Association device, control device, quantum annealing system, association method, control method, and recording medium

Abstract

This association device comprises an association means for: respectively associating two three-node closed paths, which share one edge in a graph configured by using nodes and edges, with two four-body couplers which share two quantum bit devices and in which one quantum bit device among the two shared quantum bit devices is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating an edge other than the edge shared by the two three-node closed paths among edges of the two three-node closed paths with a quantum bit device other than the quantum bit devices shared by the two four-body couplers among quantum bit devices coupled by the four-body couplers respectively associated with the closed paths.

Description

Association device, control device, quantum annealing system, association method, control method, and recording medium

[0001] The present invention relates to an association device, a control device, a quantum annealing system, an association method, a control method, and a recording medium.

[0002] In quantum annealing, one of the methods for associating a combinatorial optimization problem with an annealing machine is the LHZ method (see, for example, Patent Document 1).

[0003] Japanese Patent Application Publication No. 2022-076900

[0004] When performing quantum annealing, it is preferable that the annealing machine be small in scale.

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

[0006] According to a first aspect of the present disclosure, an association device includes association means for associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; for associating an edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and for associating an edge of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0007] According to a second aspect of the present disclosure, the correspondence apparatus includes correspondence means for repeatedly associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and for repeatedly associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler, until all edges of the graph have been associated with quantum bit devices.

[0008] According to a third aspect of the present disclosure, a control device includes: association means for associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; association means for associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and association means for associating, among the edges of the two three-node closed paths, edges other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated; and control means for controlling an annealing machine including the four-body couplers and the quantum bit devices, based on the association relationships obtained by the association means.

[0009] According to a fourth aspect of the present disclosure, a control device includes: a correspondence means that corresponds each edge of a three-node closed path in a graph constructed using nodes and edges to each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and repeats corresponding each edge of the four-node closed path in the graph to each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices; and a control means that controls the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the correspondence means.

[0010] According to a fifth aspect of the present disclosure, a quantum annealing system includes an annealing machine and a control device, wherein the annealing machine includes quantum bit devices and a four-body coupler that couples four of the quantum bit devices together, and the control device associates two three-node closed paths that share one edge in a graph formed using nodes and edges with two four-body couplers that share two quantum bit devices, one of the two shared quantum bit devices being a fixed bit, and the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths to quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers; and control means for controlling the annealing machine based on the correspondence obtained by the correspondence by the correspondence means.

[0011] According to a sixth aspect of the present disclosure, a quantum annealing system includes an annealing machine and a control device, wherein the annealing machine includes a quantum bit device and a four-body coupler that couples the quantum bit devices four-body. The control device includes: association means that associates each edge of a three-node closed path in a graph formed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine formed using a four-body coupler and quantum bit devices, and repeats associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler, until all edges of the graph have been associated with quantum bit devices; and control means that controls the annealing machine based on the correspondence obtained by the association means.

[0012] According to a seventh aspect of the present disclosure, the correspondence method includes a computer associating each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers that share two quantum bit devices, one of the two shared quantum bit devices being a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0013] According to an eighth aspect of the present disclosure, a correspondence method includes a computer repeatedly associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler, until all edges of the graph have been associated with quantum bit devices.

[0014] According to a ninth aspect of the present disclosure, a control method includes a computer: associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; associating edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated; and controlling an annealing machine including the four-body couplers and the quantum bit devices based on the correspondences obtained by the associations.

[0015] According to a tenth aspect of the present disclosure, a control method includes a computer repeatedly associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices, and controlling the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the association.

[0016] According to an eleventh aspect of the present disclosure, a recording medium is a recording medium having recorded thereon a program that causes a computer to execute the following operations: associate two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associate the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associate the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers, among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0017] According to a twelfth aspect of the present disclosure, a recording medium is a recording medium having recorded thereon a program that causes a computer to execute the following steps: assigning each edge of a three-node closed path in a graph constructed using nodes and edges to each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and assigning each edge of the four-node closed path in the graph to each of the four quantum bit devices coupled by the four-body coupler; repeating this process until all edges of the graph have been assigned to quantum bit devices.

[0018] According to a thirteenth aspect of the present disclosure, a recording medium is a recording medium having recorded thereon a program that causes a computer to execute the following steps: associate two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associate the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associate the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers, among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated; and control an annealing machine that includes the four-body couplers and the quantum bit devices based on the correspondence obtained by the association.

[0019] According to a fourteenth aspect of the present disclosure, a recording medium is a recording medium having recorded thereon a program that causes a computer to execute the following steps: assigning each edge of a three-node closed path in a graph constructed using nodes and edges to each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; repeating the process of assigning each edge of the four-node closed path in the graph to each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been assigned to quantum bit devices; and controlling the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the assignment.

[0020] According to the present invention, when quantum annealing is performed, it is expected that the scale of the annealing machine will be relatively small.

[0021] 1 is a diagram illustrating an example of the configuration of a quantum annealing system according to at least one embodiment; 2 is a diagram illustrating an example of the configuration of an annealing machine according to at least one embodiment; 3 is a diagram illustrating an example of the configuration of a control device according to at least one embodiment; 4 is a diagram illustrating an example of a sparse graph; 5 is a diagram illustrating an example of a complete graph; 6 is a diagram illustrating an example of an annealing machine in the LHZ system; 7 is a diagram illustrating an example of mapping a sparse graph to an annealing machine by a mapping unit according to at least one embodiment; 8 is a diagram illustrating an example of two three-node cycles that share one edge; 9 is a diagram illustrating an example of mapping two three-node cycles that share one edge to an annealing machine or a portion thereof by a mapping unit according to at least one embodiment; 10 is a diagram illustrating an example of mapping a three-node cycle and a four-node cycle that share two edges to an annealing machine or a portion thereof by a mapping unit according to at least one embodiment; 11 is a diagram illustrating an example of a three-node cycle and a four-node cycle that share one edge. FIG. 1 is a diagram illustrating an example of mapping a three-node cycle and a four-node cycle that share one edge to an annealing machine or a portion thereof by an association unit according to at least one embodiment. FIG. 2 is a diagram illustrating an example of two four-node cycles that share two edges. FIG. 3 is a diagram illustrating an example of mapping two four-node cycles that share two edges to an annealing machine or a portion thereof by an association unit according to at least one embodiment. FIG. 4 is a diagram illustrating an example of two four-node cycles that share one edge to an annealing machine or a portion thereof by an association unit according to at least one embodiment. FIG. 5 is a diagram illustrating an example of mapping two four-node cycles that share one edge to an annealing machine or a portion thereof by an association unit according to at least one embodiment. FIG. 6 is a diagram illustrating an example of a processing procedure by which a control device according to at least one embodiment maps a graph to an annealing machine. FIG. 7 is a diagram illustrating an example of the configuration of an association device according to at least one embodiment.1 is a diagram illustrating an example of the configuration of an association device according to at least one embodiment; 2 is a diagram illustrating an example of the configuration of a control device according to at least one embodiment; 3 is a diagram illustrating an example of the configuration of a quantum annealing system according to at least one embodiment; 4 is a diagram illustrating an example of the configuration of a quantum annealing system according to at least one embodiment; 5 is a diagram illustrating an example of the processing steps in an association method according to at least one embodiment; 6 is a diagram illustrating an example of the processing steps in an association method according to at least one embodiment; 7 is a diagram illustrating an example of the processing steps in a control method according to at least one embodiment; 8 is a schematic block diagram illustrating the configuration of a computer according to at least one embodiment;

[0022] The following describes embodiments of the present invention, but the following embodiments do not limit the scope of the invention as claimed. Furthermore, not all of the combinations of features described in the embodiments are necessarily essential to the solution of the invention.

[0023] 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 an annealing machine 100 and a control device 200.

[0024] The annealing machine 100 performs quantum annealing under the control of the control device 200. Fig. 2 is a diagram showing an example of the configuration of the annealing machine 100. In the configuration shown in Fig. 2, the annealing machine 100 includes a quantum bit device 110 and a four-body coupler 120.

[0025] The quantum bit device 110 is an element for expressing a quantum bit. The quantum bits included in the annealing machine 100 are not limited to a specific type. For example, the quantum bit device 110 may be configured using a Josephson Parametric Oscillator (JPO), but is not limited thereto.

[0026] The four-body coupler 120 couples the four qubit devices 110. The coupling of the qubit devices is also referred to as the interaction of the qubit devices.

[0027] The control device 200 controls the annealing machine 100 to perform quantum annealing. In particular, the control device 200 determines an association between the combinatorial optimization problem to be solved by quantum annealing and the annealing machine 100, and controls the annealing machine 100 in accordance with the determined association. The control device 200 may be configured using a computer.

[0028] The control device 200 is an example of an association device. The device that associates the combinatorial optimization problem with the annealing machine 100 and the device that controls the annealing machine 100 in accordance with the determined association may be configured as separate devices.

[0029] Fig. 3 is a diagram showing an example of the configuration of the control device 200. In the configuration shown in Fig. 3, the control device 200 includes a communication unit 210, a display unit 220, an operation input unit 230, a storage unit 280, and a processing unit 290. The processing unit 290 includes a graph acquisition unit 291, an association unit 292, and a control unit 293.

[0030] The communication unit 210 communicates with other devices such as the annealing machine 100. For example, the communication unit 210 transmits a control signal for controlling the annealing machine 100 to the annealing machine 100. The communication unit 210 also receives a signal indicating the result of quantum annealing from the annealing machine 100. The communication unit 210 may also receive a combinatorial optimization problem from a device that stores the combinatorial optimization problem to be solved by quantum annealing.

[0031] The display unit 220 has a display screen such as a liquid crystal panel or an LED (Light Emitting Diode) panel, and acquires various images. For example, the display unit 220 may display various information related to quantum annealing, such as combinatorial optimization problems and quantum annealing results.

[0032] The operation input unit 230 includes input devices such as a keyboard and a mouse, and accepts user operations. For example, the operation input unit 230 may accept user operations for making various settings related to quantum annealing, such as setting the number of iterations of quantum annealing.

[0033] The storage unit 280 stores various types of data. For example, the storage unit 280 may store various types of data related to quantum annealing, such as a control schedule for the annealing machine 100 and the results of each quantum annealing run. The storage unit 280 is configured using a storage device included in the control device 200.

[0034] The processing unit 290 performs various processes by controlling each unit of the control device 200. The functions of the processing unit 290 are performed, for example, by a CPU (Central Processing Unit) included in the control device 200 reading and executing a program from the storage unit 280.

[0035] The graph acquisition unit 291 acquires a graph indicating the combinatorial optimization problem to be solved by quantum annealing. For example, the communication unit 210 may receive a graph indicating the combinatorial optimization problem to be solved by quantum annealing (a graphical representation of the combinatorial optimization problem) from another device. The graph acquisition unit 291 may then extract the graph from the signal received by the communication unit 210. A graph indicating the combinatorial optimization problem to be solved by quantum annealing may also be simply referred to as a graph.

[0036] The associating unit 292 associates the graph with the annealing machine 100. In particular, the associating unit 292 associates the edges of the graph with the quantum bit devices 110. The associating unit 292 is an example of associating means.

[0037] The control unit 293 controls the annealing machine 100 in accordance with the association performed by the association unit 292. In this way, the control unit 293 causes the annealing machine 100 to perform quantum annealing. The control unit 293 corresponds to an example of control means.

[0038] The association between a graph and an annealing machine performed by the association unit 292 will be further described. For example, consider the case where a sparse graph such as that shown in FIG. 4 is associated with the annealing machine 100. The sparse graph here is a graph that is not a complete graph. The complete graph here is a graph in which all nodes are directly connected to each other by edges.

[0039] Figure 4 is a diagram showing an example of a sparse graph. The graph in Figure 4 has five nodes, numbered 1 to 5. This graph also has edges that connect each of the node number pairs 1-2, 1-3, 1-4, 2-3, 2-5, 3-4, and 3-5. On the other hand, this graph does not have edges that directly connect each of the node number pairs 1-5, 2-4, and 4-5.

[0040] Hereinafter, an edge may be indicated by putting a "-" between two node numbers. For example, the edge connecting node 1 and node 2 is also referred to as edge 1-2.

[0041] Let us consider the case where this graph is associated with an annealing machine using the Lechner-Hauke-Zoller (LHZ) method. In the LHZ method, the complete graph is associated with an annealing machine composed of a combination of quantum bit devices and four-body couplers. When representing a sparse graph with a complete graph, the connection strength between nodes that do not have a direct edge in the sparse graph is set to 0 in the complete graph.

[0042] Figure 5 is a diagram showing an example of a complete graph. The graph in Figure 5 has five nodes, numbered 1 to 5. This graph also has edges that directly connect all of the nodes. When the combinatorial optimization problem represented by the graph in Figure 4 is represented by the graph in Figure 5, the connection strength between nodes represented by edges 1-5, 2-4, and 4-5 is set to 0.

[0043] The energy function (Hamiltonian) H of a combinatorial optimization problem expressed as a complete graph such as the graph in FIG. 5 is expressed as in equation (1).

[0044]

[0045] σ ｉ denotes a binary variable in a combinatorial optimization problem. ｉ takes the value of 1 or -1. ｉｊ is a two-variable term J ｉｊ σ ｉ σ ｊ is the coefficient in ｊ is a one-variable term h ｊ σ ｊ The coefficient J ｉｊ The value of and the coefficient h ｊ The value of is determined depending on the combinatorial optimization problem.

[0046] The energy function H shown in equation (1) is transformed into equation (2).

[0047]

[0048] Here, h ｊ =J ０ｊ Also, σ ０ = 1. The energy function H shown in equation (2) is rewritten as equation (3).

[0049]

[0050] σ （ｉ，ｊ） denotes a binary variable that takes the value 1 or -1. （ｉ，ｊ） = σ ｉ σ ｊN is a positive integer indicating the maximum value of j. A sub-expression indicating a penalty for making it difficult for contradictions to occur in the variable values ​​is added to the energy function indicated by equation (3), resulting in an energy function as indicated by equation (4).

[0051]

[0052] C denotes a parameter for adjusting the value of the penalty given to the energy function H when a contradiction occurs in the variable values.

[0053] FIG. 6 is a diagram showing an example of an annealing machine in the LHZ method. In the example of FIG. 6, white circles indicate quantum bit devices. Black circles indicate four-body couplers. The notation (ij), in which two numbers are enclosed in parentheses, such as (01), (02), ..., represents the variable σ in Equation (4). （ｉ，ｊ） The notation "+1" indicates that the quantum bit device is controlled as a fixed bit with a value of 1.

[0054] 7 shows an example of how a sparse graph is associated with an annealing machine in the LHZ method. Fig. 7 shows an example of how the graph in Fig. 4 is associated with an annealing machine in the LHZ method.

[0055] The notation (ij), in which two numbers are enclosed in parentheses, such as (12), (13), ..., indicates the quantum bit device to which the edge connecting the i-th node and the j-th node corresponds. This correspondence is determined by the variable σ in Equation (4), as in the example of FIG. （ｉ，ｊ） This corresponds to associating the quantum bit device with the quantum

[0056] The notation "+1" indicates that the qubit device is controlled as a fixed bit with a value of 1, as in the example of FIG. 6. The notation "0" indicates a qubit device to which no external field is applied. Not applying an external field to a qubit device is equivalent to J ｉｊ This corresponds to .times. ...

[0057] In the example of Figure 7, the graph of Figure 4 is associated with an annealing machine equipped with 13 qubit devices and 6 four-body couplers. For ease of understanding, the graph of Figure 4 is associated with h for each of j = 1, 2, ..., 5. ｊ = 0, that is, the variable σ in the above equation (1) ｊ Offset h ｊ The value of h is set to 0. ｊ If ≠0, the variable σ ０ and associate the graph of FIG. 4 with an annealing machine with 19 qubit devices and 10 four-body couplers.

[0058] 8 is a diagram showing an example of associating a sparse graph with the annealing machine 100 by the associating unit 292. FIG. 8 shows an example of associating the graph of FIG. 4 with the annealing machine 100.

[0059] In the example of FIG. 8, for ease of explanation, in the energy function H shown in Equation (1), h is used for j=1, 2, . . . , 5. ｊ = 0. In addition, J １５ σ １ σ ５ , J ２４ σ ２ σ ４ , J ４５ σ ４ σ ５ Each subexpression of １５ =J ２４ =J ４５ =0.

[0060] h ｊ If ≠0, it is conceivable to add a node 0 to the graph of FIG. 4, and connect the node 0 to each of the nodes 1 to 5 with edges to form a graph.

[0061] The correspondence shown in Fig. 8 can be achieved by associating the edges of the closed path in the graph of Fig. 4 with the quantum bit devices 110 coupled by the four-body coupler 120. For example, the correspondence unit 292 associates the edges 1-3, 3-4, and 1-4 of the closed path including the three nodes 1, 3, and 4 with the quantum bit devices 110 indicated by "(13)," "(34)," and "(14)." The correspondence unit 292 also sets the quantum bit device 110 indicated by "(13)," "(34)," and "(14)" and another quantum bit device coupled by the four-body coupler 120 as a fixed bit with a value of 1.

[0062] Furthermore, of the edges 1-2, 2-3, and 1-3 of the closed path including the three nodes 1, 2, and 3, the edge 1-3 is associated with the quantum bit device 110 indicated by "(13)." The association unit 292 associates the edges 1-2 and 2-3 with the quantum bit devices 110 indicated by "(12)" and "(23)." Furthermore, the other quantum bit device coupled to each of the quantum bit devices 110 indicated by "(12)," "(23)," and "(13)" via the four-body coupler 120 is set to a fixed bit with a value of 1.

[0063] Furthermore, of the edges 2-3, 3-5, and 2-5 of the closed path including the three nodes 2, 3, and 5, the edge 2-3 is associated with the quantum bit device 110 indicated by "(23)." The association unit 292 associates the edges 3-5 and 2-5 with the quantum bit devices 110 indicated by "(35)" and "(25)." Furthermore, the other quantum bit device coupled to each of the quantum bit devices 110 indicated by "(23)," "(35)," and "(25)" via the four-body coupler 120 is set to a fixed bit with a value of 1.

[0064] In the example of Figure 8, the association unit 292 associates the graph of Figure 4 with an annealing machine equipped with eight quantum bit devices and three four-body couplers. The annealing machine 100 in the example of Figure 8 is smaller in scale than the annealing machine in the example of Figure 7. The smaller the scale of the annealing machine, the fewer the number of control targets during quantum annealing, and in this respect, it is expected that quantum annealing can be performed with high accuracy. In other words, improvement in the solution-finding performance of quantum annealing is expected. Furthermore, the smaller the scale of the annealing machine, the lower (cheaper) the manufacturing and operating costs of the annealing machine are expected to be.

[0065] (Matching of two three-node closed paths sharing one edge) In this way, the matching unit 292 matches each of the two three-node closed paths sharing one edge with each of the two four-body couplers 120 that share two quantum bit devices 110, one of which is a fixed bit.

[0066] Furthermore, the associating unit 292 associates the edge shared by these two three-node closed circuits with the quantum bit devices 110 other than the fixed bit among the quantum bit devices 110 shared by the two four-body couplers 120 .

[0067] Furthermore, the association unit 292 associates the edges of these two three-node closed circuits other than the edge shared by the two three-node closed circuits with quantum bit devices 110 other than the quantum bit devices 110 shared by the two four-body couplers, among the quantum bit devices 110 coupled by the four-body couplers 120 to which each closed circuit is associated.

[0068] Figure 9 shows an example of two three-node cycles that share one edge. In the example of Figure 9, the cycle with three nodes 1, 2, and 3 and the cycle with three nodes 1, 3, and 4 share the edge 1-3.

[0069] Fig. 10 is a diagram showing an example of how the associating unit 292 associates two three-node cycles that share one edge with the annealing machine 100 or a portion thereof. Fig. 10 shows an example of how the associating unit 292 associates the two three-node cycles shown in Fig. 9 with the annealing machine 100 or a portion thereof.

[0070] 10 , the association unit 292 associates the edge 1-3 shared by two three-node closed circuits with the quantum bit device 110 indicated by “(13)” among the two quantum bit devices 110 shared by the two four-body couplers 120. Furthermore, the association unit 292 sets the quantum bit devices 110 other than the quantum bit device 110 indicated by “(13)” among the two quantum bit devices 110 shared by the two four-body couplers 120 as fixed bits with a value of 1.

[0071] Furthermore, the associating unit 292 associates the edges 1-2 and 2-3 of the closed path of the three nodes 1, 2, and 3 with the quantum bit devices 110 indicated by (12) and (23). Furthermore, the associating unit 292 associates the edges 1-4 and 3-4 of the closed path of the three nodes 1, 3, and 4 with the quantum bit devices 110 indicated by (14) and (34).

[0072] In addition, the association unit 292 associates each of a first closed path, which is a three-node closed path or a four-node closed path, and a second closed path, which is a three-node closed path or a four-node closed path that shares one or two edges with the first closed path, with each of two four-body couplers 120 that share at least one quantum bit device 110.

[0073] Furthermore, the associating unit 292 associates a shared edge, which is an edge shared by the first closed circuit and the second closed circuit, with a quantum bit device 110 shared by two four-body couplers 120 .

[0074] In addition, the association unit 292 associates edges of the first closed circuit other than the shared edges with quantum bit devices 110 other than the quantum bit devices 110 shared by two four-body couplers 120, among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated.

[0075] In addition, the association unit 292 associates the edges of the second closed circuit other than the shared edges with quantum bit devices 110 other than the quantum bit devices 110 shared by two four-body couplers 120, among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0076] 9 and 10, for example, the closed path of three nodes 1, 2, and 3 in Fig. 9 corresponds to an example of the first closed path. The closed path of three nodes 1, 3, and 4 corresponds to an example of the second closed path. The edge 1-3 corresponds to an example of one shared edge.

[0077] In addition, the quantum bit devices 110 indicated by "(12)", "(13)", and "(23)" in Figure 10, and the four-body couplers 120 that couple the quantum bit devices 110 that are fixed bits, are examples of four-body couplers 120 to which the first closed circuit is associated.

[0078] The quantum bit devices 110 indicated by "(13)", "(14)", and "(34)", as well as the four-body couplers 120 that couple the quantum bit devices 110 that are fixed bits, are examples of four-body couplers 120 to which the second closed circuit is associated.

[0079] The quantum bit device 110 indicated by "(13)" and the quantum bit device 110 that is a fixed bit are examples of quantum bit devices 110 that are shared by these two four-body couplers 120.

[0080] The associating unit 292 associates the edge 1-3, which is an example of a shared edge, with the quantum bit device 110 indicated by "(13)" among the quantum bit devices 110 shared by the two four-body couplers 120.

[0081] In addition, the association unit 292 associates each of the edges 1-2 and 2-3, which are edges of the first closed circuit other than the shared edges, with each of the quantum bit devices 110 indicated by "(12)" and "(23)," which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated.

[0082] In addition, the association unit 292 associates each of the edges 1-4 and 3-4 of the second closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(14)" and "(34)," which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0083] (Matching between a three-node closed path and a four-node closed path sharing two edges) The example in FIG. 9 can also be considered as a combination of a three-node closed path (1, 2, and 3) and a four-node closed path (1, 2, 3, and 4). In this case, the three-node closed path and the four-node closed path share two edges, 1-2 and 2-3. In this case, for example, the three-node closed path (1, 2, and 3) corresponds to an example of a first closed path. The four-node closed path (1, 2, 3, and 4) corresponds to an example of a second closed path. The edges 1-2 and 2-3 correspond to an example of two shared edges.

[0084] 11 is a diagram showing an example of association of a three-node closed path and a four-node closed path that share two edges with the annealing machine 100 or a part thereof by the association unit 292. Fig. 11 shows an example of association of the three-node closed path and the four-node closed path shown in Fig. 9 with the annealing machine 100 or a part thereof by the association unit 292.

[0085] 11 , the quantum bit devices 110 indicated by "(12)," "(13)," and "(23)," and the four-body couplers 120 coupling the quantum bit devices 110 that are fixed bits, correspond to examples of four-body couplers 120 associated with the first closed path. The four-body couplers 120 coupling the quantum bit devices 110 indicated by "(12)," "(23)," "(34)," and "(14)" correspond to examples of four-body couplers 120 associated with the second closed path.

[0086] The two quantum bit devices 110 indicated by "(12)" and "(23)" are examples of quantum bit devices 110 shared by these two four-body couplers 120. The association unit 292 associates the edges 1-2 and 2-3, which are examples of shared edges, with the quantum bit devices 110 indicated by "(12)" and "(23)" that are shared by the two four-body couplers 120.

[0087] In addition, the association unit 292 associates edges 1-3, which are edges of the first closed circuit other than the shared edges, with the quantum bit device 110 indicated by "(13)" among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated, other than the quantum bit device 110 shared by two four-body couplers 120.

[0088] In addition, the association unit 292 associates each of the edges 1-4 and 3-4 of the second closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(14)" and "(34)," which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0089] (Association between a three-node closed path and a four-node closed path sharing one edge) Fig. 12 is a diagram showing an example of a three-node closed path and a four-node closed path sharing one edge. In the example of Fig. 12, the three-node closed path (1, 2, and 3) and the four-node closed path (1, 3, 4, and 5) share the 1-2 edge. The three-node closed path (1, 2, and 3) corresponds to an example of the first closed path. The four-node closed path (1, 3, 4, and 5) corresponds to an example of the second closed path.

[0090] Fig. 13 is a diagram showing an example of association of a three-node closed path and a four-node closed path that share one edge with the annealing machine 100 or a part thereof by the association unit 292. Fig. 13 shows an example of association of the three-node closed path and the four-node closed path shown in Fig. 12 with the annealing machine 100 or a part thereof by the association unit 292.

[0091] 13, the quantum bit devices 110 indicated by "(12)", "(13)", and "(23)", and the four-body couplers 120 coupling the quantum bit devices 110 that are fixed bits, correspond to examples of four-body couplers 120 to which the first closed path is associated. The four-body couplers 120 coupling the quantum bit devices 110 indicated by "(12)", "(25)", "(45)", and "(14)" correspond to examples of four-body couplers 120 to which the second closed path is associated.

[0092] The quantum bit device 110 indicated by "(12)" is an example of a quantum bit device 110 shared by these two four-body couplers 120. The association unit 292 associates the edge 1-2, which is an example of a shared edge, with the quantum bit device 110 indicated by "(12)" that is shared by the two four-body couplers 120.

[0093] In addition, the association unit 292 associates each of the edges 1-3 and 2-3 of the first closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(13)" and "(23)" among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated, other than the quantum bit devices 110 shared by the two four-body couplers 120.

[0094] In addition, the association unit 292 associates each of the edges 2-5, 4-5, and 1-4, which are edges of the second closed circuit other than the shared edges, with each of the quantum bit devices 110 indicated by "(25)", "(45)", and "(14)", which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0095] (Matching of two four-node closed paths sharing two edges) Figure 14 is a diagram showing an example of two four-node closed paths sharing two edges. In the example of Figure 14, a closed path with four nodes, 1, 2, 3, and 4, and a closed path with four nodes, 1, 2, 3, and 5, share two edges, 1-2 and 2-3. For example, the closed path with four nodes, 1, 2, 3, and 4, corresponds to an example of a first closed path. The closed path with four nodes, 1, 2, 3, and 5, corresponds to an example of a second closed path.

[0096] Fig. 15 is a diagram showing an example of how two four-node cycles sharing two edges are associated with the annealing machine 100 or a portion thereof by the association unit 292. Fig. 15 shows an example of how two four-node cycles sharing two edges shown in Fig. 14 are associated with the annealing machine 100 or a portion thereof by the association unit 292.

[0097] 15 , the four-body couplers 120 coupling the quantum bit devices 110 indicated by “(12)”, “(23)”, “(34)”, and “(14)” correspond to examples of four-body couplers 120 associated with the first closed path. The four-body couplers 120 coupling the quantum bit devices 110 indicated by “(12)”, “(23)”, “(35)”, and “(15)” correspond to examples of four-body couplers 120 associated with the second closed path.

[0098] The two quantum bit devices 110 indicated by "(12)" and "(23)" are examples of quantum bit devices 110 shared by these two four-body couplers 120. The association unit 292 associates the edges 1-2 and 2-3, which are examples of shared edges, with the quantum bit devices 110 indicated by "(12)" and "(23)" that are shared by the two four-body couplers 120.

[0099] In addition, the association unit 292 associates each of the edges 3-4 and 1-4 of the first closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(34)" and "(14)" among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated, other than the quantum bit devices 110 shared by the two four-body couplers 120.

[0100] In addition, the association unit 292 associates each of the edges 3-5 and 1-5, which are edges of the second closed circuit other than the shared edges, with each of the quantum bit devices 110 indicated by "(35)" and "(15)," which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0101] (Matching of two four-node closed paths sharing one edge) Figure 16 is a diagram showing an example of two four-node closed paths sharing one edge. In the example of Figure 16, a closed path of four nodes, numbered 1, 2, 3, and 4, and a closed path of four nodes, numbered 1, 2, 5, and 6, share an edge 1-2. For example, the closed path of four nodes, numbered 1, 2, 3, and 4, is an example of a first closed path. The closed path of four nodes, numbered 1, 2, 5, and 6, is an example of a second closed path.

[0102] Fig. 17 is a diagram showing an example of how the associating unit 292 associates two four-node cycles that share one edge with the annealing machine 100 or a portion thereof. Fig. 17 shows an example of how the associating unit 292 associates two four-node cycles that share one edge shown in Fig. 16 with the annealing machine 100 or a portion thereof.

[0103] For example, the four-body couplers 120 coupling the quantum bit devices 110 indicated by "(12)", "(24)", "(34)", and "(13)" in Fig. 17 are examples of four-body couplers 120 associated with the first closed path. The four-body couplers 120 coupling the quantum bit devices 110 indicated by "(12)", "(26)", "(56)", and "(15)" are examples of four-body couplers 120 associated with the second closed path.

[0104] One quantum bit device 110 indicated by "(12)" corresponds to an example of a quantum bit device 110 shared by these two four-body couplers 120. The association unit 292 associates the edge 1-2, which corresponds to an example of a shared edge, with the quantum bit device 110 indicated by "(12)" that is shared by the two four-body couplers 120.

[0105] In addition, the association unit 292 associates each of the edges 2-4, 3-4, and 1-3 of the first closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(24)", "(34)", and "(13)", which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated.

[0106] In addition, the association unit 292 associates each of the edges 2-6, 5-6, and 1-5 of the second closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(26)", "(56)", and "(15)", which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0107] (Matching of two four-node closed paths sharing one edge and one node) The graph in Figure 4 can also be considered as two four-node closed paths sharing one edge and one node. Specifically, the closed path of four nodes 1, 2, 3, and 4 and the closed path of four nodes 1, 2, 3, and 5 can also be considered as sharing the 1-2 edge and the 3rd node. For example, the closed path of four nodes 1, 2, 3, and 4 is an example of a first closed path. The closed path of four nodes 1, 2, 3, and 5 is an example of a second closed path.

[0108] 18 is a diagram showing an example of how the associating unit 292 associates two four-node cycles that share one edge and one node with the annealing machine 100 or a portion thereof. FIG. 18 shows an example of how the associating unit 292 associates two four-node cycles that share one edge and one node, as shown in FIG. 4, with the annealing machine 100 or a portion thereof.

[0109] For example, the four-body couplers 120 coupling the quantum bit devices 110 indicated by "(12)", "(23)", "(34)", and "(14)" in Fig. 18 are examples of four-body couplers 120 associated with the first closed path. The four-body couplers 120 coupling the quantum bit devices 110 indicated by "(12)", "(25)", "(35)", and "(15)" are examples of four-body couplers 120 associated with the second closed path.

[0110] One quantum bit device 110 indicated by "(12)" corresponds to an example of a quantum bit device 110 shared by these two four-body couplers 120. The association unit 292 associates the edge 1-2, which corresponds to an example of a shared edge, with the quantum bit device 110 indicated by "(12)" that is shared by the two four-body couplers 120.

[0111] In addition, the association unit 292 associates each of the edges 2-3, 3-4, and 1-4 of the first closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(23)", "(34)", and "(14)", which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the first closed circuit is associated.

[0112] In addition, the association unit 292 associates each of the edges 2-5, 3-5, and 1-3 of the second closed circuit, which are edges other than the shared edges, with each of the quantum bit devices 110 indicated by "(25)", "(35)", and "(13)", which are quantum bit devices 110 other than the quantum bit device 110 shared by two four-body couplers 120 among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0113] As in the examples of Figures 4 and 9, depending on how a cycle is perceived, there may be multiple ways to select a cycle and associate a single graph or subgraph (part of a graph) with the annealing machine 100 or a part thereof. When associating a graph with the annealing machine 100, the association unit 292 may determine whether or not the association is actually possible. If it determines that the association is not possible, the association unit 292 may attempt another association.

[0114] 19 is a diagram showing an example of the procedure of the process in which the control device 200 associates a graph with the annealing machine 100. In the process in FIG. 19, the graph acquisition unit 291 acquires a graph (a graph indicating an optimization problem to be subjected to quantum annealing) (step S11).

[0115] Next, the association unit 292 selects one three-node closed path or one four-node closed path from the graph (step S12). Next, the association unit 292 selects a three-node closed path or one four-node closed path that shares an edge with one of the selected closed paths (step S13). In step S13, the association unit 292 selects a closed path that includes an edge that is not included in the selected closed path.

[0116] Next, the association unit 292 determines whether all edges included in the graph have been selected by selecting the closed loop (step S14). If the association unit 292 determines that there is an edge that has not yet been selected (step S14: NO), the process returns to step S13. In this case, the association unit 292 continues to select an unselected closed loop.

[0117] On the other hand, if it is determined in step S14 that all edges have been selected (step S14: YES), the association unit 292 attempts to associate the graph with the annealing machine 100 (step S21). In accordance with the selection of the closed path in steps S12 and S13, the association unit 292 associates the closed path with the four-body coupler 120 and the edges with the quantum bit devices 110, as in the example described above. If there is a quantum bit device 110 to which no edge is associated, the association unit 292 designates that quantum bit device 110 as a quantum bit device 110 to which no external field is applied.

[0118] Next, the association unit 292 determines whether or not the association of the graph with the annealing machine 100 has been successful (step S22). If the association unit 292 determines that the association has been successful (step S22: YES), the control unit 293 controls the annealing machine 100 to perform quantum annealing (step S31).

[0119] The control device 200 then outputs the results of the quantum annealing (step S32). For example, the control unit 293 may control the display unit 220 to display the results of the quantum annealing, such as the bit values ​​of each quantum bit device 110. Alternatively, if the control device 200 is configured as a server device that provides a service for executing quantum annealing, the control unit 293 may control the communication unit 210 to transmit the results of the quantum annealing to the device that issued the request. After step S32, the control device 200 ends the processing of FIG. 19.

[0120] On the other hand, if it is determined in step S22 that the association of the graph with the annealing machine 100 has failed (step S22: NO), the association unit 292 determines whether or not a cycle selection other than the cycle selection already performed is possible (step S41). In other words, the association unit 292 determines whether or not all edges of the graph can be selected in a combination different from the cycle combinations obtained by the cycle selection already performed.

[0121] If it is determined that a closed path selection other than the closed path selection already performed is possible (step S41: YES), the association unit 292 resets the closed path selection once (step S51). After step S51, the process returns to step S12. In this case, the association unit 292 attempts to select a closed path other than the closed path selection already performed.

[0122] On the other hand, if the association unit 292 determines in step S41 that no other closed-loop selections are possible other than the closed-loop selections already performed, the control device 200 performs error processing (step S61). For example, the association unit 292 may control the display unit 220 to display an error message indicating that quantum annealing cannot be performed. Alternatively, if the control device 200 is configured as a server device that provides a quantum annealing execution service, the association unit 292 may control the communication unit 210 to transmit an error message to the requesting device. After step S61, the control device 200 ends the processing of FIG. 19.

[0123] As described above, the association unit 292 associates each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers 120 that share two quantum bit devices 110, one of which is a fixed bit. The association unit 292 also associates the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers. The association unit 292 also associates the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device 110 other than the quantum bit device 110 shared by the two four-body couplers among the quantum bit devices 110 coupled by the four-body coupler 120 to which the respective closed paths are associated.

[0124] The control device 200 can map a graph to the annealing machine 100 in the same way as mapping two three-node closed circuits that share one edge to two four-body couplers 120 that share a quantum bit device 110 that is considered a fixed bit. In this respect, the control device 200 is expected to make the annealing machine 100 relatively small in scale. For example, the control device 200 is expected to make the annealing machine 100 smaller in scale than the LHZ method.

[0125] Because the scale of the annealing machine 100 is relatively small, the control device 200 is expected to enable quantum annealing to be performed with relatively high accuracy. In other words, improvement in the solution-finding performance of quantum annealing is expected. Furthermore, the control device 200 is expected to reduce the manufacturing and operating costs of the annealing machine 100.

[0126] The associating unit 292 also associates, in the graph, a first closed path that is a three-node closed path or a four-node closed path, and a second closed path that is a three-node closed path or a four-node closed path that shares one or two edges with the first closed path, with each of the two four-body couplers 120 that share at least one quantum bit device 110. The associating unit 292 also associates a shared edge that is an edge shared by the first closed path and the second closed path, with a quantum bit device 110 shared by the two four-body couplers 120. The associating unit 292 also associates edges of the first closed path other than the shared edge with quantum bit devices 110 other than the quantum bit device 110 shared by the two four-body couplers 120, among the quantum bit devices 110 coupled by the four-body coupler 120 to which the first closed path is associated. In addition, the association unit 292 associates the edges of the second closed circuit other than the shared edges with quantum bit devices 110 other than the quantum bit devices 110 shared by two four-body couplers 120, among the quantum bit devices 110 coupled by the four-body couplers 120 to which the second closed circuit is associated.

[0127] The control device 200 can associate various graphs expressed by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, with the annealing machine 100. In this respect, the control device 200 can apply quantum annealing to various combinatorial optimization problems.

[0128] Furthermore, the association unit 292 associates each of two four-node closed paths that share two edges in the graph with each of two four-body couplers 120 that share two quantum bit devices. The association unit 292 also associates the edge shared by these two four-node closed paths with the quantum bit device 110 shared by the two four-body couplers 120. The association unit 292 also associates the edges of these two four-node closed paths other than the edge shared by the two four-node closed paths with quantum bit devices 110 other than the quantum bit device 110 shared by the two four-body couplers, among the quantum bit devices 110 coupled by the four-body couplers 120 to which the respective closed paths are associated.

[0129] According to the control device 200, a graph can be associated with the annealing machine 100 in the same way as associating two four-node closed circuits that share two edges with a four-body coupler that shares two quantum bit devices 110 that are fixed bits. In this respect, according to the control device 200, the scale of the annealing machine 100 is expected to be relatively small.

[0130] As described above, because the scale of the annealing machine 100 is relatively small, the control device 200 is expected to enable quantum annealing to be performed with relatively high accuracy. In other words, improvement in the solution-finding performance of quantum annealing is expected. Furthermore, the control device 200 is expected to reduce the manufacturing and operating costs of the annealing machine 100.

[0131] In addition, the correspondence unit 292 repeatedly associates the closed circuits with the four-body couplers 120 and the edges with the quantum bit devices 110 for all closed circuits included in the graph so that the edges included in the closed circuits are associated with the quantum bit devices 110 coupled by the four-body couplers 120.

[0132] The control device 200 allows various graphs to be associated with the annealing machine 100. For example, the control device 200 allows graphs of various sizes (various scales) to be associated with the annealing machine 100. In this respect, the control device 200 allows quantum annealing to be applied to various combinatorial optimization problems.

[0133] In addition, the correspondence unit 292 corresponds each edge of the three-node closed loop in the graph constructed using nodes and edges to each of three of the four quantum bit devices 110 coupled by one four-body coupler 120 in the annealing machine 100 constructed using the four-body coupler 120 and the quantum bit devices 110, and repeats this process of corresponding each edge of the four-node closed loop in the graph to each of the four quantum bit devices 110 coupled by the four-body coupler 120 until all edges of the graph have been corresponding to quantum bit devices 110.

[0134] The control device 200 can associate various graphs represented by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, with the annealing machine 100. For example, the control device 200 can associate graphs of various sizes (various scales) with the annealing machine 100. In this respect, the control device 200 can apply quantum annealing to various combinatorial optimization problems.

[0135] Furthermore, the associating unit 292 associates an edge shared by multiple closed circuits with one quantum bit device. The control device 200 can reflect the sharing of edges by multiple closed circuits in the association of the graph with the annealing machine 100. In this respect, the control device 200 is expected to be able to perform quantum annealing with a relatively high degree of accuracy.

[0136] Furthermore, the associating unit 292 associates, with fixed bits, the quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed circuit, among the four quantum bit devices coupled by one four-body coupler. According to the control device 200, the relationship between the variables represented by the three-node closed circuit can be reflected in the association of the graph with the annealing machine 100. In this respect, according to the control device 200, it is expected that quantum annealing can be performed with relatively high accuracy.

[0137] Second Embodiment Fig. 20 is a diagram showing an example of the configuration of an association device according to at least one embodiment. In the configuration shown in Fig. 20, an association device 610 includes an association unit 611.

[0138] In this configuration, the association unit 611 associates each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers that share two quantum bit devices and in which one of the two shared quantum bit devices is a fixed bit, associates the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers, and associates the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated. The association unit 611 is an example of association means.

[0139] The correspondence device 610 can correspond a graph to an annealing machine so that two three-node closed circuits sharing one edge are corresponded to two four-body couplers that share a qubit device that is considered a fixed bit. In this respect, the correspondence device 610 is expected to result in a relatively small annealing machine. For example, the correspondence device 610 is expected to result in an annealing machine with a smaller scale than the LHZ method.

[0140] Because the scale of the annealing machine is relatively small, the association device 610 is expected to be able to perform quantum annealing with relatively high accuracy. That is, improvement in the solution-finding performance of quantum annealing is expected. Furthermore, the association device 610 is expected to have relatively low manufacturing and operating costs for the annealing machine.

[0141] Third Embodiment Fig. 21 is a diagram showing an example of the configuration of an association device according to at least one embodiment. In the configuration shown in Fig. 21, an association device 620 includes an association unit 621.

[0142] In this configuration, the association unit 621 associates each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and repeats this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices. The association unit 621 is an example of an association means.

[0143] The association device 620 can associate various graphs represented by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, with annealing machines. For example, the association device 620 can associate graphs of various sizes (various scales) with annealing machines. In this respect, the association device 620 can apply quantum annealing to various combinatorial optimization problems.

[0144] 22 is a diagram illustrating an example of the configuration of a control device according to at least one embodiment. In the configuration illustrated in FIG. 22, a control device 630 includes an association unit 631 and a control unit 632.

[0145] In this configuration, the correspondence unit 631 corresponds each of two three-node closed paths that share one edge in a graph constructed using nodes and edges to each of two four-body couplers that share two quantum bit devices, one of which is a fixed bit; it corresponds the edge shared by the two three-node closed paths to a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and it corresponds the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths to a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0146] The control unit 632 controls the annealing machine including the four-body coupler and the quantum bit device based on the correspondence obtained by the correspondence performed by the correspondence unit 631. The correspondence unit 631 is an example of a correspondence means. The control unit 632 is an example of a control means.

[0147] The control device 630 can map a graph to an annealing machine in the same way that two three-node closed circuits sharing one edge are mapped to two four-body couplers that share a qubit device that is considered a fixed bit. In this respect, the control device 630 is expected to enable the annealing machine to be relatively small in scale. For example, the control device 630 is expected to enable the annealing machine to be smaller in scale than the LHZ method.

[0148] Because the scale of the annealing machine is relatively small, the control device 630 is expected to enable quantum annealing to be performed with relatively high accuracy. In other words, improvement in the solution-finding performance of quantum annealing is expected. Furthermore, the control device 630 is expected to reduce the manufacturing and operating costs of the annealing machine.

[0149] Fifth Embodiment Fig. 23 is a diagram illustrating an example of the configuration of a control device according to at least one embodiment. In the configuration illustrated in Fig. 23, a control device 640 includes an association unit 641 and a control unit 642.

[0150] In this configuration, the association unit 641 associates each edge of a three-node closed path in a graph formed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine formed using a four-body coupler and quantum bit devices, and repeats this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph are associated with quantum bit devices. The control unit 642 controls the annealing machine including the four-body coupler and quantum bit devices based on the association obtained by the association unit 641. The association unit 641 is an example of association means. The control unit 642 is an example of control means.

[0151] The control device 640 can associate various graphs represented by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, with the annealing machine. For example, the control device 640 can associate graphs of various sizes (various scales) with the annealing machine. In this respect, the control device 640 can apply quantum annealing to various combinatorial optimization problems.

[0152] Sixth Embodiment Fig. 24 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. 24, a quantum annealing system 650 includes an annealing machine 651 and a control device 654. The annealing machine 651 includes a quantum bit device 652 and a four-body coupler 653. The control device 654 includes an association unit 655 and a control unit 656.

[0153] With this configuration, the four-body coupler 653 couples four quantum bit devices 652. The association unit 655 associates each of two three-node closed paths that share one edge in a graph formed using nodes and edges with each of two four-body couplers 653 that share two quantum bit devices 652 and in which one of the two shared quantum bit devices 652 is a fixed bit, associates the edge shared by the two three-node closed paths with a quantum bit device 652 other than the fixed bit among the quantum bit devices 652 shared by the two four-body couplers 653, and associates the edge of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device 652 other than the quantum bit device 652 shared by the two four-body couplers 653 among the quantum bit devices 652 coupled by the four-body coupler 653 to which the respective closed paths are associated.

[0154] The control unit 656 controls the annealing machine 651 based on the correspondence obtained by the correspondence performed by the correspondence unit 655. The correspondence unit 655 is an example of correspondence means. The control unit 656 is an example of control means.

[0155] According to the quantum annealing system 650, a graph can be mapped to the annealing machine 651 in the same way as two three-node closed circuits sharing one edge are mapped to two four-body couplers that share a quantum bit device that is considered a fixed bit. According to the quantum annealing system 650, in this respect, the scale of the annealing machine 651 is expected to be relatively small. For example, according to the quantum annealing system 650, the scale of the annealing machine 651 is expected to be smaller than in the case of the LHZ method.

[0156] Because the scale of the annealing machine 651 is relatively small, the quantum annealing system 650 is expected to be able to perform quantum annealing with relatively high accuracy. In other words, improvement in the solution-finding performance of quantum annealing is expected. Furthermore, the quantum annealing system 650 is expected to have relatively low manufacturing and operating costs for the annealing machine 651.

[0157] Seventh Embodiment Fig. 25 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. 25, a quantum annealing system 660 includes an annealing machine 661 and a control device 664. The annealing machine 661 includes a quantum bit device 662 and a four-body coupler 663. The control device 664 includes an association unit 665 and a control unit 666.

[0158] With this configuration, the four-body coupler 663 couples four quantum bit devices 662. The association unit 665 associates each edge of a three-node closed path in a graph formed using nodes and edges with three of the four quantum bit devices 662 coupled by one four-body coupler 663 in an annealing machine 661 formed using a four-body coupler 663 and quantum bit devices 662, and repeats this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices 662 coupled by the four-body coupler 663 until all edges of the graph are associated with quantum bit devices 662.

[0159] The control unit 666 controls the annealing machine 661 based on the correspondence obtained by the correspondence performed by the correspondence unit 655. The correspondence unit 665 is an example of correspondence means. The control unit 666 is an example of control means.

[0160] The quantum annealing system 660 can associate various graphs expressed by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, with the annealing machine 661. For example, the quantum annealing system 660 can associate graphs of various sizes (various scales) with the annealing machine 661. In this respect, the quantum annealing system 660 can apply quantum annealing to various combinatorial optimization problems.

[0161] Eighth Embodiment Fig. 26 is a diagram showing an example of a processing procedure in an association method according to at least one embodiment. The association method shown in Fig. 26 includes performing association (step S611).

[0162] In making the correspondence (step S611), the computer corresponds each of two three-node closed paths that share one edge in a graph constructed using nodes and edges to each of two four-body couplers that share two quantum bit devices, one of which is a fixed bit; it corresponds the edge shared by the two three-node closed paths to a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and it corresponds the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths to a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0163] According to the correspondence method shown in Figure 26, a graph can be associated with an annealing machine so that two three-node closed circuits sharing one edge are associated with two four-body couplers that share a quantum bit device that is considered a fixed bit. According to the correspondence method shown in Figure 26, in this respect, the scale of the annealing machine is expected to be relatively small. For example, according to the correspondence method shown in Figure 26, the scale of the annealing machine is expected to be smaller than that of the LHZ method.

[0164] Because the scale of the annealing machine is relatively small, it is expected that quantum annealing can be performed with relatively high accuracy according to the association method shown in Figure 26. In other words, it is expected that the solution-finding performance of quantum annealing will be improved. Furthermore, according to the association method shown in Figure 26, it is expected that the manufacturing costs and operating costs of the annealing machine will be relatively small.

[0165] Ninth Embodiment Fig. 27 is a diagram showing an example of a processing procedure in an association method according to at least one embodiment. The association method shown in Fig. 27 includes performing association (step S621).

[0166] In making the correspondence (step S621), the computer corresponds each edge of a three-node closed loop in a graph constructed using nodes and edges to each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using a four-body coupler and quantum bit devices, and repeats this process of corresponding each edge of a four-node closed loop in the graph to each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been corresponding to quantum bit devices.

[0167] According to the correspondence method shown in Figure 27, various graphs expressed by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, can be associated with annealing machines. For example, according to the correspondence method shown in Figure 27, graphs of various sizes (various scales) can be associated with annealing machines. In this respect, according to the correspondence method shown in Figure 27, quantum annealing can be applied to various combinatorial optimization problems.

[0168] Tenth Embodiment Fig. 28 is a diagram showing an example of a processing procedure in a control method according to at least one embodiment. The control method shown in Fig. 28 includes performing association (step S631) and performing control (step S632).

[0169] In performing the correspondence (step S631), the computer corresponds each of two three-node closed paths that share one edge in a graph constructed using nodes and edges to each of two four-body couplers that share two quantum bit devices, one of which is a fixed bit; it corresponds the edge shared by the two three-node closed paths to a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and it corresponds the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths to a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated. In performing the control (step S632), the computer controls an annealing machine including the four-body couplers and the quantum bit devices based on the correspondence obtained by the correspondence.

[0170] According to the control method shown in Figure 28, a graph can be associated with an annealing machine in the same way that two three-node closed circuits sharing one edge are associated with two four-body couplers that share a quantum bit device that is considered a fixed bit. According to the control method shown in Figure 28, the scale of the annealing machine is expected to be relatively small in this respect. For example, according to the control method shown in Figure 28, the scale of the annealing machine is expected to be smaller than that of the LHZ method.

[0171] Because the scale of the annealing machine is relatively small, it is expected that quantum annealing can be performed with relatively high accuracy according to the control method shown in Figure 28. In other words, it is expected that the solution-finding performance of quantum annealing will be improved. Furthermore, it is expected that the manufacturing cost and operating cost of the annealing machine will be relatively small according to the control method shown in Figure 28.

[0172] 29 is a diagram illustrating an example of a processing procedure in a control method according to at least one embodiment. The control method illustrated in FIG. 29 includes performing association (step S641) and performing control (step S642).

[0173] In performing the correspondence (step S641), the computer corresponds each edge of a three-node closed path in a graph formed using nodes and edges to each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine formed using a four-body coupler and quantum bit devices, and repeats the process of corresponding each edge of the four-node closed path in the graph to each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices. In performing the control (step S642), the computer controls the annealing machine including the four-body coupler and quantum bit device based on the correspondence obtained by the correspondence.

[0174] According to the control method shown in Fig. 29, various graphs expressed by combinations of three-node and four-node loops, or combinations of either three-node or four-node loops, can be associated with the annealing machine. For example, according to the control method shown in Fig. 29, graphs of various sizes (various scales) can be associated with the annealing machine. In this respect, according to the control method shown in Fig. 29, quantum annealing can be applied to various combinatorial optimization problems.

[0175] 30 is a schematic block diagram showing the configuration of a computer according to at least one embodiment. In the configuration shown in Fig. 30, a computer 700 includes a CPU (Central Processing Unit) 710, a main memory device 720, an auxiliary memory device 730, an interface 740, and a non-volatile recording medium 750.

[0176] One or more of the control device 200, the association device 610, the association device 620, the control device 630, the control device 640, the control device 654, and the control device 664, or a part thereof, may be implemented in the computer 700. In this case, the operation of each of the above-mentioned 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-mentioned 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-mentioned storage units in accordance with the program. Communication between each device and other devices is executed by the interface 740, which has a communication function, and communicating under the control of the CPU 710.

[0177] When the control device 200 is implemented in a computer 700, the operations of the processing unit 290 and each of its units are stored in the form of a program in an 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.

[0178] Furthermore, the CPU 710 allocates a storage area for the storage unit 280 in the main storage device 720 in accordance with the program. Communication with other devices by the communication unit 210 is performed by the interface 740 having a communication function and operating under the control of the CPU 710. Display of images by the display unit 220 is performed by the interface 740 having a display device and displaying various images under the control of the CPU 710. Reception of user operations by the operation input unit 230 is performed by the interface 740 having an input device and receiving user operations under the control of the CPU 710.

[0179] When the association device 610 is implemented in the computer 700, the operation of the association unit 611 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.

[0180] Furthermore, the CPU 710, in accordance with the program, allocates a storage area in the main storage device 720 for the association device 610 to perform processing. Communication between the association device 610 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 association device 610 and a user is performed by the interface 740, which has an input device and an output device, presenting information to the user via the output device under the control of the CPU 710 and accepting user operations via the input device.

[0181] When the association device 620 is implemented in the computer 700, the operation of the association unit 621 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.

[0182] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the association device 620 to perform processing in accordance with the program. Communication between the association device 620 and other devices is performed by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the association device 620 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710 and accepting user operations via the input device.

[0183] When the control device 630 is implemented in the computer 700, the operations of the association unit 631 and the control unit 632 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-described processing in accordance with the program.

[0184] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 630 to perform processing in accordance with the program. Communication between the control device 630 and other devices is performed by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the control device 630 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0185] When the control device 640 is implemented in the computer 700, the operations of the association unit 641 and the control unit 642 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-described processing in accordance with the program.

[0186] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 640 to perform processing in accordance with the program. Communication between the control device 640 and other devices is performed by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the control device 640 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0187] When the control device 654 is implemented in the computer 700, the operations of the association unit 655 and the control unit 656 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-described processing in accordance with the program.

[0188] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 654 to perform processing in accordance with the program. Communication between the control device 654 and other devices is performed by the interface 740 having a communication function and performing communication under the control of the CPU 710. Interaction between the control device 654 and a user is performed by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0189] When the control device 664 is implemented in the computer 700, the operations of the association unit 665 and the control unit 666 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-described processing in accordance with the program.

[0190] Furthermore, the CPU 710 allocates a storage area in the main storage device 720 for the control device 664 to perform processing in accordance with the program. Communication between the control device 664 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 control device 664 and a user is achieved by the interface 740 having an input device and an output device, presenting information to the user via the output device under the control of the CPU 710, and accepting user operations via the input device.

[0191] 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.

[0192] Note that programs for executing all or part of the processing performed by control device 200, association device 610, association device 620, control device 630, control device 640, control device 654, and control device 664 may be recorded on a computer-readable recording medium, and the programs 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" herein 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 the computer system. Furthermore, the programs may be programs for implementing part of the functions described above, or may be programs that can realize the functions described above in combination with programs already recorded on the computer system.

[0193] 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.

[0194] A part or all of the above-described embodiments can be described as, but not limited to, the following supplementary notes.

[0195] (Supplementary Note 1) An association device comprising: association means for associating, in a graph constructed using nodes and edges, each of two three-node closed paths that share one edge with each of two four-body couplers that share two quantum bit devices, one of the two shared quantum bit devices being a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating, among the edges of the two three-node closed paths, the edge other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0196] (Supplementary Note 2) The association device described in Supplementary Note 1, wherein the association means associates, in the graph, each of a first closed path that is a closed path with three nodes or a closed path with four nodes, and a second closed path that is a closed path with three nodes or a closed path with four nodes that shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associates a shared edge that is an edge shared by the first closed path and the second closed path with a quantum bit device shared by the two four-body couplers; associates edges of the first closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associates edges of the second closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0197] (Supplementary Note 3) The association device described in Supplementary Note 1 or Supplementary Note 2, wherein the association means associates each of two four-node closed paths in the graph, which share two edges, with each of two four-body couplers that share two quantum bit devices; associates the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers; and associates edges of the two four-node closed paths other than the edge shared by the two four-node closed paths with quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers.

[0198] (Supplementary Note 4) The associating device according to any one of Supplementary Notes 1 to 3, wherein the associating means repeats associating closed paths with four-body couplers and associating edges with quantum bit devices for all closed paths included in the graph, such that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0199] (Supplementary Note 5) An association device comprising: association means for associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and repeating this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph are associated with quantum bit devices.

[0200] (Supplementary Note 6) The association apparatus according to Supplementary Note 5, wherein the association means associates an edge shared by a plurality of closed paths with one quantum bit device.

[0201] (Supplementary Note 7) The association apparatus according to Supplementary Note 5 or Supplementary Note 6, wherein the association means associates, among four quantum bit devices coupled by one four-body coupler, quantum bit devices other than three quantum bit devices associated with each edge of the three-node closed path, with fixed bits.

[0202] (Supplementary Note 8) A control device comprising: association means for associating, in a graph constructed using nodes and edges, each of two three-node closed paths that share one edge with each of two four-body couplers that share two quantum bit devices, one of the two shared quantum bit devices being a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating, among the edges of the two three-node closed paths, edges other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated; and control means for controlling an annealing machine including the four-body couplers and the quantum bit devices, based on the correspondence obtained by the association by the association means.

[0203] (Supplementary Note 9) The control device according to Supplementary Note 8, wherein the association means associates, in the graph, each of a first closed path that is a closed path of three nodes or a closed path of four nodes, and a second closed path that is a closed path of three nodes or a closed path of four nodes that shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associates a shared edge that is an edge shared by the first closed path and the second closed path, with a quantum bit device shared by the two four-body couplers; associates edges of the first closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associates edges of the second closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0204] (Supplementary Note 10) The control device according to Supplementary Note 8 or Supplementary Note 9, wherein the association means associates each of two four-node closed paths in the graph, which share two edges, with each of two four-body couplers which share two quantum bit devices, associates the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers, and associates edges of the two four-node closed paths other than the edge shared by the two four-node closed paths with quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers.

[0205] (Supplementary Note 11) The control device according to any one of Supplementary Notes 8 to 10, wherein the association means repeats association between closed paths and four-body couplers and association between edges and quantum bit devices for all closed paths included in the graph, such that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0206] (Supplementary Note 12) A control device comprising: a correspondence means for associating each edge of a three-node closed path in a graph formed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine formed using four-body couplers and quantum bit devices, and repeating this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices; and a control means for controlling the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the correspondence means.

[0207] (Supplementary Note 13) The control device according to Supplementary Note 12, wherein the associating means associates an edge shared by a plurality of closed paths with one quantum bit device.

[0208] (Supplementary Note 14) The control device according to Supplementary Note 12 or Supplementary Note 13, wherein the associating means associates, among the four quantum bit devices coupled by one four-body coupler, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed path, with fixed bits.

[0209] (Supplementary Note 15) An annealing machine includes an annealing machine and a control device, wherein the annealing machine includes: quantum bit devices; and a four-body coupler that couples four of the quantum bit devices, and the control device includes: association means that associates two three-node closed paths that share one edge in a graph formed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit, and associates the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers, and associates edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which each closed path is associated; and control means that controls the annealing machine based on the association relationships obtained by the association means. A quantum annealing system comprising:

[0210] (Supplementary Note 16) The quantum annealing system according to Supplementary Note 15, wherein the association means associates, in the graph, each of a first closed path that is a closed path of three nodes or a closed path of four nodes, and a second closed path that is a closed path of three nodes or a closed path of four nodes that shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associates a shared edge that is an edge shared by the first closed path and the second closed path with a quantum bit device shared by the two four-body couplers; associates edges of the first closed path other than the shared edge with quantum bit devices coupled by the four-body coupler with which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associates edges of the second closed path other than the shared edge with quantum bit devices coupled by the four-body coupler with which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0211] (Supplementary Note 17) The quantum annealing system according to Supplementary Note 15 or Supplementary Note 16, wherein the association means associates each of two four-node closed paths that share two edges in the graph with each of two four-body couplers that share two quantum bit devices, associates the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers, and associates edges of the two four-node closed paths other than the edge shared by the two four-node closed paths with quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers.

[0212] (Supplementary Note 18) The quantum annealing system according to any one of Supplementary Notes 15 to 17, wherein the association means repeats the association between closed paths and four-body couplers and the association between edges and quantum bit devices for all closed paths included in the graph, such that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0213] (Supplementary Note 19) A quantum annealing system comprising: an annealing machine; and a control device; wherein the annealing machine comprises: quantum bit devices; and a four-body coupler that couples four of the quantum bit devices; and wherein the control device comprises: association means that associates each edge of a three-node closed path in a graph formed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine formed using a four-body coupler and quantum bit devices, and repeats associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler, until all edges of the graph have been associated with quantum bit devices; and control means that controls the annealing machine based on the association obtained by the association means.

[0214] (Supplementary Note 20) The quantum annealing system according to Supplementary Note 19, wherein the associating means associates an edge shared by a plurality of closed paths with one quantum bit device.

[0215] (Supplementary Note 21) The quantum annealing system according to Supplementary Note 19 or Supplementary Note 20, wherein the associating means associates, among the four quantum bit devices coupled by one four-body coupler, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed path, with fixed bits.

[0216] (Supplementary Note 22) A correspondence method including a computer associating each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers that share two quantum bit devices, one of the two shared quantum bit devices being a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating, among the edges of the two three-node closed paths, the edge other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0217] (Supplementary Note 23) The correspondence method according to Supplementary Note 22, including the computer: associating, in the graph, each of a first closed path that is a closed path of three nodes or a closed path of four nodes, and a second closed path that is a closed path of three nodes or a closed path of four nodes that shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associating a shared edge that is an edge shared by the first closed path and the second closed path with a quantum bit device shared by the two four-body couplers; associating, among the edges of the first closed path, edges other than the shared edge with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associating, among the edges of the second closed path, edges other than the shared edge with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0218] (Supplementary Note 24) The correspondence method according to Supplementary Note 22 or Supplementary Note 23, wherein the computer: associates each of two four-node closed paths in the graph, which share two edges, with each of two four-body couplers that share two quantum bit devices; associates the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers; and associates, of the edges of the two four-node closed paths, other than the edge shared by the two four-node closed paths, with a quantum bit device other than the quantum bit device shared by the two four-body couplers, among quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0219] (Supplementary Note 25) The method of association described in any one of Supplementary Notes 22 to 24, including the computer repeatedly associating closed paths with four-body couplers and edges with quantum bit devices for all closed paths included in the graph, so that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0220] (Supplementary Note 26) A correspondence method including: a computer repeatedly associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler, until all edges of the graph have been associated with quantum bit devices.

[0221] (Supplementary Note 27) The method of association according to Supplementary Note 26, further comprising: associating an edge shared by a plurality of closed paths with one quantum bit device, by the computer.

[0222] (Supplementary Note 28) The method of association described in Supplementary Note 26 or Supplementary Note 27, including the computer associating, with fixed bits, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed path, among the four quantum bit devices coupled by one four-body coupler.

[0223] (Supplementary Note 29) A control method comprising: a computer associating each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating, among the edges of the two three-node closed paths, edges other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated; and controlling an annealing machine including the four-body couplers and the quantum bit devices based on the correspondence obtained by the association.

[0224] (Supplementary Note 30) The control method according to Supplementary Note 29, wherein the computer: associates, in the graph, each of a first closed path that is a closed path of three nodes or a closed path of four nodes, and a second closed path that is a closed path of three nodes or a closed path of four nodes that shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associates a shared edge that is an edge shared by the first closed path and the second closed path, with a quantum bit device shared by the two four-body couplers; associates, among the edges of the first closed path, edges other than the shared edge, with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associates, among the edges of the second closed path, edges other than the shared edge, with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0225] (Supplementary Note 31) The control method according to Supplementary Note 29 or Supplementary Note 30, wherein the computer: associates each of two four-node closed paths in the graph, which share two edges, with each of two four-body couplers which share two quantum bit devices; associates the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers; and associates, of the edges of the two four-node closed paths, other than the edge shared by the two four-node closed paths, with a quantum bit device other than the quantum bit device shared by the two four-body couplers, among quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated.

[0226] (Supplementary Note 32) The control method according to any one of Supplementary Notes 29 to 31, including the computer repeatedly associating closed paths with four-body couplers and edges with quantum bit devices for all closed paths included in the graph, so that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0227] (Supplementary Note 33) A control method comprising: a computer: associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using a four-body coupler and quantum bit devices; repeating this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices; and controlling the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the association.

[0228] (Supplementary Note 34) The control method according to Supplementary Note 33, further comprising: associating an edge shared by a plurality of closed paths with one quantum bit device, by the computer.

[0229] (Supplementary Note 35) The control method according to Supplementary Note 33 or Supplementary Note 34, comprising: the computer associating, among the four quantum bit devices coupled by one four-body coupler, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed path, with fixed bits.

[0230] (Supplementary Note 36) A recording medium having recorded thereon a program that causes a computer to execute the following: associating each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers that share two quantum bit devices, and one of the two shared quantum bit devices is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating, among the edges of the two three-node closed paths, the edge other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

[0231] (Supplementary Note 37) The recording medium according to Supplementary Note 36, wherein the program causes the computer to execute the following: associate a first closed path of the graph, which is a closed path with three nodes or a closed path with four nodes, and a second closed path, which is a closed path with three nodes or a closed path with four nodes and shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associate a shared edge that is an edge shared by the first closed path and the second closed path with a quantum bit device shared by the two four-body couplers; associate edges of the first closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associate edges of the second closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0232] (Supplementary Note 38) The recording medium described in Supplementary Note 36 or Supplementary Note 37, wherein the program causes the computer to execute the following: associate two four-node closed paths in the graph, each of which shares two edges, with two four-body couplers that share two quantum bit devices; associate the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers; and associate edges of the two four-node closed paths other than the edge shared by the two four-node closed paths with quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers.

[0233] (Appendix 39) The recording medium described in any one of Appendices 36 to 38, wherein the program causes the computer to execute: repeating, for all closed paths included in the graph, associations between closed paths and four-body couplers and associations between edges and quantum bit devices, such that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0234] (Supplementary Note 40) A recording medium having recorded thereon a program that causes a computer to execute the following steps: in a graph constructed using nodes and edges, each edge of a three-node closed path corresponds to each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and in the graph, each edge of a four-node closed path corresponds to each of four quantum bit devices coupled by the four-body coupler; this process is repeated until all edges of the graph are associated with quantum bit devices.

[0235] (Supplementary Note 41) The recording medium according to Supplementary Note 40, wherein the program causes the computer to execute: associating an edge shared by a plurality of closed paths with one quantum bit device.

[0236] (Supplementary Note 42) The recording medium according to Supplementary Note 40 or Supplementary Note 41, wherein the program causes the computer to execute: associating, with fixed bits, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed path, among four quantum bit devices coupled by one four-body coupler.

[0237] (Supplementary Note 43) A recording medium having recorded thereon a program that causes a computer to execute the following: associating each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with each of two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating, among the edges of the two three-node closed paths, edges other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated; and controlling an annealing machine including the four-body couplers and the quantum bit devices based on the correspondence obtained by the correspondence.

[0238] (Supplementary Note 44) The recording medium according to Supplementary Note 43, wherein the program causes the computer to execute the following: associate a first closed path of the graph, which is a closed path with three nodes or a closed path with four nodes, and a second closed path, which is a closed path with three nodes or a closed path with four nodes and shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associate a shared edge that is an edge shared by the first closed path and the second closed path with a quantum bit device shared by the two four-body couplers; associate edges of the first closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associate edges of the second closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

[0239] (Supplementary Note 45) The recording medium according to Supplementary Note 43 or Supplementary Note 44, wherein the program causes the computer to execute the following: associating two four-node closed paths in the graph, each of which shares two edges, with two four-body couplers that share two quantum bit devices; associating the edge shared by the two four-node closed paths with a quantum bit device shared by the two four-body couplers; and associating edges of the two four-node closed paths other than the edge shared by the two four-node closed paths with quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers.

[0240] (Appendix 46) The recording medium described in any one of Appendices 43 to 45, wherein the program causes the computer to execute: for all closed paths included in the graph, repeating the association between closed paths and four-body couplers and the association between edges and quantum bit devices so that edges included in the closed paths are associated with quantum bit devices coupled by the four-body couplers.

[0241] (Supplementary Note 47) A recording medium having recorded thereon a program that causes a computer to execute the following steps: correspond each edge of a three-node closed path in a graph constructed using nodes and edges to each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using a four-body coupler and quantum bit devices; and correspond each edge of the four-node closed path in the graph to each of the four quantum bit devices coupled by the four-body coupler, repeating this process until all edges of the graph are associated with quantum bit devices; and control the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the association.

[0242] (Supplementary Note 48) The recording medium according to Supplementary Note 47, wherein the program causes the computer to execute: associating an edge shared by a plurality of closed paths with one quantum bit device.

[0243] (Supplementary Note 49) The recording medium according to Supplementary Note 47 or Supplementary Note 48, wherein the program causes the computer to execute: associating, with fixed bits, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed path, among the four quantum bit devices coupled by one four-body coupler.

[0244] The present invention may be applied to an association device, a control device, a quantum annealing system, an association method, a control method, and a recording medium.

[0245] 1, 650, 660 Quantum annealing system 100, 651, 661 Annealing machine 110, 652, 662 Quantum bit device 120, 653, 663 Four-body coupling device 200, 630, 640, 654, 664 Control device 210 Communication unit 220 Display unit 230 Operation input unit 280 Storage unit 290 Processing unit 291 Graph acquisition unit 292, 611, 621, 631, 641, 655, 665 Correspondence unit 293, 632, 642, 656, 666 Control unit 610, 620 Correspondence device

Claims

1. A correspondence device comprising: a correspondence means for associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; for associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and for associating edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

2. The association apparatus according to claim 1, wherein the association means associates each of a first closed path of the graph, which is a closed path with three nodes or a closed path with four nodes, and a second closed path, which is a closed path with three nodes or a closed path with four nodes that shares one or two edges with the first closed path, with each of two four-body couplers that share at least one quantum bit device; associates a shared edge that is an edge shared by the first closed path and the second closed path with a quantum bit device shared by the two four-body couplers; associates edges of the first closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the first closed path is associated, other than the quantum bit device shared by the two four-body couplers; and associates edges of the second closed path other than the shared edge with quantum bit devices coupled by the four-body coupler to which the second closed path is associated, other than the quantum bit device shared by the two four-body couplers.

3. The correspondence apparatus according to claim 1, wherein the correspondence means corresponds each of two four-node closed paths in the graph that share two edges to each of two four-body couplers that share two quantum bit devices, corresponds the edge shared by the two four-node closed paths to a quantum bit device shared by the two four-body couplers, and corresponds edges of the two four-node closed paths other than the edge shared by the two four-node closed paths to quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated, other than the quantum bit device shared by the two four-body couplers.

4. The association device according to claim 1, wherein the association means repeats the association of closed paths with four-body couplers and the association of edges with quantum bit devices for all closed paths included in the graph, so that edges included in the closed paths are associated with quantum bit devices coupled by four-body couplers.

5. A correspondence device comprising a correspondence means for associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and for repeating this process of associating each edge of a four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices.

6. The association apparatus according to claim 5, wherein the association means associates an edge shared by a plurality of closed paths with one quantum bit device.

7. The association device according to claim 5, wherein the association means associates, among four quantum bit devices coupled by one four-body coupler, quantum bit devices other than the three quantum bit devices associated with each edge of the three-node closed circuit, with fixed bits.

8. A control device comprising: a correspondence means for associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; a correspondence means for associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and a control means for controlling an annealing machine including the four-body couplers and the quantum bit devices based on the correspondence obtained by the correspondence means.

9. A control device comprising: a correspondence means for associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices, and repeating this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices; and a control means for controlling the annealing machine including the four-body coupler and the quantum bit device based on the correspondence obtained by the correspondence means.

10. An annealing machine and a control device, wherein the annealing machine comprises: quantum bit devices; and a four-body coupler that couples four of the quantum bit devices; and the control device comprises: association means for associating two three-node closed paths that share one edge in a graph formed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit, and for associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers, and for associating edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which each closed path is associated; and control means for controlling the annealing machine based on the association relationships obtained by the association means. A quantum annealing system comprising:

11. A quantum annealing system comprising: an annealing machine; and a control device; wherein the annealing machine comprises: quantum bit devices; and a four-body coupler that couples four of the quantum bit devices; and wherein the control device comprises: association means that associates each edge of a three-node closed path in a graph formed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine formed using a four-body coupler and quantum bit devices, and repeats associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler, until all edges of the graph have been associated with quantum bit devices; and control means that controls the annealing machine based on the association obtained by the association means.

12. A correspondence method including a computer associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

13. A correspondence method comprising: a computer associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and repeating this process of associating each edge of a four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices.

14. A control method comprising: a computer associating two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associating the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associating edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body couplers to which the respective closed paths are associated; and controlling an annealing machine including the four-body couplers and the quantum bit devices based on the correspondence obtained by the association.

15. A control method comprising: a computer: associating each edge of a three-node closed path in a graph constructed using nodes and edges with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; repeating this process of associating each edge of the four-node closed path in the graph with each of the four quantum bit devices coupled by the four-body coupler until all edges of the graph have been associated with quantum bit devices; and controlling the annealing machine including the four-body coupler and the quantum bit devices based on the correspondence obtained by the association.

16. A recording medium having recorded thereon a program that causes a computer to execute the following steps: associate each of two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associate the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associate the edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated.

17. A recording medium having recorded thereon a program that causes a computer to execute the following steps: in a graph constructed using nodes and edges, each edge of a three-node closed path is associated with each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and in said graph, each edge of a four-node closed path is associated with each of the four quantum bit devices coupled by the four-body coupler; this process is repeated until all edges of said graph have been associated with quantum bit devices.

18. A recording medium having recorded thereon a program that causes a computer to execute the following steps: associate two three-node closed paths that share one edge in a graph constructed using nodes and edges with two four-body couplers that share two quantum bit devices, one of which is a fixed bit; associate the edge shared by the two three-node closed paths with a quantum bit device other than the fixed bit among the quantum bit devices shared by the two four-body couplers; and associate edges of the two three-node closed paths other than the edge shared by the two three-node closed paths with a quantum bit device other than the quantum bit device shared by the two four-body couplers among the quantum bit devices coupled by the four-body coupler to which the respective closed paths are associated; and control an annealing machine that includes the four-body couplers and the quantum bit devices based on the correspondence obtained by the correspondence.

19. A recording medium having recorded thereon a program that causes a computer to: correspond each edge of a three-node closed path in a graph constructed using nodes and edges to each of three of the four quantum bit devices coupled by one four-body coupler in an annealing machine constructed using four-body couplers and quantum bit devices; and correspond each edge of the four-node closed path in the graph to each of the four quantum bit devices coupled by the four-body coupler, repeating this process until all edges of the graph have been associated with quantum bit devices; and control the annealing machine including the four-body coupler and the quantum bit device based on the correspondence obtained by the association.

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