Parameter adjustment device, quantum annealing system, parameter adjustment method, and recording medium

Abstract

This parameter adjustment device comprises a determination means for, for a quantum annealing machine having a structure indicated by an LHZ model, performing at least one of: setting a quantum annealing time to a value that is one time the product of Dirac's constant and the reciprocal of a coefficient value of a term of a longitudinal magnetic field of the Hamiltonian of a model embedded in the LHZ model; and setting a four-body interaction coefficient value to a value the magnitude of which is at least five times the coefficient value of the term of the longitudinal magnetic field of the Hamiltonian of the model embedded in the LHZ model.

Description

Parameter adjustment device, quantum annealing system, parameter adjustment method, and recording medium

[0001] The present invention relates to a parameter adjustment device, a quantum annealing system, a parameter adjustment method, and a recording medium.

[0002] The LHZ (Lechner-Hauke-Zoller) method is sometimes used for quantum annealing (see, for example, Patent Document 1). While it is difficult to create a quantum annealing machine having a structure represented by a fully connected graph, the LHZ method makes it possible to solve combinatorial optimization problems that can be expressed by a fully connected graph using a quantum annealing machine having a structure represented by a graph that is not fully connected. In particular, the LHZ method embeds a combinatorial optimization problem that can be expressed by a fully connected graph in a quantum annealing machine having a structure represented by a graph with asymmetricity, and performs quantum annealing.

[0003] International Publication No. 2021 / 044516

[0004] When solving a combinatorial optimization problem with multiple optimal solutions using quantum annealing with the LHZ method, it is conceivable that the probability of obtaining each optimal solution will differ. On the other hand, there may be cases where it is preferable to obtain multiple optimal solutions (multiple optimal solutions), such as when it is desired to obtain all optimal solutions for a combinatorial optimization problem with multiple optimal solutions.

[0005] An example of an object of the present invention is to provide a parameter adjustment device, a quantum annealing system, a parameter adjustment method, and a recording medium that can solve the above-mentioned problems.

[0006] According to a first aspect of the present disclosure, a parameter adjustment device includes a determination means for performing at least one of the following: determining a quantum annealing time for a quantum annealing machine having a structure represented by an LHZ model to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant; and determining a four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0007] According to a second aspect of the present disclosure, a parameter adjustment device includes a determination means for determining, for a quantum annealing machine having a structure represented by an LHZ model, a quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant, and determining the magnitude of the four-body interaction coefficient value to be a value between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0008] According to a third aspect of the present disclosure, a quantum annealing system includes a quantum annealing machine having a structure represented by an LHZ model, and a parameter adjustment device, wherein the parameter adjustment device includes determination means for performing at least one of the following: determining a quantum annealing time for the quantum annealing machine to a value that is 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant; and determining a four-body interaction coefficient value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and the quantum annealing machine repeatedly performs quantum annealing in accordance with the determined quantum annealing time and four-body interaction coefficient value.

[0009] According to a fourth aspect of the present disclosure, a quantum annealing system includes a quantum annealing machine having a structure represented by an LHZ model, and a parameter adjustment device, wherein the parameter adjustment device includes determination means for determining a quantum annealing time for the quantum annealing machine to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, and the quantum annealing machine repeatedly performs quantum annealing in accordance with the determined quantum annealing time and four-body interaction coefficient value.

[0010] According to a fifth aspect of the present disclosure, a parameter adjustment method includes a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model, performing at least one of determining a quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to be 5 times or more the magnitude of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0011] According to a sixth aspect of the present disclosure, a parameter adjustment method includes a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model, determining a quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0012] According to a seventh aspect of the present disclosure, a recording medium is a recording medium having recorded thereon a program that causes a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model to perform at least one of the following: determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant; and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0013] According to an eighth aspect of the present disclosure, a recording medium is a recording medium having recorded thereon a program that causes a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model to determine the quantum annealing time to be a value that is between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and to determine the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0014] According to the present disclosure, when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved by quantum annealing using the LHZ method, it is expected that multiple optimal solutions can be obtained.

[0015] FIG. 1 is a diagram illustrating an example of the configuration of a quantum annealing system according to at least one embodiment; FIG. 2 is a diagram illustrating a first example of embedding a combinatorial optimization problem into a quantum annealing machine according to at least one embodiment; FIG. 3 is a diagram illustrating a second example of embedding a combinatorial optimization problem into a quantum annealing machine according to at least one embodiment; FIG. 4 is a diagram illustrating a first example of a relationship between quantum annealing time and a success rate according to at least one embodiment; FIG. 5 is a diagram illustrating a fifth example of a relationship between quantum annealing time and a success rate according to at least one embodiment; FIG. 6 is a diagram illustrating a sixth example of a relationship between quantum annealing time and a success rate according to at least one embodiment; FIG. 7 is a diagram illustrating a first example of a relationship between quantum annealing time and Number to Reject Fair Sampling according to at least one embodiment; FIG. 8 is a diagram illustrating a second example of a relationship between quantum annealing time and Number to Reject Fair Sampling according to at least one embodiment; FIG. 9 is a diagram illustrating a third example of a relationship between quantum annealing time and Number to Reject Fair Sampling according to at least one embodiment; 1 is a diagram showing a first example of a relationship between quantum annealing time and TTAS according to at least one embodiment; FIG. 2 is a diagram showing a second example of a relationship between quantum annealing time and TTAS according to at least one embodiment; FIG. 3 is a diagram showing a third example of a relationship between quantum annealing time and TTAS according to at least one embodiment; FIG. 4 is a diagram showing a fourth example of a relationship between quantum annealing time and TTAS according to at least one embodiment; and FIG. 5 is a diagram showing a first example of a relationship between the magnitude of a four-body bond strength coefficient and TTAS according to at least one embodiment.FIG. 1 is a diagram showing a second example of a relationship between the magnitude of a four-body bond strength coefficient and TTAS according to at least one embodiment. FIG. 2 is a diagram showing a third example of a relationship between the magnitude of a four-body bond strength coefficient and TTAS according to at least one embodiment. FIG. 3 is a diagram showing a fourth example of a relationship between the magnitude of a four-body bond strength coefficient and TTAS according to at least one embodiment. FIG. 4 is a diagram showing a first example of a relationship between the magnitude of a four-body bond strength coefficient and the minimum value of TTAS according to at least one embodiment. FIG. 5 is a diagram showing a second example of a relationship between the magnitude of a four-body bond strength coefficient and the minimum value of TTAS according to at least one embodiment. FIG. 6 is a diagram showing a third example of a relationship between the magnitude of a four-body bond strength coefficient and the minimum value of TTAS according to at least one embodiment. FIG. 7 is a diagram showing a fourth example of a relationship between the magnitude of a four-body bond strength coefficient and the minimum value of TTAS according to at least one embodiment. FIG. 8 is a diagram showing an example of a processing procedure performed by a quantum annealing system according to at least one embodiment. FIG. 9 is a diagram showing an example of a configuration of a parameter adjustment device according to at least one embodiment. FIG. 10 is a diagram showing an example of a configuration of a parameter adjustment device according to at least one embodiment. FIG. 11 is a diagram showing an example of a configuration of a quantum annealing system according to at least one embodiment. FIG. 12 is a diagram showing an example of a processing procedure in a parameter adjustment method according to at least one embodiment. 1 is a diagram illustrating an example of a processing procedure in a parameter adjustment method according to at least one embodiment.

[0016] Hereinafter, embodiments of the present invention will be described, but the following embodiments do not limit the invention according to the claims. Furthermore, not all of the combinations of features described in the embodiments are necessarily essential to the solution of the invention. Furthermore, circumflexes may be expressed by adding a "^" after a letter. For example, an h with a circumflex attached will also be written as h^. Furthermore, a dagger symbol may be expressed as " ＋ " (superscript +)

[0017] <First Embodiment> Fig. 1 is a diagram showing an example of the configuration of a quantum annealing system according to at least one embodiment. In the configuration shown in Fig. 1, the quantum annealing system 1 includes a parameter adjustment device 100, a control device 200, and a quantum annealing machine 300. The parameter adjustment device 100 includes a parameter value determination unit 110 and a parameter value output unit 120. The parameter value determination unit 110 includes a quantum annealing time determination unit 111 and a four-body interaction determination unit 112. The quantum annealing machine 300 includes a quantum bit device 310 and a four-body coupler 320.

[0018] The quantum annealing machine 300 is a quantum annealing machine based on the LHZ (Lechner-Hauke-Zoller) model. The LHZ model here is a model that shows the structure (graph structure) of a quantum annealing machine into which a combinatorial optimization problem can be embedded using the LHZ method. Embedding a combinatorial optimization problem in a quantum annealing machine here means associating a logical model with a physical model to be input to the quantum annealing machine so that a solution to the combinatorial optimization problem can be obtained from the values ​​of the quantum bits after quantum annealing is performed. The logical model is a model that represents the combinatorial optimization problem. The physical model is a model that shows the structure of the quantum annealing machine.

[0019] Embedding a combinatorial optimization problem in a quantum annealing machine is also referred to as embedding a logical model in a physical model. In the LHZ model, a quantum annealing machine is configured using a combination of a qubit device and a four-body coupler.

[0020] The quantum bit device 310 is an element for expressing the value of a quantum bit. The quantum bit device included in the quantum annealing machine 300 is not limited to a specific type. For example, the quantum bit device 310 may be configured using a Kerr nonlinear parametric oscillator (Kerr nonlinear parametric oscillator), but is not limited to this. The four-body coupler 320 couples the four quantum bit devices 310. The coupling of the quantum bit devices is also referred to as the interaction of the quantum bit devices.

[0021] The parameter adjustment device 100 adjusts the quantum annealing parameter values ​​so that when the quantum annealing machine 300 repeatedly performs quantum annealing to search for a solution to a combinatorial optimization problem with multiple optimal solutions, multiple optimal solutions (multiple optimal solutions) can be expected to be obtained.

[0022] The quantum annealing system 1 may be configured to acquire all of the multiple optimal solutions. Alternatively, if there are three or more optimal solutions, the quantum annealing system 1 may be configured to acquire two or more optimal solutions that correspond to a portion of all of the optimal solutions.

[0023] The parameter value determination unit 110 determines parameter values ​​for performing quantum annealing by the quantum annealing machine 300. In particular, the parameter value determination unit 110 determines parameter values ​​for quantum annealing so that multiple optimal solutions are expected to be obtained when the quantum annealing machine 300 repeatedly performs quantum annealing to search for a solution to a combinatorial optimization problem with multiple optimal solutions. The parameter value determination unit 110 corresponds to an example of a determination means.

[0024] The parameter value determination unit 110 may calculate the parameter values ​​and determine the calculated parameter values ​​as the parameter values ​​used by the quantum annealing machine 300 to perform quantum annealing. Alternatively, the parameter value determination unit 110 may store parameter values ​​in advance and determine the stored parameter values ​​as the parameter values ​​for quantum annealing performed by the quantum annealing machine 300. In this case, the parameter value determination unit 110 reading out the pre-stored parameter values ​​may be considered to be determining the parameter values. Alternatively, the parameter value determination unit 110 outputting the parameter values ​​to the outside of the parameter adjustment device 100 via the parameter value output unit 120 may be considered to be determining the parameter values. For example, the parameter adjustment device 100 transmitting the parameter values ​​to the control device 200 may be considered to be determining the parameter values. Alternatively, the parameter adjustment device 100 presenting the parameter values ​​to the user may be considered to be determining the parameter values.

[0025] The quantum annealing time determination unit 111 determines the quantum annealing time for the quantum annealing performed by the quantum annealing machine 300. In particular, when the quantum annealing machine 300 repeatedly performs quantum annealing to search for a solution to a combinatorial optimization problem with multiple optimal solutions, the quantum annealing time determination unit 111 determines the quantum annealing time so that multiple optimal solutions can be expected to be obtained. The quantum annealing time here refers to the execution time of one quantum annealing run. Hereinafter, the quantum annealing time will be referred to as "T ＱＡ " can also be written as ".

[0026] The four-body interaction determination unit 112 determines four-body interaction coefficient values ​​for performing quantum annealing by the quantum annealing machine 300. In particular, the four-body interaction determination unit 112 determines four-body interaction coefficient values ​​that are expected to result in obtaining multiple optimal solutions when the quantum annealing machine 300 repeatedly performs quantum annealing to search for a solution to a combinatorial optimization problem with multiple optimal solutions.

[0027] The four-body interaction coefficient here is a parameter for adjusting the balance between the strength of the influence of the local field set on the quantum bit device and the strength of the influence of the interaction of the quantum bit device due to the four-body coupler. The four-body interaction coefficient value may be reflected in quantum annealing, for example, by multiplying it by the coupling strength set for each four-body coupler depending on the optimization problem to be solved or the embedding method. Hereinafter, the four-body interaction coefficient will also be referred to as "C". The magnitude of the four-body interaction coefficient is expressed as "|C|" (the absolute value of C). The magnitude of the four-body interaction coefficient will also be referred to as the magnitude of the four-body interaction.

[0028] The parameter value output unit 120 outputs the quantum annealing time determined by the quantum annealing time determination unit 111 and the four-body interaction coefficient value determined by the four-body interaction determination unit 112. The parameter value output unit 120 may transmit the quantum annealing time determined by the quantum annealing time determination unit 111 and the four-body interaction coefficient value determined by the four-body interaction determination unit 112 to the control device 200. The transmission of the quantum annealing time and the four-body interaction coefficient value by the parameter value output unit 120 to the control device 200 can be considered as setting the quantum annealing time and the four-body interaction coefficient value.

[0029] Alternatively, the parameter value output unit 120 may present to the user the quantum annealing time determined by the quantum annealing time determination unit 111 and the four-body interaction coefficient values ​​determined by the four-body interaction determination unit 112. In this case, the user may set the presented quantum annealing time and four-body interaction coefficient values ​​in the control device 200. For example, the parameter value output unit 120 may be provided with a display screen and may display the quantum annealing time and the four-body interaction coefficient values.

[0030] The control device 200 controls the quantum annealing machine 300 to perform quantum annealing. In particular, the control device 200 controls the quantum annealing machine 300 in accordance with the quantum annealing time determined by the quantum annealing time determination unit 111 and the four-body interaction coefficient values ​​determined by the four-body interaction determination unit 112.

[0031] Here, the LHZ method deals with combinatorial optimization problems in which the evaluation function is expressed by an equation containing at most two binary variables in one term, such as the Ising model or QUBO (Quadratic Unconstrained Binary Optimization). The Ising model and QUBO are each examples of logical models. The number of binary variables contained in one term is also referred to as the degree of that term. For example, a term containing two binary variables is also referred to as a quadratic term. The evaluation function in the Ising model can be expressed as shown in Equation (1).

[0032]

[0033] The evaluation function in the Ising model is also called a Hamiltonian (energy function), and a solution (value of a binary variable) that minimizes the evaluation function value is searched for. Alternatively, the evaluation function in the Ising model can be expressed so that a solution that maximizes the evaluation function value is searched for.

[0034] σ ｉ is a binary variable that takes the value +1 or -1. ｉ are also called Ising variables. In equation (1), i and j are both indexes that identify binary variables (Ising variables).

[0035] J ｉｊ is the second-order term J ｉｊ σ ｉ σ ｊ is the coefficient in ｉｊ is the Ising variable σ ｉ and σ ｊ It can be considered as a parameter that indicates the strength of the interaction with h. ｉ is the first-order term h ｉ σ ｉ is the coefficient in ｉ can be considered as a parameter that represents a local field. The evaluation function in the Ising model can be considered as a mathematical expression of the Ising model. The evaluation function in the Ising model is also called the Ising model.

[0036] The evaluation function in QUBO can be expressed as in equation (2).

[0037]

[0038] In QUBO, the evaluation function is treated as a cost function, and a solution (value of a binary variable) that minimizes the evaluation function value is searched for. The evaluation function in QUBO is also called a Hamiltonian (energy function). Alternatively, the evaluation function in QUBO can be expressed so that a solution search is performed that maximizes the evaluation function value.

[0039] x ｉ is a binary variable that takes the value 0 or 1. In equation (2), i and j are both indexes that identify the binary variable. Q ｉｉ is the second-order term Q ｉｉ x ｉ x ｉ The Ising model and QUBO can be converted into equivalents. The evaluation function in QUBO can be considered as a mathematical expression of QUBO. The evaluation function in QUBO is also referred to as QUBO.

[0040] Both the Ising model and QUBO can be expressed as a complete graph (fully connected graph) in which binary variables are represented by nodes and connections between the binary variables are represented by edges. However, in a complete graph, the greater the number of nodes, the greater the number of edges connected to one node. In particular, when a complete graph with four or more nodes is expressed on a plane, edge intersections occur. In general, it is difficult to create a quantum annealing machine with a complete graph structure. Therefore, it is difficult to directly implement the Ising model or QUBO in a quantum annealing machine.

[0041] Therefore, in the LHZ method, a combinatorial optimization problem represented by a complete graph is converted so that the product value of two binary variables is represented by the value of one quantum bit, and this is embedded in a quantum annealing machine constructed using a combination of a quantum bit device and a four-body coupler.

[0042] The following describes an example in which the parameter adjustment device 100 determines quantum annealing parameter values ​​when an Ising model is embedded in an LHZ model. However, the parameter adjustment device 100 may also determine quantum annealing parameter values ​​when QUBO is embedded in an LHZ model. As described above, the Ising model and QUBO can be converted into equivalent values, and the processing performed by the parameter adjustment device 100 when an Ising model is embedded in an LHZ model can be replaced with the processing performed when QUBO is embedded in an LHZ model. Here, the Ising model embedded in an LHZ model and the QUBO embedded in an LHZ model are collectively referred to as a model embedded in an LHZ model.

[0043] FIG. 2 is a diagram showing a first example of embedding a combinatorial optimization problem into a quantum annealing machine 300. FIG. 2 corresponds to an example of embedding an Ising model consisting of interactions between four variables into an LHZ model. That is, in the example of FIG. 2, the Ising model embedded in the quantum annealing machine 300 consists of second-order terms and does not include first-order terms. FIG. 2 can also be considered an example of an LHZ model.

[0044] 2, the open circle indicates the qubit device 310. Two numbers, such as "12," shown in the open circle indicate the indexes of two binary variables associated with the qubit device 310. For example, the open circle with "12" indicates the index of the Ising variable σ １ and σ ２ The product of σ １ σ ２ 3 shows a qubit device 310 that represents the value of the term J ｉｊ σ ｉ σ ｊ Coefficient J in ｉｊ is the product σ ｉ σ ｊ is set as the local field for the qubit representing the value of

[0045] An open circle marked with an "F" indicates a qubit device 310 that is set to have a fixed value. In the example of FIG. 2, an open circle marked with an "F" indicates a qubit device 310 that is set to have a value of +1. A closed circle indicates a four-body coupler 320. In the example of FIG. 2, the four-body coupler 320 is set so that the product of the values ​​of the four coupled qubit devices 310 is +1 (even parity).

[0046] 2, the top row (the row of white circles with "14" written on them) in the arrangement of the quantum bit devices 310 is also referred to as the first row. The second row from the top (the row of two white circles with "13" and "24" written on them, respectively) is also referred to as the second row. The third row from the top (the row of three white circles with "12", "23", and "34" written on them, respectively) is also referred to as the third row. The bottom row (both rows with two white circles with "F" written on them) is also referred to as the bottom row.

[0047] FIG. 3 is a diagram showing a second example of embedding a combinatorial optimization problem into a quantum annealing machine 300. FIG. 3 shows an example of embedding an Ising model including interactions of three variables and a local field into an LHZ model. That is, in the example of FIG. 3, the Ising model embedded in the quantum annealing machine 300 includes a second-order term and a first-order term. As in the case of FIG. 2, FIG. 3 can also be considered an example of an LHZ model.

[0048] When the evaluation function in a combinatorial optimization problem includes a first-order term, auxiliary Ising variables are introduced in the embedding into the LHZ model. In the example of Figure 3, the Ising model includes three Ising variables σ １ , σ ２ , σ ３ and the auxiliary Ising variables σ ０ has been introduced.

[0049] 2, in the example of FIG. 3, the open circle indicates the qubit device 310. Two numbers, such as "12," shown in the open circle indicate the indexes of two binary variables associated with the qubit device 310. For example, the open circle with "12" indicates the index of the Ising variable σ １ and σ２ The product of σ １ σ ２ 3 shows a qubit device 310 that represents the value of the quadratic term J ｉｊ σ ｉ σ ｊ Coefficient J in ｉｊ is the product σ ｉ σ ｊ In the example of FIG. 3, the first-order term J ｉ σ ｉ Coefficient J in ｉ is the product σ ０ σ ｉ is set as the local field for the qubit representing the value of

[0050] As in Figure 2, in the example of Figure 3, open circles labeled "F" indicate qubit devices 310 that are set to have a fixed value. In the example of Figure 3, open circles labeled "F" indicate qubit devices 310 that are set to have a value of +1. Filled circles indicate four-body couplers 320. In the example of Figure 3, the four-body couplers 320 are set so that the product of the values ​​of the four coupled qubit devices 310 is +1 (even parity).

[0051] 3, the top row in the arrangement of the quantum bit devices 310 (the row of white circles with "03" written on them) is also referred to as the first row. The second row from the top (the row of two white circles with "02" and "13" written on them) is also referred to as the second row. The third row from the top (the row of three white circles with "01", "12", and "23" written on them) is also referred to as the third row. The bottom row (both rows with two white circles with "F" written on them) is also referred to as the bottom row.

[0052] 2 and 3, the LHZ model has one, two, ... qubit devices arranged in order from the top row, one less qubit device arranged in the bottom row than the row immediately above, and the four nearest qubit devices are coupled by a four-body coupler. All of the qubit devices in the bottom row are set to have fixed values.

[0053] In a quantum annealing machine 300 configured using the LHZ model, one, two, ... quantum bit devices 310 are arranged in order from the top row, and the bottom row has one less quantum bit device 310 than the row immediately above, with the nearest four quantum bit devices 310 being coupled by a four-body coupler 320. The quantum bit devices 310 in the bottom row are all set to have fixed values.

[0054] On the other hand, the number of rows of quantum bit devices in the LHZ model is not limited to a specific number of rows, and can vary depending on the number of binary variables included in the combinatorial optimization problem. In other words, the size of the LHZ model is not limited to a specific size, and can vary depending on the size (scale) of the combinatorial optimization problem. In the quantum annealing machine 300, the number of rows of quantum bit devices 310 is also not limited to a specific number of rows, and can vary depending on the number of binary variables included in the combinatorial optimization problem.

[0055] In a quantum annealing machine having a structure represented by an asymmetric graph, such as the LHZ model, when there are multiple optimal solutions to a combinatorial optimization problem, all optimal solutions may not be obtained with equal probability. Here, the asymmetry of the graph representing the structure of the quantum annealing machine means that the number of interactions that each quantum bit device is a target of varies depending on the quantum bit device. In this case, the asymmetry of the graph can be understood as the number of edges representing interactions that are directly connected to each node representing a quantum bit device being different.

[0056] In the LHZ model, a single qubit device can be the subject of one to four four-body interactions, i.e., a minimum of one four-body coupler is connected to a single qubit device, and a maximum of four four-body couplers can be connected to a single qubit device.

[0057] When there are multiple optimal solutions to a combinatorial optimization problem, not all optimal solutions can be obtained with equal probability is called Unfair Sampling, and obtaining all optimal solutions with equal probability is called Fair Sampling. Furthermore, the greater the variation in the probability of obtaining an optimal solution between optimal solutions, the stronger the tendency toward Unfair Sampling, or the weaker the tendency toward Fair Sampling. The smaller the variation in the probability of obtaining an optimal solution between optimal solutions, the weaker the tendency toward Unfair Sampling, or the stronger the tendency toward Fair Sampling.

[0058] Here, there may be cases where multiple optimal solutions are desired, such as when all optimal solutions of a combinatorial optimization problem are desired. Consider using one of the following two indices, or a combination of these indices, as an index of the ease of obtaining multiple optimal solutions.

[0059] The first of the two indicators is an indicator of the strength of the tendency toward fair sampling. The strength of the tendency toward fair sampling can be interpreted as the likelihood of obtaining different optimal solutions (i.e., multiple optimal solutions) when quantum annealing is repeatedly performed to obtain optimal solutions multiple times.

[0060] Specifically, the first of the two indicators is the Number to Reject Fair Sampling, which is the number of samples required to determine that a sample is not fair, with a certain statistical significance of, for example, 95%, based on Pearson's chi-square test.

[0061] Here, one sampling is one execution of quantum annealing. One execution of quantum annealing obtains one set of values ​​for each quantum bit. One set of values ​​for each quantum bit (one set of combinations of values ​​for each quantum bit for all quantum bits) indicates one candidate for the optimal solution of the combinatorial optimization problem. The term "candidate" here indicates that the obtained combination of values ​​for each quantum bit is not necessarily the optimal solution of the combinatorial optimization problem.

[0062] The larger the value of Number to Reject Fair Sampling, the greater the degree to which optimal solutions appear equally, and the stronger the tendency toward fair sampling.On the other hand, the smaller the value of Number to Reject Fair Sampling, the stronger the tendency toward unfair sampling.

[0063] Number to Reject Fair Sampling is defined as follows: For a combinatorial optimization problem with n optimal solutions, when sampling is performed R times, the optimal solution s ｉ GA O ｉ Here, n is an integer such that n≧2. R is an integer such that R≧1. i takes values ​​of 1, 2, ..., n and indicates an index for identifying the optimal solution. ｉ Yes, O ｉ is an integer greater than or equal to 0. In this case, the expected value E of the number of times that the optimal solution can be obtained among R samplings is expressed as in equation (3).

[0064]

[0065] Chi-square (χ ２ The value of is expressed as in equation (4).

[0066]

[0067] χ shown in equation (4) ２The number to reject fair sampling is the smallest sampling number R for which the value of exceeds the chi-squared value required to reject fair sampling at a 5% significance level with n-1 degrees of freedom. The chi-squared value required to reject fair sampling at a 5% significance level is 3.841 when n = 2, 5.991 when n = 3, and 7.815 when n = 4.

[0068] As the second of the two indices, the inventors of the present application have come up with a new index, which is the total quantum annealing time required to obtain all optimal solutions with a certain probability (for example, 99%). Specifically, the quantum annealing time (the time required to perform one quantum annealing) is defined as T ＱＡ When quantum annealing is repeatedly performed with the above, the probability that all optimal solutions will appear at least once is P Ｒ We consider an index that is the minimum value of the total quantum annealing time that satisfies the above. This index is called Time To All Solutions (TTAS), and TTAS (T ＱＡ , P Ｒ ) where the above "specific probability" is expressed as probability P Ｒ The probability P Ｒ The value of may be preset by the user, for example.

[0069] TTAS (T ＱＡ , P Ｒ ) is the probability that all optimal solutions appear at least once. Ｒ The minimum number of times quantum annealing is performed R ｍｉｎ and the quantum annealing time T ＱＡ The product R ｍｉｎ ×T ＱＡ Using TTAS (T ＱＡ , P Ｒ ) = R ｍｉｎ ×T ＱＡ It is expressed as: TTAS (T ＱＡ , P Ｒ ) is smaller, it is expected that multiple optimal solutions (e.g., all optimal solutions) can be obtained in a shorter time.

[0070] In order to express the total quantum annealing time required to obtain all optimal solutions with a certain probability, we first find a formula for the probability that all optimal solutions will appear at least once. Let the number of optimal solutions in a combinatorial optimization problem be n, and let the optimal solutions be s. ｉ Here, n is an integer of n≧2. i takes values ​​of 1, 2, ..., n and indicates an index for identifying the optimal solution. ｉ The probability that appears at least once is p ｓｉ The probability that the optimal solution does not appear even once when quantum annealing is performed R times is P ０ (R) is shown as formula (5).

[0071]

[0072] Here, R is an integer R≧1. When quantum annealing is performed R times, the optimal solution s ｉ１ The probability that only ｓｉ１ (R) is shown as formula (6).

[0073]

[0074] Here, the appearance of only a specific optimal solution means that the specific optimal solution appears, and no other optimal solutions appear. In this case, the "specific optimal solution" may refer to one optimal solution or multiple optimal solutions. ｉｋ ∈{s １ , s ２ , ..., s ｎ} In equation (6), k=1.

[0075] In addition, in the Σ calculation, index values ​​that are not included in the sum are indicated by using "≠". For example, Σ ｊ＝１　ｊ≠ｉ１ ｎ (p ｓｊ ) from j=1 to j=n ｓｊ When j = i1, p ｓｊ It shows that the sum of Σ ｊ＝１　ｊ≠ｉ１ ｎ (p ｓｊ ) is expressed as in equation (7).

[0076]

[0077] In equation (6), 1-Σ ｊ＝１　ｊ≠ｉ１ ｎ (p ｓｊ ) is the optimal solution s in one run of quantum annealing. ｉ１ In equation (6), this is raised to the power R, and the optimal solution s appears when quantum annealing is performed R times. ｉ１ Find the probability that no optimal solution other than ０ In equation (6), the probability P ０ (R) is the optimal solution s ｉ１ can be thought of as the probability that the

[0078] Among the optimal solutions, the optimal solution s ｉ１ and the optimal solution s ｉ２ The probability that only ｓｉ１，ｓｉ２ (R) is expressed as in equation (8).

[0079]

[0080] In the Σ calculation, j≠i1, i2 indicates that j≠i1 and j≠i2. In this way, when there are multiple index values ​​that are not to be added up in the Σ calculation, these index values ​​are listed and shown.

[0081] In equation (8), 1-Σ ｊ＝１　ｊ≠ｉ１，ｉ２ ｎ (p ｓｊ ) is the optimal solution s in one run of quantum annealing. ｉ１ and the optimal solution s ｉ２ In equation (8), this is raised to the power R, and the optimal solution s appears when quantum annealing is performed R times. ｉ１ and the optimal solution s ｉ２ Find the probability that an optimal solution other than ｓｉ１ (R) and P ｓｉ２ (R) and P ０ (R) is subtracted.

[0082] optimal solution s ｉ１ and the optimal solution s ｉ２If no other optimal solution than s appears, ｉ１ and the optimal solution s ｉ２ The case where both of these appear and the optimal solution s ｉ１ The case where only the optimal solution s appears, ｉ２ This includes cases where only the optimal solution appears, and cases where no optimal solution appears.

[0083] In equation (8), -P ｓｉ１ (R) is the optimal solution s ｉ１ This indicates that the probability of only appearing is subtracted. ｓｉ２ (R) is the optimal solution s ｉ２ This indicates that the probability of only appearing is subtracted. ０ (R) indicates that the probability that no optimal solution occurs is subtracted.

[0084] In the same way as in the case of equation (6) and the case of equation (8), the n optimal solutions s １ , s ２ , ..., s ｎ Among the m optimal solutions s ｉ１ , s ｉ２ , ..., s ｉｍ The probability that only ｓｉ１，・・・，ｓｉｍ (R) is shown as in formula (9).

[0085]

[0086] Σ （ｓｊ１，・・・，ｓｊｋ） (P ｓｊ１，・・・，ｓｊｋ (R)) is the number of m optimal solutions s obtained by performing quantum annealing R times. ｉ１ , s ｉ２ ,...s ｉｍ The k optimal solutions s ｊ１ , s ｊ２ ,...s ｊｋ The probability that only ｓｊ１，・・・，ｓｊｋ (R) is expressed as m optimal solutions s ｉ１ , s ｉ２ ,...s ｉｍ k optimal solutions s ｊ１ , s ｊ２ ,...s ｊｋ This indicates that the sum is calculated for all combinations of selecting

[0087] 1-Σ ｊ＝１　ｊ≠ｉ１，・・・，ｉｍｎ (p ｓｊ ) is the optimal solution s in one run of quantum annealing. ｉ１ , s ｉ２ , ..., s ｉｍ In equation (9), this is raised to the power R, and the optimal solution s appears when quantum annealing is performed R times. ｉ１ , s ｉ２ , ..., s ｉｍ Find the probability that an optimal solution other than ｋ＝１ ｍ－１ Σ （ｓｊ１，・・・，ｓｊｋ） (P ｓｊ１，・・・，ｓｊｋ (R)) and P ０ (R) is subtracted.

[0088] In equation (9), Σ ｋ＝１ ｍ－１ Σ （ｓｊ１，・・・，ｓｊｋ） (P ｓｊ１，・・・，ｓｊｋ (R) is the probability that only k optimal solutions appear among m optimal solutions. ｊ１ ,...s ｊｋ The sum of all combinations of selecting k from k=1 to m-1 is shown. That is, -Σ ｋ＝１ ｍ－１ Σ （ｓｊ１，・・・，ｓｊｋ） (P ｓｊ１，・・・，ｓｊｋ (R)) indicates that the probability that only some of the m optimal solutions will appear is subtracted. ０ (R) indicates that the probability that no optimal solution occurs is subtracted.

[0089] If m = n, then equation (9) can be expressed as the n optimal solutions s １ , ..., s ｎ Therefore, the probability that all of the n optimal solutions s １ , ..., s ｎ The probability that all of ｓ１，・・・，ｓｎ (R) is expressed as in formula (10).

[0090]

[0091] Probability P ｓ１，・・・，ｓｎ Using (R), when quantum annealing is performed R times, the probability that all optimal solutions will appear at least once is PＲ The above is shown by equation (11).

[0092]

[0093] The minimum R that satisfies equation (11) is R ｍｉｎ As mentioned above, TTAS (T ＱＡ , P Ｒ ) = R ｍｉｎ ×T ＱＡ It is required that:

[0094] As mentioned above, T ＱＡ denotes the quantum annealing time (the time required to perform one quantum annealing). Ｒ denotes the specific probability mentioned above. Specifically, P Ｒ is the probability that all optimal solutions appear at least once. ｓ１，・・・，ｓｎ indicates the baseline probability to be compared with.

[0095] The parameter adjustment device 100 may be configured to be able to set, as the solution search mode by quantum annealing, either a mode that equalizes the probability of obtaining each optimal solution or a mode that shortens the time required to obtain multiple optimal solutions, or both of these. The solution search mode by quantum annealing may be set by the user.

[0096] In a mode that attempts to equalize the probability of obtaining each optimal solution, the parameter value determination unit 110 may set parameter values ​​that are predetermined as parameter values ​​that make the value of Number to Reject Fair Sampling relatively large. The parameters here include the four-body interaction coefficient C and the quantum annealing time T ＱＡ Alternatively, the parameter value determining unit 110 may calculate parameter values ​​that result in a relatively large value for Number to Reject Fair Sampling.

[0097] In a mode for shortening the time required to obtain multiple optimal solutions, the parameter value determination unit 110 may set predetermined parameter values ​​that result in a relatively small TTAS value. The parameters include the four-body interaction coefficient C and the quantum annealing time T ＱＡ Alternatively, the parameter value determination unit 110 may calculate parameter values ​​that result in a relatively small TTAS value.

[0098] In the quantum annealing machine based on the LHZ model, the local field is given as the strength of the magnetic field. The magnitude of the four-body interaction coefficient |C| and the quantum annealing time T ＱＡ can be expressed as a ratio to the magnetic field strength by "appropriate unit conversion." In the following, we consider the value of the magnitude of the four-body interaction coefficient |C| and the quantum annealing time T ＱＡ Let us express and as a ratio to the local field of the qubit in the LHZ model.

[0099] In a quantum annealing machine using a Kerr nonlinear parametric oscillator as a quantum bit device, the magnitude of the four-body interaction |C| and the quantum annealing time T ＱＡ can be determined based on the coherent drive (a coefficient indicating the magnitude (strength) of the coherent drive). The coherent drive here is a microwave with a frequency and phase that is input to the Kerr nonlinear parametric oscillator. As the coherent drive, a microwave with a frequency close to the resonant frequency is input to the Kerr nonlinear parametric oscillator. This input gives a longitudinal magnetic field term. For example, the Hamiltonian (energy function that describes the physical behavior of the system) H^ of the Kerr nonlinear parametric oscillator is ｂ can be expressed as in equation (12).

[0100]

[0101] Δ denotes detuning. The detuning indicated by Δ corresponds to the transverse magnetic field term in general transverse magnetic quantum annealing. a^ ＋denotes the creation operator. a^ denotes the annihilation operator. K denotes the Kerr nonlinearity. p denotes the pump amplitude. ε denotes the coherent drive. The coherent drive ε corresponds to the local field of the qubit in the Ising model. As described above, the longitudinal magnetic field term is given by the input of the coherent drive, and there is a correlation between the value of the coherent drive ε and the value of the coefficient J of the longitudinal magnetic field term. Depending on the method of realizing the qubit device, for example, it is possible to use the value of the coefficient J of the longitudinal magnetic field term of the Hamiltonian of the Ising model as the value of the coherent drive ε.

[0102] In the Kerr nonlinear parametric oscillator, the Kerr nonlinearity K and the coherent drive ε are both expressed as frequencies. ＱＡ The ratio of ε to the inverse of the coherent drive ε is important.

[0103] Below, we will explain parameter values ​​in quantum annealing that make it easier to obtain multiple optimal solutions. Furthermore, the following four examples are used as examples of combinatorial optimization problems. As a first example of a combinatorial optimization problem, an Ising model with Hamiltonian H expressed as in Equation (13) is used.

[0104]

[0105] The example shown in Equation (13) is also referred to as Example 1. In Example 1, the number of binary variables included in the Ising model is four, and they are embedded in an LHZ model with eight quantum bits. Also, Example 1 can be considered as an Ising model in which all four binary variables exhibit antiferromagnetic interactions.

[0106] As a second example of a combinatorial optimization problem, an Ising model in which Hamiltonian H is expressed as in equation (14) is used.

[0107]

[0108] The example shown in Equation (14) is also referred to as Example 2. In Example 2, the number of binary variables included in the Ising model is five, and the number of quantum bits is embedded in an LHZ model of 13. Also, Example 2 can be regarded as an Ising model in which only one of the five binary variables exhibits a ferromagnetic interaction, and the other four binary variables all exhibit antiferromagnetic interactions.

[0109] As a third example of a combinatorial optimization problem, an Ising model in which Hamiltonian H is expressed as in equation (15) is used.

[0110]

[0111] The example shown in equation (15) is also referred to as example 3. In example 3, the number of binary variables included in the Ising model is 5, and is embedded in an LHZ model with 13 quantum bits.

[0112] As a fourth example of a combinatorial optimization problem, an Ising model in which Hamiltonian H is expressed as in equation (16) is used.

[0113]

[0114] The example shown in Equation (16) is also referred to as Example 4. In Example 4, the number of binary variables included in the Ising model is 5, and the Ising model is embedded in an LHZ model with 13 quantum bits. These Ising models were embedded in the LHZ model, and quantum annealing simulations were performed.

[0115] In the following, the quantum annealing time T ＱＡ is the inverse of the coefficient J of the longitudinal magnetic field term in the Hamiltonian and the Dirac constant h Ｄｉｒａｃ The product of Ｄｉｒａｃ When the value of the coefficient J of the longitudinal magnetic field term of the Hamiltonian of the Ising model is used as the value of the coherent drive ε, the quantum annealing time T ＱＡ is the inverse of the coherent drive ε and the Dirac constant h Ｄｉｒａｃ The product of Ｄｉｒａｃ The Dirac constant is a constant whose value is obtained by dividing the Planck constant by 2π (twice the ratio of the circumference of a circle to its diameter), and is expressed as 1.055 × 10－３４ It is measured in joules per second (J·s).

[0116] As described above, the quantum annealing time is the execution time of one quantum annealing. Here, the quantum annealing time is defined as the time from when the Hamiltonian of the Ising model that represents the combinatorial optimization problem to be solved starts to be strengthened from a state in which the Hamiltonian for performing quantum mechanical search is only the transverse magnetic field Hamiltonian, to when the transverse magnetic field Hamiltonian no longer exists. During quantum annealing, the value of the Hamiltonian of the Ising model is increased and the value of the transverse magnetic field Hamiltonian is decreased.

[0117] For example, the Hamiltonian H(t) of quantum annealing at time t (time t from the start of quantum annealing) can be expressed as in equation (17).

[0118]

[0119] T represents the quantum annealing time. t represents time. t takes a value in the range of 0≦t≦T. (t / T)×H Ｉｓｉｎｇ denotes the Ising model Hamiltonian. (1-t / T)×H ｔｒａｎｓｖｅｒｓｅ denotes the transverse magnetic field Hamiltonian. In equation (17), × denotes scalar multiplication.

[0120] In equation (17), when t = 0, the Hamiltonian H(t) is the transverse magnetic field Hamiltonian (1-t / T) × H ｔｒａｎｓｖｅｒｓｅ = H ｔｒａｎｓｖｅｒｓｅ When t = T, the Hamiltonian H(t) is the Ising model Hamiltonian (t / T) × H Ｉｓｉｎｇ = H Ｉｓｉｎｇ Only.

[0121] The Hamiltonian H^(t) obtained by adding a constraint based on four-body interactions to the Hamiltonian H(t) of equation (17) is expressed as equation (18).

[0122]

[0123] The first term on the right side of equation (18) is "-Γ(1-t / T)Σ ｉ σ ｉｘ " is the transverse magnetic field term. -Γ(1-t / T)Σ ｉ σ ｉ ｘ is the transverse magnetic field Hamiltonian (1-t / T) × H ｔｒａｎｓｖｅｒｓｅ Corresponding to σ ｉ ｘ is the x-component of the spin. The transverse magnetic field term corresponds to quantum fluctuations and is the driver of quantum annealing.

[0124] The second term on the right side of equation (18) is "-J(t / T)Σ ｉ (J ｉ / J)σ ｉ ｚ " is the longitudinal magnetic field term. -J(t / T)Σ ｉ (J ｉ / J)σ ｉ ｚ is the Ising model Hamiltonian (t / T) × H Ｉｓｉｎｇ Corresponds to J ｉ indicates a coefficient determined according to the combinatorial optimization problem to be solved by quantum annealing. σ ｉ ｚ is the z-component of the spin. σ ｉ ｚ Is J ｉ Together, they represent the combinatorial optimization problem to be solved by quantum annealing.

[0125] σ （ｉ，ｋ） ｚ , σ （ｊ，ｋ） ｚ , σ （ｋ，ｌ） ｚ , σ （ｉ，ｌ） ｚ The combination of C(t / T)Σ represents four quantum bits that are four-body coupled in the LHZ model. ｉ，ｊ，ｋ，ｌ σ （ｉ，ｋ） ｚ σ （ｊ，ｋ） ｚ σ （ｋ，ｌ） ｚ σ （ｉ，ｌ） ｚ " is a penalty term that indicates the constraint due to four-body interactions. Specifically, C<0 and σ （ｉ，ｋ） ｚ σ （ｊ，ｋ）ｚ σ （ｋ，ｌ） ｚ σ （ｉ，ｌ） ｚ If the value of is positive (even parity), then σ （ｉ，ｋ） ｚ σ （ｊ，ｋ） ｚ σ （ｋ，ｌ） ｚ σ （ｉ，ｌ） ｚ The value of the Hamiltonian H^(t) is smaller than when the value of t is negative (odd parity). This reduces the possibility that the solution candidate obtained by quantum annealing is inconsistent with the combinatorial optimization problem.

[0126] Γ, J, and C are constant coefficients for adjusting the degree of influence of each term in the Hamiltonian H^(t). The values ​​of Γ, J, and C are determined in advance (before the start of quantum annealing). C is the four-body interaction coefficient described above.

[0127] In addition, the second term on the right side of equation (18) “−J(t / T)Σ ｉ (J ｉ / J)σ ｉ ｋ " represents the interaction and local field of the Ising model. Dividing both sides of equation (18) by J is equivalent to setting the magnitude of the interaction and the magnitude of the local field of the Ising model to 1, respectively. The Hamiltonian H^(t) and the coefficient J both have the dimension of energy, and dividing both sides of equation (18) by J can be considered to make the Hamiltonian H^(t) dimensionless. Dividing both sides of equation (18) by J results in equation (19).

[0128]

[0129] Furthermore, quantum annealing evolves over time according to the Schrodinger equation shown in equation (20).

[0130]

[0131] In equation (20), i represents the imaginary unit. Ｄｉｒａｃ denotes the Dirac constant. ψ denotes the wave function. Equation (20) can be transformed into equation (21).

[0132]

[0133] t' is expressed as in equation (22).

[0134]

[0135] In equation (21), both sides of equation (20) are divided by the coefficient J to make it dimensionless, and then t is replaced by t' to add the Dirac constant h Ｄｉｒａｃ In this respect, equation (21) simplifies the numerical calculation of time evolution in quantum annealing.

[0136] In the following, we will use t' to represent time. This means that time can be expressed as the reciprocal of the coherent drive ε and the Dirac constant h Ｄｉｒａｃ The product of Ｄｉｒａｃ As mentioned above, the quantum annealing time is also expressed as a ratio of the reciprocal of the coherent drive ε and the Dirac constant h Ｄｉｒａｃ The product of Ｄｉｒａｃ / ε.

[0137] Converting time t to time t' and converting time t' to time t can both be referred to as a conversion of an appropriate unit for time t. Dividing the four-body interaction coefficient C by J to convert it into the coefficient C / J of the longitudinal magnetic field term (the third term on the right-hand side) in equation (19), and multiplying the coefficient C / J by J to convert it into the four-body interaction coefficient C can both be referred to as a conversion of an appropriate unit for the four-body interaction coefficient C.

[0138] For example, the coherent drive ε and the Dirac constant h Ｄｉｒａｃ The product of ε / h and the reciprocal of Ｄｉｒａｃ If T is 10 megahertz (MHz), this corresponds to about 100 nanoseconds (ns) when converted to time. ＱＡ= 1 indicates that the quantum annealing time is 100 nanoseconds. Here, the conversion from frequency to time can be performed by taking the reciprocal of the frequency. In addition, hereinafter, the magnitude of the four-body interaction |C| is expressed as a ratio to the coherent drive ε. For example, if the coherent drive ε is 10 MHz, |C| = 1 indicates that the magnitude of the four-body interaction is 10 MHz. Expressing the magnitude of the four-body interaction |C| as a ratio to the coherent drive ε is equivalent to expressing the magnitude of the four-body interaction |C| as a ratio to the coefficient J of the longitudinal magnetic field term of the Hamiltonian.

[0139] 4 is a diagram showing a first example of the relationship between quantum annealing time and success probability. FIG. 4 shows an example of the relationship between quantum annealing time and success probability when the four-body interaction coefficient C=-2 in the simulation of Example 1. The horizontal axis of the graph in FIG. 4 is the quantum annealing time T ＱＡ The vertical axis shows the success rate.

[0140] The success rate here is the percentage of times an optimal solution is obtained among the number of times quantum annealing is performed. The success rate can also be thought of as indicating the probability of obtaining an optimal solution.

[0141] In the case of Example 1, (σ １ , σ ２ , σ ３ , σ ４ ) = (+1, +1, -1, -1), (+1, -1, +1, -1), (+1, -1, -1, +1). １ , σ ２ , σ ３ , σ ４ The line L112 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ The line L113 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ４ ) = (+1, -1, -1, +1) for each quantum annealing time. Line L114 shows the total success rate of these three optimal solutions. In other words, line L114 shows the relationship between the quantum annealing time and the rate at which any of the optimal solutions is obtained.

[0142] The area where the three lines L111 to L113 overlap can be considered as fair sampling. On the other hand, the area where the three lines L111 to L113 do not overlap can be considered as unfair sampling. In the example of FIG. 4, the quantum annealing time T ＱＡ =10 ０ From the left side of the figure (approximately T ＱＡ ≦10 ０ ) can be understood as being fair sampling. Also, the quantum annealing time T ＱＡ = 2 x 10 ０ From the right side of the figure (approximately T ＱＡ ≧2×10 ０ ) can be seen as unfair sampling.

[0143] 5 is a diagram showing a second example of the relationship between quantum annealing time and success rate. FIG. 5 shows an example of the relationship between quantum annealing time and success rate when the four-body interaction coefficient C=-5 in the simulation of Example 1. The horizontal axis of the graph in FIG. 5 is the quantum annealing time T ＱＡ The vertical axis shows the success rate.

[0144] The line L121 is (σ １ , σ ２ , σ ３ , σ ４ The line L122 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ The line L123 shows the success rate of the optimal solution of (σ １ , σ ２ , σ３ , σ ４ ) = (+1, -1, -1, +1) for each quantum annealing time. Line L124 shows the total success rate of these three optimal solutions. In other words, line L124 shows the relationship between the quantum annealing time and the rate at which any of the optimal solutions is obtained.

[0145] The area where the three lines L121 to L123 overlap can be considered as fair sampling. On the other hand, the area where the three lines L121 to L123 do not overlap can be considered as unfair sampling. In the example of FIG. 5, the quantum annealing time T ＱＡ = 4 x 10 ０ From the left side of the figure (approximately T ＱＡ ≦4×10 ０ ) can be understood as being fair sampling. Also, the quantum annealing time T ＱＡ = 5 x 10 ０ From the right side of the figure (approximately T ＱＡ ≧5×10 ０ ) can be seen as unfair sampling.

[0146] 6 is a diagram showing a third example of the relationship between quantum annealing time and success rate. FIG. 6 shows an example of the relationship between quantum annealing time and success rate when the four-body interaction coefficient C is set to −10 in the simulation of Example 1. The horizontal axis of the graph in FIG. 6 is the quantum annealing time T ＱＡ The vertical axis shows the success rate.

[0147] The line L131 is (σ １ , σ ２ , σ ３ , σ ４ The line L132 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ The line L133 shows the success rate of the optimal solution of (σ １ , σ２ , σ ３ , σ ４ ) = (+1, -1, -1, +1) for each quantum annealing time. Line L134 shows the total success rate of these three optimal solutions. In other words, line L134 shows the relationship between the quantum annealing time and the rate at which any of the optimal solutions is obtained.

[0148] The area where the three lines L131 to L133 overlap can be considered as fair sampling. On the other hand, the area where the three lines L131 to L133 do not overlap can be considered as unfair sampling. In the example of FIG. 6, the quantum annealing time T ＱＡ =10 １ From the left side of the figure (approximately T ＱＡ ≦10 １ ) can be understood as being fair sampling. Also, the quantum annealing time T ＱＡ = 2 x 10 １ From the right side of the figure (approximately T ＱＡ ≧2×10 １ ) can be seen as unfair sampling.

[0149] 4 to 6, it can be understood that the larger the magnitude |C| of the four-body interaction, the longer the quantum annealing time that results in fair sampling, and the stronger the tendency toward fair sampling. Furthermore, with reference to lines L114, L124, and L134, it can be understood that the larger the magnitude |C| of the four-body interaction, the smaller the success rate (here, the rate at which any optimization is obtained) for the same quantum annealing time.

[0150] 4 to 6, when the value of the four-body interaction coefficient C is fixed, the longer the quantum annealing time, the higher the success rate of obtaining an optimal solution, but the stronger the tendency toward unfair sampling. Conversely, the shorter the quantum annealing time, the stronger the tendency toward fair sampling, but the lower the success rate of obtaining an optimal solution.

[0151] 7 is a diagram showing a fourth example of the relationship between quantum annealing time and success rate. FIG. 7 shows an example of the relationship between quantum annealing time and success rate when the four-body interaction coefficient C=-3 in the simulation of Example 2. The horizontal axis of the graph in FIG. 7 is the quantum annealing time T ＱＡ The vertical axis shows the success rate.

[0152] In the case of Example 2, (σ １ , σ ２ , σ ３ , σ ４ , σ ５ ) = (+1, +1, +1, -1, -1), (+1, +1, -1, +1, -1), (+1, +1, -1, -1, +1), (+1, +1, -1, -1, -1). Line L211 has four optimal solutions: (σ １ , σ ２ , σ ３ , σ ４ , σ ５ The line L212 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ , σ ５ The line L213 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ , σ ５ The line L214 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４, σ ５ ) = (+1, +1, -1, -1, -1) for each quantum annealing time. Line L215 shows the total success rate of these four optimal solutions. In other words, line L215 shows the relationship between the quantum annealing time and the rate at which any of the optimal solutions is obtained.

[0153] The area where the four lines L211 to L214 overlap can be considered as fair sampling. On the other hand, the area where the four lines L211 to L214 do not overlap can be considered as unfair sampling. In the example of FIG. 7, the quantum annealing time T ＱＡ = 2 x 10 ０ From the left side of the figure (approximately T ＱＡ ≦2×10 ０ ) can be understood as being fair sampling. Also, the quantum annealing time T ＱＡ = 3 x 10 ０ From the right side of the figure (approximately T ＱＡ ≧3×10 ０ ) can be seen as unfair sampling.

[0154] 8 is a diagram showing a fifth example of the relationship between quantum annealing time and success rate. FIG. 8 shows an example of the relationship between quantum annealing time and success rate when the four-body interaction coefficient C=-5 in the simulation of Example 2. The horizontal axis of the graph in FIG. 8 is the quantum annealing time T ＱＡ The vertical axis shows the success rate.

[0155] The line L221 is (σ １ , σ ２ , σ ３ , σ ４ , σ ５ The line L222 shows the success rate of the optimal solution of (σ ) = (+1, +1, +1, -1, -1) for each quantum annealing time. １ , σ ２ , σ ３ , σ ４ , σ ５The line L223 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ , σ ５ The line L224 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ , σ ５ ) = (+1, +1, -1, -1, -1) for each quantum annealing time. Line L225 shows the total success rate of these four optimal solutions. In other words, line L225 shows the relationship between quantum annealing time and the rate at which any of the optimal solutions is obtained.

[0156] The area where the four lines L221 to L224 overlap can be considered as fair sampling. On the other hand, the area where the four lines L221 to L224 do not overlap can be considered as unfair sampling. In the example of FIG. 8, the quantum annealing time T ＱＡ = 4 x 10 ０ From the left side of the figure (approximately T ＱＡ ≦4×10 ０ ) can be understood as being fair sampling. Also, the quantum annealing time T ＱＡ =10 １ From the right side of the figure (approximately T ＱＡ ≧10 １ ) can be seen as unfair sampling.

[0157] 9 is a diagram showing a sixth example of the relationship between quantum annealing time and success rate. FIG. 9 shows an example of the relationship between quantum annealing time and success rate when the four-body interaction coefficient C=−10 in the simulation of Example 2. The horizontal axis of the graph in FIG. 9 is the quantum annealing time T ＱＡ The vertical axis shows the success rate.

[0158] The line L231 is (σ１ , σ ２ , σ ３ , σ ４ , σ ５ The line L232 shows the success rate of the optimal solution of (σ ) = (+1, +1, +1, -1, -1) for each quantum annealing time. １ , σ ２ , σ ３ , σ ４ , σ ５ The line L233 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ , σ ５ The line L234 shows the success rate of the optimal solution of (σ １ , σ ２ , σ ３ , σ ４ , σ ５ ) = (+1, +1, -1, -1, -1) for each quantum annealing time. Line L235 shows the total success rate of these four optimal solutions. In other words, line L235 shows the relationship between the quantum annealing time and the rate at which any of the optimal solutions is obtained.

[0159] The area where the four lines L231 to L234 overlap can be considered as fair sampling. On the other hand, the area where the four lines L231 to L234 do not overlap can be considered as unfair sampling. In the example of FIG. 9, the quantum annealing time T ＱＡ =10 １ From the left side of the figure (approximately T ＱＡ ≦10 １ ) can be understood as being fair sampling. Also, the quantum annealing time T ＱＡ = 4 x 10 １ From the right side of the figure (approximately T ＱＡ ≧4×10 １ ) can be seen as unfair sampling.

[0160] 7 to 9, it can be seen that the larger the magnitude |C| of the four-body interaction, the longer the quantum annealing time that results in fair sampling, and the stronger the tendency toward fair sampling. Furthermore, with reference to lines L215, L225, and L235, it can be seen that the larger the magnitude |C| of the four-body interaction, the smaller the success rate (here, the rate at which any optimization is obtained) for the same quantum annealing time.

[0161] 7 to 9, when the value of the four-body interaction coefficient C is fixed, the longer the quantum annealing time, the higher the success rate of obtaining an optimal solution, but the stronger the tendency toward unfair sampling. Conversely, the shorter the quantum annealing time, the stronger the tendency toward fair sampling, but the lower the success rate of obtaining an optimal solution.

[0162] In the examples of Figures 4 to 9, the quantum annealing time T ＱＡ , that is, the quantum annealing time T ＱＡ is approximately 10 １ For example, in the examples of FIG. 6 and FIG. 9, the value is approximately T ＱＡ ≦10 １ When this is the case, it is Fair Sampling.

[0163] 10 is a diagram showing a first example of the relationship between quantum annealing time and Number to Reject Fair Sampling. FIG. 10 shows an example of the relationship between quantum annealing time and Number to Reject Fair Sampling in the simulation of Example 1. The horizontal axis of the graph in FIG. 10 is the quantum annealing time T ＱＡ The vertical axis shows the value of Number to Reject Fair Sampling.

[0164] Line L311 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -2. Line L312 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -3. Line L313 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -4. Line L314 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -5. Line L315 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -6. Line L316 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -7. Line L317 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -8. Line L318 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -9. Line L319 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -10.

[0165] In the example of FIG. 10, the overall trend is that the longer the quantum annealing time, the smaller the value of Number to Reject Fair Sampling. In particular, ＱＡ ≦2×10 －１ In the case of the quantum annealing time T, the value of Number to Reject Fair Sampling monotonically decreases as the quantum annealing time increases on all of the lines L311 to L319. ＱＡ ≧3×10 －１When , the value of Number to Reject Fair Sampling tends to oscillate and decrease as the quantum annealing time increases.

[0166] 11 is a diagram showing a second example of the relationship between quantum annealing time and Number to Reject Fair Sampling. FIG. 11 shows an example of the relationship between quantum annealing time and Number to Reject Fair Sampling in the simulation of Example 2. The horizontal axis of the graph in FIG. 11 is the quantum annealing time T ＱＡ The vertical axis shows the value of Number to Reject Fair Sampling.

[0167] Line L321 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -2. Line L322 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -3. Line L323 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -4. Line L324 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -5. Line L325 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -6. Line L326 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -7. Line L327 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -8. Line L328 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -9. Line L329 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -10.

[0168] In the example of FIG. 11, the overall trend is that the longer the quantum annealing time, the smaller the value of Number to Reject Fair Sampling. ＱＡ ≦2×10 －１ In the case of the quantum annealing time T, the value of Number to Reject Fair Sampling decreases monotonically as the quantum annealing time increases on all of the lines L321 to L329. ＱＡ ≧3×10 －１When , the value of Number to Reject Fair Sampling tends to oscillate and decrease as the quantum annealing time increases.

[0169] 12 is a diagram showing a third example of the relationship between quantum annealing time and Number to Reject Fair Sampling. FIG. 12 shows an example of the relationship between quantum annealing time and Number to Reject Fair Sampling in the simulation of Example 3. The horizontal axis of the graph in FIG. 12 is the quantum annealing time T ＱＡ The vertical axis shows the value of Number to Reject Fair Sampling.

[0170] Line L331 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -2. Line L332 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -3. Line L333 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -4. Line L334 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -5. Line L335 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -6. Line L336 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -7. Line L337 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -8. Line L338 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -9. Line L339 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -10.

[0171] In the example of FIG. 12, the overall trend is that the longer the quantum annealing time, the smaller the value of Number to Reject Fair Sampling. ＱＡ ≦2×10 －１ In the case of the quantum annealing time T, the value of Number to Reject Fair Sampling monotonically decreases as the quantum annealing time increases on all of the lines L331 to L339. ＱＡ ≧3×10 －１When , the value of Number to Reject Fair Sampling tends to oscillate and decrease as the quantum annealing time increases.

[0172] 13 is a diagram showing a fourth example of the relationship between quantum annealing time and Number to Reject Fair Sampling. FIG. 13 shows an example of the relationship between quantum annealing time and Number to Reject Fair Sampling in the simulation of Example 4. The horizontal axis of the graph in FIG. 13 is the quantum annealing time T ＱＡ The vertical axis shows the value of Number to Reject Fair Sampling.

[0173] Line L341 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -2. Line L342 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -3. Line L343 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -4. Line L344 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -5. Line L345 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -6. Line L346 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -7. Line L347 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -8. Line L348 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -9. Line L349 shows the value of Number to Reject Fair Sampling for each quantum annealing time when the four-body interaction coefficient C = -10.

[0174] In the example of FIG. 13, the overall trend is that the longer the quantum annealing time, the smaller the value of Number to Reject Fair Sampling. ＱＡ ≦2×10 －１ In the case of the quantum annealing time T, the value of Number to Reject Fair Sampling monotonically decreases as the quantum annealing time increases on all of the lines L341 to L349. ＱＡ ≧3×10 －１When , the value of Number to Reject Fair Sampling tends to oscillate and decrease as the quantum annealing time increases.

[0175] In the examples of FIGS. 10 to 13, for example, the quantum annealing time T ＱＡ ≦10 ０ etc., quantum annealing time T ＱＡ The shorter the quantum annealing time T ＱＡ It is also important not to make it too short.

[0176] Quantum annealing time T ＱＡ When the quantum annealing time T is relatively long, the larger the magnitude of the four-body interaction |C|, the larger the value of Number to Reject Fair Sampling tends to be. ＱＡ In order to make |C| relatively long and increase the value of Number to Reject Fair Sampling, it is preferable that |C| ≧ 5, and it is more preferable that |C| ≧ 7. If the coherent drive ε is about 10 MHz, |C| = 5 is about 50 MHz, and |C| = 7 is about 70 MHz.

[0177] Quantum annealing time T ＱＡ Regarding T ＱＡ It is preferable that T = 1. When the coherent drive ε is set to about 10 MHz, ＱＡ =1 is about 100 nanoseconds.

[0178] For example, in the example of FIG. 10, |C|≧5 and T ＱＡ = 1, C = -5, Number to Reject Fair Sampling is 10 ４ Therefore, the Number to Reject Fair Sampling is a value equal to or greater than this. Also, in the example of FIG. 10, if |C|≧7 and T ＱＡ If ≦4, then C=−7 and T ＱＡis approximately 4 x 10 －０ When the Number to Reject Fair Sampling is 10, ４ The minimum value is slightly smaller than . Therefore, the Number to Reject Fair Sampling will be a value equal to or greater than .

[0179] 14 is a diagram showing a first example of the relationship between quantum annealing time and TTAS. FIG. 14 shows an example of the relationship between quantum annealing time and TTAS in the simulation of Example 1. The horizontal axis of the graph in FIG. 14 is the quantum annealing time T ＱＡ The vertical axis indicates the TTAS value.

[0180] Line L411 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-2. Line L412 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-3. Line L413 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-4. Line L414 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-5. Line L415 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-6. Line L416 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-7. Line L417 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C=-8. Line L418 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -9. Line L419 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -10.

[0181] In the example of FIG. 14, the overall trend is that the TTAS value increases as the quantum annealing time increases. In particular, ＱＡ ≦2×10 ０ When the quantum annealing time T ＱＡ >2 x 10 ０When , the value of TTAS tends to increase monotonically or to increase with an oscillatory motion as the quantum annealing time increases.

[0182] 15 is a diagram showing a second example of the relationship between quantum annealing time and TTAS. FIG. 15 shows an example of the relationship between quantum annealing time and TTAS in the simulation of Example 2. The horizontal axis of the graph in FIG. 15 is the quantum annealing time T ＱＡ The vertical axis indicates the TTAS value.

[0183] Line L421 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -2. Line L422 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -3. Line L423 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -4. Line L424 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -5. Line L425 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -6. Line L426 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -7. Line L427 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -8. Line L428 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -9. Line L429 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -10.

[0184] In the example of FIG. 15, the quantum annealing time T ＱＡ ≦2×10 －１ When the quantum annealing time T ＱＡ ≧3×10 －１ When , the value of TTAS oscillates with respect to the quantum annealing time.

[0185] 16 is a diagram showing a third example of the relationship between quantum annealing time and TTAS. FIG. 16 shows an example of the relationship between quantum annealing time and TTAS in the simulation of Example 3. The horizontal axis of the graph in FIG. 16 is the quantum annealing time T ＱＡ The vertical axis indicates the TTAS value.

[0186] Line L431 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -2. Line L432 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -3. Line L433 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -4. Line L434 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -5. Line L435 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -6. Line L436 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -7. Line L437 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -8. Line L438 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -9. Line L439 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -10.

[0187] In the example of FIG. 16, the quantum annealing time T ＱＡ ≦2×10 －１ When the quantum annealing time T ＱＡ ≧3×10 －１ When , the value of TTAS oscillates with respect to the quantum annealing time.

[0188] 17 is a diagram showing a fourth example of the relationship between the quantum annealing time and the TTAS. FIG. 17 shows an example of the relationship between the quantum annealing time and the TTAS in the simulation of Example 4. The horizontal axis of the graph in FIG. 17 is the quantum annealing time T ＱＡ The vertical axis indicates the TTAS value.

[0189] Line L441 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -2. Line L442 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -3. Line L443 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -4. Line L444 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -5. Line L445 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -6. Line L446 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -7. Line L447 shows the TTAS value for each quantum annealing time when the four-body interaction coefficient C = -8. Line L448 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -9. Line L449 shows the value of TTAS for each quantum annealing time when the four-body interaction coefficient C = -10.

[0190] In the example of FIG. 17, the quantum annealing time T ＱＡ ≦2×10 －１ When the quantum annealing time T ＱＡ ≧3×10 －１ When , the TTAS oscillates with respect to the quantum annealing time.

[0191] In the examples of FIGS. 14 to 17, for example, T ＱＡ When T = 0.1, the larger the magnitude of the four-body interaction |C|, the smaller the value of TTAS. ＱＡ When the coherent drive ε is about 10 MHz, the value of TTAS becomes small when the magnitude of the four-body interaction |C| is about 2 to 5. ＱＡ = 0.1 is about 10 nanoseconds, and T ＱＡ = 10 is about 1 microsecond (μs). Also, if the coherent drive ε is about 10 MHz, |C| = 2 is about 20 MHz, and |C| = 5 is about 50 MHz.

[0192] 18 is a diagram showing a first example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and TTAS. ＱＡ 18 shows an example of the relationship between the magnitude of the four-body bond strength coefficient |C| and TTAS when |C|=1.0. The horizontal axis of the graph in FIG. 18 represents the magnitude of the four-body bond strength coefficient |C|, and the vertical axis represents the value of TTAS.

[0193] Line L511 shows the value of TTAS for each magnitude |C| of the four-body bond strength coefficient. In the example of Fig. 18, when |C| < 5, the value of TTAS decreases as the magnitude |C| of the four-body bond strength coefficient increases, and the value of TTAS is minimal when |C| = 5. When |C| > 5, the value of TTAS increases as the magnitude |C| of the four-body bond strength coefficient increases.

[0194] 19 is a diagram showing a second example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and TTAS. ＱＡ 19 shows an example of the relationship between the magnitude of the four-body bond strength coefficient |C| and TTAS when |C|=1.0. The horizontal axis of the graph in FIG. 19 represents the magnitude of the four-body bond strength coefficient |C|, and the vertical axis represents the value of TTAS.

[0195] Line L521 shows the value of TTAS for each magnitude |C| of the four-body bond strength coefficient. In the example of Fig. 19, when |C| < 4, the value of TTAS decreases as the magnitude |C| of the four-body bond strength coefficient increases, and the value of TTAS is minimal when |C| = 4. When |C| > 4, the value of TTAS increases as the magnitude |C| of the four-body bond strength coefficient increases.

[0196] 20 is a diagram showing a third example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and TTAS. ＱＡ 20 shows an example of the relationship between the magnitude of the four-body bond strength coefficient |C| and TTAS when |C|=1.0. The horizontal axis of the graph in FIG. 20 represents the magnitude of the four-body bond strength coefficient |C|, and the vertical axis represents the value of TTAS.

[0197] Line L531 shows the TTAS value for each magnitude |C| of the four-body bond strength coefficient. In the example of Fig. 20, when |C| < 3, the TTAS value decreases as the magnitude |C| of the four-body bond strength coefficient increases, and the TTAS values ​​are almost the same when |C| = 3 and when |C| = 4. When |C| > 4, the TTAS value increases as the magnitude |C| of the four-body bond strength coefficient increases.

[0198] 21 is a diagram showing a fourth example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and TTAS. ＱＡ 21 shows an example of the relationship between the magnitude of the four-body bond strength coefficient |C| and TTAS when |C| = 1.0. The horizontal axis of the graph in FIG. 21 represents the magnitude of the four-body bond strength coefficient |C|, and the vertical axis represents the value of TTAS.

[0199] Line L541 shows the value of TTAS for each magnitude |C| of the four-body bond strength coefficient. In the example of Fig. 21, when |C| < 4, the value of TTAS decreases as the magnitude |C| of the four-body bond strength coefficient increases, and the value of TTAS is minimal when |C| = 4. When |C| > 4, the value of TTAS increases as the magnitude |C| of the four-body bond strength coefficient increases.

[0200] In the examples of FIGS. 18 to 21, the quantum annealing time T ＱＡ When the coherent drive ε is about 10 MHz, the value of TTAS becomes small when the magnitude of the four-body interaction |C| is about 3 to 5. ＱＡ = 1 is about 100 nanoseconds. Also, if the coherent drive ε is about 10 megahertz, |C| = 3 is about 30 megahertz, and |C| = 5 is about 50 megahertz.

[0201] 22 is a diagram showing a first example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and the minimum value of TTAS. ＱＡ22 shows an example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and the minimum value of TTAS when the magnitude is changed within the range of ≦10. Changing the quantum annealing time here means performing quantum annealing simulations with various quantum annealing times. The horizontal axis of the graph in FIG. 22 represents the magnitude |C| of the four-body coupling strength coefficient. The vertical axis represents the minimum value of TTAS.

[0202] A line L611 indicates the minimum value of TTAS for each magnitude of the four-body bond strength coefficient |C|. In the example of Fig. 22, the value of TTAS monotonically decreases as the magnitude of the four-body bond strength coefficient |C| increases.

[0203] 23 is a diagram showing a second example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and the minimum value of TTAS. ＱＡ 23 shows an example of the relationship between the magnitude |C| of the four-body bond strength coefficient and the minimum value of TTAS when the magnitude is changed within the range of |C|≦10. The horizontal axis of the graph in FIG. 23 represents the magnitude |C| of the four-body bond strength coefficient, and the vertical axis represents the minimum value of TTAS.

[0204] Line L621 shows the minimum value of TTAS for each magnitude of the four-body bond strength coefficient |C|. In the example of Figure 23, the minimum value of TTAS decreases when |C| = 3 compared to when |C| = 2, and the minimum value of TTAS is minimal when |C| = 3. Furthermore, when 3 < |C| < 7, the minimum value of TTAS increases as |C| increases, and the minimum value of TTAS is minimal when |C| = 7. Furthermore, when |C| > 7, the minimum value of TTAS decreases as |C| increases.

[0205] 24 is a diagram showing a third example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and the minimum value of TTAS. ＱＡ 24 shows an example of the relationship between the magnitude |C| of the four-body bond strength coefficient and the minimum value of TTAS when the magnitude is changed within the range of |C|≦10. The horizontal axis of the graph in FIG. 24 represents the magnitude |C| of the four-body bond strength coefficient, and the vertical axis represents the minimum value of TTAS.

[0206] Line L631 shows the minimum value of TTAS for each magnitude of the four-body bond strength coefficient |C|. In the example of Figure 24, the minimum value of TTAS decreases when |C| = 3 compared to when |C| = 2, and the minimum value of TTAS is minimal when |C| = 3. Furthermore, when 3 < |C| < 7, the minimum value of TTAS increases as |C| increases, and the minimum value of TTAS is minimal when |C| = 7. Furthermore, when |C| > 7, the minimum value of TTAS decreases as |C| increases.

[0207] 25 is a diagram showing a fourth example of the relationship between the magnitude |C| of the four-body coupling strength coefficient and the minimum value of TTAS. ＱＡ 25 shows an example of the relationship between the magnitude |C| of the four-body bond strength coefficient and the minimum value of TTAS when the magnitude is changed within the range of |C|≦10. The horizontal axis of the graph in FIG. 25 represents the magnitude |C| of the four-body bond strength coefficient, and the vertical axis represents the minimum value of TTAS.

[0208] Line L641 shows the minimum value of TTAS for each magnitude of the four-body bond strength coefficient |C|. In the example of Figure 25, when |C| < 7, the minimum value of TTAS increases as |C| increases, and when |C| = 7, the minimum value of TTAS becomes maximum. Furthermore, when |C| > 7, the minimum value of TTAS decreases as |C| increases.

[0209] In the examples of FIGS. 22 to 25, 2≦|C|≦10 and 0.1≦T ＱＡ Within the range of |C|≦10, the TTAS value is small when 2≦|C|≦4 or when |C|=10. In particular, in the example of FIG. 22, the TTAS value is smallest when |C|=10. In the examples of FIG. 23 and FIG. 24, the TTAS value is smallest when |C|=3. In the example of FIG. 25, the TTAS value is smallest when |C|=2.

[0210] When the coherent drive ε is about 10 MHz, |C|=2 is about 20 MHz, |C|=4 is about 40 MHz, |C|=5 is about 50 MHz, |C|=7 is about 70 MHz, and |C|=10 is about 100 MHz. ＱＡ = 0.1 is about 10 nanoseconds, and T ＱＡ =10 is about 1 microsecond.

[0211] Thus, the quantum annealing time T ＱＡ However, 1≦T ＱＡ When the magnitude of the four-body interaction |C| is set to 2≦|C|≦5, it is expected that the value of TTAS will be small. For example, in the examples of FIGS. 16 and 17, when 1≦T ＱＡ In the range of ≦10, when C=−2, −3, −4, or −5, the TTAS value is relatively small.

[0212] In the example of FIG. 14, approximately 4≦T ＱＡ In the range of 1≦T ＱＡ ≦4 and approximately 8≦T ＱＡ In the range of ≦10, when C=−3, −4, or −5, the TTAS value is relatively small.

[0213] In the example of FIG. 15, approximately 1≦T ＱＡ In the range of C≦2, when C=−2, −3, −4, or −5, the TTAS value is relatively small. ＱＡ In the range of ≦10, when C=−3, −4, or −5, the TTAS value is relatively small.

[0214] Also, the quantum annealing time T ＱＡ But, T ＱＡ When |C| is about 0.1, if the magnitude of the four-body interaction |C| is set to a relatively large value, for example, |C|=10, it can be expected that the value of TTAS will become smaller. For example, in any of the examples of FIGS. 14 to 17, T ＱＡWhen |C| is about 0.1, the larger the magnitude of the four-body interaction, the smaller the value of TTAS.

[0215] When the TTAS value is small, it is expected that multiple optimal solutions can be obtained relatively quickly, for example, when the TTAS value is small, it is expected that all optimal solutions can be obtained relatively quickly.

[0216] However, while the evaluation of TTAS only takes into account the quantum annealing time, it is important to note that in an actual quantum annealing machine, it takes time to perform the preliminary setup for quantum annealing and to read the results, so a short quantum annealing time does not necessarily mean that all optimal solutions will be obtained quickly.

[0217] For example, the quantum annealing time T ＱＡ To, T ＱＡ It may be set to a relatively large value, such as approximately 1 or a larger value. By lengthening the quantum annealing time to a certain extent, it is possible to increase the accuracy of quantum annealing (the possibility of obtaining an optimal solution), and it is expected that the number of times quantum annealing is repeated until multiple optimal solutions (e.g., all optimal solutions) are obtained can be relatively reduced. This is expected to make it possible to relatively shorten the total time required to obtain multiple optimal solutions, including the time required for prior setup for quantum annealing and reading the results.

[0218] 26 is a diagram showing an example of the procedure of the process performed by the quantum annealing system 1. In the process shown in FIG. 26, the parameter adjustment device 100 determines the values ​​of parameters for quantum annealing (step S101). In particular, the parameter adjustment device 100 determines the four-body interaction coefficient C and the quantum annealing time T ＱＡ Determine values ​​for parameters including

[0219] The parameter adjustment node 100 then transmits the determined parameter value to the control device 200 (step S102). The parameter adjustment node 100's transmission of the parameter value to the control device 200 can be considered as setting the parameter value.

[0220] The control device 200, which has received the parameter values ​​from the parameter adjustment device 100, controls the quantum annealing machine 300 based on the received parameter values ​​to repeatedly execute quantum annealing (step S111). The quantum annealing machine 300 repeatedly executes quantum annealing in accordance with the control of the control device 200 (step S121).

[0221] As described above, the parameter value determination unit 110 performs at least one of the following for a quantum annealing machine having a structure represented by the LHZ model: determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant; and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0222] The parameter adjustment device 100 is expected to obtain multiple optimal solutions when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved using quantum annealing with the LHZ method. In particular, the parameter adjustment device 100 is expected to provide a relatively large value for the Number to Reject Fair Sampling, an index indicating the strength of the tendency toward fair sampling. In this respect, the parameter adjustment device 100 is expected to obtain different optimal solutions (i.e., multiple optimal solutions) when an optimal solution is obtained multiple times.

[0223] The quantum annealing time only needs to be approximately 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and does not need to be exactly 1. If the quantum annealing time is approximately 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, it is expected that multiple optimal solutions will be obtained when quantum annealing is repeated.

[0224] Furthermore, a Kerr nonlinear parametric oscillator is used as the quantum bit device 310 of the quantum annealing machine 300. The parameter value determination unit 110 performs at least one of determining the quantum annealing time to be 1 times the product of the reciprocal of the coherent drive ε and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coherent drive ε.

[0225] According to the parameter adjustment device 100, when a combinatorial optimization problem with multiple optimal solutions is embedded in a quantum annealing machine 300 using a Kerr nonlinear parametric oscillator as the quantum bit device 310 using the LHZ method and quantum annealing is repeatedly performed, it is expected that multiple optimal solutions will be obtained.

[0226] Furthermore, when the solution search mode by quantum annealing is set to a mode that attempts to equalize the probability of obtaining each optimal solution, the parameter value determination unit 110 performs at least one of determining the quantum annealing time to be 1 time the product of the reciprocal of the coefficient value of the vertical magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the vertical magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and when the solution search mode is set to a mode that attempts to shorten the time it takes to obtain multiple optimal solutions, the parameter value determination unit 110 determines the quantum annealing time to be 1 time or more and 10 times the product of the reciprocal of the coefficient value of the vertical magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is 2 times or more and 5 times or less the coefficient value of the vertical magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0227] The parameter adjustment device 100 is expected to be able to obtain multiple optimal solutions in both a mode that aims to equalize the probability of obtaining each optimal solution and a mode that aims to shorten the time required to obtain multiple optimal solutions.

[0228] In a mode that attempts to equalize the probability of obtaining each optimal solution, the parameter value determination unit 110 sets parameter values ​​that result in a relatively large value for Number to Reject Fair Sampling. This expects that when quantum annealing is repeatedly performed to obtain multiple optimal solutions, different optimal solutions (i.e., multiple optimal solutions) will be obtained. At least one of determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, corresponds to an example of setting parameter values ​​that result in a relatively large value for Number to Reject Fair Sampling.

[0229] In a mode for shortening the time required to obtain multiple optimal solutions, the parameter value determination unit 110 sets parameter values ​​that result in a relatively small TTAS value. This is expected to shorten the time required to obtain multiple optimal solutions. Determining the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, are examples of setting parameter values ​​that result in a relatively small TTAS value.

[0230] The solution search mode may include both a mode that equalizes the probability of obtaining each optimal solution and a mode that shortens the time required to obtain multiple optimal solutions. In this case, the parameter value determination unit 110 may determine the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and may determine the four-body interaction coefficient value to be 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. This parameter value is common to the mode that equalizes the probability of obtaining each optimal solution and the mode that shortens the time required to obtain multiple optimal solutions.

[0231] Furthermore, a Kerr nonlinear parametric oscillator is used as the quantum bit device 310 of the quantum annealing machine 300. When the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the parameter value determination unit 110 determines the quantum annealing time to be a value that is between 1 and 10 times the product of the reciprocal of the coherent drive ε and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive ε.

[0232] According to the parameter adjustment device 100, when a combinatorial optimization problem with multiple optimal solutions is embedded using the LHZ method in the quantum annealing machine 300, which uses a Kerr nonlinear parametric oscillator as the quantum bit device 310, and quantum annealing is repeatedly performed, it is expected that multiple optimal solutions will be obtained in either a mode that attempts to equalize the probability of obtaining each optimal solution, or a mode that attempts to shorten the time required to obtain multiple optimal solutions.

[0233] Furthermore, when the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the parameter value determination unit 110 determines the quantum annealing time to be a value that is between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0234] With the parameter adjustment device 100, when the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, it is expected that the possibility of obtaining multiple optimal solutions will be further increased. In particular, with the parameter adjustment device 100, when the mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, it is expected that the TTAS value will be further reduced. In this respect, with the parameter adjustment device 100, it is expected that the time required to obtain multiple optimal solutions will be further shortened.

[0235] Furthermore, a Kerr nonlinear parametric oscillator is used as the quantum bit device 310 of the quantum annealing machine 300. When the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the parameter value determination unit 110 determines the quantum annealing time to be a value that is between 1 and 10 times the product of the reciprocal of the coherent drive ε and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive ε.

[0236] According to the parameter adjustment device 100, when a combinatorial optimization problem with multiple optimal solutions is embedded using the LHZ method in the quantum annealing machine 300, which uses a Kerr nonlinear parametric oscillator as the quantum bit device 310, and quantum annealing is performed repeatedly, it is expected that the possibility of obtaining multiple optimal solutions will be further increased.

[0237] In particular, the TTAS value is expected to be further reduced when the parameter adjustment device 100 is set to a mode that aims to shorten the time required to obtain multiple optimal solutions. In this respect, the parameter adjustment device 100 is expected to further shorten the time required to obtain multiple optimal solutions.

[0238] Furthermore, for a quantum annealing machine having a structure represented by the LHZ model, when the magnitude of the interaction and local field of the model embedded in the LHZ model is set to 1, the parameter value determination unit 110 determines the quantum annealing time as a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, as values ​​after performing appropriate unit conversion, and determines the four-body interaction coefficient value as a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0239] The parameter adjustment device 100 is expected to be able to obtain multiple optimal solutions when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved using quantum annealing with the LHZ method. In particular, the parameter adjustment device 100 is expected to provide a relatively small TTAS value, which is an index indicating the total quantum annealing time required to obtain all specific optimal solutions. In this respect, the parameter adjustment device 100 is expected to provide a relatively short time required to obtain multiple optimal solutions.

[0240] Second Embodiment Fig. 27 is a diagram showing an example of the configuration of a parameter adjustment node according to at least one embodiment. In the configuration shown in Fig. 27, a parameter adjustment node 610 includes a determination unit 611.

[0241] With this configuration, the determination unit 611 performs at least one of the following for a quantum annealing machine having a structure represented by the LHZ model: determining the quantum annealing time to a value equal to or less than the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant; and determining the four-body interaction coefficient value to a value whose magnitude is equal to or greater than five times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The determination unit 611 corresponds to an example of a determination means.

[0242] The parameter adjustment device 610 is expected to obtain multiple optimal solutions when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved using quantum annealing with the LHZ method. In particular, the parameter adjustment device 610 is expected to obtain a relatively large value for the Number to Reject Fair Sampling, which is an index indicating the strength of the tendency toward fair sampling. In this respect, the parameter adjustment device 610 is expected to obtain different optimal solutions (i.e., multiple optimal solutions) when an optimal solution is obtained multiple times.

[0243] Third Embodiment Fig. 28 is a diagram showing an example of the configuration of a parameter adjustment node according to at least one embodiment. In the configuration shown in Fig. 28, a parameter adjustment node 620 includes a determination unit 621.

[0244] With this configuration, the determination unit 621 determines the quantum annealing time for a quantum annealing machine having a structure represented by the LHZ model to be a value that is between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be between 2 and 5 times the magnitude of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0245] The parameter adjustment device 620 is expected to be able to obtain multiple optimal solutions when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved using quantum annealing with the LHZ method. In particular, the parameter adjustment device 620 is expected to provide a relatively small TTAS value, which is an index indicating the total quantum annealing time required to obtain all specific optimal solutions. In this respect, the parameter adjustment device 620 is expected to provide a relatively short time required to obtain multiple optimal solutions.

[0246] 29 is a diagram showing an example of the configuration of a quantum annealing system according to at least one embodiment. In the configuration shown in Fig. 29, a quantum annealing system 630 includes a quantum annealing machine 631 and a parameter adjustment device 632. The parameter adjustment device 632 includes a determination unit 633.

[0247] In this configuration, the quantum annealing machine 631 has a structure shown in the LHZ model. The determination unit 633 performs at least one of the following: determining the quantum annealing time for the quantum annealing machine 631 to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant; and determining the four-body interaction coefficient value to be a value whose magnitude is at least five times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The quantum annealing machine 631 repeatedly performs quantum annealing in accordance with the determined quantum annealing time and four-body interaction coefficient value. The determination unit 633 is an example of a determination means.

[0248] According to the quantum annealing system 630, when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved by quantum annealing using the LHZ method, it is expected that multiple optimal solutions will be obtained. In particular, according to the quantum annealing system 630, it is expected that the value of the Number to Reject Fair Sampling, which is an index value indicating the strength of the tendency toward fair sampling, will be relatively large. In this respect, according to the quantum annealing system 630, when an optimal solution is obtained multiple times, it is expected that different optimal solutions (i.e., multiple optimal solutions) will be obtained.

[0249] Fifth Embodiment Fig. 30 is a diagram showing an example of the configuration of a quantum annealing system according to at least one embodiment. In the configuration shown in Fig. 30, a quantum annealing system 640 includes a quantum annealing machine 641 and a parameter adjustment device 642. The parameter adjustment device 642 includes a determination unit 643.

[0250] With this configuration, the quantum annealing machine 641 has a structure shown in the LHZ model. The determination unit 643 determines the quantum annealing time for the quantum annealing machine 641 to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The quantum annealing machine 641 repeatedly performs quantum annealing in accordance with the determined quantum annealing time and four-body interaction coefficient value. The determination unit 643 corresponds to an example of a determination means.

[0251] According to the quantum annealing system 640, when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved by quantum annealing using the LHZ method, it is expected that multiple optimal solutions will be obtained. In particular, according to the quantum annealing system 640, it is expected that the TTAS value, which is an index value indicating the total quantum annealing time until all specific optimal solutions are obtained, will be relatively small. In this respect, according to the quantum annealing system 640, it is expected that the time required to obtain multiple optimal solutions will be relatively short.

[0252] Sixth Embodiment Fig. 31 is a diagram showing an example of a processing procedure in a parameter adjustment method according to at least one embodiment. The parameter adjustment method shown in Fig. 31 includes determining a parameter value (step S611).

[0253] In determining the parameter values ​​(step S611), a computer that determines the parameter values ​​for a quantum annealing machine having a structure represented by the LHZ model performs at least one of the following: determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant; and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0254] According to the parameter adjustment method shown in Figure 31, when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved by quantum annealing using the LHZ method, it is expected that multiple optimal solutions will be obtained. In particular, according to the parameter adjustment method shown in Figure 31, it is expected that the value of Number to Reject Fair Sampling, which is an index value indicating the strength of the tendency toward fair sampling, will be relatively large. In this respect, according to the parameter adjustment method shown in Figure 31, when an optimal solution is obtained multiple times, it is expected that different optimal solutions (i.e., multiple optimal solutions) will be obtained.

[0255] Seventh Embodiment Fig. 32 is a diagram showing an example of a processing procedure in a parameter adjustment method according to at least one embodiment. The parameter adjustment method shown in Fig. 32 includes determining a parameter value (step S621).

[0256] In determining the parameter values ​​(step S621), a computer that determines the parameter values ​​for a quantum annealing machine having a structure represented by the LHZ model determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0257] According to the parameter adjustment method shown in Figure 32, when a combinatorial optimization problem with multiple optimal solutions is repeatedly solved by quantum annealing using the LHZ method, it is expected that multiple optimal solutions will be obtained. In particular, according to the parameter adjustment method shown in Figure 32, it is expected that the value of TTAS, which is an index value indicating the total quantum annealing time until all specific optimal solutions are obtained, will be relatively small. In this respect, according to the parameter adjustment method shown in Figure 32, it is expected that the time required to obtain multiple optimal solutions will be relatively short.

[0258] 33 is a diagram illustrating the configuration of a computer according to at least one embodiment. In the configuration shown in FIG. 33, a computer 700 includes a CPU (Central Processing Unit) 710, a main memory device 720, an auxiliary memory device 730, and an interface 740.

[0259] One or more of the parameter adjustment node 100, control device 200, parameter adjustment node 610, parameter adjustment node 620, parameter adjustment node 632, and parameter adjustment node 642, or a portion thereof, may be implemented in the computer 700. In this case, the operation of each of the above-described processing units is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-described processing in accordance with the program. The CPU 710 also allocates storage areas in the main storage device 720 corresponding to each of the above-described storage units in accordance with the program. Communication between each device and other devices is achieved by the interface 740 having a communication function and communicating under the control of the CPU 710.

[0260] When the parameter adjustment device 100 is implemented in the computer 700, its operations are stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-mentioned processing in accordance with the program.

[0261] The CPU 710 also allocates a storage area in the main memory device 720 for the parameter adjustment node 100 to perform processing in accordance with the program. Communication between the parameter adjustment node 100 and other devices is achieved by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the parameter adjustment node 100 and a user is achieved by the interface 740 having a display device and input device, displaying various images under the control of the CPU 710, and accepting user operations.

[0262] When the control device 200 is implemented in the computer 700, its operation is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-described processing in accordance with the program.

[0263] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 200 to perform processing in accordance with the program. Communication between the control device 200 and other devices is performed by the interface 740, which has a communication function and performs communication under the control of the CPU 710. Interaction between the control device 200 and a user is performed by the interface 740, which has a display device and an input device, displaying various images under the control of the CPU 710 and accepting user operations.

[0264] When the parameter adjustment device 610 is implemented in the computer 700, its operation is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-described processing in accordance with the program.

[0265] The CPU 710 also allocates a storage area in the main storage device 720 for the parameter adjustment device 610 to perform processing in accordance with the program. Communication between the parameter adjustment device 610 and other devices is achieved by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the parameter adjustment device 610 and a user is achieved by the interface 740 having a display device and input device, displaying various images under the control of the CPU 710, and accepting user operations.

[0266] When the parameter adjustment device 620 is implemented in the computer 700, its operation is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-described processing in accordance with the program.

[0267] The CPU 710 also allocates a storage area in the main memory 720 for the parameter adjustment device 620 to perform processing in accordance with the program. Communication between the parameter adjustment device 620 and other devices is achieved by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the parameter adjustment device 620 and a user is achieved by the interface 740 having a display device and an input device, displaying various images under the control of the CPU 710, and accepting user operations.

[0268] When the parameter adjustment device 632 is implemented in the computer 700, its operation is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-described processing in accordance with the program.

[0269] Furthermore, the CPU 710, in accordance with the program, allocates a storage area in the main storage device 720 for the parameter adjustment device 632 to perform processing. Communication between the parameter adjustment device 632 and other devices is achieved by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the parameter adjustment device 632 and a user is achieved by the interface 740 having a display device and an input device, displaying various images under the control of the CPU 710, and accepting user operations.

[0270] When the parameter adjustment device 642 is implemented in the computer 700, its operation is stored in the form of a program in the auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-described processing in accordance with the program.

[0271] Furthermore, the CPU 710, in accordance with the program, allocates a storage area in the main storage device 720 for the parameter adjustment device 642 to perform processing. Communication between the parameter adjustment device 642 and other devices is achieved by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the parameter adjustment device 642 and a user is achieved by the interface 740 having a display device and an input device, displaying various images under the control of the CPU 710, and accepting user operations.

[0272] One or more of the above-described programs may be recorded on nonvolatile recording medium 750. In this case, interface 740 may read the programs from nonvolatile recording medium 750. Then, CPU 710 may directly execute the programs read by interface 740, or may temporarily store the programs in main storage device 720 or auxiliary storage device 730 and then execute them.

[0273] Note that a program for executing all or part of the processing performed by the parameter adjustment device 100, the control device 200, the parameter adjustment device 610, the parameter adjustment device 620, the parameter adjustment device 632, and the parameter adjustment device 642 may be recorded on a computer-readable recording medium, and the program recorded on the recording medium may be loaded into a computer system and executed to perform the processing of each unit. Note that the term "computer system" here includes hardware such as an operating system (OS) and peripheral devices. Furthermore, the term "computer-readable recording medium" refers to portable media such as flexible disks, optical magnetic disks, read-only memories (ROMs), and compact disc read-only memories (CD-ROMs), as well as storage devices such as hard disks built into computer systems. The program may be designed to implement part of the aforementioned functions, or may be capable of implementing the aforementioned functions in combination with a program already recorded on the computer system.

[0274] Although the embodiments of the present invention have been described above in detail with reference to the drawings, the specific configuration is not limited to these embodiments and includes designs within the scope of the present invention. Furthermore, the above-described embodiments may be combined with other embodiments as appropriate.

[0275] Some or all of the above-described embodiments can be described as, but are not limited to, the following supplementary notes.

[0276] (Supplementary Note 1) A parameter adjustment device comprising: a determination means for performing at least one of the following: determining a quantum annealing time for a quantum annealing machine having a structure represented by an LHZ model to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of a Hamiltonian of a model embedded in the LHZ model and the Dirac constant; and determining a four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of a Hamiltonian of a model embedded in the LHZ model.

[0277] (Supplementary Note 2) The parameter adjustment device according to Supplementary Note 1, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determination means performs at least one of determining the quantum annealing time to be a value equal to or less than the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is equal to or greater than five times the coherent drive.

[0278] (Appendix 3) When the solution search mode by quantum annealing is set to a mode that aims to equalize the probability of obtaining each optimal solution, the determination means performs at least one of determining the quantum annealing time to a value that is 1 time the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, the determination means determines the quantum annealing time to a value that is 1 time or more and 10 times or less the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to a value whose magnitude is 2 times or more and 5 times or less the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. 2. The parameter adjustment device of claim 1.

[0279] (Supplementary Note 4) The parameter adjustment device according to Supplementary Note 3, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determination means, when the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, determines the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of a coherent drive and a Dirac constant, and determines the four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coherent drive.

[0280] (Supplementary Note 5) The parameter adjustment device according to Supplementary Note 3, wherein when the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0281] (Supplementary Note 6) The parameter adjustment device according to Supplementary Note 5, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determination means, when the solution search mode is set to a mode that measures the reduction of the time required to obtain multiple optimal solutions, determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of a coherent drive and a Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive.

[0282] (Supplementary Note 7) A parameter adjustment device comprising: a determination means for determining, for a quantum annealing machine having a structure represented by an LHZ model, a quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of a Hamiltonian of a model embedded in the LHZ model and a Dirac constant, and determining a four-body interaction coefficient value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0283] (Supplementary Note 8) The parameter adjustment device according to Supplementary Note 7, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of a coherent drive and a Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive.

[0284] (Supplementary Note 9) The parameter adjustment device according to Supplementary Note 7, wherein the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0285] (Supplementary Note 10) The parameter adjustment device according to Supplementary Note 9, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of a coherent drive and a Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive.

[0286] (Supplementary Note 11) A quantum annealing system comprising: a quantum annealing machine having a structure represented by an LHZ model; and a parameter adjustment device; wherein the parameter adjustment device comprises determination means for the quantum annealing machine that at least one of: determining a quantum annealing time to be equal to or less than the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and a Dirac constant; and determining a four-body interaction coefficient value to be equal to or greater than five times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and wherein the quantum annealing machine repeatedly performs quantum annealing in accordance with the determined quantum annealing time and four-body interaction coefficient value.

[0287] (Supplementary Note 12) The quantum annealing system described in Supplementary Note 11, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determining means performs at least one of determining the quantum annealing time to a value equal to or less than the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is equal to or greater than five times the coherent drive.

[0288] (Appendix 13) When the solution search mode by quantum annealing is set to a mode that aims to equalize the probability of obtaining each optimal solution, the determination means performs at least one of determining the quantum annealing time to a value that is 1 time the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, the determination means determines the quantum annealing time to a value that is 1 time or more and 10 times or less the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to a value whose magnitude is 2 times or more and 5 times or less the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. 12. The quantum annealing system of claim 11.

[0289] (Supplementary Note 14) A quantum annealing system according to Supplementary Note 13, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and when the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive.

[0290] (Supplementary Note 15) The quantum annealing system according to Supplementary Note 13, wherein, when the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0291] (Supplementary Note 16) A quantum annealing system according to Supplementary Note 15, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and when the solution search mode is set to a mode that measures the reduction in the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive.

[0292] (Supplementary Note 17) A quantum annealing system comprising: a quantum annealing machine having a structure represented by an LHZ model; and a parameter adjustment device; wherein the parameter adjustment device comprises determination means for determining, for the quantum annealing machine, a quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, as values ​​after appropriate unit conversion, when the magnitudes of the interaction and local fields of the Ising model embedded in the LHZ model are 1; and determining a four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and wherein the quantum annealing machine repeatedly performs quantum annealing in accordance with the determined quantum annealing time and four-body interaction coefficient value.

[0293] (Supplementary Note 18) The quantum annealing system according to Supplementary Note 17, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determining means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive.

[0294] (Supplementary Note 19) The quantum annealing system according to Supplementary Note 17, wherein the determining means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0295] (Supplementary Note 20) The quantum annealing system according to Supplementary Note 19, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the determining means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive.

[0296] (Supplementary Note 21) A parameter adjustment method, comprising: a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model, performing at least one of the following: determining a quantum annealing time to a value that is 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant; and determining a four-body interaction coefficient value to a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model.

[0297] (Supplementary Note 22) The parameter adjustment method according to Supplementary Note 21, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes the computer determining the quantum annealing time to be 1 times or less the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coherent drive.

[0298] (Supplementary Note 23) When the computer is set in a mode of solution search by quantum annealing that equalizes the probability of obtaining each optimal solution, at least one of determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant and determining the four-body interaction coefficient value to be 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model is determined. and determining the four-body interaction coefficient value to a value whose magnitude is five times or more of the coefficient value of a longitudinal magnetic field term of a Hamiltonian of a model to be embedded in the LHZ model, and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value whose magnitude is one to ten times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of a Hamiltonian of the model to be embedded in the LHZ model and a Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is two to five times the coefficient value of the longitudinal magnetic field term of a Hamiltonian of the model to be embedded in the LHZ model.

[0299] (Supplementary Note 24) The parameter adjustment method according to Supplementary Note 23, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value that is between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes, when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value that is between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coherent drive, by the computer.

[0300] (Supplementary Note 25) When the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes, when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, by the computer. 24. The parameter adjustment method according to claim 23.

[0301] (Supplementary Note 26) The parameter adjustment method according to Supplementary Note 25, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value that is between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes, when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value that is between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 4 times the coherent drive, by the computer.

[0302] (Supplementary Note 27) A parameter adjustment method comprising: a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model determines a quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant, and determines a four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0303] (Supplementary Note 28) The parameter adjustment method according to Supplementary Note 27, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes the computer determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive.

[0304] (Supplementary Note 29) The parameter adjusting method according to Supplementary Note 27, wherein determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and a Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes the computer determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and a Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0305] (Supplementary Note 30) The parameter adjustment method according to Supplementary Note 29, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, includes the computer determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive.

[0306] (Supplementary Note 31) A recording medium having recorded thereon a program that causes a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model to perform at least one of the following: determining a quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant; and determining a four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model.

[0307] (Appendix 32) The recording medium described in Appendix 31, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the program causes the computer to execute at least one of determining the quantum annealing time to be equal to or less than the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be equal to or more than five times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, and determining the quantum annealing time to be equal to or less than the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be equal to or more than five times the coherent drive.

[0308] (Supplementary Note 33) When at least one of determining the quantum annealing time to be one time the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant and determining the four-body interaction coefficient value to be five times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model is performed, the program can determine that when the mode of solution search by quantum annealing is set to a mode that equalizes the probability of obtaining each optimal solution, the quantum annealing time is set to be one time the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant. and determining the four-body interaction coefficient value to a value whose magnitude is five times or more of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, determining the quantum annealing time to a value whose magnitude is one to ten times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is two to five times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0309] (Supplementary Note 34) The recording medium according to Supplementary Note 33, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, the quantum annealing time is determined to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and the four-body interaction coefficient value is determined to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, wherein the program causes the computer to execute the following when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions: determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive.

[0310] (Appendix 35) When the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, the quantum annealing time is determined to be a value that is 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and the four-body interaction coefficient value is determined to be a value whose magnitude is 2 to 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. In this case, the program causes the computer to execute the following when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions: determining the quantum annealing time to be a value that is 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is 2 to 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. 34. The recording medium according to claim 33.

[0311] (Supplementary Note 36) The recording medium according to Supplementary Note 35, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, the quantum annealing time is determined to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and the four-body interaction coefficient value is determined to be a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, wherein the program causes the computer to execute the following when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions: determining the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determining the four-body interaction coefficient value to be a value whose magnitude is between 2 and 4 times the coherent drive.

[0312] (Supplementary Note 37) A recording medium having recorded thereon a program that causes a computer that determines parameter values ​​for a quantum annealing machine having a structure represented by an LHZ model to execute the following: determining a quantum annealing time to a value that is 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to a value whose magnitude is 2 to 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of a model embedded in the LHZ model.

[0313] (Appendix 38) The recording medium described in Appendix 37, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the quantum annealing time is determined to be 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and the four-body interaction coefficient value is determined to be a value whose magnitude is 2 to 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, the program causing the computer to determine the quantum annealing time to be 1 to 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determine the four-body interaction coefficient value to be a value whose magnitude is 2 to 5 times the coherent drive.

[0314] (Supplementary Note 39) The recording medium according to Supplementary Note 37, wherein determining the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, comprises the program causing the computer to determine the quantum annealing time to a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is between 2 and 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model.

[0315] (Appendix 40) The recording medium described in Appendix 39, wherein a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine, and the quantum annealing time is determined to be 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and the four-body interaction coefficient value is determined to be a value whose magnitude is 2 to 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model, the program causing the computer to determine the quantum annealing time to be 1 to 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determine the four-body interaction coefficient value to be a value whose magnitude is 2 to 4 times the coherent drive.

[0316] The present invention may be applied to a parameter adjustment device, a quantum annealing system, a parameter adjustment method, and a recording medium.

[0317] 1, 630, 640 Quantum annealing system 100, 610, 620, 632, 642 Parameter adjustment device 110 Parameter value determination unit 111 Quantum annealing time determination unit 112 Four-body interaction determination unit 120 Parameter value output unit 200 Control device 300, 631, 641 Quantum annealing machine 310 Qubit device 320 Four-body coupler 611, 621, 633, 643 Determination unit

Claims

a determination means for determining, for a quantum annealing machine having a structure represented by an LHZ model, at least one of determining a quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of a Hamiltonian of a model embedded in the LHZ model and a Dirac constant, and determining a four-body interaction coefficient value to be 5 times or more the coefficient value of the longitudinal magnetic field term of a Hamiltonian of a model embedded in the LHZ model; A parameter adjustment device comprising: 　 a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine; The determining means determines the quantum annealing time to be 1 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coherent drive. The parameter adjustment device according to claim 1 . 　 When the solution search mode by quantum annealing is set to a mode that aims to equalize the probability of obtaining each optimal solution, the determination means performs at least one of determining the quantum annealing time to a value that is 1 time the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; and when the solution search mode is set to a mode that aims to shorten the time required to obtain a plurality of optimal solutions, the determination means determines the quantum annealing time to a value that is 1 time or more and 10 times or less the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to a value whose magnitude is 2 times or more and 5 times or less the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The parameter adjustment device according to claim 1 . 　 a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine; When the solution search mode is set to a mode that shortens the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coherent drive. The parameter adjustment device according to claim 3 . 　 When the solution search mode is set to a mode that aims to shorten the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to be a value that is 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determines the four-body interaction coefficient value to be a value that is 2 to 4 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The parameter adjustment device according to claim 3 . 　 a Kerr nonlinear parametric oscillator is used as a quantum bit device of the quantum annealing machine; When the solution search mode is set to a mode that measures the reduction of the time required to obtain multiple optimal solutions, the determination means determines the quantum annealing time to be a value that is 1 to 10 times the product of the reciprocal of the coherent drive and the Dirac constant, and determines the four-body interaction coefficient value to be a value that is 2 to 4 times the coherent drive. The parameter adjustment device according to claim 5 . a determining means for determining a quantum annealing time for a quantum annealing machine having a structure represented by an LHZ model to be 1 to 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of a Hamiltonian of a model embedded in the LHZ model and a Dirac constant, and determining a four-body interaction coefficient value to be 2 to 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; A parameter adjustment device comprising: A quantum annealing machine having a structure represented by an LHZ model and a parameter adjustment device, the parameter adjustment device, a determination means for determining, for the quantum annealing machine, at least one of determining a quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to be a value whose magnitude is 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; Equipped with the quantum annealing machine repeatedly performs quantum annealing according to the determined quantum annealing time and four-body interaction coefficient value; Quantum annealing system. A quantum annealing machine having a structure represented by an LHZ model and a parameter adjustment device, the parameter adjustment device, a determination means for determining a quantum annealing time for the quantum annealing machine to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; Equipped with the quantum annealing machine repeatedly performs quantum annealing according to the determined quantum annealing time and four-body interaction coefficient value; Quantum annealing system. A computer that determines parameter values ​​for a quantum annealing machine having a structure represented by the LHZ model, At least one of determining the quantum annealing time to be 1 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining the four-body interaction coefficient value to be 5 times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The parameter adjustment method includes: A computer that determines parameter values ​​for a quantum annealing machine having a structure represented by the LHZ model, The quantum annealing time is determined to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and the four-body interaction coefficient value is determined to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model. The parameter adjustment method includes: A computer that determines parameter values ​​for a quantum annealing machine having a structure represented by the LHZ model, determining a quantum annealing time to be one time the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to be five times or more the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; A recording medium that records a program that executes the above. A computer that determines parameter values ​​for a quantum annealing machine having a structure represented by the LHZ model, determining a quantum annealing time to be a value between 1 and 10 times the product of the reciprocal of the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model and the Dirac constant, and determining a four-body interaction coefficient value to be a value whose magnitude is between 2 and 5 times the coefficient value of the longitudinal magnetic field term of the Hamiltonian of the model embedded in the LHZ model; A recording medium that records a program that executes the above.

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