Information processing device, information processing method, and information processing program

Abstract

The present invention provides an information processing device that causes an Ising machine to execute a process of solving an optimization problem by obtaining the value of an unknown variable using a first objective function, and when the value of the unknown variable is related to the number of quantum bits when the optimization problem is solved using the Ising machine, the following control is performed: using a second objective function different from the first objective function, a value related to the unknown variable that is minimum within a range of executable solutions to the optimization problem is derived, and causing the Ising machine to execute a process of solving the optimization problem, wherein the optimization problem is specified by a mathematical model including the derived value related to the unknown variable and the first objective function.

Description

Technical Field

[0001] The present invention relates to an information processing device, an information processing method and an information processing program. Background Art

[0002] Japanese Patent Application Laid-Open No. 2021-117977 discloses a technology in which not only a quantum computer performs arithmetic processing for finding a solution to a combinatorial optimization problem, but also a classical computer performs part of the arithmetic processing.

[0003] Japanese Patent Application Laid-Open No. 2020-184759 discloses a technology in which multiple antennas included in multiple base stations are grouped using quantum annealing. Summary of the Invention

[0004] Technical issues to be solved by the invention

[0005] As a quantum computer specifically designed to solve optimization problems, the Ising Machine is known. Among the Ising Machines, there are quantum annealing machines that utilize quantum mechanical properties, coherent Ising machines that utilize optical properties, and digital annealing furnaces composed of digital circuits. In addition, in order to be able to use the Ising Machine to solve the optimization problem, the optimization problem is modeled. As examples of models that can be solved using the Ising Machine, there are the QUBO (Quadratic Unconstrained Binary Optimization) model that models the optimization problem using a quadratic form of a binary variable of 0 or 1, and the Ising model that models the optimization problem using a quadratic form of a binary variable of -1 or 1. In addition, the QUBO model and the Ising model can be converted into each other.

[0006] However, the scale of the optimization problem that can be solved by the Ising machine is smaller than the scale of the optimization problem that can be solved by the previous general-purpose computer (also known as the classical computer) such as the Neumann computer. This is because it is difficult to increase the number of quantum bits as the computing unit of the quantum computer. In the technology described in Japanese Patent Application Publication No. 2021-117977 and Japanese Patent Application Publication No. 2020-184759, the number of quantum bits when the Ising machine is used to calculate the optimization problem is not considered.

[0007] The present invention has been made in view of the above circumstances, and its object is to provide an information processing device, an information processing method, and an information processing program that can reduce the number of quantum bits when solving an Ising machine operation optimization problem.

[0008] Means for solving technical problems

[0009] The information processing device of the present invention has at least one processor, and causes the Ising machine to perform the following processing: solving the optimization problem by using a first objective function to obtain the value of an unknown variable, in the above processing, the value of the unknown variable is related to the number of quantum bits when the optimization problem is solved using the Ising machine, in the above information processing device, the processor performs the following control: using a second objective function different from the first objective function, deriving the smallest value related to the unknown variable within the range of executable solutions to the optimization problem, causing the Ising machine to perform the processing of solving the optimization problem, and the above optimization problem is specified by a mathematical model including the derived value related to the unknown variable and the first objective function.

[0010] In the information processing device of the present invention, the second objective function may be an objective function that can relax the constraint condition compared with the first objective function. This can reduce the amount of calculation.

[0011] Furthermore, the information processing device of the present invention may store the unknown variable in a qubit group including a plurality of qubits, and the value of the unknown variable may be represented at a position in the qubit group where the qubit is 0 or 1. This can reduce the possibility of not being able to obtain an executable solution.

[0012] Furthermore, the information processing device of the present invention may further include an Ising machine having at least one processor, wherein the processor of the Ising machine performs the following processing: solving the optimization problem defined by the mathematical model.

[0013] Furthermore, the information processing method of the present invention is executed by a processor of an information processing device, which has at least one processor and causes the Ising machine to perform the following processing: solving the optimization problem by using a first objective function to obtain the value of an unknown variable, in which the value of the unknown variable is related to the number of quantum bits when the optimization problem is solved using the Ising machine, and the following control is performed in the information processing method: using a second objective function different from the first objective function, deriving the smallest value related to the unknown variable within the range of executable solutions to the optimization problem, causing the Ising machine to perform processing to solve the optimization problem, and the optimization problem is specified by a mathematical model including the derived value related to the unknown variable and the first objective function.

[0014] Furthermore, the information processing program of the present invention is used to cause the processor of the information processing device to perform the following processing, wherein the information processing device has at least one processor and causes the Ising machine to perform the following processing: solving the optimization problem by using the first objective function to obtain the value of the unknown variable, wherein the value of the unknown variable is related to the number of quantum bits when the optimization problem is solved using the Ising machine, and the information processing program performs the following control: using a second objective function different from the first objective function, deriving the smallest value related to the unknown variable within the range of executable solutions to the optimization problem, causing the Ising machine to perform the processing of solving the optimization problem, wherein the optimization problem is specified by a mathematical model including the derived value related to the unknown variable and the first objective function.

[0015] Effects of the Invention

[0016] According to the present invention, the number of quantum bits when solving an optimization problem on an Ising machine can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a block diagram showing an example of the hardware configuration of an information processing device.

[0018] Figure 2 This is a block diagram showing an example of the hardware configuration of an Ising machine.

[0019] Figure 3 This is a schematic diagram for explaining the optimization problem involved in the first embodiment.

[0020] Figure 4 This is a schematic diagram showing an example of a solution to the optimization problem according to the first embodiment.

[0021] Figure 5 This diagram shows an example of quantum bits that express the first rotation of a truck.

[0022] Figure 6 This diagram shows an example of quantum bits that express the solution for the first rotation of a truck.

[0023] Figure 7 This diagram shows an example of quantum bits that represent multiple cycles of a truck.

[0024] Figure 8 This diagram shows an example of quantum bits that represent multiple cycles of multiple trucks.

[0025] Figure 9 This is a block diagram showing an example of the functional configuration of an information processing device.

[0026] Figure 10 This is a diagram for explaining the reduced quantum bits involved in the first embodiment.

[0027] Figure 11 This is a block diagram showing an example of the functional structure of an Ising machine.

[0028] Figure 12 This is a flowchart showing an example of model generation processing.

[0029] Figure 13 This is a flowchart showing an example of a solution process.

[0030] Figure 14 This is a schematic diagram for explaining the optimization problem involved in the second embodiment.

[0031] Figure 15 This is a diagram for explaining an example of a method of expressing a quantum bit according to the second embodiment.

[0032] Figure 16 This is a diagram for explaining an example of a method of expressing a quantum bit according to the second embodiment.

[0033] Figure 17 This is a diagram for explaining another example of the method of expressing quantum bits according to the second embodiment.

[0034] Figure 18 This is a diagram for explaining another example of the method of expressing quantum bits according to the second embodiment.

[0035] Figure 19 This is a diagram for explaining the reduced quantum bits involved in the second embodiment. DETAILED DESCRIPTION

[0036] Hereinafter, embodiments for implementing the technology of the present invention will be described in detail with reference to the accompanying drawings. In the following embodiments, examples using the QUBO model will be described as a mathematical model representing an optimization problem to be solved using an Ising machine.

[0037] [First embodiment]

[0038] First, refer to Figure 1 and Figure 2 , the hardware structure of the information processing device 10 involved in this embodiment is described. As an example of the information processing device 10, a server computer etc. can be cited. Figure 1As shown, the information processing device 10 includes a CPU (Central Processing Unit) 20, a memory 21 serving as a temporary storage area, and a nonvolatile storage unit 22. Furthermore, the information processing device 10 includes a display 23 such as a liquid crystal display, an input device 24 such as a keyboard and a mouse, a network interface (I / F) 25 for connecting to a network, and an Ising machine 26. The CPU 20, memory 21, storage unit 22, display 23, input device 24, network I / F 25, and Ising machine 26 are connected to a bus 27. The information processing device 10 may include multiple Ising machines 26.

[0039] The storage unit 22 is implemented by an HDD (Hard Disk Drive), an SSD (Solid State Drive), a flash memory, or the like. The storage unit 22, serving as a storage medium, stores an information processing program 30. The CPU 20 reads the information processing program 30 from the storage unit 22, expands it into the memory 21, and executes the expanded information processing program 30.

[0040] Furthermore, the storage unit 22 stores problem data 32 for modeling the optimization problem to be solved by the information processing device 10. Details of the optimization problem represented by the problem data 32 will be described later.

[0041] The Ising machine 26 is dedicated hardware for operating the QUBO model and is installed, for example, in an expansion card slot of the information processing device 10. The Ising machine 26 is implemented, for example, as a digital circuit such as an FPGA (Field Programmable Gate Array). When the QUBO model is input to the Ising machine 26 via the bus 27 by the CPU 20, the Ising machine 26 solves the optimization problem defined by the QUBO model and outputs the results to the CPU 20. Alternatively, the Ising machine 26 may be a computer external to the information processing device 10, such as a cloud server connected via a network.

[0042] like Figure 2 As shown, the Ising machine 26 includes a processor 40, an interactive clock generator 42, a random number generator 44, and multiple Ising chips 46. The processor 40, the interactive clock generator 42, the random number generator 44, and the multiple Ising chips 46 are connected to each other so as to be able to send and receive information. The processor 40 solves the optimization problem by controlling the interactive clock generator 42, the random number generator 44, and the Ising chips 46.

[0043] Interaction clock generator 42 generates a clock used for bit-to-bit interaction when Ising chip 46 operates the QUBO model. Random number generator 44 generates random numbers, which are random bit strings used to prevent the solution search process performed by Ising chip 46 from becoming trapped in a local optimum. Ising chip 46 includes a memory unit for storing bits, interaction coefficients, external magnetic field coefficients, and the like.

[0044] Next, refer to Figure 3 and Figure 4 , an example of the optimization problem represented by the problem data 32 involved in this embodiment is described. Figure 3 As shown, in this embodiment, as an example of an optimization problem, an example of a problem of determining a route for delivering goods from one warehouse to multiple stores using multiple trucks (hereinafter referred to as a "route determination problem") is described. Figure 3 In FIG, an example is shown in which there are three trucks and nine stores. Figure 3 The number written on the inside of the truck indicates the maximum amount of goods that the truck can load (hereinafter referred to as the "maximum load"). Figure 3 The numbers written on the inside of the store indicate the demand quantity of the goods in the store.

[0045] Furthermore, in this embodiment, the number of stores, the number of products required at each store, the number of trucks, the maximum load capacity of each truck, the distance a truck travels between the warehouse and each store, and the distance a truck travels between each store are all known. The route determination problem involved in this embodiment is explained using the example of finding a delivery route that minimizes the total distance traveled by a truck from a warehouse, delivering the required quantity of products to each store, and returning to the warehouse. Furthermore, a single truck can make multiple loops. Looping here means that a truck departs from a warehouse, delivers products to one or more stores, and then returns to the warehouse. Figure 4 Shown in Figure 3 An example of a solution to the path determination problem of an example. Figure 4 The solid arrow in represents the path of a truck with a maximum load of "6", and the dotted arrow represents the path of a truck with a maximum load of "8". Figure 4 The single-dot chain arrow in represents the first round route of the truck with the maximum load capacity of "10", and the double-dot chain arrow represents the second round route of the truck with the maximum load capacity of "10".

[0046] The following describes the case of using the Ising machine 26 to solve the aforementioned routing problem. First, to solve the routing problem using the Ising machine 26, qubits are prepared to represent the number of which store each truck visits during the week. Below, let t represent the truck, s represent the store, n represent the week of the truck's movement, and i represent the store number visited by the truck during the week.

[0047] In the following, let S be the number of stores to which the goods are delivered, T be the number of trucks, N be the maximum number of round trips for each truck, and I be the maximum number of stores that each truck can visit in a week. In this case, each variable is s∈S s ={1, 2,...,S,S+1},t∈T s ={1, 2,...,T}, n∈N s ={1, 2,...,N},i∈I s ={1, 2, ..., I}. In addition, when the subscript "s" is given, it means a set. s , S+1 is added to the last element of the set to indicate that the truck finally returns to the warehouse. Furthermore, N is assumed to be a number greater than 1. This is because the routing problem above sets a maximum truck load capacity, and even if all trucks share the responsibility of delivery, it may not be possible to deliver goods to all stores within a week.

[0048] Next, the method of allocating qubits for constructing a QUBO model that can be executed by the Ising machine 26 is described. First, the first cycle of a truck (i.e., n=1) is defined. As an example, Figure 5 As shown, all stores become candidates for the truck's visit destinations in the first week, and the number of stores visited in the first week is unknown, so (S+1)×I bits of quantum bits are prepared for one week. Figure 5 In the example, quantum bits are arranged two-dimensionally, with the vertical axis representing the variable i and the horizontal axis representing the variable s.

[0049] The result of solving the path determination problem is used as an example. Figure 6 As shown. Figure 6 In the , the position where the quantum bit value is "1" indicates that the store is visited, and the position where the quantum bit value is "0" indicates that the store is not visited. Figure 6 In the case where the value of a quantum bit is "0", the "0" is omitted and left blank. This will be discussed later. Figure 7 、 Figure 8 The same is true in . Figure 6In the example of , it is shown that the truck visits store 2 for the first time, visits store 3 for the second time, and returns to the warehouse for the third time in the first week.

[0050] Figure 5 and Figure 6 The qubits shown are one-way quantities, so as an example, Figure 7 As shown in , by preparing N quantum bits, it is possible to define the quantum bits of one truck. That is, the number of quantum bits required to express one truck is (S+1)×N×I. And, as an example, Figure 8 As shown, by preparing a truckload of qubits, the number of trucks can be expressed as Figure 3 The path shown determines the solution to the problem. That is, in Figure 8 In the example shown, the required number of bits is T×(S+1)×N×I.

[0051] Next, an example of the constraint conditions and objective function of the path determination problem included in the problem data 32 is shown. First, notations are defined as follows.

[0052] [Formula 1]

[0053] Q t,s,n,i ∈{0,1}: qubit indicating whether truck t visits store s for the i-th time in week n

[0054] Maximum load capacity of truck t

[0055] The demand quantity of the product in store s

[0056] The distance the truck travels between store s and store s'

[0057] The distance the truck travels between the warehouse and store s

[0058] The constraints are expressed by the following equations (1) to (6). Equation (1) indicates that a truck can only visit all stores once. Equation (2) indicates that a truck can visit one store at a time. Equation (3) indicates that each truck can visit stores in sequence, such as the first, second, and so on. Specifically, Equation (3) indicates the following condition: Figure 6 As shown, starting from the first store to the last store returned to the warehouse, the stores are visited in order of the second, third, ... That is, there is no row whose quantum bit value is only "0" between the first row and the row indicating the return to the warehouse.

[0059] Formula (4) represents the condition that the number of goods delivered by each truck is less than the maximum load capacity of each truck. Formula (5) represents the condition that each truck returns to the warehouse after each round. Formula (6) represents the condition that each truck does not visit a store after returning to the warehouse after each round.

[0060] [Formula 2]

[0061]

[0062] [Formula 3]

[0063]

[0064] [Formula 4]

[0065]

[0066] [Formula 5]

[0067]

[0068] [Formula 6]

[0069]

[0070] [Formula 7]

[0071]

[0072] The objective function for minimizing the total value of the truck's travel distance is represented by the following equation (7): This objective function is used to solve the above-mentioned route determination problem and is hereinafter referred to as the "first objective function."

[0073] [Formula 8]

[0074]

[0075] The QUBO model defined by equations (1) to (7) can be solved by the Ising machine 26. In this case, S and T are uniquely determined according to the problem setting, but N and I become arbitrary values, for example, set to values ​​that the user has room for. This is because the user cannot know in advance the values ​​of N and I that cannot be executed when solving using the Ising machine 26. For example, Figure 3 In the routing problem of the example shown, the truck "10" with the largest maximum load capacity satisfies the above constraints and can visit a maximum of 4 stores in a week, so I is set to a value greater than 4.

[0076] In this way, when the user sets the values ​​of N and I based on the problem setting and empirical equations to avoid impossibility, the values ​​of N and I become large enough to accommodate the problem, thereby increasing the number of qubits. This is because the values ​​of the unknown variables i and n in the path determination problem are related to the number of qubits used to solve the path determination problem using the Ising machine 26. Since it is difficult to increase the number of qubits, which are the computational units of a quantum computer, it is preferable to reduce the number of qubits used when the Ising machine 26 computes the path determination problem.

[0077] Furthermore, the data size of the QUBO model input to the Ising machine 26 is proportional to the quantum bit Q obtained by equations (1) to (7). t,s,n,i The coefficients of Q and the multiplication of two qubits t,s,n,i ×Q t’,s’,n’,i’ The coefficients of the equations are arranged in a way that is proportional to the number of qubits times the number of qubits, or the square of the number of qubits. Therefore, as the number of qubits increases, the data size of the QUBO model also increases. Therefore, from the perspective of data size, it is preferable to reduce the number of qubits when using the Ising machine 26 to solve the path determination problem.

[0078] Therefore, the information processing device 10 according to this embodiment has a function of reducing the number of quantum bits when the Ising machine 26 calculates the path determination problem.

[0079] Next, refer to Figure 9 , the functional structure of the information processing device 10 involved in this embodiment is described. Figure 9 As shown, the information processing device 10 includes a derivation unit 50, a generation unit 52, a control unit 54, and an acquisition unit 56. The derivation unit 50, the generation unit 52, the control unit 54, and the acquisition unit 56 function as the CPU 20 executing the information processing program 30.

[0080] The deriving unit 50 uses a second objective function different from the first objective function to derive the minimum value of unknown variables i and n within a range where an executable solution to the path determination problem can be obtained. The second objective function is represented by the following equation (8).

[0081] [Formula 9]

[0082]

[0083] In the second objective function, the value to be minimized is the sum of the upper limit of variable i, I, and the upper limit of variable n, N. In equation (8), by including variables i and n in the objective function, a solution can be obtained in which the number of stores visited and the number of loops per truck are minimized.

[0084] Specifically, the deriving unit 50 performs the following processing: solves the path determination problem in which the objective function is changed from the first objective function to the second objective function. t,s,n,i The maximum value of i and n when the value of becomes 1 corresponds to the minimum value of I and N within the range that can obtain an executable solution to the path determination problem. Hereinafter, these minimum values ​​of I and N will be referred to as I' and N'. That is, I' and N' correspond to the upper limit values ​​I and N of the variables i and n that are the minimum within the range that can obtain an executable solution to the path determination problem, derived using the second objective function.

[0085] The second objective function is an objective function that can relax constraints compared to the first objective function. Specifically, in equation (8) representing the second objective function, there is no need to calculate the truck's travel distance. Therefore, the constraints related to the store visit order, equations (3) and (6), can be ignored among the constraints in equations (1) to (6). This reduces the amount of computation required.

[0086] In the solution process by the derivation unit 50 , for example, well-known methods such as the branch-and-bound method, the local search method, an evolutionary computing method such as a genetic algorithm, and a swarm intelligence optimization method such as an ant colony optimization can be used.

[0087] The generator 52 generates a QUBO model that includes N' and I' derived by the derivation unit 50 and the first objective function. Specifically, the generator 52 uses N' and I' derived by the derivation unit 50 and equations (1) to (7) to generate a QUBO model in a data format that enables the Ising machine 26 to solve the path determination problem. The QUBO model includes information necessary for solving the path determination problem, such as the values ​​of N' and I', constraints, the first objective function, a method for expressing qubits, and a problem setting.

[0088] In the QUBO model generated by the generator 52, the upper limit values ​​I' and N' of the unknown variables i and n are smaller than I and N set by the user with a margin so that an executable solution can be obtained. Figure 10 As shown, the number of qubits required to solve the path determination problem in the Ising machine 26 can be reduced. Specifically, when qubits are arranged two-dimensionally, the qubits from the 1′+1th row to the 1st row can be reduced from the 1st to the N′th round. Furthermore, in this case, the total number of qubits from the 1st to the 1st row can be reduced from the N′+1th to the Nth round.

[0089] The control unit 54 controls the Ising machine 26 to execute a process for solving the path determination problem defined by the QUBO model generated by the generation unit 52. Specifically, the control unit 54 outputs the QUBO model generated by the generation unit 52 to the Ising machine 26 via the bus 27. Furthermore, the control unit 54 controls the storage unit 22 to store the results of the solution process, which are acquired by the acquisition unit 56 (described later). The control unit 54 can also control the display 23 to display the results of the solution process.

[0090] The acquisition unit 56 acquires the result of the solution process of the path determination problem performed by the Ising machine 26 from the Ising machine 26 via the bus 27 .

[0091] Next, refer to Figure 11 , the functional structure of the Ising machine 26 involved in this embodiment is described. Figure 11 As shown, the Ising engine 26 includes an acquisition unit 60, an execution unit 62, and an output unit 64. The processor 40 functions as the acquisition unit 60, the execution unit 62, and the output unit 64.

[0092] The acquisition unit 60 acquires the QUBO model input from the CPU 20. The execution unit 62 performs processing to solve the path determination problem defined by the QUBO model acquired by the acquisition unit 60. The output unit 64 outputs the result of the path determination problem solution processing performed by the execution unit 62 to the CPU 20 via the bus 27.

[0093] Next, refer to Figure 12 and Figure 13 The function of the information processing device 10 of this embodiment will be described. The CPU 20 executes the information processing program 30. Figure 12 The model generation process shown. Figure 12 The model generation process shown is executed when a command to start the execution is input by the user via the input device 24 , for example.

[0094] exist Figure 12 In step S10, as described above, the derivation unit 50 uses a second objective function different from the first objective function to derive the minimum values ​​associated with the unknown variables i and n within a range that yields an executable solution to the path determination problem. In step S12, as described above, the generation unit 52 generates a QUBO model that includes N' and I' derived in step S10 and the first objective function.

[0095] In step S14, the control unit 54 outputs the QUBO model generated in step S12 to the Ising machine 26 via the bus 27. In step S16, the acquisition unit 56 acquires the result of the solution process of the path determination problem performed using the Ising machine 26 from the Ising machine 26 via the bus 27. In step S18, the control unit 54 controls the storage unit 22 to store the result of the solution process acquired in step S16. When the process of step S18 is completed, the model generation process ends.

[0096] When the QUBO model is input from the CPU 20 to the Ising machine 26 in step S14 of the model generation process, the processor 40 executes Figure 13 The solution process shown.

[0097] exist Figure 13 In step S20, the acquisition unit 60 acquires the QUBO model input from the CPU 20. In step S22, the execution unit 62 performs processing to solve the path determination problem defined by the QUBO model acquired in step S20. In step S24, the output unit 64 outputs the result of solving the path determination problem based on the processing in step S22 to the CPU 20 via the bus 27. When the processing in step S24 is completed, the solution process ends. The solution result input to the CPU 20 in step S24 is acquired in step S16 of the model generation process described above.

[0098] As described above, according to this embodiment, the number of quantum bits when the Ising machine 26 calculates the path determination problem can be reduced.

[0099] [Second embodiment]

[0100] A second embodiment of the inventive technique will be described. Note that the hardware configurations of the information processing device 10 and the Ising machine 26 according to this embodiment are the same as those of the first embodiment, and therefore their description will be omitted.

[0101] refer to Figure 14 , an example of the optimization problem represented by the problem data 32 involved in this embodiment is described. Figure 14 As shown, in this embodiment, as an example of an optimization problem, an example is described of the problem of determining the delivery quantity of goods in a manner that meets the demand quantity of goods in each warehouse and minimizes the delivery cost when delivering inventory goods from multiple factories to multiple warehouses (hereinafter referred to as "inventory delivery problem").

[0102] In the following, let f be the variable representing the factory, w be the variable representing the warehouse, and C be the variable representing the delivery cost per product when delivering products from the factory to the warehouse. f、wThe quantity of goods delivered from the factory to the warehouse is set to x f、w In the following, let the number of factories be F and the number of warehouses be W. In this case, the variable f becomes f∈f s ={1, 2, ..., F}, the variable w becomes w∈w s ={1, 2, ..., W}. In addition, when the subscript "s" is given, it represents a set.

[0103] The first objective function in the inventory distribution problem is represented by the following equation (9). The inventory distribution problem becomes a problem of finding the unknown variable x f、w The value problem.

[0104] [Formula 10]

[0105]

[0106] As a constraint condition for solving the inventory distribution problem, for example, the total value of the demand quantity of goods for each warehouse and the quantity of goods delivered from each factory to the warehouse can be given as the production quantity FM of the goods in each factory. f The following etc.

[0107] In order to solve the inventory distribution problem using the Ising machine 26, we use quantum bits to express x as a positive integer in decimal. f、w As examples of its expression method, the following two examples can be given.

[0108] The first expression method is a method of preparing a qubit group including a plurality of qubits represented by the following equation (10), and expressing the unknown variable x at positions where the qubits are 1 in the qubit group. f、w The value of .

[0109] [Formula 11]

[0110]

[0111] Specifically, as an example, Figure 15 As shown in the figure, the quantum bits are arranged two-dimensionally, with the vertical direction indicating the warehouse number and the horizontal direction indicating the number of goods delivered to the warehouse. Figure 15 In the example, the above qubit group is a qubit array. The number of bits in the horizontal direction is set to be equal to the number of qubits that can be produced FM. f The same amount, according to the previous Figure 15 In the example of the left end, the value of the first quantum bit is 1 to represent the number of goods delivered to the warehouse. Alternatively, the value of the first quantum bit from the end of the horizontal direction ( Figure 15 In the example on the right, the value of the nth quantum bit is 1 to represent the number of goods delivered to the warehouse.

[0112] For example, the position where the value of the qubit becomes 1 is Figure 16 In the case of the location shown, 6 items are delivered to warehouse 1 and 3 items are delivered to warehouse 2. Figure 16 In the case where the value of a quantum bit is "0", the "0" is omitted and left blank. This will be discussed later. Figure 18 The same is true in . Figure 16 In the example, it indicates the number of goods delivered to the warehouse at the position where the quantum bit becomes 1, but it can also indicate the number of goods delivered to the warehouse at the position where the quantum bit becomes 0. In this case, Figure 16 The values ​​of the qubits 0 and 1 are shown swapped.

[0113] The second expression method is to prepare a number of qubits represented by the following formula (11), so that one qubit corresponds to one bit of a binary number, and express the unknown variable x as a binary number obtained by combining multiple qubits. f、w The value of .

[0114] [Formula 12]

[0115]

[0116] Specifically, as an example, Figure 17 As shown, the quantum bits are arranged two-dimensionally, with the vertical direction indicating the warehouse number and the horizontal direction indicating the number of goods delivered to the warehouse. The number of bits in the horizontal direction is set to be equal to log2(FM f ) the same number, the horizontal bit string represents a binary number. For example, the position where the value of the quantum bit becomes 1 is Figure 18 In the case of the positions shown, 6 products are delivered to warehouse 1 and 3 products are delivered to warehouse 2.

[0117] The first expression method requires more qubits than the second, but due to the simpler constraints, the probability of obtaining an executable solution is higher. The second expression method requires fewer qubits than the first, but due to the additional constraints required to associate the qubit corresponding to the binary number with the decimal integer representing the delivery quantity of the product, the probability of not obtaining an executable solution is higher. The following describes an example using the first expression method.

[0118] Next, refer to Figure 9 , the functional structure of the information processing device 10 involved in this embodiment is described. Functional parts having the same functions as those in the first embodiment are marked with the same symbols as those in the first embodiment and their descriptions are omitted. Figure 9As shown, information processing device 10 includes deriving unit 50A, generating unit 52A, control unit 54, and acquiring unit 56. When CPU 20 executes information processing program 30, deriving unit 50A, generating unit 52A, control unit 54, and acquiring unit 56 function.

[0119] The derivation unit 50A uses a second objective function different from the first objective function to derive the smallest value related to the unknown variable x within the range of an executable solution to the inventory distribution problem. f、w The second objective function is represented by the following equation (12). Equation (12) minimizes the maximum value of the number of products delivered from factory f to warehouse w.

[0120] [Formula 13]

[0121]

[0122] Specifically, the derivation unit 50A performs the following processing: solves the inventory distribution problem with the objective function changed from the first objective function to the second objective function. Let the solution obtained by this processing be x' f、w , setting its minimum value to The M is equivalent to the unknown variable x in the range of executable solutions to the inventory distribution problem. f、w The minimum value of M. Furthermore, this M can be considered the minimum number of goods that can be delivered among all combinations of factories and warehouses required for delivering goods. Therefore, the number of quantum bits required at this time is expressed using M as shown in the following formula (13).

[0123] [Formula 14]

[0124]

[0125] As an example, Figure 19 As shown, Equation (13) indicates that in the set of factories and warehouses required to deliver goods, there is no need to represent quantum bits less than the minimum delivery quantity M. Figure 19 The qubits filled in gray in the figure are not needed. Figure 19 In the example above, for the warehouse required to deliver goods, the number of quantum bits required is reduced by M-1 bits.

[0126] Generator 52A generates a QUBO model that includes M derived by deriving unit 50A and the first objective function. Specifically, generator 52A uses M derived by deriving unit 50A, the constraints, and the first objective function to generate a QUBO model in a data format that enables the Ising machine 26 to solve the inventory distribution problem.

[0127] The function of the Ising machine 26 according to the present embodiment differs from that of the first embodiment only in the optimization problem to be processed, and therefore description thereof will be omitted.

[0128] Furthermore, regarding the function of the information processing device 10 involved in this embodiment, only the optimization problem of the processing object is different from that of the first embodiment, and the processing flow is the same as that of the first embodiment (refer to Figure 12 and Figure 13 ), so the description is omitted. Specifically, only Figure 12 The unknown variable x derived in step S10 f、w The value M and the QUBO model generated in step S12 are different from those in the first embodiment.

[0129] As described above, according to this embodiment, the number of quantum bits when the Ising machine 26 is caused to calculate the inventory distribution problem can be reduced.

[0130] In addition, in the above embodiments, the QUBO model is used as the mathematical model operated by the Ising machine 26, but this is not limiting. Alternatively, the Ising model can be used as the mathematical model. While the QUBO model models the optimization problem using a quadratic form of binary variables of 0 or 1, the Ising model models the optimization problem using a quadratic form of binary variables of -1 or 1. Furthermore, the QUBO model and the Ising model can be converted to each other using known methods.

[0131] Furthermore, in the above-described embodiment, for example, various processors described below can be used as the hardware configuration of processing units that perform various processes, such as the derivation unit 50, 50A, the generation unit 52, 52A, the control unit 54, and the acquisition unit 56. As described above, the various processors include general-purpose processors (CPUs) that execute software (programs) and function as various processing units, as well as processors such as FPGAs (Programmable Logic Devices: PLDs) whose circuit configuration can be modified after manufacture, and processors such as ASICs (Application Specific Integrated Circuits) that have circuit configurations specifically designed to perform specific processes (special purpose circuits).

[0132] A single processing unit may be composed of one of these various processors, or a combination of two or more processors of the same or different types (e.g., a combination of multiple FPGAs, or a combination of a CPU and an FPGA). Furthermore, a single processor may constitute multiple processing units.

[0133] Examples of multiple processing units composed of a single processor include, firstly, a method typified by computers such as clients and servers, where a single processor is composed of a combination of one or more CPUs and software, and the processor functions as multiple processing units. Secondly, a method typified by system-on-chip (SoC) systems uses a single integrated circuit (IC) chip to implement the functions of the entire system including multiple processing units. In this way, various processing units are constructed as hardware using one or more of the various processors described above.

[0134] Furthermore, as the hardware configuration of these various processors, more specifically, a circuit formed by combining circuit elements such as semiconductor elements can be used.

[0135] Furthermore, in the above embodiment, the information processing program 30 is described as being pre-stored (installed) in the storage unit 22, but the present invention is not limited thereto. The information processing program 30 may also be provided in a form recorded on a recording medium such as a CD-ROM (Compact Disc Read Only Memory), a DVD-ROM (Digital Versatile Disc Read Only Memory), or a USB (Universal Serial Bus) memory device. Furthermore, the information processing program 30 may be downloaded from an external device via a network.

[0136] The invention of Japanese Patent Application No. 2021-191810 filed on November 26, 2021, is incorporated herein by reference in its entirety. Furthermore, all documents, patent applications, and technical specifications described in this specification are incorporated herein by reference as if each individual document, patent application, or technical specification were specifically and individually indicated as being incorporated by reference.

Claims

1. An information processing device comprising at least one processor and an Ising machine, wherein the Ising machine is configured to perform processing for solving an optimization problem by using a first objective function to determine a value of an unknown variable, wherein the value of the unknown variable is related to the number of qubits used to solve the optimization problem using the Ising machine. The processor uses a second objective function different from the first objective function to derive a value related to the unknown variable that is minimum within a range where an executable solution to the optimization problem can be obtained. The processor generates a mathematical model including the derived minimum value related to the unknown variable and the first objective function, The processor outputs the generated mathematical model to the Ising machine, and causes the Ising machine to execute a process of solving the optimization problem specified by the mathematical model. The second objective function is an objective function that can relax the constraint condition compared to the first objective function.

2. The information processing device according to claim 1, wherein The unknown variable is stored in a quantum bit group comprising a plurality of quantum bits, The value of the unknown variable is represented by the position where the quantum bit in the quantum bit group becomes 0 or 1.

3. The information processing device according to claim 1 or 2, wherein: The Ising machine has at least one processor. The processor of the Ising machine performs the following processing: solving the optimization problem specified by the mathematical model.

4. An information processing method, executed by a processor of an information processing device, the information processing device comprising at least one processor and an Ising machine, wherein the Ising machine is caused to perform processing to solve an optimization problem by finding a value of an unknown variable using a first objective function, wherein the value of the unknown variable is related to the number of qubits used to solve the optimization problem using the Ising machine, wherein: The processor uses a second objective function different from the first objective function to derive a value related to the unknown variable that is minimum within a range where an executable solution to the optimization problem can be obtained. The processor generates a mathematical model including the derived minimum value related to the unknown variable and the first objective function, The processor outputs the generated mathematical model to the Ising machine, and causes the Ising machine to execute a process of solving the optimization problem specified by the mathematical model. The second objective function is an objective function that can relax the constraint condition compared to the first objective function.

5. A computer-readable storage medium storing an information processing program configured to cause a processor of an information processing device to execute the following processing, wherein the information processing device comprises at least one of the processors and an Ising machine, and the Ising machine is configured to execute the following processing: solving an optimization problem by finding a value of an unknown variable using a first objective function, wherein the value of the unknown variable is related to the number of qubits used when solving the optimization problem using the Ising machine; The processor uses a second objective function different from the first objective function to derive a value related to the unknown variable that is minimum within a range where an executable solution to the optimization problem can be obtained. The processor generates a mathematical model including the derived minimum value related to the unknown variable and the first objective function, The processor outputs the generated mathematical model to the Ising machine, and causes the Ising machine to execute a process of solving the optimization problem specified by the mathematical model. The second objective function is an objective function that can relax the constraint condition compared to the first objective function.

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