JP7795741B2 - Ising machine selection device, Ising machine selection method, and program - Google Patents

Description

Article 30, paragraph 2 of the Patent Act applies (1) Date: February 3, 2022 (Period: February 3, 2022 - February 4, 2022) Name and location of the event Name of the event: Kyushu University Master's Thesis Presentation 2021 Venue: Kyushu University West Building 1 (W1-D-413 IMI Auditorium) 744 Motooka, Nishi-ku, Fukuoka City, Fukuoka Prefecture, 819-0395

The present invention relates to a technology for selecting an Ising machine to be used to solve an optimization problem.

In recent years, Ising machines, a type of non-von Neumann computer, have been attracting attention. Ising machines have been applied to the calculation of combinatorial optimization problems, machine learning, and model calculations in physics and chemistry. For example, they are used to solve problems such as route selection problems aimed at avoiding traffic congestion, route optimization problems for automated guided vehicles in factories, portfolio optimization problems for financial products, optimization problems for ad delivery, rectangle packing problems, slot placement problems, induced subgraph isomorphism problems, and binary neural network problems.

An Ising machine is a computer based on a new principle of minimizing the Hamiltonian of the Ising model (hereinafter referred to as the Ising Hamiltonian). In order to solve the above problem with an Ising machine, the problem is first converted into an Ising Hamiltonian that represents the problem, and then the Ising Hamiltonian is minimized using the Ising machine. The Ising Hamiltonian H is expressed by the following equation.

where s _i (i=1, …, N) is the spin, J=(J _ij ) is the interaction matrix, and h=(h _i ) is the external magnetic field vector, where s _i is a variable that takes the value +1 or -1, J is an N×N real matrix, and h is an N-dimensional real vector.

When an interaction matrix J and an external magnetic field vector h are input to an Ising machine, it outputs a combination of spins s ₁ , ..., s _N that reduces the value of the Ising Hamiltonian H.

Note that some Ising machines minimize the QUBO (Quadratic Unconstrained Binary Optimization) instead of the Ising Hamiltonian. However, QUBO and the Ising Hamiltonian can easily be converted to each other (see Non-Patent Document 1).

In general, the smaller the value of the Ising Hamiltonian, the better the quality of the solution to the problem before transformation, so it is preferable to solve the problem using an Ising machine that can reduce the value of the Ising Hamiltonian.

Currently, several Ising machines, hardware that solves basis search problems for the Ising model, have been developed, but there are differences in their implementation methods. As a result, the characteristics of each Ising machine also differ, and the quality of the solution is greatly influenced by the Ising machine (see Non-Patent Document 2). Specific explanations follow. The relationship between the time elapsed since the start of calculation and the value of the Ising Hamiltonian at that elapsed time will differ for each Ising machine, even for the same problem. Furthermore, the relationship between the time elapsed since the start of calculation and the value of the Ising Hamiltonian at that elapsed time will differ for different problems, even if the same Ising machine is used. In other words, the Ising machine that can obtain the highest quality solution will vary depending on both the problem corresponding to the Ising Hamiltonian and the time spent on calculation.

Comparisons of performance when solving the same problem using an Ising machine and a classical computer have been conducted in the past (see Non-Patent Document 3), but no comparisons have been made of performance when solving the same problem using various Ising machines. Therefore, to select the optimal Ising machine for solving a certain problem, it is necessary to actually solve the problem and compare the results.

Zhengbing Bian, Fabian Chudak, William G. Macready, and Geordie Rose, “The Ising model: teaching an old problem new tricks,” [online], [accessed August 1, 2022], Internet <URL: https://www.dwavesys.com/media/vbklsvbh/weightedmaxsat_v2.pdf>. Hamerly, Ryan, et al., “Experimental investigation of performance differences between coherent Ising machines and a quantum annealer,” Science advances, vol.5, no.5, 2019. Charles Moussa, Henri Calandra, and Vedran Dunjko, “To quantum or not to quantum: towards algorithm selection in near-term quantum optimization,” Quantum Science and Technology, vol.5, no.4, 2020.

As mentioned above, to select an Ising machine to use to solve a certain problem, the results of solving that problem are compared, but this trial-and-error selection process requires human effort and time, and is a significant burden. If an Ising machine that is charged according to calculation time is used, the selection process will incur costs. Furthermore, the burden of the selection process will be incurred for each problem to be solved. In other words, there is a problem in that the burden of selecting an Ising machine to use to calculate the Ising Hamiltonian is extremely large.

The present invention therefore aims to provide technology for efficiently selecting an Ising machine to use in calculating the Ising Hamiltonian.

In one aspect of the present invention, M, N, and K are integers of 2 or more, _Hm (m=1, ..., M) is an Ising Hamiltonian that serves as a benchmark, _In (n=1, ..., N) is an Ising machine used to calculate the Ising Hamiltonian, and _Tk (k=1, ..., K) is an allowable time for calculating the Ising Hamiltonian (hereinafter referred to as allowable calculation time), and the present invention includes a recording unit that records a relationship _R1 between the Ising Hamiltonian _Hm , the Ising machine _{In ,} the allowable calculation time _Tk , and the value Vm _,n,k of the Ising Hamiltonian _Hm at the time when the allowable calculation time _Tk has elapsed since the Ising machine In started calculation, and a relationship _R2 between the Ising Hamiltonian _Hm and a feature vector _Xm of a graph corresponding to the Ising Hamiltonian _Hm ; a feature vector calculation unit that calculates a feature vector of a graph corresponding to an Ising Hamiltonian that is to be selected as an Ising machine to be used for calculation (hereinafter referred to as a selection target Ising Hamiltonian); a first selection unit that selects an Ising Hamiltonian H _{m_0} (where m ₀ satisfies 1≦m ₀ ≦M) corresponding to the feature vector that has the smallest distance from the feature vector using relation _{R 2} ; and a second selection unit that selects an allowable calculation time T _{k_0} (where k ₀ satisfies 1≦k ₀ ≦K) that is closest to the time allowable for calculating the Ising Hamiltonian to be selected, and selects a predetermined number of Ising machines corresponding to the Ising machines with the smallest value V _{m_0,n,k_0} using relation R ₁ .

The present invention makes it possible to efficiently select an Ising machine to use in calculating the Ising Hamiltonian.

FIG. 10 is a diagram showing an example of a table representing a relationship _R1 . FIG. 10 is a diagram showing an example of a table representing a relationship _R1 . FIG. 10 is a diagram showing an example of a table representing a relationship _R2 . FIG. 1 is a block diagram showing a configuration of an Ising machine selection device 100. 10 is a flowchart showing the operation of the Ising machine selection device 100. FIG. 2 is a diagram illustrating an example of the functional configuration of a computer that realizes each device according to an embodiment of the present invention.

Embodiments of the present invention will be described in detail below. Components with the same functions will be assigned the same numbers, and duplicate explanations will be omitted.

Before explaining each embodiment, we will explain the notation used in this specification.

The ^ (caret) represents a superscript. For example, x ^{y^z} means that y ^z is a superscript to x, and x _y^z means that y ^z is a subscript to x. The _ (underscore) represents a subscript. For example, x ^y_z means that y _z is a superscript to x, and x _{y_z} means that y _z is a subscript to x.

The superscripts "^" and "~" for a certain letter x, such as ^x and ~x, should actually be written directly above the "x", but due to limitations on the notation used in the specification, they are written as ^x and ~x.

<Technical background>
It is believed that the behavior of an Ising machine is similar to that of an Ising Hamiltonian with similar characteristics. Therefore, in an embodiment of the present invention, data related to a benchmark Ising Hamiltonian is generated in advance, and the data is used to select an Ising machine to be used in calculating the Ising Hamiltonian to be selected. In this case, taking into consideration that a graph can be associated with an Ising Hamiltonian and that an Ising Hamiltonian can be associated with a graph, the Ising Hamiltonian and the graph are treated as being the same.

A detailed explanation is given below. It is assumed that there are N Ising machines (where N is an integer of 2 or more) used to calculate the Ising Hamiltonian, and these are represented as I ₁ , ..., _IN .

(1) Generation of data related to benchmark Ising Hamiltonians First, a plurality of graphs are generated using a graph generation algorithm. Then, Ising Hamiltonians corresponding to the generated graphs are obtained, and these Ising Hamiltonians are used as benchmark Ising Hamiltonians. Note that, for example, the methods described in Reference Non-Patent Document 1, Reference Non-Patent Document 2, and Reference Non-Patent Document 3 can be used as the graph generation algorithm.

(Reference non-patent document 1: P. Erdos and A. Renyi, “On random graphs i,” Publicationes Mathematicae Debrecen, vol.6, pp.290-297, 1959.)
(Reference non-patent document 2: Duncan J. Watts and Steven H. Strogatz, “Collective dynamics of 'small-world' networks,” Nature, vol.393, pp.440-442, 1998.)
(Reference Non-Patent Document 3: Albert-Laszlo Barabasi and Reka Albert, “Emergence of scaling in random networks,” Science, vol. 286, pp. 509-512, 1999.)
Next, multiple allowable times for calculating the Ising Hamiltonian (hereinafter referred to as allowable calculation times) are determined. Below, the benchmark Ising Hamiltonian will be represented as H ₁ , ..., H _M (where M is an integer greater than or equal to 2), and the allowable calculation times will be represented as T ₁ , ..., T _K (where K is an integer greater than or equal to 2). Then, the benchmark Ising Hamiltonian H _m is solved by the Ising machine I _n , and the value V _m,n,k of the Ising Hamiltonian H _m at the point when the allowable calculation time T _k has elapsed since the Ising machine I _n started the calculation is obtained.

Finally, a graph feature vector _Xm corresponding to the Ising Hamiltonian _Hm is calculated. Here, the graph feature vector is a vector whose elements are the graph feature quantities, and the following can be used as graph feature quantities, for example:

(a) Edge Density For a graph G, the edge density D is a feature defined by the following equation:

where |V| represents the number of vertices in graph G, and |E| represents the number of edges in graph G.

Edge density D is an index that indicates how densely edges are in graph G relative to the complete graph.

(b) Scale-Free Property The scale-free property D _KL (P||P _z ) for a graph G is a feature defined by the following equation.

where P(k)=n _k /|V| (k=1, ..., |V|, |V| is the number of vertices in graph G, and n _k is the number of vertices in graph G with degree k) represents the degree distribution. Also, P _z (k)=f(k; a, |V|) represents the probability density function of the Zipf distribution. Note that a is the value obtained by fitting P(k) using maximum likelihood estimation.

The scale-free property D _KL (P||P _z ) is an index that indicates the degree to which the degree distribution follows a power law.

(c) Average Path Length The average path length _Lc for a graph G is a feature defined by the following equation:

where |V| is the number of vertices in graph G, v _i , v _j (i=1, ..., |V|, j=1, ..., |V|, i≠j) are the vertices in graph G, and d(v _i , v _j ) is the shortest distance between vertex v _i and vertex v _j . If vertex v _j cannot be reached from vertex v _i , then d(v _i , v _j )=0.

The average path length _Lc is the average value of the shortest path lengths between all pairs of vertices in graph G, and is one of the indices that represents small-world property. Here, small-world property is the property that any two vertices in a graph are connected via a small number of intermediate vertices.

(d) Average Clustering Coefficient The average clustering coefficient C for a graph G is a feature defined by the following equation:

where |V| is the number of vertices in graph G, C _i = 2m _i /{k _i (k _i -1)} (i=1, …, |V|, m _i is the number of edges connecting adjacent vertices of vertex v _i in graph G, and k _i is the degree of vertex v _i in graph G) represents the clustering coefficient of vertex v _i in graph G.

The average clustering coefficient C is the average value of the clustering coefficients for all vertices in a graph G, and is one of the indicators of small-world nature.

In this way, the relationship R1 between the Ising Hamiltonian H _m , the Ising machine I _n , the allowable calculation time T _k , and the value V _m,n,k of the Ising Hamiltonian H _m at the time when the allowable calculation time T _k has elapsed since the Ising machine I _n started calculation, and the relationship _R2 between the Ising Hamiltonian H _m and the feature quantity vector X _m of the graph corresponding to the Ising Hamiltonian H _m are generated as data related to the Ising Hamiltonian _that serves as a benchmark.

The relationships _R1 and _R2 can each be expressed using a table. FIGS. 1 and 2 are diagrams showing examples of tables representing the relationship _R1 . The relationship _R1 is expressed using two tables, FIGS. 1 and 2. FIG. 1 is a table showing the value V m,n,1 of the Ising Hamiltonian H _m (m=1, ..., 12) when the allowable calculation time T ₁ =10 ms has elapsed since the Ising machine _{I n (} n=1, ..., 5) started calculation, and FIG. 2 is a table showing the value V _{m,n, 2} of the Ising Hamiltonian H _m (m=1, ..., 12) when the allowable calculation time T ₂ =1000 ms has elapsed since the Ising machine I n (n=1, ..., 5) started calculation. FIG. 3 is a diagram showing an example of a table representing the relationship _R2 . FIG. 3 is a table showing the feature vector X _m of a graph corresponding to an Ising Hamiltonian H _m (m=1, ..., 12) (where the first, second, and third elements of the feature vector X _m are the branch density, average path length, and average clustering coefficient of the graph corresponding to the Ising Hamiltonian H _m, respectively).

(2) Selection of Ising Machine First, an Ising Hamiltonian to be selected as an Ising machine to be used in calculation (hereinafter referred to as a selected Ising Hamiltonian) and an allowable time for calculation of the selected Ising Hamiltonian are input.

Next, we calculate the feature vector of the graph corresponding to the target Ising Hamiltonian. This feature vector is the same as the feature vector of the relation _R2 generated in advance.

Then, using the relationship _R2 , the Ising Hamiltonian H _{m_0} (where m ₀ satisfies 1≦m ₀ ≦M) corresponding to the feature vector that has the smallest distance from the feature vector calculated earlier is selected. Any distance can be used as the distance between vectors. For example, the Euclidean distance can be used as the distance between vectors.

Finally, from the allowable calculation times T _k (k=1, ..., K), an allowable calculation time T _{k_0} (where k ₀ satisfies 1≦k ₀ ≦K) that is closest to the time allowable for calculating the Ising Hamiltonian to be selected is selected, and a predetermined number of Ising machines corresponding to the smallest value V _{m_0,n,k_0} are selected using the relationship _R1 . The selected Ising machines may be output as a list in order from the smallest value V _{m_0,n,k_0} . Here, the reason for selecting in order from the smallest value is that it is considered that the Ising machine that gives the higher quality solution is the smaller the value.

An example of Ising machine selection will be explained below using the relationship _R1 in Figures 1 and 2 and the relationship _R2 in Figure 3. If the feature vector of the graph corresponding to the Ising Hamiltonian to be selected is (0.421, 1.589, 0.378) and the allowable time for calculating the Ising Hamiltonian to be selected is 10 ms, and Euclidean distance is used as the distance between vectors, _H6 is selected as the Ising Hamiltonian corresponding to the feature vector with the smallest distance from Figure 3. Then, if the number of Ising machines to be selected is 5, a list of Ising machines sorted from smallest to largest value is output, as shown in Figure 1: ( _I3 , _I5 , _I4 , _I2 , _I1 ).

First Embodiment
Let M, N, and K be integers of 2 or greater, _Hm (m=1, ..., M) be the benchmark Ising Hamiltonian, _In (n=1, ..., N) be the Ising machine used to calculate the Ising Hamiltonian, and _Tk (k=1, ..., K) be the allowable time for calculating the Ising Hamiltonian (hereinafter referred to as the allowable calculation time), and the Ising machine selection device 100 selects a predetermined number of Ising machines to be used for calculating the Ising Hamiltonian to be selected (hereinafter referred to as the selected Ising Hamiltonian) from the Ising Hamiltonian to be used for calculation and the allowable time for calculating the selected Ising Hamiltonian.

The Ising machine selection device 100 will be described below with reference to FIGS. 4 and 5. FIG. 4 is a block diagram showing the configuration of the Ising machine selection device 100. FIG. 5 is a flowchart showing the operation of the Ising machine selection device 100. As shown in FIG. 4, the Ising machine selection device 100 includes a feature vector calculation unit 110, a first selection unit 120, a second selection unit 130, and a recording unit 190. The recording unit 190 is a component that appropriately records information necessary for the processing of the Ising machine selection device 100. The recording unit 190 records in advance a relationship R1 between the Ising Hamiltonian H _m , the Ising machine I _n , the allowable calculation time T _k , and the value V _{m ,n,k} of the Ising Hamiltonian H _m at the time when the allowable calculation time T _k has elapsed since the Ising machine I n started calculation, and a relationship _R2 between the Ising Hamiltonian H _m and the feature quantity vector X _m of the graph corresponding to the Ising Hamiltonian _{H m} .

The operation of the Ising machine selection device 100 will be explained with reference to Figure 5.

In S110, the feature vector calculation unit 110 receives the Ising Hamiltonian to be selected as input, calculates the feature vector of the graph corresponding to the Ising Hamiltonian to be selected, and outputs it. The number of elements of the graph feature vector is arbitrary, and the elements can be the features of any graph.

In S120, the first selection unit 120 receives the feature vector calculated in S110 as input, selects and outputs the Ising Hamiltonian H _{m_0} (where m ₀ satisfies 1≦m ₀ ≦M) corresponding to the feature vector that has the smallest distance from the feature vector using the relationship R _2. Any distance can be used as the distance between the vectors.

In S130, the second selection unit 130 receives as input the allowable time for calculating the Ising Hamiltonian to be selected and the Ising Hamiltonian H _{m_0} selected in S120, selects from the allowable calculation times T _k (k= ₁ , ..., K) the allowable calculation time T _{k_0} (where k ₀ satisfies 1≦k ₀ ≦K) that is closest to the allowable time for calculating the Ising Hamiltonian to be selected, selects a predetermined number of Ising machines corresponding to the Ising machines with the smallest value V _{m_0,n,k_0} using the relationship R1, and outputs a list of Ising machines sorted in order from the smallest value V _{m_0,n,k_0} . The predetermined number is arbitrary. If the predetermined number is N, the user can select the optimal Ising machine from among the available Ising machines based on the output list.

According to an embodiment of the present invention, it is possible to efficiently select an Ising machine to be used in calculating an Ising Hamiltonian. When making the selection, it is not necessary to actually solve the Ising Hamiltonian using an Ising machine. Furthermore, by inputting the time allowable for calculating the Hamiltonian, an Ising machine can be efficiently selected even when it is desired to obtain a solution in a short time or when calculation time is prioritized over solution quality.

<Additional Notes>
The processing of each unit of each of the above-mentioned devices may be realized by a computer, in which case the processing content of the functions to be possessed by each device is described by a program. Then, by loading this program into the recording unit 2020 of the computer 2000 shown in Fig. 6 and operating the arithmetic processing unit 2010, the input unit 2030, the output unit 2040, the auxiliary recording unit 2025, etc., the processing functions of each of the above-mentioned devices are realized on the computer.

The device of the present invention, for example, comprises, as a single hardware entity, an input unit capable of inputting signals from outside the hardware entity, an output unit capable of outputting signals to outside the hardware entity, a communication unit to which a communication device (e.g., a communication cable) can be connected for communication with an external device to the hardware entity, a CPU (which may also include a central processing unit, cache memory, registers, etc.) as an arithmetic processing unit, RAM and ROM as memory, an external storage device such as a hard disk, and buses connecting these input unit, output unit, communication unit, CPU, RAM, ROM, and external storage device so that data can be exchanged between them. If necessary, the hardware entity may also be provided with a device (drive) capable of reading and writing to recording media such as a CD-ROM. An example of a physical entity equipped with such hardware resources is a general-purpose computer.

The external storage device of the hardware entity stores the programs required to realize the above-mentioned functions and the data required to process these programs (the program is not limited to an external storage device; for example, it may be stored in ROM, a read-only storage device). In addition, data obtained by processing these programs is stored appropriately in RAM, external storage, etc.

In a hardware entity, each program stored in an external storage device (or ROM, etc.) and the data required to process each program are loaded into memory as needed, and interpreted, executed, and processed by the CPU as appropriate. As a result, the CPU realizes the specified functions (each component represented as a "... unit," "... means," etc., above). In other words, each component in an embodiment of the present invention may be configured using processing circuitry.

As mentioned above, when the processing functions of the hardware entities (devices of the present invention) described in the above embodiments are implemented by a computer, the processing content of the functions that the hardware entities should have is described by a program. Then, by executing this program on a computer, the processing functions of the hardware entities are implemented on the computer.

The program describing this processing can be recorded on a computer-readable recording medium. A computer-readable recording medium is, for example, a non-transitory recording medium, such as a magnetic recording device or optical disk.

This program may be distributed, for example, by selling, transferring, or lending portable recording media such as DVDs or CD-ROMs on which the program is recorded. Furthermore, the program may be stored in a storage device of a server computer, and then distributed by transferring the program from the server computer to other computers via a network.

A computer that executes such a program, for example, first temporarily stores the program recorded on a portable recording medium or transferred from a server computer in its own non-transitory storage device, auxiliary storage unit 2025. Then, when executing a process, the computer loads the program stored in its own non-transitory storage device, auxiliary storage unit 2025, into storage unit 2020 and executes processing in accordance with the loaded program. As an alternative execution form of this program, the computer may load the program directly from a portable recording medium into storage unit 2020 and execute processing in accordance with the program. Furthermore, each time a program is transferred from a server computer to this computer, the computer may execute processing in accordance with the received program. Alternatively, the above-mentioned processing may be executed using a so-called ASP (Application Service Provider) type service, which realizes processing functions simply by issuing execution instructions and obtaining results, without transferring the program from the server computer to this computer. In this embodiment, the program includes information used for processing by an electronic computer that is equivalent to a program (such as data that is not a direct command to a computer but has properties that dictate computer processing).

In addition, in this embodiment, the device is configured by executing a specific program on a computer, but at least part of the processing may be implemented in hardware.

The present invention is not limited to the above-described embodiments, and modifications can be made as appropriate without departing from the spirit of the present invention.

Claims (3)

Let M, N, and K be integers equal to or greater than 2, H _m (m=1, …, M) be the benchmark Ising Hamiltonian, I _n (n=1, …, N) be the Ising machine used to calculate the Ising Hamiltonian, and T _k (k=1, …, K) be the allowable time for calculating the Ising Hamiltonian (hereinafter referred to as the allowable calculation time),
a recording unit that records a relationship R1 between an Ising Hamiltonian H _m , an Ising machine _{I n} , an allowable calculation time T _k , and a value V _m,n,k of the Ising Hamiltonian H _m at a time point when the allowable calculation time T _k has elapsed since the Ising machine I n started calculation, and a relationship _R2 between the Ising Hamiltonian H _m and a feature vector X _m of a graph corresponding to the Ising Hamiltonian _{H m} ;
a feature vector calculation unit that calculates a feature vector of a graph corresponding to an Ising Hamiltonian that is a selection target for an Ising machine to be used in calculation (hereinafter referred to as a selection target Ising Hamiltonian);
a first selection unit that selects an Ising Hamiltonian H _{m_0} (where m ₀ satisfies 1≦m ₀ ≦M) corresponding to a feature vector that has a minimum distance from the feature vector using a relation R ₂ ;
a second selection unit that selects an allowable calculation time T _{k_0} (where k ₀ satisfies 1≦k ₀ ≦K) that is closest to the allowable time for calculation of the Ising Hamiltonian to be selected, and selects a predetermined number of Ising machines corresponding to the Ising machines having the smallest value V _{m_0,n,k_0} using a relationship R _1;
An Ising machine selection device including: Let M, N, and K be integers equal to or greater than 2, H _m (m=1, …, M) be the benchmark Ising Hamiltonian, I _n (n=1, …, N) be the Ising machine used to calculate the Ising Hamiltonian, and T _k (k=1, …, K) be the allowable time for calculating the Ising Hamiltonian (hereinafter referred to as the allowable calculation time),
a feature vector calculation step in which an Ising machine selection device including a recording unit that records a relationship _R1 between an Ising Hamiltonian _Hm , an Ising _{machine In ,} an allowable calculation time Tk, and a value Vm _,n,k of the Ising _{Hamiltonian Hm} at the time when the allowable calculation time _Tk has elapsed since the Ising machine In started calculation, and a relationship _R2 between the Ising Hamiltonian _Hm and a feature vector _Xm of a graph corresponding to the Ising Hamiltonian _Hm , calculates a feature vector of a graph corresponding to an Ising Hamiltonian that is a selection target for an Ising machine to be used in calculation (hereinafter referred to as a selection target Ising Hamiltonian);
a first selection step in which the Ising machine selection device selects an Ising Hamiltonian H _{m_0} (where m ₀ satisfies 1≦m ₀ ≦M) corresponding to a feature vector that has a minimum distance from the feature vector using a relationship R ₂ ;
a second selection step in which the Ising machine selection device selects an allowable calculation time T _{k_0} (where k ₀ satisfies 1≦k ₀ ≦K) that is closest to the allowable time for calculation of the Ising Hamiltonian to be selected, and selects _a predetermined number of Ising machines corresponding to the Ising machine having the smallest value V _{m_0,n,k_0} using a relationship R 1;
An Ising machine selection method including: A program for causing a computer to function as the Ising machine selection device described in claim 1.