Processing system, processing device, processing method, and processing program

Abstract

To achieve both reduction in processing time and high-accuracy output of optimal solutions.SOLUTION: An optimization process for sequentially determining, for each of binary variable qubits that constitute an optimal solution, an optimal value of contribution of an orthogonal magnetic field function based on a final state in the annealing process, includes: when an optimal qubit is defined as a qubit providing an optimal evaluation index for the final state in which a strength parameter of a pre-optimization qubit is varied for having a maximum value of the orthogonal magnetic field function, extracting the optimal qubit based on the evaluation index, which is phase information of a controlled qubit whose final states before and after the variation of the strength parameter are phase kicked-back states by a quantum gate circuit; determining the strength parameter, which is the optimal value of the extracted optimal qubit, according to the evaluation index; and outputting the optimal solution by mapping a set of the strength parameters determined for all qubits.SELECTED DRAWING: Figure 10

Description

[Technical Field]

[0001] The present disclosure relates to a processing technique for solving combinatorial optimization problems with two variables. [Background technology]

[0002] As a processing technique for solving combinatorial optimization problems, quantum annealing, which processes quantum bits corresponding to binary variables, has been proposed in, for example, Non-Patent Document 1. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Tadashi Kadowaki and Hidetoshi Nishimori, "Quantum annealing in the transverse ising model." Phys. Rev. E 58, 5355 (1998) Summary of the Invention [Problem to be solved by the invention]

[0004] However, when quantum annealing, which merely varies the transverse magnetic field over time, is applied as in Non-Patent Document 1, there are limitations to outputting the optimal solution with high precision in the short processing time expected of a quantum computing system.

[0005] An object of the present disclosure is to provide a processing system that achieves both a reduction in processing time and a highly accurate output of an optimal solution. Another object of the present disclosure is to provide a processing device that achieves both a reduction in processing time and a highly accurate output of an optimal solution. Yet another object of the present disclosure is to provide a processing method that achieves both a reduction in processing time and a highly accurate output of an optimal solution. Yet another object of the present disclosure is to provide a processing program that achieves both a reduction in processing time and a highly accurate output of an optimal solution. [Means for solving the problem]

[0006] The technical means of the present disclosure for solving the problems will be described below. Note that the claims and the reference symbols in parentheses in this section indicate the correspondence with the specific means described in the embodiments described later in detail, and do not limit the technical scope of the present disclosure.

[0007] A first aspect of the present disclosure is A processing system for solving combinatorial optimization problems involving binary variables by controlling quantum annealing and quantum gates that process quantum bits corresponding to the binary variables, the processing system comprising: a processor (12); The processor an annealing process that individually controls the contribution of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining, for each quantum bit corresponding to a binary variable constituting an optimal solution to a combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on the final state in the annealing process; The quantum bit for which the evaluation index for evaluating the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as the optimal quantum bit. The optimization process is Extracting an optimal quantum bit based on an evaluation index that is phase information of a control quantum bit in which each final state before and after the fluctuation of the intensity parameter is phase-kicked back by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value for the extracted optimal quantum bit in accordance with the evaluation index; and outputting an optimal solution by mapping the set of intensity parameters determined for all qubits.

[0008] A second aspect of the present disclosure is A processing device that controls quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, the processing device comprising: a processor (12); The annealing process is a process of individually controlling the contribution of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function, over time; The optimization process is a process of sequentially determining the optimal value of the contribution of the orthogonal magnetic field function for each quantum bit corresponding to a binary variable that constitutes an optimal solution to the combinatorial optimization problem based on the final state in the annealing process, The quantum bit for which the evaluation index for evaluating the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as the optimal quantum bit. The processor Extracting an optimal quantum bit based on an evaluation index that is phase information of a control quantum bit in which each final state before and after the fluctuation of the intensity parameter is phase-kicked back by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value for the extracted optimal quantum bit in accordance with the evaluation index; and outputting an optimal solution by mapping the set of intensity parameters determined for all qubits.

[0009] A third aspect of the present disclosure is a processing method executed by a processor (12) to control quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, the method comprising: an annealing process that individually controls the contribution of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining the optimal value of the contribution of the orthogonal magnetic field function for each quantum bit corresponding to a binary variable constituting an optimal solution of the combinatorial optimization problem based on the final state of the annealing process; The quantum bit for which the evaluation index for evaluating the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as the optimal quantum bit. The optimization process is Extracting an optimal quantum bit based on an evaluation index that is phase information of a control quantum bit in which each final state before and after the fluctuation of the intensity parameter is phase-kicked back by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value for the extracted optimal quantum bit in accordance with the evaluation index; and outputting an optimal solution by mapping the set of intensity parameters determined for all qubits.

[0010] A fourth aspect of the present disclosure is A processing method executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, comprising: The annealing process is a process of individually controlling the contribution of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function, over time; The optimization process is a process of sequentially determining the optimal value of the contribution of the orthogonal magnetic field function for each quantum bit corresponding to a binary variable that constitutes an optimal solution to the combinatorial optimization problem based on the final state in the annealing process, The quantum bit for which the evaluation index is optimal for the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as the optimal quantum bit. 、 strengthextracting an optimal quantum bit based on an evaluation index that is phase information of a control quantum bit in which each final state before and after a change in the degree parameter is phase-kicked back by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value for the extracted optimal quantum bit in accordance with the evaluation index; and outputting an optimal solution by mapping the set of intensity parameters determined for all qubits. Run the optimization process .

[0011] A fifth aspect of the present disclosure is A processing program including instructions stored in a storage medium (10) and executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, an annealing process that individually controls the contribution of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining the optimal value of the contribution of the orthogonal magnetic field function for each quantum bit corresponding to a binary variable constituting an optimal solution to the combinatorial optimization problem based on the final state in the annealing process; The quantum bit for which the evaluation index for evaluating the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as the optimal quantum bit. The optimization process is Extracting an optimal quantum bit based on an evaluation index that is phase information of a control quantum bit in which each final state before and after the fluctuation of the intensity parameter is phase-kicked back by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value for the extracted optimal quantum bit in accordance with the evaluation index; and outputting an optimal solution by mapping the set of intensity parameters determined for all qubits.

[0012] A sixth aspect of the present disclosure is A processing program including instructions stored in a storage medium (10) and executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, The annealing process is a process of individually controlling the contribution of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function, over time; The optimization process is a process of sequentially determining the optimal value of the contribution of the orthogonal magnetic field function for each quantum bit corresponding to a binary variable that constitutes an optimal solution to the combinatorial optimization problem based on the final state in the annealing process, The quantum bit for which the evaluation index for evaluating the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as the optimal quantum bit. Extracting an optimal quantum bit based on an evaluation index that is phase information of a control quantum bit in which each final state before and after the fluctuation of the intensity parameter is phase-kicked back by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value for the extracted optimal quantum bit in accordance with the evaluation index; and outputting an optimal solution by mapping the set of strength parameters determined for all of the qubits.

[0013] In the optimization processes of these first to sixth aspects, the optimal value of the contribution of the orthogonal magnetic field function is sequentially determined for each quantum bit corresponding to a binary variable based on the final state of the annealing process, which individually controls the contributions of the cost function, the transverse magnetic field function, and the orthogonal magnetic field function over time.Therefore, an optimal quantum bit is extracted, which has an optimal evaluation index that evaluates the final state of the annealing process, which varies the intensity parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization.At this time, the extraction of the optimal quantum bit is based on the evaluation index, which is the phase information of the control quantum bit whose phase is kicked back by the quantum gate circuit, for each final state before and after the variation of the intensity parameter.

[0014] According to this, even if the annealing time in the annealing process is shortened, the solution space of the combinatorial optimization problem can be narrowed down by sequentially determining the strength parameters that are optimal values ​​for the extracted optimal quantum bits according to the evaluation index. Therefore, by mapping the set of strength parameters determined for all quantum bits, the optimal solution can be output with high accuracy. This makes it possible to achieve both a shortened annealing time and a highly accurate output of the optimal solution. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a block diagram showing the overall configuration of a processing system according to an embodiment. [Figure 2] FIG. 1 is a block diagram illustrating a functional configuration of a processing system according to an embodiment. [Figure 3] FIG. 1 is a time transition diagram for explaining an annealing process according to an embodiment. [Figure 4] 1 is a graph illustrating an annealing process according to an embodiment. [Figure 5] FIG. 1 is a block diagram showing a quantum gate circuit according to an embodiment. [Figure 6] 10 is a table for explaining an optimization process according to an embodiment. [Figure 7] 10 is a table for explaining an optimization process according to an embodiment. [Figure 8] 10 is a table for explaining an optimization process according to an embodiment. [Figure 9] 10 is a table for explaining an optimization process according to an embodiment. [Figure 10] 1 is a sequence chart illustrating a processing method according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[0017] The processing system 1 of one embodiment shown in FIG. 1 is a quantum computing system for controlling quantum annealing having quantum bits corresponding to binary variables to solve combinatorial optimization problems involving the binary variables. The processing system 1 includes, as multiple dedicated computers, an annealing quantum computer that performs operations using quantum bits using a quantum annealing method and a gate quantum computer that performs operations using quantum bits using a quantum gate method. The processing system 1 may also include, as a dedicated computer, a classical computer that performs operations using classical bits in combination with the annealing quantum computer and the gate quantum computer. At least one of the annealing quantum computer and the gate quantum computer, which are essential components of the processing system 1, may be, for example, a noisy intermediate scale quantum (NISQ) device.

[0018] The dedicated computer constituting the processing system 1 has a plurality of memories 10 and processors 12. The plurality of memories 10 are non-transitory tangible storage media, such as semiconductor memory, magnetic media, and optical media, that non-temporarily store computer-readable programs, data, and the like. The plurality of processors 12 include at least a quantum processing unit capable of implementing a quantum annealing method and a quantum processing unit capable of implementing a quantum gate method. The processor 12 of a classical computer combined with a quantum computer as the dedicated computer constituting the processing system 1 may include at least one of a central processing unit (CPU), a graphics processing unit (GPU), and a reduced instruction set computer (RISC)-CPU, for example.

[0019] In the processing system 1, the processor 12 controls quantum annealing and quantum gates that process quantum bits corresponding to binary variables, and executes instructions included in processing programs stored in multiple memories 10 to solve combinatorial optimization problems involving the binary variables. In this way, the processor 12 constructs multiple functional blocks for controlling quantum annealing and quantum gates to solve combinatorial optimization problems. The multiple functional blocks constructed in the processing system 1 include an annealing block 100, a gate block 110, and an optimization block 120, as shown in FIG. 2.

[0020] The annealing block 100 is realized by the processor 12 in the annealing quantum computer, or by a combination of the processor 12 and the memory 10 in the classical computer. The annealing block 100 executes the annealing process of the quantum annealing method. Specifically, the annealing block 100 of this embodiment executes the annealing process of the quantum annealing method using the cost function H z and the transverse magnetic field function Hx and the orthogonal magnetic field function H y The annealing process is performed so that the contributions of the annealing block 100 and the annealing block 101 are individually controlled over time. Hereinafter, the annealing process performed by the annealing block 100 is referred to as a quantum annealing (QA) process.

[0021] The QA process is based on the Ising model (i.e., the spin glass model), which associates binary variables of a combinatorial optimization problem with quantum bits. The QA process is based on the cost function H z and the transverse magnetic field function H x and the orthogonal magnetic field function H y In equation (1), t is the elapsed time in the QA process, and in this embodiment, as shown in FIGS. 3 and 4, it is defined as the time until the annealing time T, which will be described later, and varies within the range of 0 to T.

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[0022] Cost function H z is defined as the z-direction component of the total Hamiltonian H shown in Figure 3. The cost function H z is expressed by Equation 2 as a function that converges through optimization in a combinatorial optimization problem. i z ,σ j z is the Pauli matrix of the z-direction component corresponding to the qubit pair with index i and j whose combination is optimized. ij is the weight matrix w of the combinatorial optimization problem ij For example, the coupling constant J ij is defined as a random variable that satisfies equations 4 and 5 so that interactions based on the SK (Sherrington-Kirkpatrick) model are applied to combinatorial optimization problems. In equation 5, N is the number of quantum bits corresponding to the number of binary variables, and the cost function H zis the number of spins that make up the cost function H z In combinatorial optimization problems using N The combination of these will be optimized.

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[0023] In Equation 1, the cost function H z The coefficient function A(t) acting on the cost function H z 4 for individually controlling the time, is expressed by Equation 6. In Equation 6, t is the elapsed time as in Equation 1. In Equation 6, T is the annealing time from the start to the end of the QA process, and is simplified to the numerical value 1 in this embodiment. In Equation 6, a is an intensity parameter for giving the maximum value of the coefficient function A(t), and is simplified to the numerical value 1 in this embodiment.

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[0024] Transverse magnetic field function H x is defined as the x-direction component of the total Hamiltonian H shown in Figure 3. The transverse magnetic field function H x is the cost function H in the z direction z is expressed as a function of quantum fluctuations representing the uniform magnetic field component in the x direction perpendicular to the i x is the Pauli matrix with the x-direction component corresponding to the qubit with index i whose combination is being optimized.

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[0025] In equation 1, the transverse magnetic field function H x The coefficient function B(t) acting on the transverse magnetic field function H x 4 for individually controlling the time, is expressed by Equation 8. In Equation 8, t is the elapsed time as in Equation 1. In Equation 8, T is the annealing time as in Equation 6. In Equation 8, b is an intensity parameter for giving the maximum value of the coefficient function B(t), and in this embodiment in particular, it is set to an optimal parameter such as 0.43 that has been verified in advance by demonstration experiments.

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[0026] Orthogonal magnetic field function H y is defined as the y-direction component of the total Hamiltonian H shown in Figure 3. The orthogonal magnetic field function H y is the cost function H in the z direction z and the transverse magnetic field function H in the x direction x The non-uniform magnetic field component in the y direction, which is perpendicular to both the y direction and the y direction, is expressed by Equation 9. In Equation 9, σ i y is the Pauli matrix with the y-direction component corresponding to the qubit with index i whose combination is being optimized.

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[0027] In equation 9, the orthogonal magnetic field function H y The coefficient function C that constitutes i (t) is the orthogonal magnetic field function H y 4 for individually controlling the time, is expressed by Equation 10. In Equation 10, t is the elapsed time as in Equation 1. In Equation 10, T is the annealing time as in Equation 6. In Equation 10, c i is the coefficient function C for the qubit with index i. iThis is a strength parameter for giving the maximum value of (t), and in this embodiment in particular, it is set by the optimization block 120 as described below.

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[0028] The QA process is based on the time control of the assumed total Hamiltonian H by quantum annealing, and the final state ψ of the wave function ψ for the total Hamiltonian H is shown in Figure 3. _f Under the time control of the total Hamiltonian H in the QA process, the final state ψ at time t=1 is obtained according to the Schrodinger equation expressed by Equation 11. _f will be obtained.

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[0029] Here, as shown in Figures 3 and 4, the time control in the QA process is performed by using the cost function H for the total Hamiltonian H. z The coefficient function A(t), which can be said to be the contribution of the total Hamiltonian H, is gradually increased from 0 to the final value as time t elapses. In particular, the time control of this embodiment increases the output value of the coefficient function A(t) proportionally to the elapsed time t up to the set value of the intensity parameter a, which is the final value. At the same time, the time control in the QA processing is performed by increasing the transverse magnetic field function H x The coefficient function B(t), which can be said to be the contribution of the total Hamiltonian H, is decreased from the initial value to 0 as time t elapses. In particular, the time control in this embodiment decreases the output value of the coefficient function B(t) from the set value of the intensity parameter b, which is the initial value, in proportion to the elapsed time t. Furthermore, the time control in the QA processing is performed by using the magnetic field function H y Coefficient function C, which can be said to be the contribution of i (t) is increased from 0 to the maximum value as time t passes, and then decreased to 0 as time t passes. In particular, the time control of this embodiment is performed by increasing the intensity parameter c i The coefficient function C is set to oscillate at the midpoint of the elapsed time t.i The output value of (t) is changed proportionally to the square of the sine function.

[0030] The gate block 110 shown in Fig. 2 is realized by a processor 12 in a gate-type quantum computer, or by cooperation of the processor 12 and a memory 10 in a classical computer. The gate block 110 constructs a quantum gate circuit QG of the quantum gate type as shown in Fig. 5. Specifically, the quantum gate circuit QG has a control qubit Q for one qubit. a Here, the control qubit Q a is an ancillary qubit whose input state is initialized to |0>. N register qubits Q r has its input state initialized to |0>.

[0031] The quantum gate circuit QG is a quantum gate that converts the input control qubit Q a On the other hand, the revolving gate G r Rotating gate G r is expressed as the control qubit Q by Equation 12. a into a superposition state of state |0> and state |1>. The state |ψ1> thus transformed is expressed by equation 13.

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[0032] The quantum gate circuit QG has a control qubit Q a For the final state ψ of the wave function ψ for the total Hamiltonian H in the QA treatment, _f Among these, the reference final state ψ b_f The reference unitary gate U b The reference unitary gate U b is the control qubit Q in the superposition state a The register qubit Q of the branch whose state is |0> rQA processing is performed on the register qubit Q of the corresponding branch. r The state of the reference final state ψ b_f Thus, the state |ψ2> after the phase kickback is expressed by Equation 14.

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[0033] The quantum gate circuit QG has a control qubit Q a For the final state ψ of the wave function ψ for the total Hamiltonian H in the QA treatment, _f Among these, the final analytical state ψ i_f The analytical unitary gate U kicks back the phase according to i Apply the analytical unitary gate U i is the control qubit Q in the superposition state a The register qubit Q of the branch whose state is |1> r QA processing is performed on the register qubit Q of the corresponding branch. r Analyze the state of the final state ψ i_f Thus, the state |ψ3> after further phase kickback is expressed by Equation 15.

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[0034] The quantum gate circuit QG has a final state ψ b_f ,ψ i_f The phase-kicked back control qubit Q a For the Hadamard gate G h Hadamard gate G h is the quantum bit Q controlled by the Hadamard matrix of number 16. a Thus, the state |ψ4> after the Hadamard transformation is expressed by equation 17. As a result, in the quantum gate circuit QG, there are two types of unitary gates U b ,U i The effect of this is to create the strength parameter c i The final state ψ before and after the fluctuationb_f ,ψ i_f However, as shown in Equation 17, the control quantum bit Q a It can be said that the phase is kicked back relative to

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[0035] The quantum gate circuit QG has a control qubit Q a The output measurement data reflects the phase information of the control qubit Q. The output measurement data has two types of probabilities P0 and P1. One of the probabilities P0 is the probability of a The other probability P1 is defined by the control qubit Q a The state |1> of |0> is defined by Equation 19. In this embodiment, the probability values ​​of the emergence of the states |0> and |1> by repeated (for example, 1000 times or more) calculations using the quantum gate circuit QG are output as estimated measurement data with probabilities P0 and P1, respectively.

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[0036] The optimization block 120 shown in FIG. 2 is realized by a combination of a processor 12 and a memory 10 in a classical computer, or by a combination of the combination and at least one of a processor 12 in an annealing quantum computer and a processor 12 in a gate quantum computer. In order to solve a combinatorial optimization problem of binary variables, the optimization block 120 executes an optimization process that narrows down the solution space of the problem. Specifically, the optimization block 120 calculates an orthogonal magnetic field function H y The optimal value of the contribution of the final state ψ in the QA process _fHereinafter, the combinatorial optimization process by the optimization block 120 will be referred to as quantum greedy optimization (QGO) process.

[0037] QGO processing is 2 N For all N qubits before optimization, i.e., all qubits with index i=1 to N, the orthogonal magnetic field function H y The strength parameter c that gives the maximum value of i Both of these are based on the reference intensity parameter c i_b At this time, each reference intensity parameter c i_b In this embodiment, N is set to a value of 0 for any quantum bit with index i, as shown in Fig. 6. Note that Fig. 6 and Figs. 7 to 9 described below illustrate the case where N=8 (i.e., i=an integer from 1 to 8).

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[0038] The QGO process calculates the corresponding strength parameter c for each qubit with index i before optimization. i As shown in Equation 21, the reference intensity parameter c i_b The fluctuation intensity parameter c is given by a small amount of fluctuation Δ. i_f , the reference intensity parameter c i_b This is set separately from the reference intensity parameter c i_b In the QGO process, where is initialized to zero, the fluctuation strength parameter c i_f This means that the setting of Δ=Δ is performed as shown in Fig. 6. Therefore, the minute amount Δ in this embodiment is set to an optimum amount, such as 0.1, which has been verified in advance by a demonstration experiment.

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[0039] The QGO process uses the strength parameter c i The reference intensity parameter ci_b and the reference intensity parameter c i_b The fluctuation intensity parameter c i_f Specifically, in the sensitivity analysis subroutine, as shown in Figure 2, for each quantum bit before optimization, the strength parameter c i_b ,c i_f is passed from the optimization block 120 to the annealing block 100.

[0040] In the sensitivity analysis subroutine, the gate block 110 determines the intensity parameter c i_b ,c i_f The annealing block 100 controls the annealing block 100 to which the register qubit Q r As shown in Figure 6, the quantum annealing process is performed on the quantum gate circuit QG. b and analytical unitary gate U i is the register qubit Q r This QA process is performed on the strength parameter c i The reference strength parameter c before fluctuation i_b The reference final state ψ corresponding to b_f and the intensity parameter c i The fluctuation intensity parameter c after the fluctuation i_f The analytical final state ψ corresponding to i_f and the control qubit Q a A controlled superposition state is obtained depending on the state of the

[0041] Here, the QA process calculates all indices i commonly used for all qubits before optimization as the reference strength parameter c i_b The standard final state ψ is prepared using the total Hamiltonian H with b_f is the standard unitary gate U b At the same time, in the QA process, for each qubit before optimization, the corresponding fluctuation strength parameter c i_f and the uncorresponding reference intensity parameter c of index ii_b The fluctuation intensity parameter c is prepared using the total Hamiltonian H including i_f The analytical final state ψ corresponding to i_f But the analytical unitary gate U i It is implemented by

[0042] In the sensitivity analysis subroutine, the strength parameter c i The final state ψ before and after the fluctuation b_f ,ψ i_f The gate block 110, which is obtained by controlling the annealing block 100, controls the control quantum bit Q a The probabilities P0 and P1 for each state |0>, |1> of the quantum gate circuit QG are output for each quantum bit before optimization. The probabilities P0 and P1 output in this way are passed to the optimization block 120 as measurement data by the quantum gate circuit QG in the gate block 110, as shown in FIG.

[0043] In the sensitivity analysis subroutine, the optimization block 120 selects one quantum bit Q that has the optimum evaluation index F among all the quantum bits before optimization corresponding to the measurement data of the probabilities P0 and P1 that have been handed over. o At this time, the evaluation index F is the final analysis state ψ of the index i used in the measurement data output of the probabilities P0 and P1. i_f The analytical evaluation index F of the index i is evaluated as follows: i Therefore, the analytical evaluation index F i is defined as the probability difference between probabilities P0 and P1 according to equation 22.

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[0044] Here, Equation 22 can be transformed into an equation according to Equation 23. From Equation 21, the analytical evaluation index F i is the control qubit Q a As the evaluation index F, which is the phase information of the quantum gate circuit QG, the intensity parameter ci Each final state ψ before and after the fluctuation b_f ,ψ i_f Imaginary part of the inner product of two b_f |ψ i_f >.

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[0045] Therefore, the optimization calculation based on the evaluation index F in the sensitivity analysis subroutine is performed by using the analysis evaluation index F i The optimal qubit Q that maximizes the absolute value of o is extracted as shown in FIG. 6 according to Equation 24. In Equation 24, the optimal quantum bit Q o The index i before the optimization operation is formally expressed using k and m so that the index of is treated as i after the optimization operation. Note that Figure 6 shows the optimal qubit Q with index i=8 in the first sensitivity analysis subroutine. o The following shows an example of the extracted

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[0046] In the sensitivity analysis subroutine, optimization block 120 extracts the optimal qubit Q o The optimal value of the strength parameter c i Assuming that the optimal qubit Q o Analysis evaluation index F corresponding to i The optimal strength parameter c that satisfies Equation 25 according to i_o is determined as shown in Figure 6. Here, c in Equation 25 c is a constant parameter common to all N quantum bits, and in this embodiment, is set to an optimal parameter such as π / 2 (i.e., 1.57), which has been verified in advance by a demonstration experiment. Note that FIG. 6 shows the optimal quantum bit Q with index i=8 in the first sensitivity analysis subroutine. o is extracted and the optimal strength parameter c i_o 1 shows a determined example of

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[0047] The optimization block 120 then passes the sensitivity analysis subroutine to the annealing block 100 as shown in FIG. 2 to generate the strength parameter c i_b ,c i_f , the optimal strength parameter c i_o Each time the sensitivity analysis subroutine is performed, it is changed as shown in Figures 7 to 9 and repeated. That is, in the second and subsequent sensitivity analysis subroutines, all optimal quantum bits Q optimized by the previous sensitivity subroutines are analyzed. o For index i, the corresponding reference strength parameter c i_b Instead, the corresponding optimal strength parameter c of index i i_o will be handed over.

[0048] As a result, in the second and subsequent sensitivity analysis subroutines, the reference final state ψ b_f In the QA process to obtain the optimal intensity parameter c i_o The corresponding reference intensity parameter c of index i is i_b is the optimal strength parameter c i_o In the second and subsequent sensitivity analysis subroutines, the final state of the analysis ψ i_f When performing the QA process to obtain the optimal qubit Q o For each qubit before optimization, excluding the uncorresponding reference strength parameter c i_b and the optimal strength parameter c i_o is the corresponding reference intensity parameter c of index i. i_b is the optimal strength parameter c i_o is replaced by

[0049] In this way, in the sensitivity analysis subroutine from the second time onwards, the optimal qubit Q o Among the remaining qubits before optimization, excluding a Based on the evaluation index F, which is the phase information ofo Furthermore, in the second and subsequent sensitivity analysis subroutines, the extracted optimal qubit Q o With respect to the control qubit Q, the phase is kicked back by the quantum gate circuit QG. a Based on the evaluation index F, which is the phase information of i_o is determined.

[0050] In addition, Figure 7 shows the optimal qubit Q for index i=8 in the first sensitivity analysis subroutine. o is extracted and the optimal strength parameter c i_o After the determination of , the optimal qubit Q for index i = 6 is obtained by the QGO process in the second sensitivity analysis subroutine. o is extracted and the optimal strength parameter c i_o 8 shows an example of the optimal qubit Q for index i=8 and 6 determined in the first and second sensitivity analysis subroutines. o is extracted and the optimal strength parameter c i_o After the determination of , the optimal qubit Q for index i = 2 is obtained by the QGO process in the third sensitivity analysis subroutine. o is extracted and the optimal strength parameter c i_o 9 shows an example of the optimal qubit Q other than index i=5 in the first to seventh sensitivity analysis subroutines. o is extracted and the optimal strength parameter c i_o After the determination of , the optimal qubit Q for index i = 5 is obtained by the QGO process in the eighth sensitivity analysis subroutine. o is extracted and the optimal strength parameter c i_o 1 shows a determined example of

[0051] In the QGO process, the optimization block 120 repeats the sensitivity analysis subroutine a number of times equal to the number of qubits N to find the optimal strength parameter c i_o is determined for all N qubits. In this way, the optimal strength parameter c for all qubits is i_o After determining the optimal strength parameters ci_o The set of ∑ ∑ i = ∑ j ...

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[0052] The processing method in which the processing system 1 controls quantum annealing having quantum bits corresponding to binary variables and solves a combinatorial optimization problem of the binary variables through the cooperation of the blocks 100 and 110 described above is executed according to the sequence chart shown in Fig. 10. This sequence chart is executed in response to, for example, an instruction from an operator of the processing system 1. Note that each "S" in the sequence chart represents a plurality of steps executed by a plurality of instructions included in each processing program of the plurality of memories 10.

[0053] In S10 of the QGO process, the optimization block 120 calculates the strength parameters c for all qubits before optimization. i Both are based on the reference intensity parameter c i_b In S11 of the QGO process, the optimization block 120 initializes the reference strength parameter c i_b The fluctuation intensity parameter c i_f In S12 of the QGO process, the optimization block 120 repeatedly executes a sensitivity analysis subroutine including S120 to S124.

[0054] Specifically, in S120 of the sensitivity analysis subroutine, the optimization block 120 calculates the reference strength parameter c i_b and the fluctuation intensity parameter c i_fis transferred to the annealing block 100. In response to this transfer, the gate block 110 controls the annealing block 100 in step S20. In response to this control, the annealing block 100 then transfers the transferred reference strength parameter c i_b and the control qubit Q of the gate block 110 a Using the reference final state ψ b_f and the analytical final state ψ i_f In step S40, the gate block 110 prepares a superposition state of these final states ψ b_f ,ψ i_f The phase of the control qubit Q is kicked back. a The measurement data of the probabilities P0 and P1 for the states |0> and |1> are output by the quantum gate circuit QG for each pre-optimization quantum bit and handed over to the optimization block 120.

[0055] In S121 of the sensitivity analysis subroutine, the optimization block 120 calculates an analytical evaluation index F, which is the probability difference between the probabilities P0 and P1 delivered from the gate block 110 in S40. i , the control qubit Q a The optimization block 120 performs optimization calculations using the evaluation index F, which is the phase information of the intensity parameter c i Each final state ψ before and after the fluctuation b_f ,ψ i_f Imaginary part of the inner product of two b_f |ψ i_f >, the analytical evaluation index F i The optimal qubit Q for which o are extracted in S121.

[0056] In S122 of the sensitivity analysis subroutine, the optimization block 120 calculates the optimal qubit Q extracted by S121. o Analysis evaluation index F as the evaluation index F corresponding to i Depending on o The optimal strength parameter c with respect to i_oIn S123 of the sensitivity analysis subroutine, the optimization block 120 determines the optimal strength parameters c for all N qubits. i_o It is determined whether the determination of the above has been completed.

[0057] If a negative determination is made in S123, S124 is executed instead of S120 so that the sensitivity analysis subroutine is repeated. In S124, the optimization block 120 calculates the optimum strength parameter c i_o The corresponding reference intensity parameter c of index i i_b Instead of and other reference intensity parameters c i_b and the fluctuation intensity parameter c i_f In accordance with S120, S20, S30, S40, S121, S122, S123, and S124 are handed over to the annealing block 100. In response to this handover, S20, S30, S40, S121, S122, S123, and S124 are handed over to the annealing block 100. o The remaining qubits before optimization are used as the qubits other than the qubits.

[0058] On the other hand, if a positive determination is made in S123, the sensitivity analysis subroutine ends, and the sequence chart proceeds to S13. In S13 of the QGO process, the optimization block 120 calculates the optimal strength parameters c i_o Then, in S125, the optimization block 120 stores the output optimal solution OA in the memory 10. This completes one execution of the sequence chart.

[0059] (Action and effect) In this way, in the QGO process of this embodiment, the cost function H z and the transverse magnetic field function H x and the orthogonal magnetic field function H y The final state ψ in QA processing in which the contributions of _f By using the orthogonal magnetic field function H yThe optimal value of the contribution of is then determined sequentially. Then, for the quantum bit before optimization, the orthogonal magnetic field function H y The strength parameter c that gives the maximum value of i The final state ψ in QA processing with varying _f The optimal qubit Q that gives the best evaluation index F is o is extracted. Then, the optimal qubit Q o The extraction of the intensity parameter c i Each final state ψ before and after the fluctuation _f is phase-kicked back by the quantum gate circuit QG. a The evaluation index F is based on the phase information of the

[0060] According to this, even if the annealing time T in the QA process is shortened, the extracted optimal qubit Q o The optimal value of the strength parameter c i By sequentially determining the strength parameters c for all qubits, the solution space of the combinatorial optimization problem can be narrowed down. i By mapping the set of , the optimal solution OA can be output with high accuracy. This makes it possible to achieve both a reduction in the annealing time T and a high-accuracy output of the optimal solution OA. Note that a high-accuracy optimal solution OA, in other words, a high solution accuracy, may mean that the probability of the optimal solution OA is high, or the cost function H after optimization z This may mean that the value of ∇ ...

[0061] (Other embodiments) Although one embodiment has been described above, the present disclosure should not be construed as being limited to the embodiment described above, and can be applied to various embodiments within the scope that does not deviate from the gist of the present disclosure.

[0062] In the variant optimization block 120, the optimal qubit Q o may be extracted multiple times in one sensitivity analysis subroutine, in which case the optimal strength parameter c i_o is the optimal qubit for eacho In the modified annealing block 100, the Pauli matrix σ of the y-direction component of Equation 9 is determined by a time-controlled unitary transformation. i y is the time-controlled x-direction component of the Pauli matrix σ i x and the Pauli matrix σ in the z direction i z and obtain a new total Hamiltonian H, thereby realizing the time control.

[0063] In addition to the above, the above-described embodiments and variations may be implemented using a computer device or semiconductor device (e.g., a semiconductor chip) having a processor 12 and memory 10 that executes at least the QGO processing of the processing system 1.

[0064] (Additional remarks) This specification discloses the following technical ideas and combinations thereof.

[0065] (Technical thought 1) A processing system for solving combinatorial optimization problems involving binary variables by controlling quantum annealing and quantum gates that process quantum bits corresponding to the binary variables, the processing system comprising: a processor (12); The processor: an annealing process that individually controls the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution of the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. The optimization process includes: Extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the qubits.

[0066] (Technical thought 2) The optimization process includes: The processing system according to Technical Idea 1 includes extracting the optimal quantum bit based on the evaluation index, which is the imaginary part of the inner product between the final states before and after the fluctuation of the intensity parameter, from the phase kicked back phase information.

[0067] (Technical Thought 3) The optimization process includes: The processing system according to Technical Idea 2 includes determining the intensity parameter that becomes the optimal value of the optimal quantum bit according to the evaluation index, which is the imaginary part of the inner product of the final states before and after the fluctuation of the intensity parameter, from the phase information that has been phase kicked back.

[0068] (Technical Thought 4) The optimization process includes: The processing system according to any one of Technical Ideas 1 to 3, further comprising: extracting the optimal quantum bit for which the evaluation index is optimal when the intensity parameter initialized to a value of 0 for the quantum bit before optimization is varied.

[0069] (Technical Thought 5) The optimization process includes: The initialized intensity parameters are set as reference intensity parameters, When the intensity parameter varied from the reference intensity parameter is defined as a varied intensity parameter, The processing system according to Technical Idea 4 includes extracting the optimal quantum bit based on the evaluation index, which is the phase information obtained by phase kickback between the final state corresponding to the reference intensity parameter before fluctuation and the final state corresponding to the fluctuation intensity parameter after fluctuation.

[0070] (Technical Thought 6) The optimization process includes: The processing system according to Technical Idea 5 includes determining the intensity parameter that becomes the optimal value of the optimal quantum bit according to the evaluation index, which is the phase information obtained by phase kickback between the final state corresponding to the reference intensity parameter before fluctuation and the final state corresponding to the fluctuating intensity parameter after fluctuation.

[0071] (Technical Thought 7) A storage medium (10) is provided. The optimization process includes: The processing system according to any one of Technical Ideas 1 to 6, further comprising storing the optimal solution in the storage medium.

[0072] (Technical Thought 8) The annealing treatment is The processing system according to any one of technical ideas 1 to 7, includes obtaining the final state of the wave function for the total Hamiltonian of the cost function, the transverse magnetic field function, and the orthogonal magnetic field function based on time control of the total Hamiltonian by quantum annealing.

[0073] (Technical Thought 9) The annealing treatment is Increasing the contribution of the cost function over time from a zero value to a closing value; Decreasing the contribution of the transverse magnetic field function from an initial value to a value of 0 over time; The processing system according to technical idea 8, further comprising: increasing the contribution of the orthogonal magnetic field function from 0 to the maximum value over time, and then decreasing the contribution to 0 over time.

[0074] (Technical Thought 10) A processing device that controls quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, the processing device comprising: a processor (12); a process of individually controlling the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function over time is defined as an annealing process; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution to the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. The processor: Extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

[0075] The above-mentioned technical ideas 1 to 10 may be realized in the form of a method or a program. [Explanation of symbols]

[0076] 1: Processing system, 10: Memory, 12: Processor, QG: Quantum gate circuit

Claims

1. A processing system for solving combinatorial optimization problems involving binary variables by controlling quantum annealing and quantum gates that process quantum bits corresponding to the binary variables, the processing system comprising: a processor (12); The processor: an annealing process that individually controls the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining an optimal value of the contribution of the orthogonal magnetic field function for each quantum bit corresponding to the binary variable constituting an optimal solution of the combinatorial optimization problem based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. The optimization process includes: extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the qubits.

2. The optimization process includes:

2. The processing system according to claim 1, further comprising: extracting the optimal quantum bit based on the evaluation index, which is an imaginary part of an inner product between the final states before and after the fluctuation of the intensity parameter, from the phase information subjected to phase kickback.

3. The optimization process includes:

3. The processing system according to claim 2, further comprising: determining the intensity parameter that becomes the optimal value of the optimal quantum bit according to the evaluation index that is an imaginary part of an inner product between the final states before and after a variation in the intensity parameter, among the phase information that has been phase kicked back.

4. The optimization process includes:

4. The processing system according to claim 1, further comprising: extracting the optimal quantum bit for which the evaluation index is optimal when the strength parameter initialized to a value of 0 for the quantum bit before optimization is varied.

5. The optimization process includes: The initialized intensity parameters are set as reference intensity parameters, When the intensity parameter varied from the reference intensity parameter is defined as a varied intensity parameter, 5. The processing system according to claim 4, further comprising: extracting the optimum quantum bit based on the evaluation index, which is the phase information obtained by phase kicking back the final state corresponding to the reference intensity parameter before fluctuation and the final state corresponding to the fluctuation intensity parameter after fluctuation.

6. The optimization process includes:

6. The processing system according to claim 5, further comprising: determining the intensity parameter that becomes the optimal value of the optimal quantum bit according to the evaluation index, which is the phase information obtained by phase kicking back the final state corresponding to the reference intensity parameter before fluctuation and the final state corresponding to the fluctuating intensity parameter after fluctuation.

7. A storage medium (10) is provided, The optimization process includes:

4. The processing system according to claim 1, further comprising storing the optimal solution in the storage medium.

8. The annealing treatment is The processing system according to any one of claims 1 to 3, further comprising: obtaining the final state of a wave function for a total Hamiltonian of the cost function, the transverse magnetic field function, and the orthogonal magnetic field function based on time control of the total Hamiltonian by quantum annealing.

9. The annealing treatment is Increasing the contribution of the cost function over time from a value of 0 to a final value; Decreasing the contribution of the transverse magnetic field function from an initial value to a zero value over time; The processing system of claim 8 , further comprising: increasing the contribution of the orthogonal magnetic field function from a value of 0 to the maximum value over time, and then decreasing the contribution to a value of 0 over time.

10. A processing device that controls quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, the processing device comprising: a processor (12); a process of individually controlling the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function over time is defined as an annealing process; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution to the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. The processor: extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

11. A processing method executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, comprising: an annealing process that individually controls the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution of the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. The optimization process includes: extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the qubits.

12. A processing method executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, comprising: a process of individually controlling the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function over time is defined as an annealing process; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution to the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

13. A processing program including instructions stored in a storage medium (10) and executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, an annealing process that individually controls the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution of the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. The optimization process includes: extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

14. A processing program including instructions stored in a storage medium (10) and executed by a processor (12) for controlling quantum annealing and quantum gates that process quantum bits corresponding to binary variables to solve combinatorial optimization problems of the binary variables, a process of individually controlling the contribution of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component orthogonal to the cost function, and an orthogonal magnetic field function that defines a magnetic field component orthogonal to the cost function and the transverse magnetic field function over time is defined as an annealing process; an optimization process for sequentially determining, for each quantum bit corresponding to the binary variable constituting an optimal solution to the combinatorial optimization problem, an optimal value of the contribution of the orthogonal magnetic field function based on a final state in the annealing process; The quantum bit for which the evaluation index that evaluates the final state in the annealing process in which the strength parameter that gives the maximum value of the orthogonal magnetic field function for the quantum bit before optimization is varied is defined as an optimal quantum bit. extracting the optimal quantum bit based on the evaluation index, which is phase information of a control quantum bit whose final states before and after the fluctuation of the intensity parameter are phase kicked back by a quantum gate circuit (QG); determining the intensity parameter that is the optimum value of the extracted optimum quantum bit in accordance with the evaluation index; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

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