple variational parameters improves the probability that the value of the variable sequence corresponding to the combination of measurement results of the Z component of the Pauli spin operator for each qubit in the trial quantum state is a good solution to the combinatorial optimization problem.

[0017] The process of setting the initial quantum state is implemented, for example, by a classical computer. The process of evolving the initial quantum state to obtain a trial quantum state is implemented, for example, by a gate-type quantum computer. The process of calculating the expected value of the energy represented by the cost function is implemented, for example, by a gate-type quantum computer. The process of updating multiple variational parameters is implemented, for example, by a classical computer.

[0018] For updating multiple variational parameters, methods such as the Grid method, BFGS (Broyden-Fletcher-Goldfarb-Shanno) method, and Powell's method can be used. For information on QAOA, see, for example, reference 1 below.

[0019] Reference 1: Farhi, Edward, Jeffrey Goldstone, and Sam Gutmann. “A quantum approximate optimization algorithm.” arXiv preprint arXiv:1411.4028 (2014).

[0020] Specifically, according to the Ising model, a combinatorial optimization problem involves a variable z that takes a value of +1 or -1. i This problem can be expressed as minimizing a cost function C(z) such that i = 1 to N. Specifically, the cost function is defined by the following equation (1), where z is a sequence of variables. Specifically, z = z N ...z2z1 is c i c is the first-order weighting coefficient. i,j This is a second-order weighting coefficient. The cost function may include terms of order three or higher.

[0021]

number

[0022] Specifically, the trial function of QAOA is defined by equation (1) above, which represents the cost function, and equations (2) to (10) below. The trial function is, for example, a variational trial function. P is the number of layers in the quantum circuit. P ≥ 1. z is the sequence of variables described above. Equation (2) below represents the energy operator. The energy operator is also called the cost operator. σ Z i σ is the Z component of the Pauli spin operator. Equation (3) below represents the mixer operator. X i is the X component of the Pauli spin operator. The mixer operator may be other types of mixer operators, such as the XY-Mixer. For other types of mixer operators, such as the XY-Mixer, see, for example, reference 2 below.

[0023]

number

[0024]

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[0025] Reference 2: Hadfield, Stuart, et al. “From the quantum approximate optimization algorithm to a quantum alternating operator ansatz.” Algorithms 12.2 (2019): 34.

[0026] The following formula (4) represents a cost unitary operator. The cost unitary operator is an exponential function that includes an energy operator with a variational parameter γ l in its exponent. l = 1 to P. The variational parameter γ l is set for each layer of the quantum circuit. The cost unitary operator represents the action on the problem setting in the quantum circuit. The following formula (5) represents a mixer unitary operator. The mixer unitary operator is an exponential function that includes a mixer operator with a variational parameter β l in its exponent. The variational parameter β l is set for each layer of the quantum circuit. The mixer unitary operator represents the action on the search space in the quantum circuit.

[0027]

Number

[0028]

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[0029] The following formula (6) represents an initial quantum state. The initial quantum state is, for example, the ground state of the mixer operator. The following formula (7) represents a trial quantum state. γ = (γ1, γ2, ···, γ P) is the case. β=(β1,β2,···,β P ) is. γ1,γ2,···,γ P These are real numbers. β1, β2, ..., β P is a real number. Equation (8) below represents the expectation value of the energy operator. Equation (8) below corresponds to energy.

[0030]

number

[0031]

number

[0032]

number

[0033] Here, by making the number of layers P in the quantum circuit approach infinity, it is possible to simulate quantum annealing. Simulating quantum annealing is γ l From γ1 to γ P We increase it to this extent, and also the β corresponding to the strength of the transverse magnetic field. l From β1 to β P This corresponds to reducing the size to a certain extent. Theoretically, in QAOA, although the number of layers P is finite, increasing the number of layers P improves the ability to represent the quantum state corresponding to the solution, thereby improving the accuracy of solving combinatorial optimization problems.

[0034] On the other hand, in practice, it can be difficult to solve combinatorial optimization problems accurately. For example, increasing the number of layers P in a quantum circuit increases the number of variational parameters, making it difficult to find appropriate values ​​for these parameters. Specifically, this leads to an increase in the processing load and processing time required to find appropriate values ​​for variational parameters. Therefore, there is a problem in that it is difficult to increase the number of layers P in order to improve the accuracy of solving combinatorial optimization problems.

[0035] In contrast, one approach is to expand the aforementioned variational parameters using sine and cosine functions, and then modify QAOA so that the expansion coefficients applied to the sine and cosine functions are the ones whose values ​​are updated, instead of the variational parameters themselves. This approach is also known as the Fourier method. The expansion formulas for expanding the variational parameters are defined, for example, by equations (9) and (10) below.

[0036]

number

[0037]

number

[0038] This method can reduce the number of parameters whose values ​​need to be updated. For example, the number of parameters whose values ​​need to be updated can be reduced to less than 2P. For more information on this method, please refer to, for example, the above-mentioned Patent Document 2.

[0039] However, in this method, from the perspective of approximating quantum annealing, it may not be desirable to expand multiple variational parameters using sine and cosine functions. Therefore, it may be difficult to solve combinatorial optimization problems accurately.

[0040] Therefore, this embodiment describes an information processing method that can improve the accuracy of solving combinatorial optimization problems. Specifically, with this information processing method, even if the number of layers P is increased and the ability to represent quantum states is improved, the number of parameters whose values ​​are to be updated can be reduced, thereby improving the accuracy of solving combinatorial optimization problems.

[0041] In Figure 1, the information processing device 100 stores a quantum circuit 110 used when solving a combinatorial optimization problem. The quantum circuit 110 has P layers 111. The quantum circuit 110 defines the actions on N qubits. The quantum circuit 110 includes a plurality of gates, each representing an action on one or more qubits. The quantum circuit 110 includes a measurement unit 112 for each qubit. P is the number of layers.

[0042] Each layer 111 of the quantum circuit 110 includes a first subcircuit 121 representing the action of a mixer unitary operator and a second subcircuit 122 representing the action of a cost unitary operator.

[0043] The mixer unitary operator is a mathematical formula that defines the action of layer 111. The mixer unitary operator represents, for example, an action on the search space. The mixer unitary operator includes, for example, the first variational parameter 131. The first variational parameter 131 is, for example, the β1, β2, ..., β mentioned above. P The mixer unitary operator corresponds, for example, to equation (5) above. Therefore, the first subcircuit 121 representing the action of the mixer unitary operator has a first variational parameter 131. The information processing device 100 stores, for example, the first variational parameter 131 relating to the first subcircuit 121.

[0044] The cost unitary operator is a mathematical formula that defines the action of layer 111. The cost unitary operator represents, for example, the action on the problem setting. The cost unitary operator includes, for example, a second variational parameter 132. The second variational parameter 132 is, for example, the aforementioned γ1, γ2, ..., γ P The cost unitary operator corresponds, for example, to equation (4) above. Therefore, the second subcircuit 122 representing the action of the cost unitary operator has a second variational parameter 132. The information processing device 100 stores, for example, the second variational parameter 132 relating to the second subcircuit 122.

[0045] Furthermore, the information processing device 100 stores a cost function corresponding to the combinatorial optimization problem. The cost function represents, for example, energy. The cost function corresponds, for example, to equation (1) above. For example, the expected value of the energy represented by the cost function is the object to be optimized in order to solve the combinatorial optimization problem. Optimization is, for example, minimization.

[0046] (1-1) The information processing device 100 sets a first function for the quantum circuit 110, which is a combination of a monotonically decreasing function and a first sine function, representing the first variational parameter 131 relating to the first subcircuit 121. The first function represents the relationship between the order of each layer 111 from the beginning of the quantum circuit 110 and the value of the first variational parameter 131 relating to the first subcircuit 121 that the layer 111 possesses. Graph 140 represents the first function. The horizontal axis of graph 140 represents the variable l indicating the order of the layers 111. The vertical axis of graph 140 represents, for example, the value of the first variational parameter 131.

[0047] The monotonically decreasing function is, for example, a function that represents a monotonically decreasing straight line 141. Monotonically decreasing may be, for example, monotonically decreasing in a broad sense. The monotonically decreasing function may also represent a monotonically decreasing curve rather than a straight line. The first sine function is, for example, a function that represents a sine wave whose value is zero for the first layer 111 and the Pth layer 111 from the beginning of the quantum circuit 110. The first function is, for example, a function that represents a curve 142 by combining the monotonically decreasing function and the first sine function. Specifically, each point on the curve 142 corresponding to the order of the layers 111 represents the value of the first variational parameter 131 relating to the first subcircuit 121 of that layer 111.

[0048] (1-2) The information processing device 100 sets a second function for the quantum circuit 110, which is a combination of a monotonically increasing function and a second sine function, representing the second variational parameter 132 relating to the second subcircuit 122. The second function represents the relationship between the order of each layer 111 from the beginning of the quantum circuit 110 and the value of the second variational parameter 132 relating to the second subcircuit 122 of that layer 111. Graph 150 represents the second function. The horizontal axis of graph 150 represents the variable l indicating the order of the layers 111. The vertical axis of graph 140 represents, for example, the value of the second variational parameter 132.

[0049] The monotonically increasing function is, for example, a function that represents a monotonically increasing straight line 151. Monotonically increasing may be, for example, a broadly defined monotonically increasing function. The monotonically increasing function may also represent a monotonically increasing curve rather than a straight line. The second sine function is, for example, a function that represents a sine wave whose value is zero for the first layer 111 and the Pth layer 111 from the beginning of the quantum circuit 110. The second function is, for example, a function that represents a curve 152 by combining the monotonically increasing function and the second sine function. Specifically, each point on the curve 152 corresponding to the order of the layers 111 represents the value of the second variational parameter 132 that applies to the second subcircuit 122 of that layer 111.

[0050] (1-3) The information processing device 100 uses the quantum circuit 110 to calculate the solution to the combinatorial optimization problem. The information processing device 100 calculates the solution to the combinatorial optimization problem by updating the values ​​of the first transformation parameter 161 and the second transformation parameter 162, for example, to optimize the expected value of the cost function.

[0051] Specifically, the information processing device 100 sets initial values ​​for the first transformation parameter 161 and the second transformation parameter 162. Subsequently, the information processing device 100 calculates the solution to the combinatorial optimization problem by repeatedly performing the following series of processes based on QAOA using an external quantum computer until the termination condition is met. The series of processes consists of multiple processes for appropriately updating the values ​​of the first transformation parameter 161 and the second transformation parameter 162.

[0052] The series of processes includes, for example, process 1, process 2, and process 3 below, in order. Process 1 is, for example, calculating the value of the first variational parameter and the value of the second variational parameter based on the value of the first transformation parameter and the value of the second transformation parameter. Process 2 is, for example, calculating the expected value of the cost function based on the calculated value of the first variational parameter and the calculated value of the second variational parameter. Process 3 is, for example, updating the value of the first transformation parameter and the value of the second transformation parameter based on the calculated expected value if a predetermined termination condition is not met.

[0053] This allows the information processing device 100 to improve the accuracy of solving combinatorial optimization problems. For example, when increasing the number of layers P of the quantum circuit 110 to improve the quantum circuit 110's ability to represent quantum states, the information processing device 100 can reduce the number of parameters whose values ​​need to be updated. Therefore, even when increasing the number of layers P, the information processing device 100 is less likely to encounter problems where the processing burden and processing time required to solve combinatorial optimization problems increase, thereby improving the accuracy of solving combinatorial optimization problems. Furthermore, the information processing device 100 can reduce the processing burden and processing time required to solve combinatorial optimization problems.

[0054] Here, we have described the case in which the information processing device 100 utilizes an externally existing quantum computer, but it is not limited to this. For example, the information processing device 100 may be an actual quantum computer. Also, for example, the information processing device 100 may utilize an internally existing quantum simulator.

[0055] Here, we have described the case where the functions of the information processing device 100 are realized by a single computer, but this is not the only case. For example, the functions of the information processing device 100 may be realized through the collaboration of multiple computers. For example, the functions of the information processing device 100 may be realized on the cloud.

[0056] (An example of information processing system 200) Next, using Figure 2, we will describe an example of an information processing system 200 to which the information processing device 100 shown in Figure 1 is applied.

[0057] Figure 2 is an explanatory diagram showing an example of an information processing system 200. In Figure 2, the information processing system 200 includes an information processing device 100, a quantum computing device 201, and a client device 202.

[0058] In the information processing system 200, the information processing device 100 and the quantum computing device 201 are connected via a wired or wireless network 210. The network 210 is, for example, a LAN (Local Area Network), a WAN (Wide Area Network), or the Internet. Also in the information processing system 200, the information processing device 100 and the client device 202 are connected via a wired or wireless network 210.

[0059] The information processing device 100 is a computer that controls the quantum computing device 201. The information processing device 100 receives processing requests that request the solution of combinatorial optimization problems. The information processing device 100 may receive processing requests, for example, by receiving them from the client device 202. The information processing device 100 may also receive processing requests, for example, by accepting input of processing requests based on user operation input.

[0060] A processing request includes, for example, definition information that defines a combinatorial optimization problem. This definition information may include definitions of, for example, a cost function, an energy operator, a mixer operator, a cost unitary operator, or a mixer unitary operator. The definition information may also include definitions of, for example, the first variational parameter of the mixer unitary operator and the second variational parameter of the cost unitary operator.

[0061] The definition information may include, for example, the definition of a first transformation parameter that defines a first function representing the first variational parameter, and the definition of a second transformation parameter that defines a second function representing the second variational parameter. The definition of the first transformation parameter includes, for example, a first transformation formula that makes the first variational parameter and the first transformation parameter interchangeable with each other. The definition of the second transformation parameter includes, for example, a second transformation formula that makes the second variational parameter and the second transformation parameter interchangeable with each other.

[0062] The information processing device 100 sets up a quantum circuit having P layers in response to the acquired processing request. The information processing device 100 acquires a cost function in response to the acquired processing request. The information processing device 100 acquires a first transformation formula and a second transformation formula based on definition information in response to the acquired processing request. The information processing device 100 sets initial values ​​for the first transformation parameter and the second transformation parameter.

[0063] The information processing device 100 calculates the solution to a combinatorial optimization problem by repeatedly performing a series of processes to update the first transformation parameter and the second transformation parameter using a set quantum circuit until a termination condition is met. The termination condition is, for example, that the series of processes is performed a predetermined number of times. The termination condition may also be, for example, that the expected value of the energy represented by the cost function falls below a predetermined threshold.

[0064] The series of processes includes, for example, process 1, process 2, and process 3 below, in order. Process 1 is, for example, calculating the value of the first variational parameter and the value of the second variational parameter based on the value of the first transformation parameter and the value of the second transformation parameter, by referring to the first transformation formula and the second transformation formula. Process 2 is, for example, calculating the expected value of the energy represented by the cost function based on the calculated value of the first variational parameter and the calculated value of the second variational parameter. Process 3 is, for example, updating the value of the first transformation parameter and the value of the second transformation parameter based on the calculated expected value if a predetermined termination condition is not met.

[0065] The information processing device 100 performs the above process 1 by, for example, referring to the first transformation formula and the second transformation formula, and calculating the value of the first variational parameter and the value of the second variational parameter based on the value of the first transformation parameter and the value of the second transformation parameter.

[0066] The information processing device 100 performs the above process 2 by, for example, controlling the quantum computer 201 to execute a set quantum circuit, and calculating the expected value of the energy represented by the cost function based on the result of executing the quantum circuit. Specifically, the information processing device 100 sends an execution request to the quantum computer 201 requesting that the quantum circuit be executed. The execution request includes, for example, the set quantum circuit. The execution request includes, for example, the calculated value of the first variational parameter and the calculated value of the second variational parameter. Specifically, the information processing device 100 receives a trial quantum state from the quantum computer 201 as a result of executing the quantum circuit. The information processing device 100 calculates the expected value of the energy based on the received trial quantum state.

[0067] For example, if the predetermined termination conditions are not met, the information processing device 100 performs process 3 by updating the values ​​of the first transformation parameter and the second transformation parameter based on the calculated expected value. Specifically, the information processing device 100 determines whether or not the predetermined termination conditions are met. Specifically, if the predetermined termination conditions are not met, the information processing device 100 updates the values ​​of the first transformation parameter and the second transformation parameter based on the calculated expected value in a direction that minimizes the expected value of the energy represented by the cost function.

[0068] The information processing device 100 outputs the calculated solution to the combinatorial optimization problem. The information processing device 100 transmits the solution to the combinatorial optimization problem to the client device 202, for example. The information processing device 100 may also output the solution to the combinatorial optimization problem for the user to refer to. The information processing device 100 is, for example, a server or a PC.

[0069] The quantum computing device 201 is a computer that performs requested computational processing. The quantum computing device 201 is capable of performing quantum computations. The quantum computing device 201 may also be capable of performing classical computations. The quantum computing device 201 executes quantum circuits according to the control of the information processing device 100. For example, when the quantum computing device 201 receives an execution request from the information processing device 100 that requests the execution of a quantum circuit, it executes the quantum circuit. Specifically, the quantum computing device 201 evolves the initial quantum state and identifies a trial quantum state by executing the quantum circuit.

[0070] The quantum computing device 201 returns the result of executing the quantum circuit to the information processing device 100. For example, the quantum computing device 201 returns the trial quantum state to the information processing device 100 as a result of executing the quantum circuit. The quantum computing device 201 is, for example, a physical quantum computer. The quantum computing device 201 may also be, for example, a classical computer that starts a quantum simulator. A classical computer is, for example, a server or a PC.

[0071] The client device 202 is a computer used by a user who wishes to solve a combinatorial optimization problem. Based on the user's input, the client device 202 generates a processing request to solve the combinatorial optimization problem and sends it to the information processing device 100. The client device 202 receives the solution to the combinatorial optimization problem from the information processing device 100. The client device 202 outputs the solution to the combinatorial optimization problem so that the user can refer to it. The client device 202 may be, for example, a PC, a tablet terminal, or a smartphone.

[0072] This section describes a case where the information processing device 100 and the quantum computing device 201 are different devices, but is not limited to this case. For example, the information processing device 100 may have the functionality of a quantum computing device 201 and may operate as a quantum computing device 201. Similarly, this section describes a case where the information processing device 100 and the client device 202 are different devices, but is not limited to this case. For example, the information processing device 100 may have the functionality of a client device 202 and may operate as a client device 202.

[0073] (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 using Figure 3.

[0074] Figure 3 is a block diagram showing an example of the hardware configuration of the information processing device 100. In Figure 3, the information processing device 100 includes a CPU (Central Processing Unit) 301, a memory 302, and a network interface 303. The information processing device 100 also includes a recording medium interface 304, a recording medium 305, a display 306, and an input device 307. Each component is connected by a bus 300.

[0075] Here, the CPU 301 is responsible for the overall control of the information processing device 100. The memory 302 includes, for example, ROM (Read Only Memory), RAM (Random Access Memory), and flash ROM. Specifically, for example, flash ROM and ROM store various programs, and RAM is used as the work area for the CPU 301. Programs stored in memory 302 are loaded into the CPU 301, causing the CPU 301 to execute the coded processes.

[0076] The network interface 303 is connected to network 210 via a communication line, and then connects to other computers via network 210. The network interface 303 manages the internal interface with network 210 and controls the input and output of data from other computers. The network interface 303 is, for example, a modem or a LAN adapter.

[0077] The recording medium interface (I / F) 304 controls the reading and writing of data to the recording medium 305 according to the control of the CPU 301. The recording medium interface (I / F) 304 is, for example, a disk drive, an SSD (Solid State Drive), or a USB (Universal Serial Bus) port. The recording medium 305 is a non-volatile memory that stores the data written under the control of the recording medium interface (I / F) 304. The recording medium 305 is, for example, a disk, semiconductor memory, or USB memory. The recording medium 305 may be detachable from the information processing device 100.

[0078] Display 306 displays data such as cursors, icons, toolboxes, documents, images, or functional information. Display 306 is, for example, a CRT (Cathode Ray Tube), a liquid crystal display, or an organic EL (Electroluminescence) display. Input device 307 has keys for inputting characters, numbers, or various instructions, and performs data input. Input device 307 is, for example, a keyboard or a mouse. Input device 307 may also be, for example, a touch panel input pad or a numeric keypad.

[0079] The information processing device 100 may have, in addition to the components described above, a camera, for example. Furthermore, the information processing device 100 may have, in addition to the components described above, a printer, scanner, microphone, or speaker, for example. Also, the information processing device 100 may have multiple recording medium interfaces 304 and recording mediums 305, for example. Furthermore, the information processing device 100 does not necessarily have, for example, a display 306 or an input device 307. Also, the information processing device 100 does not necessarily have, for example, recording medium interfaces 304 and recording mediums 305.

[0080] (Example hardware configuration of quantum computing device 201) In the case where the quantum computing device 201 is a classical computer that starts a quantum simulator, the hardware configuration example of the quantum computing device 201 is specifically the same as the hardware configuration example of the information processing device 100 shown in Figure 3, so the explanation is omitted.

[0081] On the other hand, it is possible that the quantum computing device 201 is a physical quantum computer. Here, using Figure 4, we will explain an example of the hardware configuration of the quantum computing device 201 when it is a physical quantum computer.

[0082] Figure 4 is a block diagram showing an example of the hardware configuration of the quantum computing device 201. In Figure 4, the quantum computing device 201 includes a CPU 401, memory 402, network interface 403, recording medium interface 404, and recording medium 405. The quantum computing device 201 further includes a chassis interface 406 and a quantum computing chassis 407. Each component is connected by a bus 400.

[0083] Here, the CPU 401 is responsible for the overall control of the quantum computing device 201. Memory 402 includes, for example, ROM, RAM, and flash ROM. Specifically, for example, flash ROM and ROM store various programs, and RAM is used as the work area for CPU 401. Programs stored in memory 402 are loaded into CPU 401, causing CPU 401 to execute the coded processes.

[0084] The network interface 403 is connected to network 210 via a communication line, and then connects to other computers via network 210. The network interface 403 manages the internal interface with network 210 and controls the input and output of data from other computers. The network interface 403 is, for example, a modem or a LAN adapter.

[0085] The recording medium interface (I / F) 404 controls the reading and writing of data to the recording medium (SSD) 405 according to the control of the CPU 401. The recording medium interface (I / F) 404 is, for example, a disk drive, SSD, or USB port. The recording medium (SSD) 405 is a non-volatile memory that stores the data written under the control of the recording medium interface (I / F) 404. The recording medium (SSD) 405 is, for example, a disk, semiconductor memory, or USB memory. The recording medium (SSD) 405 may be detachable from the quantum computing device (SSD) 201.

[0086] The chassis interface 406 controls access to the quantum computing chassis 407 according to the control of the CPU 401. The chassis interface 406 uses a microwave pulse generator to convert the output signal from the CPU 401 into an input signal for the quantum computing chassis 407 and transmits it to the quantum computing chassis 407. The chassis interface 406 uses a microwave pulse demodulator to convert the output signal from the quantum computing chassis 407 into an input signal for the CPU 401 and transmits it to the CPU 401.

[0087] The quantum computing chassis 407 is a computing device equipped with one or more qubit chips, cooled to an extremely low temperature of 10 mK. Each qubit chip represents, for example, a logical qubit. The quantum computing chassis 407 uses one or more qubit chips to perform predetermined operations in response to input signals and outputs an output signal corresponding to the result of the predetermined operations.

[0088] In addition to the components described above, the quantum computing device 201 may also have, for example, a keyboard, mouse, display, printer, scanner, microphone, speaker, etc. Furthermore, the quantum computing device 201 may have multiple recording medium interfaces 404 and 405. Alternatively, the quantum computing device 201 may not have recording medium interfaces 404 and 405. Also, the qubit chip in the quantum computing enclosure 407 may be controlled by methods other than microwaves. For example, the qubit chip in the quantum computing enclosure 407 may implement optical qubits.

[0089] (Example hardware configuration for client device 202) The hardware configuration example for client device 202 is specifically the same as the hardware configuration example for information processing device 100 shown in Figure 3, so a detailed explanation will be omitted.

[0090] (Example of the functional configuration of the information processing device 100) Next, an example of the functional configuration of the information processing device 100 will be described using Figure 5.

[0091] Figure 5 is a block diagram showing an example of the functional configuration of the information processing device 100. The information processing device 100 includes a storage unit 500, an acquisition unit 501, a setting unit 502, an update unit 503, and an output unit 504.

[0092] The storage unit 500 is implemented by a storage area such as the memory 302 or recording medium 305 shown in Figure 3. The following description will focus on the case where the storage unit 500 is included in the information processing device 100, but is not limited to this case. For example, the storage unit 500 may be included in a device different from the information processing device 100, and the contents of the storage unit 500 may be accessible from the information processing device 100.

[0093] The acquisition unit 501 to the output unit 504 function as an example of a control unit. Specifically, the acquisition unit 501 to the output unit 504 realize their functions, for example, by having the CPU 301 execute a program stored in a storage area such as the memory 302 or recording medium 305 shown in Figure 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 recording medium 305 shown in Figure 3.

[0094] The memory unit 500 stores various information that is referenced or updated during the processing of each functional unit. The memory unit 500 stores, for example, the structure of a predetermined quantum circuit used when solving a combinatorial optimization problem. The predetermined quantum circuit implements the function of evolving an initial quantum state, which is the input, to obtain a trial quantum state, which is the output. The predetermined quantum circuit has P layers, where P is the number of layers, and P ≥ 1. The predetermined quantum circuit defines the action on N qubits that represent the quantum state, where N ≥ 1.

[0095] A given quantum circuit includes, for each layer, a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator. The action of each layer is defined by a mixer unitary operator and a cost unitary operator. The mixer unitary operator represents, for example, an action on the search space. The cost unitary operator represents, for example, an action on the problem setting. The action of each layer is defined by a mixer unitary operator and a cost unitary operator.

[0096] The mixer unitary operator includes, for example, a first variational parameter. Therefore, the first subcircuit representing the action of the mixer unitary operator has the first variational parameter. The cost unitary operator includes, for example, a second variational parameter. Therefore, the second subcircuit representing the action of the cost unitary operator has the second variational parameter. The structure of a predetermined quantum circuit is acquired, for example, by the acquisition unit 501. The structure of a predetermined quantum circuit may be set in advance by, for example, the user.

[0097] The memory unit 500 stores, for example, a cost function corresponding to a combinatorial optimization problem. The cost function is the object to be minimized or maximized. The cost function corresponds to the objective function. The cost function is retrieved, for example, by the retrieval unit 501. The cost function may be pre-set by the user, for example.

[0098] The memory unit 500 stores, for example, the values ​​of the first variational parameters relating to the first subcircuits that represent the action of the mixer unitary operators in each layer. The initial values ​​of the first variational parameters are calculated and set, for example, by the update unit 503. The initial values ​​of the first variational parameters may also be set, for example, by the setting unit 502. The initial values ​​of the first variational parameters may also be set in advance by the user, for example. The values ​​of the first variational parameters are calculated and updated, for example, by the update unit 503.

[0099] The memory unit 500 stores, for example, the values ​​of the second variational parameters relating to the second subcircuits that represent the action of the cost unitary operator in each layer. The initial values ​​of the second variational parameters are calculated and updated, for example, by the update unit 503. The initial values ​​of the second variational parameters may also be set, for example, by the setting unit 502. The initial values ​​of the second variational parameters may also be set in advance by the user, for example. The values ​​of the second variational parameters are calculated and updated, for example, by the update unit 503.

[0100] The memory unit 500 stores, for example, a first function which is a combination of a monotonically decreasing function and a first sine function, representing a combination of values ​​for the first variational parameter applied to the first subcircuit representing the action of the mixer unitary operator in each layer. The first function is set, for example, by the setting unit 502.

[0101] The storage unit 500 stores, for example, the value of the first conversion parameter relating to the first function. The initial value of the first conversion parameter is set, for example, by the setting unit 502. The initial value of the first conversion parameter may also be set in advance by, for example, the user. The value of the first conversion parameter is calculated and updated, for example, by the update unit 503.

[0102] The memory unit 500 stores, for example, a second function which is a combination of a monotonically increasing function and a second sine function, representing a combination of values ​​for the second variational parameter applied to the second subcircuit representing the action of the cost unitary operator in each layer. The second function is set, for example, by the setting unit 502.

[0103] The memory unit 500 stores, for example, the value of the second transformation parameter relating to the second function. The initial value of the second transformation parameter is set, for example, by the setting unit 502. The initial value of the second transformation parameter may also be set in advance by, for example, the user. The value of the second transformation parameter is calculated and updated, for example, by the update unit 503.

[0104] The memory unit 500 stores, for example, predetermined termination conditions. The predetermined termination conditions control the number of times a defined series of processes are repeatedly performed in order to solve a combinatorial optimization problem. The predetermined termination condition is, for example, performing the series of processes a predetermined number of times. The predetermined termination condition may also be, for example, that the expected value of the energy falls within a predetermined range. The predetermined range is, for example, a range below a predetermined threshold.

[0105] The predetermined termination condition may be, for example, that the change in the expected value of energy falls below a predetermined threshold. The change is, for example, the difference between the expected value of energy calculated when the series of processes was performed this time and the expected value of energy calculated when the series of processes was performed last time. The predetermined termination condition is acquired, for example, by the acquisition unit 501. The predetermined termination condition may be set in advance by the user, for example.

[0106] The series of processes includes, for example, setting an initial quantum state. The series of processes includes, for example, using a quantum circuit to evolve the set initial quantum state and identify a trial quantum state. The series of processes includes, for example, calculating the expected value of the energy represented by the cost function corresponding to the identified trial quantum state.

[0107] The series of processes includes, for example, updating the values ​​of the first transformation parameter and the second transformation parameter in a direction that minimizes the expected value of the energy represented by the cost function, based on the expected value of the energy represented by the calculated cost function. The series of processes also includes, for example, updating the values ​​of the first variational parameter and the second variational parameter based on the updated values ​​of the first transformation parameter and the updated values ​​of the second transformation parameter. The series of processes is performed, for example, by the update unit 503.

[0108] The acquisition unit 501 acquires various types of information used in the processing of each functional unit. The acquisition unit 501 stores the acquired information in the storage unit 500 or outputs it to each functional unit. The acquisition unit 501 may also output the information stored in the storage unit 500 to each functional unit. The acquisition unit 501 acquires various types of information, for example, based on user input. The acquisition unit 501 may also receive various types of information from a device other than the information processing device 100, for example.

[0109] The acquisition unit 501 acquires, for example, a processing request that requests solving a combinatorial optimization problem. The processing request may include, for example, the structure of a predetermined quantum circuit. The processing request may include, for example, a cost function. The processing request may include, for example, an energy operator, a cost unitary operator, a mixer operator, and a mixer unitary operator.

[0110] A processing request may include, for example, initial values ​​for the first variational parameter and the second variational parameter. A processing request may include, for example, the first function and the second function. A processing request may include, for example, initial values ​​for the first transformation parameter and the second transformation parameter. A processing request may include, for example, a predetermined termination condition.

[0111] Specifically, the acquisition unit 501 acquires processing requests by receiving input of processing requests based on user operation input. Specifically, the acquisition unit 501 may acquire processing requests by receiving processing requests from other computers. Other computers are, for example, client devices 202.

[0112] The acquisition unit 501 acquires, for example, the structure of a predetermined quantum circuit. Specifically, the acquisition unit 501 acquires the structure of a predetermined quantum circuit by receiving input of the structure of a predetermined quantum circuit based on user operation input. Specifically, the acquisition unit 501 may acquire the structure of a predetermined quantum circuit by receiving the structure of a predetermined quantum circuit from another computer. The other computer is, for example, a client device 202. Specifically, the acquisition unit 501 may acquire the structure of a predetermined quantum circuit by extracting the structure of a predetermined quantum circuit from a processing request.

[0113] The acquisition unit 501 acquires, for example, a cost function. Specifically, the acquisition unit 501 acquires a cost function by accepting input of a cost function based on user operation input. Specifically, the acquisition unit 501 may acquire a cost function by receiving a cost function from another computer. The other computer may be, for example, a client device 202. Specifically, the acquisition unit 501 may acquire a cost function by extracting a cost function from a processing request.

[0114] The acquisition unit 501 acquires, for example, predetermined termination conditions. Specifically, the acquisition unit 501 acquires predetermined termination conditions by receiving input of predetermined termination conditions based on user operation input. Specifically, the acquisition unit 501 may acquire predetermined termination conditions by receiving predetermined termination conditions from another computer. The other computer is, for example, a client device 202. Specifically, the acquisition unit 501 may acquire predetermined termination conditions by extracting predetermined termination conditions from processing requests.

[0115] The acquisition unit 501 may receive a start trigger to initiate processing in any of the functional units. A start trigger may be, for example, a predetermined operation input by a user. A start trigger may also be, for example, the receipt of predetermined information from another computer. A start trigger may also be, for example, the output of predetermined information by any of the functional units. The acquisition unit 501 accepts, for example, the acquisition of a processing request as a start trigger to initiate processing in the setting unit 502 and the update unit 503.

[0116] The setting unit 502 sets a first function for the quantum circuit, which is a combination of a monotonically decreasing function and a first sine function, representing the first variational parameter applied to the first subcircuit. The monotonically decreasing function is, for example, a function that represents a monotonically decreasing straight line. The monotonically decreasing function may also be, for example, a function that represents a monotonically decreasing curve. Specifically, the monotonically decreasing function is a function that represents a monotonically decreasing straight line or curve with its endpoints being the value of the first variational parameter applied to the first subcircuit of the first layer of the quantum circuit and the value of the first variational parameter applied to the first subcircuit of the last layer of the quantum circuit. Specifically, the first sine function is a function that represents a sine wave that is zero for the first and last layers of the quantum circuit. As a result, the setting unit 502 can convert the first transformation parameter into the first variational parameter using the first function.

[0117] The setting unit 502 sets, for example, the initial value of the first conversion parameter. Specifically, the setting unit 502 sets the initial value of the first conversion parameter by receiving input of the initial value of the first conversion parameter based on user operation input. Specifically, the setting unit 502 may set the initial value of the first conversion parameter by receiving the initial value of the first conversion parameter from another computer. The other computer may be, for example, the client device 202. Specifically, the setting unit 502 may set the initial value of the first conversion parameter by extracting the initial value of the first conversion parameter from the processing request. In this way, the setting unit 502 can set the initial value of the first conversion parameter in preparation for the update unit 503 to start processing.

[0118] The setting unit 502 may, for example, set an initial value for the first variation parameter. For example, if the update unit 503 does not calculate an initial value for the first variation parameter based on the initial value of the first transformation parameter, the setting unit 502 may set an initial value for the first variation parameter. Specifically, the setting unit 502 may set an initial value for the first variation parameter by accepting an input of an initial value for the first variation parameter based on user input.

[0119] The setting unit 502 may, specifically, set the initial value of the first variational parameter by receiving the initial value of the first variational parameter from another computer. The other computer may be, for example, the client device 202. The setting unit 502 may, specifically, set the initial value of the first variational parameter by extracting the initial value of the first variational parameter from the processing request. This allows the setting unit 502 to set the initial value of the first variational parameter in preparation for the update unit 503 to start processing.

[0120] The setting unit 502 sets a second function for the quantum circuit, which is a combination of a monotonically increasing function and a second sine function, representing the second variational parameter applied to the second subcircuit. The monotonically increasing function is, for example, a function that represents a monotonically increasing straight line. The monotonically increasing function may also be, for example, a function that represents a monotonically increasing curve. Specifically, the monotonically increasing function is a function that represents a monotonically increasing straight line or curve with its endpoints being the value of the second variational parameter applied to the second subcircuit of the first layer of the quantum circuit and the value of the second variational parameter applied to the second subcircuit of the last layer of the quantum circuit. Specifically, the second sine function is a function that represents a sine wave that is zero for the first and last layers of the quantum circuit. As a result, the setting unit 502 can convert the second transformation parameter to the second variational parameter using the second function.

[0121] The setting unit 502 sets, for example, the initial value of the second conversion parameter. Specifically, the setting unit 502 sets the initial value of the second conversion parameter by receiving input of the initial value of the second conversion parameter based on user operation input. Specifically, the setting unit 502 may set the initial value of the second conversion parameter by receiving the initial value of the second conversion parameter from another computer. The other computer may be, for example, the client device 202. Specifically, the setting unit 502 may set the initial value of the second conversion parameter by extracting the initial value of the second conversion parameter from the processing request. In this way, the setting unit 502 can set the initial value of the second conversion parameter in preparation for the update unit 503 to start processing.

[0122] The setting unit 502 may, for example, set an initial value for the second variation parameter. For example, if the update unit 503 does not calculate an initial value for the second variation parameter based on the initial value of the second transformation parameter, the setting unit 502 may set an initial value for the second variation parameter. Specifically, the setting unit 502 may set an initial value for the second variation parameter by accepting an input of an initial value for the second variation parameter based on user input.

[0123] Specifically, the setting unit 502 may set the initial value of the second variational parameter by receiving the initial value of the second variational parameter from another computer. The other computer may be, for example, the client device 202. Specifically, the setting unit 502 may set the initial value of the second variational parameter by extracting the initial value of the second variational parameter from the processing request. This allows the setting unit 502 to set the initial value of the second variational parameter in preparation for the update unit 503 to start processing.

[0124] After the setting unit 502 sets the first function and the second function, the update unit 503 uses a quantum circuit to optimize the expected value of the energy represented by the cost function by updating the values ​​of the first and second transformation parameters. In this case, the update unit 503 may execute the quantum circuit on the information processing device 100. The update unit 503 may also cooperate with an actual quantum computer capable of executing the quantum circuit. An example of an actual quantum computer is the quantum computing device 201. Based on the updated values ​​of the first and second transformation parameters, the update unit 503 calculates the solution to the combinatorial optimization problem.

[0125] The update unit 503 calculates the solution to a combinatorial optimization problem by, for example, repeatedly performing a series of processes until a predetermined termination condition is met. Specifically, the series of processes includes a process for setting the initial quantum state. Specifically, the series of processes includes a process for calculating the value of the first variational parameter and the value of the second variational parameter based on the value of the first transformation parameter and the value of the second transformation parameter, with reference to the first function and the second function.

[0126] The series of processes specifically includes a process to evolve the set initial quantum state and identify a trial quantum state using a quantum circuit that has been set with the calculated values ​​of the first variational parameter and the calculated values ​​of the second variational parameter. The series of processes specifically includes a process to calculate the expected value of the energy represented by the cost function corresponding to the identified trial quantum state. The series of processes specifically includes a process to update the values ​​of the first transformation parameter and the second transformation parameter in a direction that minimizes the expected value of the energy represented by the cost function, based on the calculated expected value of the energy represented by the cost function.

[0127] The update unit 503, for example, sets the initial quantum state. Specifically, when the update unit 503 performs the first series of operations, it sets the initial quantum state randomly. Specifically, when the update unit 503 performs the second and subsequent series of operations, it sets the trial quantum state identified during the previous series of operations as the initial quantum state. In this way, the update unit 503 can appropriately set the initial quantum state to be developed in preparation for executing the quantum circuit.

[0128] The update unit 503, for example, refers to the first function set in the setting unit 502 and calculates the value of the first variational parameter based on the value of the first transformation parameter. This allows the update unit 503 to set the initial value of the first variational parameter when performing the first series of processes. When performing the second and subsequent series of processes, the update unit 503 can appropriately update the value of the first variational parameter.

[0129] The update unit 503, for example, refers to the second function set in the setting unit 502 and calculates the value of the second variational parameter based on the value of the second transformation parameter. This allows the update unit 503 to set the initial value of the second variational parameter when performing the first series of processes. When performing subsequent series of processes, the update unit 503 can appropriately update the value of the second variational parameter.

[0130] The update unit 503, for example, uses a quantum circuit set with the calculated values ​​of the first variational parameter and the calculated values ​​of the second variational parameter to evolve the set initial quantum state, identify the trial quantum state, and calculate the expected value of the energy represented by the cost function. The expected value of the energy corresponds to, for example, the trial quantum state. Specifically, the update unit 503 sends an execution request to the actual quantum computer requesting that the quantum circuit be executed. The execution request may include, for example, a quantum circuit set with the values ​​of the first variational parameter and the second variational parameter, and the initial quantum state.

[0131] The update unit 503 receives the results of executing the quantum circuit from the actual quantum computer. The results of executing the quantum circuit include, for example, the results of measuring the identified trial quantum state. Based on the results of executing the quantum circuit, the update unit 503 calculates the expected value of the energy represented by the cost function. In this way, the update unit 503 can work in conjunction with the actual quantum computer to identify the trial quantum state and calculate the expected value of the energy represented by the cost function.

[0132] The update unit 503 updates the values ​​of the first transformation parameter and the second transformation parameter in a direction that minimizes the expected value of the energy represented by the cost function, for example, based on the expected value of the energy represented by the calculated cost function. The update is achieved by methods such as the Grid method, BFGS method, or Powell method. In this way, the update unit 503 can optimize the values ​​of the first transformation parameter and the second transformation parameter, and indirectly optimize the values ​​of the first variational parameter and the second variational parameter.

[0133] The update unit 503, for example, if a predetermined termination condition is met, uses a quantum circuit with the values ​​of the first variational parameter and the second variational parameter set to identify and measure the trial quantum state multiple times. Specifically, the update unit 503 identifies and measures the trial quantum state multiple times by sending an execution request to the actual quantum computer requesting that the quantum circuit be executed multiple times.

[0134] The update unit 503 calculates the solution to the combinatorial optimization problem by, for example, statistically processing the results of measuring the trial quantum states. This allows the update unit 503 to reduce the number of parameters whose values ​​are directly updated, thereby reducing the processing burden and processing time required when calculating the solution to the combinatorial optimization problem. The update unit 503 can also easily increase the depth of the quantum circuit, making it easier to calculate the solution to the combinatorial optimization problem with higher accuracy.

[0135] The output unit 504 outputs the processing result of at least one of the functional units. The output format can be, for example, display on a screen, print to a printer, transmit to an external device via the network interface 303, or store in a storage area such as the memory 302 or recording medium 305. This allows the output unit 504 to notify the user of the processing result of at least one of the functional units, thereby improving the usability of the information processing device 100.

[0136] The output unit 504 outputs, for example, the solution to the combinatorial optimization problem calculated by the update unit 503. Specifically, the output unit 504 outputs the solution to the combinatorial optimization problem calculated by the update unit 503 in a way that is accessible to the user. Specifically, the output unit 504 transmits the solution to the combinatorial optimization problem calculated by the update unit 503 to another computer. The other computer is, for example, the client device 202. This allows the output unit 504 to make the solution to the combinatorial optimization problem available externally.

[0137] (An example of the operation of the information processing device 100) Next, an example of the operation of the information processing device 100 will be described using Figures 6 and 7.

[0138] Figures 6 and 7 are explanatory diagrams showing an example of the operation of the information processing device 100. In Figure 6, the information processing device 100 stores a variable sequence z corresponding to a combinatorial optimization problem. The variable sequence z is a bit sequence variable z N ...z2z1. i = +1 or z i = -1. The information processing device 100 stores the cost function C(z) expressed by the Ising model. Specifically, the cost function C(z) is defined by equation (1) above.

[0139] The information processing device 100 calculates the first variational parameter β = (β1, β2, ..., β) applied to the mixer unitary operator. P ) and the second variational parameter γ = (γ1, γ2, ..., γ P ) and memorize. β1, β2, ..., β P These are real numbers. γ1, γ2, ..., γ P It is a real number.

[0140] The information processing device 100 has a first variational parameter β l The system stores a first transformation formula that expresses the first transformation parameter as a number less than P. The first transformation formula uses the first transformation parameter as the first variational parameter β. l This makes it possible to convert between the two. The first conversion equation is, for example, a combination of a first linear function representing a monotonically decreasing line and a first sine function. The first linear function is a function that represents a line whose value monotonically decreases as the variable l, which indicates the order of the layers, increases. The first linear function is, for example, the first variational parameter β1 in the first layer of the quantum circuit and the first variational parameter β in the last layer of the quantum circuit. P This is a function that represents a monotonically decreasing straight line with and as its endpoints. Specifically, the first sine function is a function that represents a sine wave that is zero for the first and last layers of a quantum circuit. Specifically, the first transformation equation is defined by equation (11) below.

[0141]

number

[0142] The information processing device 100 stores the first transformation parameters relating to the first transformation equation. Specifically, the first transformation parameters are β1 relating to the first linear function and β P This includes the first transformation parameters, specifically v1, v2, ..., v applied to the first sine function. q' It includes. q' is preferably less than P-2.

[0143] The information processing device 100 uses the second variational parameter γ l A second transformation formula is stored that expresses this using a second transformation parameter less than P. The second transformation formula uses the second transformation parameter as the second variation parameter γ. l This makes it convertible. The second transformation formula is, for example, a combination of a second linear function representing a monotonically increasing straight line and a second sine function. The second linear function is a function that represents a straight line whose value increases monotonically as the variable l, which indicates the order of the layers, increases. The second linear function is, for example, the second variational parameter γ1 in the first layer of the quantum circuit and the second variational parameter γ in the last layer of the quantum circuit. P This is a function that represents a monotonically increasing straight line with and as its endpoints. Specifically, the second sine function is a function that represents a sine wave that is zero for the first and last layers of the quantum circuit. Specifically, the second transformation equation is defined by equation (12) below.

[0144]

number

[0145] The information processing device 100 stores the second transformation parameters relating to the second transformation equation. Specifically, the second transformation parameters are γ1 relating to the second linear function and γ P This includes the second transformation parameter, specifically u1, u2, ..., u applied to the second sine function. q It includes. q is preferably less than P-2.

[0146] Now, let's move on to the explanation of Figure 7 and specifically explain the second transformation formula. The first transformation formula is the same as the second transformation formula, so we will omit its explanation. In the example in Figure 7, P=7. The second transformation formula is, for example, a combination of the first linear function corresponding to line segment 701 and the first sine function. As shown in Figure 7, the first linear function is γ1 and γ P This represents a monotonically increasing straight line with and as its endpoints. As shown in Figure 7, the second transformation equation corresponds to the curve 702 defined by equation (12) above, which is represented by a combination of the first linear function and the first sine function.

[0147] As shown in Figure 7, the information processing device 100 can easily represent linear parameter changes corresponding to linear operation in quantum annealing by setting a second transformation equation. Furthermore, the information processing device 100 can expand the correction term for linear changes in the second transformation equation using a first sine function.

[0148] Furthermore, by setting P-2>q>0 and P-2>q'>0, the information processing device 100 can retain relatively important low-frequency components while removing relatively unimportant high-frequency components. As a result, the information processing device 100 can reduce the number of parameters whose values ​​are directly updated, thereby reducing the processing burden and processing time required when updating parameter values.

[0149] Returning to the explanation of Figure 6, the information processing device 100 sets the initial value β of the first conversion parameter. i 1,β i P ,v i 1,v i 2,···,v i q' The information processing device 100 sets the initial value β of the first conversion parameter, for example. i 1,β i P ,v i 1,v i 2,···,v iq' Set it randomly.

[0150] The information processing device 100 sets the initial value γ of the second transformation parameter. i 1,γ i P ,u i 1,u i 2,···,u i q The information processing device 100 sets the initial value γ of the second transformation parameter, for example. i 1,γ i P ,u i 1,u i 2,···,u i q Set it randomly.

[0151] The information processing device 100 stores an optimization algorithm. The optimization algorithm defines a processing procedure for optimizing the first transformation parameter and the second transformation parameter. The optimization algorithm is based on, for example, the BFGS method.

[0152] (6-1) The information processing device 100, according to the optimization algorithm, refers to the first transformation equation and, based on the current value of the first transformation parameter, calculates the first variational parameter β = (β1, β2, ..., β P The information processing device 100 calculates the value of the second variational parameter γ = (γ1, γ2, ..., γ) according to the optimization algorithm by referring to the second transformation formula and based on the current value of the second transformation parameter. P Calculate the value of ).

[0153] (6-2) The information processing device 100 causes the quantum computing device 201 to execute a multilayer quantum circuit 600 according to an optimization algorithm. The quantum circuit 600 has P layers 610. Each layer 610 of the quantum circuit 600 has a first subcircuit 611 representing the action of a mixer unitary operator and a second subcircuit 612 representing the action of a cost unitary operator. The quantum circuit 600 includes, for example, a measurement unit 620 for each qubit.

[0154] The information processing device 100 generates an execution request, for example, that requests the quantum circuit 600 to be executed one or more times, and transmits it to the quantum computing device 201. The execution request includes, for example, the structure of the quantum circuit 600. The execution request includes, for example, the calculated first variational parameter β=(β1,β2,···,β P The value of ) and the calculated second variational parameter γ=(γ1,γ2,···,γ P The execution request includes the value of ). For example, the number of times to execute quantum circuit 600.

[0155] (6-3) The quantum computer 201 has a control function for qubits. The quantum computer 201 receives an execution request from the information processing device 100. The quantum computer 201 sets the initial quantum state for the qubits in response to the execution request. The quantum computer 201 measures the variable sequence z one or more times by executing the quantum circuit 600 one or more times in response to the execution request.

[0156] The quantum computer 201, for example, executes the quantum circuit 600 and applies a mixer unitary operator and a cost unitary operator to the initial quantum state to evolve the initial quantum state and identify a trial quantum state. The quantum computer 201 obtains a variable sequence z by measuring the identified trial quantum state with the measurement unit 620. The quantum computer 201 transmits the variable sequence z, which has been obtained one or more times, to the information processing device 100.

[0157] (6-4) The information processing device 100 refers to the cost function C(z) and calculates the expected value of the energy represented by the cost function C(z) based on one or more variable sequences z. Based on the calculated expected value of the energy, the information processing device 100 updates the values ​​of the first transformation parameter and the second transformation parameter in a direction that minimizes the expected value of the energy represented by the cost function C(z). In this way, the information processing device 100 can optimize the values ​​of the first transformation parameter and the second transformation parameter.

[0158] The information processing device 100 and the quantum computing device 201 repeatedly perform a series of processes including the process described in (6-1), the process described in (6-2), the process described in (6-3), and the process described in (6-4) until a predetermined termination condition is met. In this way, the information processing device 100 can repeatedly optimize the value of the first transformation parameter and the value of the second transformation parameter.

[0159] (6-5) If the predetermined termination conditions are met, the information processing device 100 calculates the solution to the combinatorial optimization problem based on the updated value of the first transformation parameter and the updated value of the second transformation parameter. The information processing device 100, for example, uses a quantum circuit 600 in which the values ​​of the first variational parameter and the second variational parameter have been set to identify and measure the trial quantum state multiple times.

[0160] Specifically, the information processing device 100 generates an execution request that requests the quantum circuit 600 to be executed one or more times, and transmits it to the quantum computing device 201, thereby identifying and measuring the trial quantum state multiple times. The information processing device 100 receives the results of identifying and measuring the trial quantum state multiple times from the quantum computing device 201. The information processing device 100 calculates the solution to the combinatorial optimization problem by statistically processing the results of measuring the trial quantum state multiple times.

[0161] As a result, the information processing device 100 can reduce the number of parameters whose values ​​are directly updated, thereby reducing the processing burden and processing time required when calculating the solution to a combinatorial optimization problem. The information processing device 100 can also easily increase the depth of the quantum circuit 600. Therefore, the information processing device 100 can easily calculate the solution to a combinatorial optimization problem with high accuracy.

[0162] Next, using Figures 8 to 11, we will compare the method for solving combinatorial optimization problems using the information processing device 100 with conventional methods and explain an example of the effects of the information processing device 100. In the following explanation, the method for solving combinatorial optimization problems using the information processing device 100 may be referred to as "this method." Conventional methods are QAOA or Fourier method.

[0163] Figures 8 to 11 are explanatory diagrams showing an example of the effect. Here, the Approximation Ratio (AR) is evaluated when calculating the solution to the energy minimization problem using this method and the conventional method. The Approximation Ratio is the approximation ratio. AR is (E max -E) / (E max -E min ) AR is between 0 and 1. The closer the AR value is to 1, the better the quality of the solution to the minimization problem.

[0164] E max E represents the highest energy. min This represents the minimum energy. The minimum energy corresponds, for example, to the energy at the optimal solution. max and E min This can be obtained, for example, by exhaustive search of the Ising model. E represents the expected value of the energy. The expected value of the energy is E min The closer it gets to , the closer the value of AR approaches 1. Therefore, the expected value of energy is E min The closer it gets to 1, the closer the value of 1-AR approaches 0.

[0165] Furthermore, in both this method and conventional methods, the probability of obtaining the optimal solution is calculated by summing the squares of the absolute values ​​of the probability amplitudes for the optimal solution previously obtained through a brute-force search of the Ising model, based on the final quantum state vector. In the following explanation, the probability of obtaining the optimal solution may be referred to as the "correct solution probability."

[0166] In the examples in Figures 8 to 11, specifically, the coefficient c in an Ising model that does not include a first-order term. i,jAssume that 100 energy minimization problems are prepared, using uniformly distributed real random numbers. The mathematical formula for the Ising model that does not include the first-order term is defined, for example, by equation (13) below. The parameter optimization algorithm used in this method and conventional methods is the L-BFGS-B method. Furthermore, in the L-BFGS-B method, there is no differential equation input. Furthermore, in the L-BFGS-B method, the search range is not specified.

[0167]

number

[0168] For the solutions to 100 energy minimization problems prepared using this method and conventional methods, we calculate the average values ​​of 1-AR, the probability of finding the correct solution, and the number of calculations required for the expected value of the energy. In the following explanation, the number of calculations required for the expected value of the energy may be referred to as the "number of energy evaluations." Now, let's move on to the explanation of Figure 8.

[0169] Graphs 800-802 in Figure 8 correspond to the calculation of solutions to 100 energy minimization problems for different numbers of qubits using the conventional QAOA method. Here, the initial value of the variational parameter [γ l ,β l Let ] = [0, 0.01π] (l = 1 to P). Graph 800 shows the change in the average value of 1-AR with respect to the change in P. Graph 801 shows the change in the average value of the correct answer probability with respect to the change in P. Graph 802 shows the change in the average value of the number of energy evaluations with respect to the change in P. Now we move on to the explanation of Figure 9.

[0170] Graphs 900-902 in Figure 9 correspond to the calculation of solutions to 100 energy minimization problems using the conventional Fourier method. The Fourier method uses eight transformation parameters. Here, the initial values ​​of the transformation parameters are [u1,u2,u3,u4;v1,v2,v3,v4]=[0.1π,0,0,0;0.1π,0,0,0]. Graph 900 shows the change in the average value of 1-AR with respect to the change in P. Graph 901 shows the change in the average value of the correct probability with respect to the change in P. Graph 902 shows the change in the average number of energy evaluations with respect to the change in P. Now, we move on to the explanation of Figure 10.

[0171] Graphs 1000-1002 in Figure 10 correspond to the calculation of solutions to 100 energy minimization problems using this method. This method uses eight transformation parameters. Here, the initial values ​​of the transformation parameters are [γ1,γ P ,u1,u2;β1,β P Let v1,v2] = [0.01π,0.1π,0,0;0.1π,0.01π,0,0]. Graph 1000 shows the change in the average value of 1-AR with respect to the change in P. Graph 1001 shows the change in the average value of the correct answer probability with respect to the change in P. Graph 1002 shows the change in the average value of the number of energy evaluations with respect to the change in P.

[0172] As shown in Figures 8 to 10, in this method, the average value of 1-AR and the average value of the correct answer probability are the same as those of the conventional QAOA method. In other words, this method can calculate the solution to the energy minimization problem with the same accuracy as the conventional QAOA method. Furthermore, in this method, the average number of energy evaluations can be reduced as P increases. In other words, this method can reduce the processing load and processing time required to calculate the solution to the energy minimization problem. Now, let's move on to the explanation of Figure 11.

[0173] Graph 1100 in Figure 11 shows the ratio of the average value of 1-AR in the conventional Fourier method to the average value of 1-AR in the present method. As shown in Figure 11, the average value of 1-AR in the present method is better than that of the conventional Fourier method. In other words, the present method can calculate the solution to the energy minimization problem with greater accuracy than the conventional Fourier method.

[0174] Thus, the information processing device 100 can represent the first variational parameter β and the second variational parameter γ using a transformation parameter that specifies a straight line connecting the values ​​at l=1 and l=P, and a transformation parameter that specifies a sine wave that is zero for l=1 and l=P. The sine wave represents the correction term. P is the number of layers of the quantum circuit 600.

[0175] Therefore, the information processing device 100 can reduce the number of parameters that are directly updated. The parameters that the information processing device 100 directly updates are the transformation parameters. The information processing device 100 indirectly updates the first variational parameter β and the second variational parameter γ based on the transformation parameters.

[0176] Therefore, the information processing device 100 can reduce the processing burden and processing time required when solving combinatorial optimization problems. For example, the information processing device 100 can reduce the number of energy evaluations. Furthermore, the information processing device 100 can improve the average value of 1-AR and the average value of the correct answer probability.

[0177] (Overall processing procedure) Next, an example of the overall processing procedure executed by the information processing device 100 will be described using Figure 12. The overall processing is realized, for example, by the CPU 301 shown in Figure 3, storage areas such as memory 302 and recording medium 305, and network I / F 303.

[0178] Figure 12 is a flowchart showing an example of the overall processing procedure. In Figure 12, the information processing device 100 obtains a cost function C(z) corresponding to the combinatorial optimization problem (step S1201).

[0179] Next, the information processing device 100 sets the conversion formula for variational parameter γ and the conversion formula for variational parameter β (step S1202). Then, the information processing device 100 sets the initial values ​​of the conversion parameters (step S1203).

[0180] Next, the information processing device 100 refers to the set transformation formula and calculates the values ​​of the variational parameter γ and the variational parameter β based on the values ​​of the transformation parameters (step S1204). Next, the information processing device 100 uses a quantum circuit to calculate the expected value of the energy by performing the calculation process described later in Figure 13 (step S1205).

[0181] The information processing device 100 then determines whether or not the termination condition is met (step S1206). If the termination condition is not met (step S1206: No), the information processing device 100 proceeds to the process in step S1207. On the other hand, if the termination condition is met (step S1206: Yes), the information processing device 100 proceeds to the process in step S1208.

[0182] In step S1207, the information processing device 100 updates the conversion parameters according to the search algorithm (step S1207). Then, the information processing device 100 returns to the process in step S1204.

[0183] In step S1208, the information processing device 100 determines whether or not the termination condition is met (step S1208). If the termination condition is not met (step S1208: No), the information processing device 100 proceeds to the process in step S1209. On the other hand, if the termination condition is met (step S1208: Yes), the information processing device 100 proceeds to the process in step S1210.

[0184] In step S1209, the information processing apparatus 100 generates and measures a trial quantum state of a quantum circuit based on the values of the variational parameter γ and the variational parameter β (step S1209). Then, the information processing apparatus 100 returns to the process of step S1208.

[0185] In step S1210, the information processing apparatus 100 selects and outputs a solution to the combinatorial optimization problem based on the measurement result (step S1210). Then, the information processing apparatus 100 ends the overall process. Thereby, the information processing apparatus 100 can accurately solve the combinatorial optimization problem.

[0186] (Calculation processing procedure) Next, an example of a calculation processing procedure that the information processing apparatus 100 executes using a physical quantum computer will be described with reference to FIG. 13. The physical quantum computer is, for example, a quantum computing device 201 or the like. The information processing apparatus 100 may be a physical quantum computer. The calculation processing is realized by, for example, the CPU 301 shown in FIG. 3, a storage area such as the memory 302 and the recording medium 305, and the network I / F 303.

[0187] FIG. 13 is a flowchart showing an example of the calculation processing procedure. In FIG. 13, the information processing apparatus 100 generates a trial quantum state by executing a quantum circuit using a physical quantum computer (step S1301).

[0188] Next, the information processing apparatus 100 measures σ Z i using the physical quantum computer based on the trial quantum state (step S1302). Then, the information processing apparatus 100 calculates the energy based on the measurement result of σ Z i (step S1303). The information processing apparatus 100, for example, the z Z i obtained as a result of measuring σ iBy substituting ±1 into the cost function, sample values ​​of energy are obtained, and the energy is calculated based on the average of the multiple sample values ​​obtained.

[0189] Subsequently, the information processing device 100 determines whether the termination condition for the accuracy of the expected value of the energy is met (step S1304). If the termination condition is not met (step S1304: No), the information processing device 100 returns to the process in step S1301. On the other hand, if the termination condition is met (step S1304: Yes), the information processing device 100 calculates the expected value of the energy (step S1305) and terminates the calculation process.

[0190] Here, the information processing device 100 may execute some steps of the flowcharts in Figures 12 and 13 in a different order. Alternatively, the information processing device 100 may omit some steps of the flowcharts in Figures 12 and 13. The overall process shown in Figure 12 could be executed, for example, when the information processing device 100 receives a processing request to solve a combinatorial optimization problem.

[0191] (Examples of applications of the information processing device 100) Next, examples of applications 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 that searches for the movement path of a moving object. The information processing device 100 can be applied, for example, to solving a combinatorial optimization problem that creates employee work schedules. The information processing device 100 can be applied, for example, to solving a combinatorial optimization problem that creates a product manufacturing plan.

[0192] As explained above, the information processing device 100 can set up a quantum circuit that includes, layer by layer, a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator, which are used when solving combinatorial optimization problems. The information processing device 100 can set up a first function for the quantum circuit, which is a combination of a monotonically decreasing function and a first sine function, representing the first variational parameter applied to the first subcircuit. The information processing device 100 can set up a second function for the quantum circuit, which is a combination of a monotonically increasing function and a second sine function, representing the second variational parameter applied to the second subcircuit. The information processing device 100 can update the values ​​of the first transformation parameter applied to the first function and the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem using the quantum circuit. As a result, the information processing device 100 can accurately calculate the solution to the combinatorial optimization problem. The information processing device 100 can reduce the processing burden and processing time required when calculating the solution to the combinatorial optimization problem.

[0193] According to the information processing device 100, the first function can be set using a monotonically decreasing function that represents a monotonically decreasing straight line. According to the information processing device 100, the second function can be set using a monotonically increasing function that represents a monotonically increasing straight line. Thus, the information processing device 100 can appropriately set the first function and the second function from the perspective of quantum annealing.

[0194] According to the information processing device 100, a monotonically decreasing function can be used, which represents a monotonically decreasing straight line with the value of the first variational parameter applied to the first subcircuit of the first layer of the quantum circuit and the value of the first variational parameter applied to the first subcircuit of the last layer of the quantum circuit as its endpoints. According to the information processing device 100, a first sine function that is zero for both the first and last layers of the quantum circuit can be used. According to the information processing device 100, a monotonically increasing function can be used, which represents a monotonically increasing straight line with the value of the second variational parameter applied to the second subcircuit of the first layer of the quantum circuit and the value of the second variational parameter applied to the second subcircuit of the last layer of the quantum circuit as its endpoints. According to the information processing device 100, a second sine function that is zero for both the first and last layers of the quantum circuit can be used. As a result, the information processing device 100 can appropriately set the first function and the second function from the viewpoint of quantum annealing.

[0195] According to the information processing device 100, a series of processes can be repeatedly performed until a predetermined termination condition is met. According to the information processing device 100, in a series of processes, the values ​​of the first variational parameter and the second variational parameter can be calculated based on the values ​​of the first transformation parameter and the second transformation parameter. According to the information processing device 100, in a series of processes, the expected value of the cost function can be calculated based on the calculated values ​​of the first variational parameter and the second variational parameter. According to the information processing device 100, if a predetermined termination condition is not met in a series of processes, the values ​​of the first transformation parameter and the second transformation parameter can be updated based on the calculated expected value. As a result, the information processing device 100 can optimize the first transformation parameter and the second transformation parameter, and can accurately calculate the solution to the combinatorial optimization problem.

[0196] According to the information processing device 100, the first function can be set using a monotonically decreasing function that represents a monotonically decreasing curve. According to the information processing device 100, the second function can be set using a monotonically increasing function that represents a monotonically increasing curve. Thus, the information processing device 100 can appropriately set the first function and the second function from the perspective of quantum annealing.

[0197] In the embodiments disclosed herein, the explanation was based on the assumption that the values ​​of β and γ are positive. However, considering that the energy minimization problem can also be treated as an energy maximization problem by reversing the sign of the cost function, the values ​​of β and γ may be negative. In that case, for example, the line 141 shown in Figure 1 is a monotonically decreasing line, and the line 151 is a monotonically increasing line. In other words, the line 141 can be said to be a line whose absolute value is monotonically decreasing, and the line 151 can be said to be a line whose absolute value is monotonically increasing. Similarly, a monotonically decreasing curve can be said to be a curve whose absolute value is monotonically increasing, and a monotonically increasing curve can be said to be a curve whose absolute value is monotonically increasing.

[0198] The information processing method described in this embodiment can be implemented by executing a pre-prepared program on a computer such as a PC or 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 can be a hard disk, flexible disk, CD (Compact Disc)-ROM, MO (Magneto Optical Disc), DVD (Digital Versatile Disc), etc. Furthermore, the information processing program described in this embodiment may be distributed via a network such as the Internet.

[0199] With regard to the embodiments described above, the following additional information is disclosed.

[0200] (Note 1) For a quantum circuit used when solving combinatorial optimization problems, which includes a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator in each layer, a first function is set to represent the first variational parameter applied to the first subcircuit, which is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function, and a second function is set to represent the second variational parameter applied to the second subcircuit, which is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function, Using the quantum circuit after setting the first function and the second function, the solution to the combinatorial optimization problem is calculated by updating the value of the first transformation parameter applied to the first function and the value of the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem. An information processing program characterized by having a computer perform the processing.

[0201] (Note 2) The monotonically decreasing function is a function that represents a straight line whose absolute value decreases monotonically. The information processing program according to Appendix 1, characterized in that the monotonically increasing function is a function that represents a straight line whose absolute value increases monotonically.

[0202] (Note 3) The monotonically decreasing function represents a straight line whose absolute value is monotonically decreasing, with the value of the first variational parameter relating to the first subcircuit of the first layer of the quantum circuit as its endpoints and the value of the first variational parameter relating to the first subcircuit of the last layer of the quantum circuit as its endpoints. The first sine function is zero for the first and last layers of the quantum circuit. The monotonically increasing function represents a straight line whose absolute value is monotonically increasing, with its endpoints being the value of the second variational parameter relating to the second subcircuit of the first layer of the quantum circuit and the value of the second variational parameter relating to the second subcircuit of the last layer of the quantum circuit. The information processing program according to Appendix 2, characterized in that the second sine function is zero for the first and last layers of the quantum circuit.

[0203] (Note 4) The calculation process described above is: An information processing program according to any one of the appendices 1 to 3, characterized in that it repeatedly performs a series of processes until the predetermined termination conditions are met, which include calculating the values ​​of the first variational parameter and the second variational parameter based on the values ​​of the first transformation parameter and the second transformation parameter, calculating the expected value of the cost function based on the calculated values ​​of the first variational parameter and the second variational parameter, and updating the values ​​of the first transformation parameter and the second transformation parameter based on the calculated expected value if the predetermined termination conditions are not met.

[0204] (Note 5) The monotonically decreasing function is a function that represents a curve whose absolute value decreases monotonically, The information processing program according to Appendix 1, characterized in that the monotonically increasing function is a function that represents a curve whose absolute value increases monotonically.

[0205] (Note 6) For a quantum circuit used when solving combinatorial optimization problems, which includes a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator in each layer, a first function is set to represent the first variational parameter of the first subcircuit, which is a combination of a monotonically decreasing function with an absolute value that decreases monotonically and a first sine function, and a second function is set to represent the second variational parameter of the second subcircuit, which is a combination of a monotonically increasing function with an absolute value that increases monotonically and a second sine function, Using the quantum circuit after setting the first function and the second function, the solution to the combinatorial optimization problem is calculated by updating the value of the first transformation parameter applied to the first function and the value of the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem. An information processing method characterized in that the processing is performed by a computer.

[0206] (Note 7) For a quantum circuit used when solving combinatorial optimization problems, which includes a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator in each layer, a first function is set representing the first variational parameter of the first subcircuit, which is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function, and a second function is set representing the second variational parameter of the second subcircuit, which is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function, Using the quantum circuit after setting the first function and the second function, the solution to the combinatorial optimization problem is calculated by updating the value of the first transformation parameter applied to the first function and the value of the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem. An information processing device characterized by having a control unit. [Explanation of Symbols]

[0207] 100 Information Processing Devices 110,600 quantum circuits 111,610 layers 112,620 Measuring section 121,611 1st partial circuit 122,612 Second part circuit 131 First Variational Parameter 132 Second Variational Parameter 140, 800~802, 900~902, 1000~1002, 1100 graph 141 straight line 142,152,702 curve 161 First Transformation Parameter 162 Second Transformation Parameter 200 Information Processing Systems 201 Quantum computing device 202 Client Devices 210 Network 300,400 buses 301,401 CPU 302,402 memory 303,403 Network I / F 304,404 Recording medium I / F 305,405 recording media 306 displays 307 Input device 406 Chassis I / F 407 Quantum Computing Enclosure 500 storage section 501 Acquisition Department 502 Settings Section 503 Update Department 504 Output section 701 line segment

Claims

1. For a quantum circuit used to solve combinatorial optimization problems, which includes a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator in each layer, a first function is set to represent the first variational parameter of the first subcircuit, which is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function, and a second function is set to represent the second variational parameter of the second subcircuit, which is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function, Using the quantum circuit after setting the first function and the second function, the solution to the combinatorial optimization problem is calculated by updating the value of the first transformation parameter applied to the first function and the value of the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem. An information processing program characterized by having a computer perform the processing.

2. The aforementioned monotonically decreasing function is a function that represents a straight line whose absolute value decreases monotonically, The information processing program according to claim 1, characterized in that the monotonically increasing function is a function that represents a straight line whose absolute value increases monotonically.

3. The monotonically decreasing function represents a straight line whose absolute value is monotonically decreasing, with the value of the first variational parameter relating to the first subcircuit of the first layer of the quantum circuit as its endpoints and the value of the first variational parameter relating to the first subcircuit of the last layer of the quantum circuit as its endpoints. The first sine function becomes zero for the first and last layers of the quantum circuit. The monotonically increasing function represents a straight line whose absolute value is monotonically increasing, with the value of the second variational parameter relating to the second subcircuit of the first layer of the quantum circuit and the value of the second variational parameter relating to the second subcircuit of the last layer of the quantum circuit as its endpoints. The information processing program according to claim 2, characterized in that the second sine function is zero for the first and last layers of the quantum circuit.

4. The calculation process described above is: An information processing program according to any one of claims 1 to 3, characterized in that it repeatedly performs a series of processes until the predetermined termination conditions are met, which include calculating the value of the first variational parameter and the value of the second variational parameter based on the value of the first transformation parameter and the value of the second transformation parameter, calculating the expected value of the cost function based on the calculated value of the first variational parameter and the calculated value of the second variational parameter, and updating the value of the first transformation parameter and the value of the second transformation parameter based on the calculated expected value if the predetermined termination conditions are not met.

5. For a quantum circuit used to solve combinatorial optimization problems, which includes a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator in each layer, a first function is set to represent the first variational parameter of the first subcircuit, which is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function, and a second function is set to represent the second variational parameter of the second subcircuit, which is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function, Using the quantum circuit after setting the first function and the second function, the solution to the combinatorial optimization problem is calculated by updating the value of the first transformation parameter applied to the first function and the value of the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem. An information processing method characterized in that the processing is performed by a computer.

6. For a quantum circuit used to solve combinatorial optimization problems, which includes a first subcircuit representing the action of a mixer unitary operator and a second subcircuit representing the action of a cost unitary operator in each layer, a first function is set to represent the first variational parameter of the first subcircuit, which is a combination of a monotonically decreasing function with a monotonically decreasing absolute value and a first sine function, and a second function is set to represent the second variational parameter of the second subcircuit, which is a combination of a monotonically increasing function with a monotonically increasing absolute value and a second sine function, Using the quantum circuit after setting the first function and the second function, the solution to the combinatorial optimization problem is calculated by updating the value of the first transformation parameter applied to the first function and the value of the second transformation parameter applied to the second function in order to optimize the expected value of the cost function corresponding to the combinatorial optimization problem. An information processing device characterized by having a control unit.

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