Combinatorial Optimization Calculation Method and Combinatorial Optimization Calculation System

Abstract

To obtain a feasible solution even for a problem for which the feasible solution cannot be obtained by FALQON.SOLUTION: A method for calculating combinatorial optimization uses a quantum computer that performs quantum calculation using a quantum circuit having a parameter representing an amount of phase rotation, and a classical computer that calculates a feedback amount based on the output of the quantum computer and newly adds the quantum circuit with the calculated feedback amount as the parameter to the quantum computer. In the classical computer, the feedback amount is multiplied by a positive gain whose magnitude approaches zero with the addition of the quantum circuit.SELECTED DRAWING: Figure 11

Description

Technical Field

[0001] The present disclosure relates to a combinatorial optimization calculation method and a combinatorial optimization calculation system.

Background Art

[0002] As an algorithm for solving combinatorial optimization problems using a quantum computer based on the quantum gate method, QAOA (Quantum Approximate Optimization Algorithm) is known (see, for example, Non-Patent Document 1). QAOA approximately calculates the state in which the energy of the cost function is minimized by searching for the optimal parameters of the quantum circuit using a classical computer.

[0003] In QAOA, the parameter search process by a classical computer becomes a bottleneck, and FALQON (Feedback-based ALgorithm for Quantum OptimizatioN) is known as an algorithm that eliminates this process (see, for example, Non-Patent Document 2).

[0004] FALQON sequentially determines the parameters of the quantum circuit according to the Lyapunov stability in classical control technology. More specifically, for a quantum circuit connected in multiple stages, the output result of the previous-stage quantum circuit is fed back, and based on this, the parameters in the next-stage quantum circuit are sequentially determined.

Prior Art Documents

Non-Patent Documents

[0005]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0006] When solving a combinatorial optimization problem using FALQON, the feedback amount for determining the parameters of the quantum circuit may not converge, and it may not be possible to obtain an executable solution.

[0007] The present disclosure aims to enable obtaining an executable solution even for problems for which an executable solution cannot be obtained with FALQON.

Means for Solving the Problems

[0008] The present disclosure provides a method for calculating combinatorial optimization using a quantum computer that performs quantum computing with a quantum circuit having a parameter representing a phase rotation amount, and a classical computer that calculates a feedback amount based on the output of the quantum computer and newly adds the quantum circuit with the calculated feedback amount as the parameter to the quantum computer, wherein in the classical computer, the feedback amount is multiplied by a gain having a positive value that approaches zero as the quantum circuit is added.

[0009] The present disclosure provides a combinatorial optimization calculation system including: a quantum computer that performs quantum calculation using a quantum circuit having a parameter representing a phase rotation amount; and a classical computer that calculates a feedback amount based on an output of the quantum computer and newly adds the quantum circuit having the calculated feedback amount as a parameter to the quantum computer, wherein the classical computer multiplies the feedback amount by a gain having a positive value that approaches zero as the quantum circuit is added.

Advantages of the Invention

[0010] According to the present disclosure, it is possible to obtain an executable solution even for a problem for which an executable solution cannot be obtained by FALQON.

Brief Description of the Drawings

[0011]

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Embodiments for Carrying Out the Invention

[0012] Hereinafter, embodiments of the present disclosure will be described in detail with appropriate reference to the drawings. However, a more detailed description than necessary may be omitted. For example, detailed descriptions of well-known matters and redundant descriptions of substantially the same configurations may be omitted. This is to avoid making the following description unnecessarily redundant and to facilitate the understanding of those skilled in the art. Note that the accompanying drawings and the following description are provided to enable those skilled in the art to fully understand the present disclosure, and are not intended to limit the subject matter described in the claims.

[0013] (This embodiment) <Overview of FALQON> FALQON is an algorithm that obtains the feedback amount based on the Lyapunov function used in classical control theory and sequentially determines the parameters of the quantum circuit that minimizes the energy. Therefore, the search process for the parameters of the quantum circuit by the classical computer in QAOA becomes unnecessary.

[0014] The following describes the theoretical background of FALQON. The time evolution of FALQON is represented by the following (Equation 1).

[0015]

Number

[0016] Here, H P represents the target Hamiltonian, that is, the energy function of the problem to be solved. H d is the quantum fluctuation term. β(t) represents the feedback amount. The Lyapunov function in FALQON is as follows (Equation 2).

[0017]

Number

[0018] Here, ψ(t) is the quantum state at time t. According to the Lyapunov stability theorem of classical control, when the time derivative of V(t) satisfies the following (Equation 3), the quantum state ψ(t) converges as t → ∞.

[0019]

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[0020] The feedback amount β(t) that satisfies the above is given by the following (Equation 4) and (Equation 5).

[0021]

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[0022]

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[0023] FIG. 1 shows a circuit block diagram of FALQON. Assuming the initial quantum state is |ψ0〉, the quantum state output from the first-stage (hereinafter, the stage may also be referred to as a layer) quantum circuit using the time evolution gates for the time step Δt shown in the following (Equation 6) and (Equation 7) is as follows in the following (Equation 8).

[0024]

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[0025]

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[0026]

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[0027] Assuming the measured value of (Equation 4) in this state is A1, the feedback amount β2 for the next stage is obtained as β2 = -A1. The FALQON algorithm repeats this process k times, where k is the number of layers of the quantum circuit, and sequentially determines β1, β2, …, β k to give the ground state of the target Hamiltonian. Note that k indicates the layer index.

[0028] FIG. 2 is a block diagram showing a configuration example of a combinatorial optimization calculation system 10 that controls the parameters of a quantum circuit by the above-described FALQON algorithm.

[0029] The combinatorial optimization calculation system 10 includes a quantum computer 20 using a quantum gate method and a classical computer. The quantum computer 20 and the classical computer can transmit and receive information through, for example, a predetermined communication network. Examples of the communication network include the Internet, a cellular network, a LAN (Local Area Network), a dedicated line, and the like.

[0030] The quantum computer 20 performs quantum computing using a quantum circuit having a parameter representing a phase rotation amount, and includes a quantum circuit device 21 and a measurement device 22.

[0031] As illustrated in FIG. 1, the quantum circuit device 21 includes at least one quantum circuit.

[0032] The measurement device 22 measures (observes) the output (i.e., quantum state) from the quantum circuit device 21.

[0033] The classical computer 30 realizes the function of the feedback amount calculation processing unit 31. As shown in FIG. 13, the classical computer 30 includes at least a processor 1001 and a memory 1002, and the processor 1001 may realize this function by reading and executing a computer program stored in the memory 1002.

[0034] The feedback amount calculation processing unit 31 calculates a feedback amount β based on the quantum state measured by the measurement device 22. Then, the feedback amount calculation processing unit 31 newly adds to the quantum circuit device 21 a quantum circuit having the calculated feedback amount β as a parameter representing the above phase rotation amount. As a result, the number of stages of the quantum circuit in FIG. 1 increases by one.

[0035] FIG. 3 is a flowchart showing an operation example of the combinatorial optimization calculation system 10 that controls the parameters of a quantum circuit by the above-described FALQON algorithm.

[0036] The feedback amount calculation processing unit 31 sets k = 1 for the layer (S101). Here, k represents a layer index. That is, k = t / Δt. In other words, t = kΔt. The layer k corresponds to the k-th stage quantum circuit in FIG. 1.

[0037] The feedback amount calculation processing unit 31 sets the feedback amount β1 of the quantum circuit of layer 1 to 0 (S102).

[0038] The feedback amount calculation processing unit 31 determines whether layer k is greater than a predetermined maximum layer (S103).

[0039] When layer k is less than or equal to the maximum layer (S103: NO), the feedback amount calculation processing unit 31 advances the process to S104.

[0040] The measurement device 22 measures the output state from the quantum circuit device 21 (S104).

[0041] Based on the measurement result of step S104, the feedback amount calculation processing unit 31 calculates the feedback amount β (S105).

[0042] The feedback amount calculation processing unit 31 adds the quantum circuit with the feedback amount β set in step S105 (that is, the (k + 1)-th stage quantum circuit) to the quantum circuit device 21 (S106).

[0043] The feedback amount calculation processing unit 31 adds 1 to layer k (S107) and returns the process to step S103.

[0044] In the determination of step S103, when layer k is greater than a predetermined maximum layer (S103: YES), the measurement device 22 measures the output state from the quantum circuit device 21 and outputs the measurement result (S108). The classical computer 30 may display the output measurement result as a graph or the like. Then, this process ends.

[0045] Through the above process, quantum circuits of layers 1 to k with the feedback amounts β1 to β k respectively set as shown in FIG. 1 are configured in the quantum circuit device 21 of the quantum computer 20. And the measurement device 22 can measure the output state from the quantum circuit device 21 configured in this way.

[0046] <Problems of FALQON> The applicant conducted evaluations under different types and scales of problems in order to verify what problems would arise when applying FALQON to actual problems.

[0047] First, regarding the MaxCut problem of finding a partitioning method that maximizes the number of edges between groups when dividing the vertices of a graph into two groups, the expected solution was obtained.

[0048] Next, an evaluation was conducted on the traveling salesman problem of finding the shortest route when a single salesman visits multiple cities.

[0049] Figure 4 shows the simulation conditions when evaluating the traveling salesman problem.

[0050] In the case of the traveling salesman problem, the optimal solution was obtained for a problem scale of 3 cities, but when the problem scale was increased to 4 cities, it became difficult to obtain an executable solution.

[0051] Figure 5 is a graph showing the results of the energy expectation value at each stage of the quantum circuit when solving the traveling salesman problem for 4 cities. Figure 6 is a graph showing the results of the feedback amount β at each stage of the quantum circuit when solving the traveling salesman problem for 4 cities. Figure 7 is a diagram showing an executable solution to the traveling salesman problem for 4 cities.

[0052] In Figures 5 and 6, the solid line indicates the average value of 10 evaluations, and the range sandwiched by the dotted lines indicates the standard deviation of the data. From these results, it can be seen that both the energy expectation value and the feedback amount have not converged. Also, the probability that the solution with the highest observation frequency becomes an executable solution as shown in Figure 7 is approximately 7%, and in the remaining 93%, unexecutable solutions including the result of not visiting any city were observed with the highest frequency.

[0053] From the above, the applicant confirmed that FALQON may not operate as expected depending on the type and scale of the problem to be solved. That is, for FALQON, which is an algorithm for solving combinatorial optimization problems on a quantum computer using the quantum gate method, there are cases where it may not operate as expected depending on the type and scale of the problem to be solved.

[0054] <Method for Solving the Problems of FALQON> The time evolution of FALQON shown in the above (Equation 1) is the same as that of the quantum annealing method. Therefore, by applying the convergence condition for the weight of the quantum fluctuation term in the quantum annealing method to FALQON, it is expected that the result of FALQON will also converge to the ground state of the target Hamiltonian.

[0055] A sufficient condition for the state changing with time in the quantum annealing method to converge to the ground state of the target Hamiltonian is that there exists a positive number t0, and when t > t0, the weight Γ(t) of the quantum fluctuation term is given by the following (Equation 9). Note that the weight Γ of the quantum fluctuation term may also be read as the gain function Γ.

[0056]

Equation

[0057] Here, N is the number of qubits, a and c are constants, and δ is an infinitesimal amount satisfying δ << 1.

[0058] Figure 8 is a graph showing an example of the weight Γ(t) of the quantum fluctuation term according to the present embodiment. In Figure 8, the lower graph is an enlarged view of the dotted-line frame part of the upper graph. As shown in Figure 8, the weight Γ(t) of the quantum fluctuation term has a positive value that approaches zero as the quantum circuit is added, that is, as the number of layers increases.

[0059] Since the amount of feedback β(t) in FALQON may change with time as in (Equation 9), consider controlling the gain of β(t) so that the envelope of β(t) is proportional to (Equation 9). More specifically, replace the feedback amount β(t) calculated in (Equation 5) with the following (Equation 10).

[0060] [Number]

[0061] When calculating β(t) using (Equation 10), the results of the energy expectation value and the feedback amount when solving the traveling salesman problem for 4 cities are shown in FIGS. 9 and 10.

[0062] FIG. 9 is a graph showing the results of the energy expectation value at each stage of the quantum circuit when solving the traveling salesman problem for 4 cities using the weight of the quantum fluctuation term according to this embodiment. FIG. 10 is a graph showing the results of the feedback amount β at each stage of the quantum circuit when solving the traveling salesman problem for 4 cities using the weight of the quantum fluctuation term according to this embodiment. In FIGS. 9 and 10, as in FIGS. 5 and 6, the solid line indicates the average value of 10 evaluations, and the range sandwiched between the dotted lines indicates the standard deviation of the data.

[0063] Looking at the results shown in FIGS. 9 and 10, it can be confirmed that both converge by adding control of the weight of the quantum fluctuation term. Also, since the average of the energy expectation value is monotonically decreasing and the width of the standard deviation of the energy is shrinking by increasing the number of stages of the quantum circuit, the observed state is gradually approaching a single low-energy state. Therefore, the observation frequency of the low-energy state that minimizes the cost function increases. In fact, the probability that the solution with the maximum observation frequency becomes an executable solution has been improved from 7% to 100% by adding control of the weight of the quantum fluctuation term to the feedback amount.

[0064] The above disclosure presents a feedback gain control method that applies the convergence condition for the weight of the quantum fluctuation term in the quantum annealing method to FALQON. And the applicant confirmed its effectiveness through simulation.

[0065] Note that the calculation method of the weight (gain function) Γ of the quantum fluctuation term is not limited to the above-mentioned (Equation 9). As the weight (gain function) Γ of the quantum fluctuation term, other functions with positive values that approach zero in magnitude along with the addition of quantum circuits may be used. For example, the weight (gain function) Γ of the quantum fluctuation term may be calculated by the following (Equation 11). In (Equation 11), L represents the total number of layers.

[0066]

Equation

[0067] FIG. 11 is a block diagram showing a configuration example of the combinatorial optimization calculation system 10 according to the present embodiment to which the above feedback gain control method is applied.

[0068] The combinatorial optimization calculation system 10 according to the present embodiment includes a quantum computer 20 using a quantum gate method and a classical computer 30, similar to the combinatorial optimization calculation system 10 shown in FIG. 2.

[0069] Since the configuration of the quantum computer 20 is the same as that shown in FIG. 2, the description thereof is omitted here.

[0070] The classical computer 30 realizes the functions of a feedback amount calculation processing unit 31, a gain control unit 32, and a synthesis unit 33. As shown in FIG. 13, the classical computer 30 includes at least a processor 1001 and a memory 1002, and these functions may be realized by the processor 1001 reading and executing a computer program stored in the memory 1002.

[0071] Similar to FIG. 2, the feedback amount calculation processing unit 31 calculates a feedback amount based on the quantum state measured (observed) by the measuring device 22. That is, the feedback amount calculation processing unit 31 calculates "-A(t)" in the above (Equation 10).

[0072] The gain control unit 32 calculates the weight Γ(t) of the quantum fluctuation term in the above (Equation 9) and (Equation 10).

[0073] As shown in (Equation 10), the synthesizing unit 33 multiplies "-A(t)" output from the feedback amount calculation processing unit 31 by Γ(t) output from the gain control unit 32 to obtain a feedback amount β(t). Similar to FIG. 2, the synthesizing unit 33 adds a quantum circuit to the quantum circuit device 21 using the feedback amount β(t).

[0074] FIG. 12 is a flowchart showing an operation example of the combinatorial optimization calculation system 10 that controls the parameters of a quantum circuit by the classical computer 30 according to the present embodiment.

[0075] The feedback amount calculation processing unit 31 sets the layer k to 1 (S201). Here, k represents a layer index. Here, k = t / Δt. In other words, t = kΔt. The layer k corresponds to the k-th stage quantum circuit in FIG. 1.

[0076] The synthesizing unit 33 sets the feedback amount β1 of the quantum circuit of layer 1 to the initial value Γ(0) (S202). That is, the feedback amount calculation processing unit 31 outputs 1, the gain control unit 32 outputs Γ(0), and the synthesizing unit 33 sets β(0) = Γ(0) to the first-stage quantum circuit.

[0077] The feedback amount calculation processing unit 31 determines whether the layer k is greater than a predetermined maximum layer (S203).

[0078] When the layer k is less than or equal to the maximum layer (S203: NO), the feedback amount calculation processing unit 31 advances the process to S204.

[0079] The measuring device 22 measures the output state from the quantum circuit device 21 (S204).

[0080] The feedback amount calculation processing unit 31 calculates "-A(t)" based on the measurement result of step S204 (S205).

[0081] The gain control unit 32 calculates Γ(t) (S206).

[0082] The combining unit 33 multiplies "-A(t)" calculated by the feedback amount calculation processing unit 31 in step S205 by Γ(t) calculated by the gain processing unit in step S206, and calculates the feedback amount β(t)=-A(t)Γ(t) (S207).

[0083] The combining unit 33 adds the quantum circuit (that is, the quantum circuit of layer (k + 1)) with the feedback amount β(t) calculated in step 207 set thereto to the quantum circuit device 21 (S208).

[0084] The feedback amount calculation processing unit 31 adds 1 to layer k (S209), and returns the process to S203.

[0085] In the determination of step S203, when layer k is greater than a predetermined maximum layer (S203: YES), the measuring device 22 measures the output state from the quantum circuit device 21, and outputs the measurement result (S210). The classical computer 30 may display the output measurement result as a graph or the like on the output device 1005 (see FIG. 13). Then, this process ends.

[0086] Through the above processing, to the quantum circuit device 21 of the quantum computer 20, as shown in FIG. 1, feedback amounts β1 to β calculated using the weights Γ(t) of the quantum fluctuation terms kQuantum circuits of layers 1 to k are respectively configured. And the measurement device 22 can measure the output state from the quantum circuit device 21 configured in this way. The measurement results can converge as shown in, for example, FIGS. 9 and 10, as compared with FIGS. 5 and 6 that did not converge in the conventional FALQON. Therefore, according to the combinatorial optimization calculation system 10 according to the present embodiment shown in FIGS. 11 and 12, there may be a case where an executable solution can be obtained even for a problem for which an executable solution could not be obtained by FALQON.

[0087] In the above description, the traveling salesman problem has been taken as an example of the combinatorial optimization problem for explanation, but the application target of the present embodiment is not limited to the traveling salesman problem. For example, the present embodiment is applicable to various combinatorial optimization problems such as optimization of a freight delivery plan, optimization of a personnel shift plan, and optimization of an AGV movement route in a factory.

[0088] <Configuration of classical computer> FIG. 13 is a block diagram showing an example of the hardware configuration of a classical computer 30 according to the present disclosure.

[0089] The classical computer 30 includes a processor 1001, a memory 1002, a storage 1003, an input device 1004, an output device 1005, a communication device 1006, a GPU (Graphics Processing Unit) 1007, a reading device 1008, and a bus 1009. Each of the devices 1001 to 1008 is connected to the bus 1009 and can transmit and receive data bidirectionally via the bus 1009.

[0090] The processor 1001 is a device that executes a computer program stored in the memory 1002 and realizes the functions described above. Examples of the processor 1001 include a CPU (Central Processing Unit), an MPU (Micro Processing Unit), a controller, an LSI (Large Scale Integration), an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), and an FPGA (Field-Programmable Gate Array).

[0091] The memory 1002 is a device that stores computer programs and data handled by the classical computer 30. The memory 1002 may include a ROM (Read-Only Memory) and a RAM (Random Access Memory). Examples of the ROM include an EEPROM (Electrically Erasable Programmable Read-Only Memory) and a flash memory. Examples of the RAM include a DRAM (Dynamic Random Access Memory) and a flash memory.

[0092] The storage 1003 is composed of a non-volatile storage medium and is a device that stores computer programs and data handled by the computer 1000. Examples of the storage 1003 include an HDD (Hard Disk Drive), an SSD (Solid State Drive), and a flash memory.

[0093] The input device 1004 is a device that receives data input to the processor 1001. Examples of the input device 1004 include a keyboard, a mouse, a touch pad, and a microphone.

[0094] The output device 1005 is a device that outputs data generated by the processor 1001. Examples of the output device 1005 include a display and a speaker.

[0095] The communication device 1006 is a device that transmits and receives data via a communication network with the quantum computer 20. The communication device 1006 may include a transmission unit that transmits data and a reception unit that receives data. The communication device 1006 may support either wired communication or wireless communication. Examples of wired communication include Ethernet (registered trademark). Examples of wireless communication include Wi-Fi (registered trademark), Bluetooth, LTE (Long Term Evolution), 4G, and 5G.

[0096] The GPU 1007 is a device that processes image rendering at high speed. Note that the GPU 1007 may also be used for AI (artificial intelligence) processing (e.g., deep learning).

[0097] The reading device 1008 is a device that reads data from a recording medium such as a DVD-ROM (Digital Versatile Disk Read Only Memory) or a USB (Universal Serial Bus) memory.

[0098] Note that the functions of the classical computer 30 may be implemented as an LSI which is an integrated circuit. These functions may be individually integrated into one chip, or may be integrated into one chip so as to include some or all of them. Here, we refer to it as an LSI, but depending on the degree of integration, it may also be referred to as an IC, a system LSI, a super LSI, or an ultra LSI. Furthermore, if a technology for integrating functions using an integrated circuit that replaces the LSI appears due to the progress of semiconductor technology or a derivative technology, naturally, the technology may be used for function integration.

[0099] (Summary of the present disclosure) The content of the present disclosure can be expressed as follows.

[0100] <Expression 1> A quantum computer 20 that performs quantum computing using a quantum circuit having a parameter representing a phase rotation amount, and a classical computer 30 that calculates a feedback amount β based on the output of the quantum computer 20 and newly adds a quantum circuit having the calculated feedback amount β as a parameter to the quantum computer 20. In the combinatorial optimization calculation method for calculating combinatorial optimization using these, in the classical computer 30, a gain Γ having a positive value that approaches zero as the quantum circuit is added is multiplied by the feedback amount β.

[0101] <Expression 2> In the combinatorial optimization calculation method according to Expression 1, the feedback amount β may be the feedback amount in the FALQON (Feedback-based ALgorithm for Quantum OptimizatioN) algorithm.

[0102] <Expression 3> In the combinatorial optimization calculation method according to Expression 1 or 2, as the gain function Γ for calculating the gain, the convergence condition for the weight of the quantum fluctuation term in quantum annealing may be used.

[0103] <Expression 4> In the combinatorial optimization calculation method according to Expression 3, the gain function Γ is

[0104]

Equation

[0105] where t is a time variable, N is the number of qubits, a and c are constants, and δ is a small amount satisfying δ << 1.

[0106] According to the method described above, even for problems for which a feasible solution cannot be obtained by FALQON, a feasible solution may be obtained.

[0107] <Expression 5> A quantum computer 20 that performs quantum computing using a quantum circuit having a parameter representing a phase rotation amount, and a classical computer that calculates a feedback amount based on the output of the quantum computer 20 and newly adds a quantum circuit having the calculated feedback amount as a parameter to the quantum computer. In the combinatorial optimization calculation system 10 including the classical computer 30, the classical computer 30 is characterized by multiplying the feedback amount by a gain having a positive value that approaches zero as the quantum circuit is added.

[0108] According to the above-described configuration, even for a problem for which a feasible solution cannot be obtained by FALQON, a feasible solution may be obtained.

[0109] As described above, the embodiments have been described with reference to the accompanying drawings, but the present disclosure is not limited to such examples. It is obvious that those skilled in the art can conceive of various modification examples, correction examples, substitution examples, addition examples, deletion examples, and equivalent examples within the scope described in the claims, and it is understood that they also belong to the technical scope of the present disclosure. Further, within the scope not departing from the gist of the invention, the components in the above-described embodiments may be arbitrarily combined.

Industrial Applicability

[0110] The technology of the present disclosure is useful for a method, apparatus, or system for solving a combinatorial optimization problem by applying quantum mechanics.

Explanation of Signs

[0111] 10 Combinatorial optimization calculation system 20 Quantum computer 21 Quantum circuit device 22 Measuring device 30 Classical computer 31 Feedback amount calculation processing unit 32 Gain control unit 33 Synthesis unit

Claims

1. A quantum computer that performs quantum computing using a quantum circuit having a parameter representing a phase rotation amount, A classical computer that calculates a feedback amount based on the output of the quantum computer and newly adds the quantum circuit having the calculated feedback amount as the parameter to the quantum computer, and a method for calculating combinatorial optimization using the classical computer, In the classical computer, a gain having a positive value that approaches zero in magnitude as the quantum circuit is added is multiplied by the feedback amount, Combinatorial optimization calculation method.

2. The feedback amount is the feedback amount in the FALQON (Feedback-based ALgorithm for Quantum OptimizatioN) algorithm, The combinatorial optimization calculation method according to claim 1.

3. As a gain function for calculating the gain, a convergence condition for the weight of the quantum fluctuation term in quantum annealing is used, The combinatorial optimization calculation method according to claim 1 or 2.

4. The gain function is 【Equation 1】 where t is a time variable, N is the number of qubits, a and c are constants, and δ is a small amount satisfying δ << 1, The combinatorial optimization calculation method according to claim 3.

5. A quantum computer that performs quantum computing using a quantum circuit having a parameter representing a phase rotation amount, A combinatorial optimization calculation system including a classical computer that calculates a feedback amount based on the output of the quantum computer and newly adds the quantum circuit having the calculated feedback amount as a parameter to the quantum computer, The classical computer is characterized by multiplying a positive gain having a value approaching zero along with the addition of the quantum circuit with respect to the feedback amount. Combinatorial optimization calculation system.

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