Processing system, processing device, processing method, processing program

Abstract

To balance shortened processing time with optimal high-precision output.SOLUTION: Optimization processing for sequentially determining an optimal value of a contribution of an orthogonal magnetic field function for each qubit corresponding to a binary variable constituting an optimal solution on the basis of a final state in annealing processing includes: extracting an optimal qubit on the basis of phase information of a control qubit in which a variation of an evaluation index caused by a variation in a field-strength parameter is phase-kicked back by a quantum gate circuit, wherein a qubit with an optimal evaluation index for the final state in which the field-strength parameter that provides a maximum value of the orthogonal magnetic field function for the qubit before optimization is varied is defined as the optimal qubit; determining the field-strength parameter being an optimal value of the extracted optimal qubit in accordance with the phase information of the control qubit in which the variation is phase-kicked back by the quantum gate circuit; and outputting the optimal solution by mapping a set of the field-strength parameter determined for all qubits.SELECTED DRAWING: Figure 12

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 optimal solutions with high precision in the short processing times expected of quantum computing systems.

[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 characters in parentheses in this section indicate the corresponding relationship 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 a combinatorial optimization problem of a binary variable by controlling quantum annealing and quantum gates for processing quantum bits corresponding to the binary variable, the processing system comprising: a processor (12); The processor An annealing process that individually controls the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 a binary variable constituting an optimal solution of a combinatorial optimization problem based on a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of determined strength parameters for all quantum bits.

[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); A process of individually controlling the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function defining a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function defining a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; an optimization process is a process of sequentially determining an 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 a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of strength parameters determined for all quantum bits.

[0009] A third aspect of the present disclosure is a processing method executed by a processor (12) to control quantum annealing and quantum gates for processing 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 each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 a 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 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of determined strength parameters for all quantum bits.

[0010] A fourth aspect of the present disclosure is A processing method executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, comprising: A process of individually controlling the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function defining a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function defining a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; an optimization process is a process of sequentially determining an 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 a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of determined strength parameters for all quantum bits.

[0011] A fifth aspect of the present disclosure is a method for manufacturing a semiconductor device comprising: A processing program including instructions stored in a storage medium (10) and executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, An annealing process that individually controls the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 a 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 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of determined strength parameters for all quantum bits.

[0012] A sixth aspect of the present disclosure is a method for manufacturing a semiconductor device comprising: A processing program including instructions stored in a storage medium (10) and executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, A process of individually controlling the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function defining a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function defining a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; an optimization process is a process of sequentially determining an 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 a 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 performs the optimization process as follows: Extracting an optimal quantum bit based on phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of strength parameters determined for all of the quantum bits.

[0013] In the optimization process of the 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 in which the contribution of each of the cost function, the transverse magnetic field function, and the orthogonal magnetic field function is individually time-controlled.Therefore, according to the optimization process of the first to sixth aspects, the optimal quantum bit that provides the optimal evaluation index for the final state of the annealing process in which the intensity parameter that provides the maximum value of the orthogonal magnetic field function is varied with respect to the quantum bit before optimization is extracted based on the phase information of the control quantum bit in which the fluctuation amount of the evaluation index caused by the fluctuation of the intensity parameter is phase-kicked back by the quantum gate circuit.

[0014] According to this, even if the annealing time in the annealing process is shortened, the strength parameters that are the optimal values ​​of the extracted optimal quantum bits are sequentially determined according to the phase information of the control quantum bit whose phase is kicked back by the quantum gate circuit, and the fluctuation amount of the evaluation index is determined. Therefore, the optimal solution can be output with high accuracy by mapping the set of strength parameters determined for all quantum bits. This makes it possible to achieve both shortening the annealing time and outputting the optimal solution with high accuracy. [Brief description of the drawings]

[0015] [Figure 1] 1 is a block diagram showing an overall configuration of a processing system according to an embodiment. [Diagram 2] 1 is a block diagram showing a functional configuration of a processing system according to an embodiment. [Diagram 3] FIG. 2 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. [Diagram 5] 1 is a table for explaining an optimization process according to an embodiment. [Figure 6] FIG. 2 is a block diagram showing a quantum gate circuit according to an embodiment. [Figure 7]1 is a table for explaining an optimization process according to an embodiment. [Figure 8] 1 is a table for explaining an optimization process according to an embodiment. [Figure 9] 1 is a table for explaining an optimization process according to an embodiment. [Figure 10] 1 is a graph for explaining an optimization process according to an embodiment; [Figure 11] 1 is a graph for explaining an optimization process according to an embodiment; [Figure 12] 1 is a sequence chart showing a processing method according to an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] Hereinafter, one 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 of the binary variables. The processing system 1 includes, as a plurality of dedicated computers, an annealing type quantum computer that performs operations using quantum bits by a quantum annealing method, and a gate type quantum computer that performs operations using quantum bits by a quantum gate method. The processing system 1 may include, as a dedicated computer, a classical computer that performs operations using classical bits in combination with each of the annealing type and gate type quantum computers. At least one of the annealing type and gate type quantum computers that are essential components of the processing system 1 in this way may be, for example, a NISQ (noisy intermediate scale quantum) device or the like.

[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 memories, magnetic media, and optical media, that non-temporarily store computer-readable programs and data. 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.

[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 a processing program stored in each of the multiple memories 10 in order to solve a combinatorial optimization problem of the binary variables. In this way, the processor 12 constructs multiple functional blocks for controlling the quantum annealing and quantum gates to solve the combinatorial optimization problem. 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 a set of a processor 12 and a memory 10 in an annealing type quantum computer, or by a combination of the set and a set of a processor 12 and a memory 10 in a classical computer. The annealing block 100 executes an annealing process of the quantum annealing method. Specifically, the annealing block 100 of this embodiment executes an annealing process of the quantum annealing method using a cost function H zand the transverse magnetic field function H x and the orthogonal magnetic field function H y The annealing process is performed so that the contributions of the two are individually controlled over time. Hereinafter, the annealing process by the annealing block 100 will be 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 maps binary variables of a combinatorial optimization problem to quantum bits. The QA process uses a cost function H z and the transverse magnetic field function H x and the orthogonal magnetic field function H y In the formula 1, t is the elapsed time in the QA process, and in this embodiment, t is defined as the time until the annealing time T described later, and varies within the range of 0 to T, as shown in Figs.

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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 the formula 2 as a function that converges by optimization in a combinatorial optimization problem. In the formula 2, σ i z ,σ j z is the Pauli matrix of the z-direction components corresponding to the qubit pair with indexes 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. Here, 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 a combinatorial optimization problem using N The combination of these is 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 3 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 in the z direction H z The quantum fluctuation function σ represents the uniform magnetic field component in the x direction perpendicular to the x direction. i x is the Pauli matrix with x-direction components 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 3 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 defined as an optimal parameter such as 0.43 that has been verified in advance by a demonstration experiment.

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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 in the z direction H z and the transverse magnetic field function H in the x direction x The non-uniform magnetic field component in the y direction perpendicular to both the y direction and the y direction is expressed by the following equation (9). 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 In order to individually control the time, the time function is expressed by the formula 10 as shown in FIG. 3. In the formula 10, t is the elapsed time as in the formula 1. In the formula 10, T is the annealing time as in the formula 6. In the formula 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, is set by the optimization block 120 as described below.

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[0028] The QA process is based on time control by quantum annealing of the total Hamiltonian H assumed in this way, and the final state ψ _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 Schrödinger equation expressed by Equation 11. _f will be obtained.

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[0029] Here, as shown in Figs. 3 and 4, the time control in the QA process is a cost function H z The coefficient function A(t), which can be said to be the contribution of the intensity parameter a, is gradually increased from 0 to the final value as time t elapses. In particular, the time control in this embodiment increases the output value of the coefficient function A(t) in proportion 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 process increases the transverse magnetic field function H x The coefficient function B(t), which can be said to be the contribution of the strength parameter b, 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 strength parameter b, which is the initial value, in proportion to the elapsed time t. Furthermore, the time control in the QA process reduces the output value of the coefficient function B(t) from the set value of the strength parameter b, which is the initial value, in proportion to the elapsed time t. y The coefficient function C, which can be said to be the contribution of i (t) is increased from 0 to a 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 strength parameter c i The coefficient function C is set so that the amplitude at the midpoint of the elapsed time t isi The output value of (t) is changed in proportion to the square of a sine function.

[0030] The gate block 110 shown in Fig. 2 is realized by a combination of a processor 12 and a memory 10 in a gate-type quantum computer, or by a combination of the combination and a processor 12 and a memory 10 in a classical computer. The gate block 110 constitutes a quantum gate circuit QG of a quantum gate type as shown in Fig. 5. Specifically, the quantum gate circuit QG includes a control quantum bit Q c , analysis qubit Q i , and the reference qubit Q b Here, the control qubit Q c is an ancillary qubit whose input state is initialized to |0>. i The input state is the final analysis state ψ i_f The reference qubit Q is a set of N target qubits that are initialized to b The input state is the reference final state ψ b_f These are the N target qubits that are initialized to . From this, we can see that the qubit Q c ,Q i ,Q b (i.e., the quantum bit Q in the operation step O1 of FIG. 5) c ,Q i ,Q b The direct product state of is expressed by the formula 12. In the formulas 15 to 19 and 21 to 24 explained below, τ is a control variable given as described later.

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[0031] The quantum gate circuit QG is a quantum gate circuit that converts the input control quantum bit Q c For the first stage Hadamard gate H p The Hadamard gate H p is the quantum bit Q controlled by the Hadamard matrix of equation 13. cThis is a rotation gate that transforms the state |0> into a superposition state of |1> through the Hadamard transform. c ,Q i ,Q b (i.e., the quantum bit Q in the operation step O2 of FIG. 5) c ,Q i ,Q b The direct product state of is expressed by the following equation 14:

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[0032] The quantum gate circuit QG is a Hadamard transformed control qubit Q c By this, the analysis of the input qubit Q i Analyze unitary gate U i Then, the analytical unitary gate U i is the eigenvalue of the unitary matrix defined in Equation 15, and the control qubit Q c The analytical unitary gate U i So, let's analyze the qubit Q. i The final analytical state ψ i_f Regarding the analytical evaluation index F i is calculated. Thus, the quantum bit Q that has undergone the phase kickback c ,Q i ,Q b (i.e., the quantum bit Q in the operation step O3 of FIG. 5) c ,Q i ,Q b The direct product state of is expressed by the following equation 16:

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[0033] The quantum gate circuit QG is a phase-kicked back control qubit Q c Then, the input reference qubit Q b For the reference unitary gate U b The reference unitary gate U b is the eigenvalue of the unitary matrix defined in Equation 17, and the control quantum bit Q c The reference unitary gate U b Now, the reference qubit Q b The reference final state ψ b_f Regarding the standard evaluation index F b is calculated. Thus, the quantum bit Q c ,Q i ,Q b (i.e., the quantum bit Q in the operation step O4 of FIG. 5) c ,Q i ,Q b The direct product state of the quantum gate circuit QG is expressed by the following equation 18. i ,U b The analytical evaluation index F, which constitutes the evaluation index F as described below, is generated by the action of i and standard evaluation index F b The amount of fluctuation δF between the control qubit Q c It can also be said that the phase is kicked back against the

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[0034] The quantum gate circuit QG is a control quantum bit Q with a phase kickback of the fluctuation amount δF of the evaluation index F. c For the phase shift gate T sThe phase shift gate T s The quantum gate circuit QG is controlled by the shift matrix of Equation 21 according to the control variable ε of the input, as described later. c This is a rotation gate that shifts the phase of the quantum bit Q c ,Q i ,Q b (i.e., the quantum bit Q in the operation step O5 of FIG. 5) c ,Q i ,Q b The direct product state of is expressed by the following equation 22:

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[0035] The quantum gate circuit QG is a phase-shifted control qubit Q c For the latter stage Hadamard gate H l The latter stage Hadamard gate H l is a quantum bit Q controlled by a Hadamard matrix according to equation 13. c This is a rotation gate that performs the Hadamard transform again. The quantum bit Q c ,Q i ,Q b (i.e., the quantum bit Q in the operation step O6 of FIG. 5) c ,Q i ,Q b The direct product state of is expressed by the following equation 23.

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[0036] The quantum gate circuit QG is a Hadamard-transformed control qubit Q c The measurement data output at this time is the control quantum bit Q cIn order to extract information on the phase change according to the fluctuation amount ΔF of the evaluation index F as the probability amplitude for the state |0> of i Here, in this embodiment, the probability that the state |0> appears by repeated (for example, 1000 or more) calculations using the quantum gate circuit QG is P i The estimated measurement data of (0,ε) is output for each quantum bit.

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[0037] The optimization block 120 shown in Fig. 2 is realized by a set of the processor 12 and memory 10 in an annealing type quantum computer, a set of the processor 12 and memory 10 in a gate type quantum computer, a set of the processor 12 and memory 10 in a classical computer, or a combination of at least two of these sets. 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 is the final state ψ _f Hereinafter, the combinatorial optimization process by the optimization block 120 is referred to as quantum greedy optimization (QGO) process.

[0038] 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 In both cases, the reference strength parameter c i_b At this time, each reference intensity parameter c i_bIn 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 11, which will be described later, illustrate the case where N=8 (i.e., i=an integer from 1 to 8).

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[0039] The QGO process calculates the corresponding strength parameter c for each qubit with index i before optimization. i As a result, the reference intensity parameter c i_b The fluctuation intensity parameter c is given a small amount of fluctuation Δ. i_f , the reference intensity parameter c i_b This is set separately from the reference strength 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 optimal amount, such as 0.1, verified in advance by a verification experiment.

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[0040] The QGO process uses the strength parameter c i The reference intensity parameter c i_b and the reference strength parameter c i_b The fluctuation intensity parameter c i_f Based on this, the sensitivity analysis subroutine is repeatedly executed. In the sensitivity analysis subroutine of the QGO process, the strength parameter c i_b ,c i_f As shown in FIG. 2, each pre-optimized quantum bit is handed over from the optimization block 120 to the QA process in the annealing block 100.

[0041] In response to these deliveries, in the annealing block 100, for each pre-optimization quantum bit, as shown in FIG. 6, the corresponding fluctuation intensity parameter ci_f and the non-corresponding reference intensity parameter c of index i i_b For the entire Hamiltonian H, including H, the QA process is performed using quantum annealing. As a result, the final state ψ of the wave function ψ for the entire Hamiltonian H is _f The final analysis state ψ i_f is obtained individually for each quantum bit before optimization. At the same time, in the annealing block 100, the reference strength parameter c i_b For the entire Hamiltonian H, including H, the QA process is performed using quantum annealing. As a result, the final state ψ of the wave function ψ for the entire Hamiltonian H is _f As the reference final state ψ b_f is obtained in common for all qubits before optimization.

[0042] The final analysis state ψ for each quantum bit before optimization obtained in this way i_f and the reference final state ψ b_f 2, is passed to the gate block 110 in accordance with a command from the optimization block 120 in the sensitivity analysis subroutine as measurement data by the QA process in the annealing block 100. At the same time, in the sensitivity analysis subroutine, the control variable ε, which is set to a value of 0 for all quantum bits before optimization, is passed from the optimization block 120 to the gate block 110.

[0043] In such a sensitivity analysis subroutine, the final analysis state ψ i_f As shown in Figure 6, the evaluation index F that gives an individual evaluation for each quantum bit before optimization is the analytical evaluation index F i Here, the analytical evaluation index F i is the strength parameter c for each quantum bit before optimization i Let c be the reference intensity parameter i_b from the fluctuation intensity parameter c i_f The final analysis state ψ i_fThe energy value of ψ is expressed by the formula 27. In addition, in the sensitivity analysis subroutine, the reference final state ψ b_f As shown in Figure 6, the evaluation index F that gives a common standard evaluation to all quantum bits before optimization is the standard evaluation index F b Here, the standard evaluation index F b is the analytical evaluation index F i The reference final state ψ is expressed by the following equation (28): b_f The energy value is specified as:

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[0044] In response to the above data transfer in the sensitivity analysis subroutine, the gate block 110 calculates the final state ψ i_f , ψ b_f and the control variable ε set to 0 are input to the quantum gate circuit QG. As a result, the probability P i (0,ε), the control qubit Q c Regarding the state |0> of i ,F b The probability P for measuring the magnitude of the phase change according to the amount of fluctuation δF i (0,0) is output for each quantum bit before optimization. The probability P i (0,0) is passed to the optimization block 120 as measurement data by the quantum gate circuit QG in the gate block 110 as shown in FIG.

[0045] In the sensitivity analysis subroutine, the optimization block 120 optimizes the probability P i Of all the pre-optimization qubits to which (0,0) was handed over, the analytical evaluation index F i The optimal qubit Q is shown in Figure 10. o The optimization calculation is performed to extract the evaluation index Fi ,F b The intensity parameter c for the energy value between i The reference intensity parameter c i_b from the fluctuation intensity parameter c i_f The amount of fluctuation δF caused by the change to c Among the phase information of i Based on the magnitude of the phase change measured as (0,0).

[0046] Therefore, the optimization calculation in the sensitivity analysis subroutine is performed according to Equation 29, and the probability P i The optimal qubit Q that minimizes (0,0) o Here, in this embodiment, the optimal quantum bit Q o Since the index of is treated as i after the optimization calculation, the index i before the optimization calculation is formally expressed using k, m in Equation 29. Also, in this embodiment, the probability P i P contains (0,0) i Since (0, ε) is expressed by the above formula 24 using a cosine function, the condition for making the control variable τ sufficiently small as a condition for properly operating the algorithm is given by formula 30. Note that in Figures 6 and 10, the quantum bit with index i=8 is the optimal quantum bit Q o The following shows the cases extracted.

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[0047] In the sensitivity analysis subroutine, the optimization block 120 shown in FIG. 2 optimizes the extracted optimal qubit Q o The analytical final state ψ i_f and the reference final state ψ b_fto the gate block 110. At the same time, the sensitivity analysis subroutine determines the optimal qubit Q o The control variable ε, which is set to a value exceeding 0 in response to the control variable ε, is passed from the optimization block 120 to the gate block 110. Here, particularly in this embodiment, the control variable ε exceeding 0 is set to an optimal value, such as 0.1, that is verified in advance by a demonstration experiment.

[0048] In response to these deliveries, the gate block 110 receives the optimal quantum bit Q o The final state ψ i_f , ψ b_f and a control variable ε that is greater than zero are input to the quantum gate circuit QG. As a result, the probability P i (0,ε), the control qubit Q c Regarding the state |0> of i ,F b The probability P for measuring the direction of the phase change according to the amount of fluctuation δF i (0,0) is the optimal qubit Q o The output probability P i As shown in FIG. 2, (0, ε) is passed to the optimization block 120 as measurement data by the quantum gate circuit QG in the gate block 110.

[0049] In the sensitivity analysis subroutine, the optimization block 120 calculates the probability P i (0,0),P i The optimal qubit Q that is handed over (0, ε) o The optimal value of the strength parameter c i , the optimal strength parameter c i_o In this case, the evaluation index F i ,F b The intensity parameter c for the energy value between i The reference intensity parameter c i_b from the fluctuation intensity parameter c i_f The amount of fluctuation δF caused by the change toc Among the phase information of i (0,0),P i Depending on the direction of the phase change measured as the magnitude relationship between (0, ε), the optimal intensity parameter c i_o Then, the optimal strength parameter c i_o The determination is performed according to numbers 31 and 32, with probability P i (0,0),P i The sign of the difference δP between (0, ε) is the optimal strength parameter c i_o Here, c in number 31 is reflected in 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) that has been verified in advance by a demonstration experiment. o 4 shows an example of the sign of the difference ΔP for the quantum bit with index i=8 extracted in

number

number

[0050] The sensitivity analysis subroutine, via optimization block 120, selects the optimum strength parameter c i_o Each time the sensitivity analysis subroutine is determined, the target to be handed over to the QA process by the annealing block 100 is changed as shown in FIGS. 7 to 9, and the process is repeated. That is, in the second and subsequent sensitivity analysis subroutines, all optimal quantum bits Q optimized by the previous or previous sensitivity subroutines are o For index i, the corresponding reference strength parameter c i_b Instead, the corresponding optimal strength parameter c i_o is delivered. At this time, the final analysis state ψ i_f In the QA process to obtain the unmatched reference strength parameter c i_bwhere the optimal strength parameter c i_o is the corresponding reference intensity parameter c i_b is the optimal strength parameter c i_o At the same time, 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 i_b is the optimal strength parameter c i_o is replaced by

[0051] In this way, in the second and subsequent sensitivity analysis subroutines, the optimal quantum bit Q o Among the remaining quantum bits before optimization, excluding o In the second and subsequent sensitivity analysis subroutines, the extracted optimal quantum bit Q o Regarding the phase change measured by the quantum gate circuit QG of the gate block 110, the optimal intensity parameter c i_o In addition, in FIG. 7, the quantum bit with index i=8 is determined to be the optimal quantum bit Q o After being extracted, the qubit with index i = 6 is selected as the optimal qubit Q o In the first and second sensitivity analysis subroutines, the qubits with indexes i = 8 and 6 are extracted as optimal qubits Q o After being extracted, the qubit with index i = 2 is selected as the optimal qubit Q by the QGO process in the third sensitivity analysis subroutine. o Figure 9 shows the cases where the qubits other than index i=5 are extracted as optimal qubits Q o After being extracted, the qubit with index i=5 is selected as the optimal qubit Q by the QGO process in the eighth sensitivity analysis subroutine. o The following shows the cases extracted.

[0052] In the QGO process, the optimization block 120 repeats the sensitivity analysis subroutine a number of times equal to the number of quantum bits N to find the optimal strength parameter c i_o For all N qubits, the optimal strength parameters c i_o After determining the optimal strength parameters c i_o into a solution of the combinatorial optimization problem using equation 33, and outputs an optimal solution OA for the combinatorial optimization problem. At this time, the QGO process stores the output optimal solution OA in the memory 10. Here, storing may mean that data is retained even when the processing system 1 is turned off, or may mean that data is erased when the processing system 1 is turned off.

number

[0053] The processing method in which the processing system 1 controls quantum annealing having quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables through cooperation of the blocks 100 and 110 described above is executed according to the sequence chart shown in Fig. 12. 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.

[0054] In S10 of the QGO process, the optimization block 120 calculates the strength parameters c i In both cases, 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_fIn S12 of the QGO process, the optimization block 120 repeatedly executes a sensitivity analysis subroutine including S120 to S127.

[0055] Specifically, in S120 of the sensitivity analysis subroutine, the optimization block 120 optimizes the reference strength parameter c i_b and the fluctuation intensity parameter c i_f to the annealing block 100. In S20 of the QA process that starts in response to this delivery, the annealing block 100 generates an individual analysis final state ψ i_f At the same time, in S20, the annealing block 100 obtains a reference final state ψ b_f The final analysis state ψ i_f This is obtained by quantum annealing separate from the above.

[0056] In S121 of the sensitivity analysis subroutine, the optimization block 120 calculates the analysis final state ψ for each quantum bit before optimization obtained in S20. i_f and the reference final state ψ b_f The gate block 110 then instructs the annealing block 100 to deliver the control variable ε set to 0 in S121 to the gate block 110. In response to these deliveries, in S30, the gate block 110 delivers the individual probability P i (0,0) is output from the quantum gate circuit QG.

[0057] In S122 of the sensitivity analysis subroutine, the optimization block 120 determines the probability P i Based on the magnitude of the phase change measured as (0,0), the optimal qubit Q o That is, the optimal qubit Q in S122 is extracted. o The extraction of the evaluation index F i ,F b The control qubit Q is a quantum gate circuit QG that kicks back the phase of the control qubit Q cThis is based on the phase information of

[0058] In S123 of the sensitivity analysis subroutine, the optimization block 120 calculates the analysis final state ψ for each quantum bit before optimization obtained in S20. i_f and the reference final state ψ b_f Among them, the optimal qubit Q o The analytical final state ψ i_f and the reference final state ψ b_f In response to these transfers, in S40, the gate block 110 instructs the annealing block 100 to transfer the optimal quantum bit Q extracted in S122. o With respect to probability P i (0,ε) is output from the quantum gate circuit QG.

[0059] In S124 of the sensitivity analysis subroutine, the optimization block 120 calculates the probability P i (0,0),P i Depending on the direction of the phase change measured as the magnitude relationship between (0, ε), the optimal quantum bit Q o The optimal strength parameter c i_o In S125 of the sensitivity analysis subroutine, the optimization block 120 determines the optimal strength parameters c i_o It is determined whether the determination of the above has been completed.

[0060] If a negative determination is made in S125, S126 is executed instead of S120 so that the sensitivity analysis subroutine is repeated. In S126, 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 than the reference strength parameter c i_b and the fluctuation intensity parameter c i_fIn accordance with S120, the annealing block 100 is handed over to the annealing block 100. In response to this handover, S20, S121, S30, S122, S123, S40, S124, and S125 are annealed by the optimal quantum bit Q o The quantum bits other than are treated as the remaining quantum bits before optimization.

[0061] On the other hand, if a positive determination is made in S125, the sensitivity analysis subroutine ends and the sequence chart proceeds to S127. In S127 of the QGO process, the optimization block 120 optimizes the optimal strength parameters c i_o Then, in S127, the optimization block 120 stores the output optimal solution OA in the memory 10. This completes one execution of the sequence chart.

[0062] (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 Based on this, for each quantum bit corresponding to a binary variable, an orthogonal magnetic field function H y Therefore, according to the QGO process of this embodiment, the orthogonal magnetic field function H y The strength parameter c that gives the maximum value of i The final state ψ in the QA process with _f For the evaluation index F that gives the evaluation, the optimal quantum bit Q o is the intensity parameter c i The fluctuation amount δF of the evaluation index F caused by the fluctuation of c The phase information is extracted based on the phase information of the

[0063] According to this, even if the annealing time in the QA process is shortened, the extracted optimal qubit Q oThe optimal value of the strength parameter c i The fluctuation amount δF of the evaluation index F is the control quantum bit Q c By sequentially determining the phase information of the quantum bit, the solution space of the combinatorial optimization problem can be narrowed down. Therefore, the strength parameters c 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 annealing time and a high-accuracy output of the optimal solution OA. Note that a high-accuracy optimal solution OA, in other words, 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 lower the value of .

[0064] (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 not departing from the gist of the present disclosure.

[0065] In the optimization block 120 that executes S122 to S124 of the modified example, the optimal quantum bit 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 each o In the annealing block 100 that executes the modified S20, the Pauli matrix σ of the y-direction component of the formula 9 is determined by a time-controlled unitary transformation. i y 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 deriving a new total Hamiltonian H, thereby realizing the time control.

[0066] In addition to the above, the above-described embodiments and modifications may be implemented using a computer device or a semiconductor device (e.g., a semiconductor chip, etc.) having a processor 12 that executes at least the QGO processing of the processing system 1 and a memory 10.

[0067] (Additional remarks) This specification discloses the following technical ideas and combinations thereof.

[0068] (Technical thought 1) A processing system for solving a combinatorial optimization problem of a binary variable by controlling quantum annealing and quantum gates for processing quantum bits corresponding to the binary variable, the processing system comprising: a processor (12); The processor An annealing process that individually controls the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 a binary variable constituting an optimal solution of a combinatorial optimization problem based on a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of determined strength parameters for all of the quantum bits.

[0069] (Technical thought 2) The optimization process is The processing system according to Technical Idea 1 includes extracting an optimal quantum bit based on the magnitude of phase change from the phase information of a control quantum bit whose fluctuation amount is kicked back in phase by a quantum gate circuit.

[0070] (Technical Thought 3) The optimization process is The processing system according to Technical Idea 1 or 2, which includes determining an intensity parameter that is an optimal value for an optimal quantum bit according to a direction of phase change from among phase information of a control quantum bit whose fluctuation amount is kicked back in phase by a quantum gate circuit.

[0071] (Technical Thought 4) The optimization process is The processing system according to any one of Technical Ideas 1 to 3, comprising extracting an optimal quantum bit that provides an optimal energy value in the final state as an evaluation index.

[0072] (Technical Thought 5) The optimization process is The processing system according to any one of Technical Ideas 1 to 4, further comprising extracting an optimal quantum bit that provides an optimal evaluation index when an intensity parameter initialized to a value of 0 is varied for a quantum bit before optimization.

[0073] (Technical Thought 6) The optimization process is The initialized intensity parameters are set as reference intensity parameters. If the intensity parameter fluctuated from the reference intensity parameter is defined as a fluctuating intensity parameter, The processing system according to technical idea 5 includes extracting an optimal quantum bit based on phase information in which the amount of fluctuation caused by fluctuations in the reference intensity parameter and the fluctuation intensity parameter is phase kicked back by a quantum gate circuit.

[0074] (Technical Thought 7) A storage medium (10), The optimization process is The processing system according to any one of Technical Ideas 1 to 6, further comprising storing the optimal solution in a storage medium.

[0075] (Technical Thought 8) The annealing process is The processing system according to any one of technical ideas 1 to 7, comprising obtaining the final state of the wave function for the total Hamiltonian of the cost function, transverse magnetic field function, and orthogonal magnetic field function based on time control of the total Hamiltonian by quantum annealing.

[0076] (Technical Thought 9) The annealing process is Increasing the contribution of the cost function over time from 0 to the closing price; 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 a value of 0 to a maximum value over time, and then decreasing the contribution to a value of 0 over time.

[0077] (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 each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function defining a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function defining a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; an optimization process is a process of sequentially determining an 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 a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of determined strength parameters for all quantum bits.

[0078] (Technical Thought 11) A processing method executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, comprising: An annealing process that individually controls the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 a 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 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of strength parameters determined for all of the quantum bits.

[0079] (Technical Thought 12) A processing method executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, comprising: A process of individually controlling the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function defining a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function defining a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; an optimization process is a process of sequentially determining an 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 a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of strength parameters determined for all of the quantum bits.

[0080] (Technical Thought 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 for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, An annealing process that individually controls the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 a 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 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of strength parameters determined for all of the quantum bits.

[0081] (Technical Thought 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 for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, A process of individually controlling the contribution of each of a cost function to be optimized in a combinatorial optimization problem, a transverse magnetic field function defining a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function defining a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; an optimization process is a process of sequentially determining an 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 a 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 phase information of a control quantum bit in which a fluctuation amount of an evaluation index caused by a fluctuation of an intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining an intensity parameter that is an optimal value of the extracted optimal quantum bit in accordance with phase information of a control quantum bit whose fluctuation amount has been phase-kicked back by a quantum gate circuit; and outputting an optimal solution by mapping the set of intensity parameters determined for all quantum bits. [Explanation of symbols]

[0082] 1: Processing system, 10: Memory, 12: Processor, QG: Quantum gate circuit

Claims

1. A processing system for solving a combinatorial optimization problem of a binary variable by controlling quantum annealing and quantum gates for processing quantum bits corresponding to the binary variable, the processing system comprising: a processor (12); The processor, An annealing process that individually controls the contribution of each of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular to the cost function and the transverse magnetic field function; An optimization process is configured to sequentially determine 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 phase information of a control quantum bit whose phase is kicked back by a quantum gate circuit (QG) according to a fluctuation amount of the evaluation index caused by a fluctuation of the intensity parameter; determining the intensity parameter that is the optimal value of the extracted optimal quantum bit in accordance with phase information of the control quantum bit whose fluctuation amount has been phase kicked back by the quantum gate circuit; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

2. The optimization process includes: The processing system according to claim 1 , further comprising: extracting the optimum quantum bit based on a magnitude of a phase change from the phase information of the control quantum bit whose fluctuation amount has been kicked back in phase by the quantum gate circuit.

3. The optimization process includes:

2. The processing system according to claim 1, further comprising: determining the intensity parameter that becomes the optimal value of the optimal quantum bit according to a direction of phase change in phase information of the control quantum bit whose fluctuation amount is kicked back in phase by the quantum gate circuit.

4. The optimization process includes:

4. The processing system according to claim 1, further comprising: extracting the optimum quantum bit for which an energy value of the final state is optimum as the evaluation index.

5. The optimization process includes: The processing system according to any one of claims 1 to 3, 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.

6. The optimization process includes: The initialized intensity parameters are set as reference intensity parameters, If the intensity parameter fluctuated from the reference intensity parameter is a fluctuating intensity parameter, The processing system according to claim 5 , further comprising: extracting the optimum quantum bit based on the phase information obtained by phase kicking back the amount of fluctuation caused by fluctuations in the reference intensity parameter and the fluctuation intensity parameter by the quantum gate circuit.

7. A storage medium (10), The optimization process includes: The processing system according to any one of claims 1 to 3, 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 zero value to a final value; Decreasing the contribution of the transverse magnetic field function from an initial value to a value of 0 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 having a processor (12), A process of individually controlling the contribution of each of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; 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 processor, extracting the optimal quantum bit based on phase information of a control quantum bit whose phase is kicked back by a quantum gate circuit (QG) according to a fluctuation amount of the evaluation index caused by a fluctuation of the intensity parameter; determining the intensity parameter that is the optimal value of the extracted optimal quantum bit in accordance with phase information of the control quantum bit whose fluctuation amount has been phase kicked back by the quantum gate circuit; and outputting the optimal solution by mapping the set of strength parameters determined for all of the quantum bits.

11. A processing method executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, comprising: An annealing process that individually controls the contribution of each of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular 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 of the quantum bits corresponding to the binary variables 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 phase information of a control quantum bit whose phase is kicked back by a quantum gate circuit (QG) according to a fluctuation amount of the evaluation index caused by a fluctuation of the intensity parameter; determining the intensity parameter that is the optimal value of the extracted optimal quantum bit in accordance with phase information of the control quantum bit whose fluctuation amount has been phase kicked back by the quantum gate circuit; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

12. A processing method executed by a processor (12) for controlling quantum annealing and quantum gates for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, comprising: A process of individually controlling the contribution of each of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; 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 phase information of a control quantum bit whose phase is kicked back by a quantum gate circuit (QG) according to a fluctuation amount of the evaluation index caused by a fluctuation of the intensity parameter; determining the intensity parameter that is the optimal value of the extracted optimal quantum bit in accordance with phase information of the control quantum bit whose fluctuation amount has been phase kicked back by the quantum gate circuit; 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 for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, the processing program comprising: An annealing process that individually controls the contribution of each of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular to the cost function and the transverse magnetic field function; an optimization process for sequentially determining an optimal value of the contribution degree of the orthogonal magnetic field function for each of the quantum bits corresponding to the binary variables 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 phase information of a control quantum bit in which a fluctuation amount of the evaluation index caused by a fluctuation of the intensity parameter is kicked back in phase by a quantum gate circuit (QG); determining the intensity parameter that is the optimal value of the extracted optimal quantum bit in accordance with phase information of the control quantum bit whose fluctuation amount has been phase kicked back by the quantum gate circuit; and outputting the optimal solution by mapping the set of strength 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 for processing quantum bits corresponding to binary variables to solve a combinatorial optimization problem of the binary variables, the processing program comprising: A process of individually controlling the contribution of each of a cost function to be optimized in the combinatorial optimization problem, a transverse magnetic field function that defines a magnetic field component perpendicular to the cost function, and an orthogonal magnetic field function that defines a magnetic field component perpendicular to the cost function and the transverse magnetic field function, is defined as an annealing process; 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. extracting the optimal quantum bit based on phase information of a control quantum bit whose phase is kicked back by a quantum gate circuit (QG) according to a fluctuation amount of the evaluation index caused by a fluctuation of the intensity parameter; determining the intensity parameter that is the optimal value of the extracted optimal quantum bit in accordance with phase information of the control quantum bit whose fluctuation amount has been phase kicked back by the quantum gate circuit; and outputting the optimal solution by mapping the set of intensity parameters determined for all of the quantum bits.

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