Calculation program and information processing method

Abstract

This computational model can be applied to an Ising model or QUBO, and has a plurality of Ising bits and a first auxiliary bit. Each of the plurality of Ising bits and the first auxiliary bit is a binary variable. The plurality of Ising bits represent each choice in a combinational optimization problem as a combination of the variables, and the first auxiliary bit indicates a value obtained by performing a logical operation on two or more of the plurality of values representing the choices.

Description

[Technical field]

[0001] The present invention is Program and Information Processing By law Regarding. [Background technology]

[0002] Attempts are being made to find optimal solutions to combinatorial optimization problems using quantum annealing (for example, Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Hiroto Teranishi, Shota Nagayama, "Utilizing excited states of quantum annealing in the simple graph minimum cut problem", Institute of Electronics, Information and Communication Engineers, Second-class research materials, Quantum Information Technology Study Group, QIT2019-89 (Nov. 2019) Summary of the Invention [Problem to be solved by the invention]

[0004] Quantum annealing machines can sometimes experience errors due to unintended quantum transitions or noise, which can prevent the optimal solution from being found properly.

[0005] The present invention has been made in consideration of the above circumstances, and has an object to provide a calculation model, an information processing method, a calculation program, and an information processing device that are less susceptible to errors caused by noise or the like. [Means for solving the problem]

[0006] In order to solve the above problems, the present invention provides the following means.

[0007] (1) A computational model according to a first aspect is a computational model applicable to an Ising model or QUBO. This computational model has a plurality of Ising bits and a first auxiliary bit. Each of the plurality of Ising bits and the first auxiliary bit is a binary variable. The plurality of Ising bits represent each of options in a combinatorial optimization problem by a combination of the variables. The first auxiliary bit represents a value obtained by performing a logical operation on two or more values ​​among a plurality of values ​​representing the options.

[0008] (2) In the above computation model, the logical operation may be an exclusive OR.

[0009] (3) In the above computation model, the logical operation may be a logical sum.

[0010] (4) In the above computation model, the logical operation may be a logical AND.

[0011] (5) The computation model may further include a second auxiliary bit, the second auxiliary bit indicating a value obtained by logically adding two or more values ​​among the plurality of values ​​indicating the options.

[0012] (6) In the above computational model, the plurality of Ising bits may represent the options in binary numbers.

[0013] (7) In the above computation model, the auxiliary variable may further include a third auxiliary bit, which indicates a value obtained by performing a logical operation on a value of the first auxiliary bit and a value, among a plurality of values ​​indicating the options, that has not been used in the logical operation to obtain the first auxiliary bit.

[0014] (8) In the above computational model, the Ising model or the QUBO may be executed by a quantum annealing machine.

[0015] (9) An information processing method according to a second aspect is an information processing method using the above-mentioned calculation model, and includes a comparison step of comparing the value of the first auxiliary bit with a result of performing the same logical operation as that used in determining the value of the first auxiliary bit on an Ising bit corresponding to a value used in the logical operation of the first auxiliary bit.

[0016] (10) The information processing method according to the above aspect may include an extraction step of enumerating combinations of the variables that the plurality of Ising bits can select from the value of the first auxiliary bit when the comparison step results in a mismatch; a calculation step of performing a calculation using the calculation model for each of the enumerated combinations; and a replacement step of replacing the combination of variables of the plurality of Ising bits when an error is detected with the combination of variables that the plurality of Ising bits can select and that results in the smallest calculation result.

[0017] (11) In the extraction step of the information processing method according to the above aspect, a combination having a small Hamming distance with the plurality of Ising bits may be extracted from among combinations of the variables that can be selected by the plurality of Ising bits.

[0018] (12) A calculation program according to a third aspect includes a calculation program that performs calculations using the calculation model according to the above aspect, and a comparison program. The comparison program compares the value of the first auxiliary bit with a result of performing the same logical operation as that performed when determining the value of the first auxiliary bit on an Ising bit corresponding to a value used in the logical operation of the first auxiliary bit.

[0019] (13) The calculation program according to the above aspect may further include an extraction program and a correction program. When the comparison program results in a mismatch, the extraction program lists possible combinations of the variables for the options that result in a mismatch based on the value of the first auxiliary bit. The correction program replaces the variables for the comparison result that result in a mismatch with the combination of variables that results in the smallest calculation result using the calculation program among the possible combinations of the variables for the options.

[0020] (14) An information processing device according to a fourth aspect includes the calculation program according to the above aspect. Effect of the Invention

[0021] The computational model, information processing method, computational program, and information processing device according to the present invention are less susceptible to errors caused by noise or the like. [Brief description of the drawings]

[0022] [Figure 1] This is an image of the Ising model, QUBO. [Diagram 2] FIG. 2 is an image diagram of a calculation model according to the present embodiment. [Diagram 3] This is an example of displaying options using one-hot representation. [Figure 4] This is an example of options displayed in binary notation. [Diagram 5] 1 is a specific example of a calculation model according to the present embodiment. [Figure 6] FIG. 2 is a flow diagram of an information processing method according to the embodiment. [Figure 7] 13 is another example of a calculation model according to the present embodiment. [Figure 8] 13 is another example of a calculation model according to the present embodiment. [Figure 9] 13 is another example of a calculation model according to the present embodiment. [Figure 10] 13 is another example of a calculation model according to the present embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] The present embodiment will be described in detail below with reference to the drawings as appropriate. The drawings used in the following description may show characteristic parts in an enlarged scale for the sake of convenience in order to make the features of the present embodiment easier to understand, and the dimensional ratios of each component may differ from the actual ones. The materials, dimensions, etc. exemplified in the following description are merely examples, and the present invention is not limited thereto, and may be appropriately modified and implemented within the scope of the present invention.

[0024] "First embodiment" The computational model according to the first embodiment is a computational model applicable to the Ising model or QUBO used in quantum annealing. Quantum annealing is an algorithm for finding a state (ground state) with the minimum energy according to the computational model.

[0025] The Ising model is a model that predicts a stable overall state when multiple elements interact with each other and each element is subjected to a forcing force.

[0026] Figure 1 is an image of the Ising model. The Ising model has multiple bits b that interact with each other through a forcing force F. Each bit b consists of a spin s. The spin s can be either up or down. Each bit b is represented by a variable that indicates a binary state. Depending on the setting of the forcing force F, the stable state can be an equilibrium state of adjacent spins s, or an antiparallel state. The forcing force F is called the interaction parameter.

[0027] The Ising model is expressed by the following energy function (cost function).

[0028]

number

[0029] where σ i , σ j are input variables. σ i , σ j indicates one of the two values, +1 or -1. σ i , σ j corresponds to the state of spin s in Figure 1. J ij is the interaction parameter. J ij corresponds to the forcing force F in Figure 1. h i is a parameter associated with external factors.

[0030] QUBO (Quadratic Unconstrained Binary Optimization) is a computational model that can be converted to be equivalent to the Ising model. In the Ising model, each bit b is represented by a binary variable of +1 or -1, whereas in QUBO, each bit b is represented by a binary variable of 0 or 1. QUBO can be applied to computational models similar to the Ising model. QUBO is expressed by the following energy function (cost function).

[0031]

number

[0032] Here, q i , q j are input variables. q i , q j indicates one of the two values, 1 or 0. i , q j corresponds to the state of spin s in the Ising model. Q ij is the interaction parameter in QUBO. Q ij corresponds to the forcing force F in the Ising model. The Ising energy is expressed by the energy function with the input variable q i , q j This is the output when the value of is input.

[0033] The Ising model and QUBO can be applied to combinatorial optimization problems. For example, when applying QUBO to a combinatorial optimization problem, first solve the combinatorial optimization problem using QUBO.ij and express it as an energy function, and each option in the combinatorial optimization problem is treated as an input variable q i , q j The next step is to express the Ising energy as smaller q i , q j Combinatorial optimization problems can be solved by finding combinations of the values ​​of

[0034] The computation model according to this embodiment has a plurality of Ising bits and auxiliary bits. Fig. 2 is an image diagram of an example of the computation model according to this embodiment.

[0035] The Ising bits x1 to x3 and the auxiliary bit y1 are each a binary variable. The number of the Ising bits x1 to x3 is not limited to three. The number of the auxiliary bit y1 is also not limited to one.

[0036] The Ising bits x1 to x3 and the auxiliary bit y1 each indicate, for example, 1 or 0. The Ising bits x1 to x3 and the auxiliary bit y1 may each indicate, for example, +1 or -1. Each of the Ising bits x1 to x3 and the auxiliary bit y1 corresponds to bit b in FIG.

[0037] Ising bits x1 to x3 represent each of the options in a combinatorial optimization problem as a combination of binary variables. For example, in the case of a traveling salesman problem, there is a choice of which cities to visit and in what order. For example, the choice of visiting city M as the Nth city is choice A.

[0038] The options based on the Ising bits x1 to x3 may be expressed as one-hot or as binary.

[0039] Figure 3 is an example of options displayed in one-hot representation. One-hot representation is a method of expressing N types of information with N bits. With one-hot representation, only one of the N bits will be "1", and all other bits will be "0". In Figure 3, option A is assigned to (1,0,0), option B is assigned to (0,1,0), and option C is assigned to (0,0,1).

[0040] Figure 4 is an example of options displayed in binary notation. Binary notation is a way of expressing N types of information in binary numbers. Binary notation allows multiple bits to be "1" at the same time. In Figure 4, option A is assigned to (1,0,0), option B is assigned to (0,1,0), option C is assigned to (0,0,1), option D is assigned to (1,1,0), option E is assigned to (0,1,1), option F is assigned to (1,0,1), option G is assigned to (0,0,0), and option H is assigned to (1,1,1).

[0041] Binary representation has the advantage that it can express multiple states with a small number of bits. On the other hand, if one bit of binary representation is rewritten by noise, etc., it will express a different state. Therefore, measures against noise are required for binary representation.

[0042] FIG. 5 is an image diagram of an example of allocation of options for an optimization problem to a computational model according to this embodiment. The auxiliary bit y1 indicates a value obtained by logically operating two or more values ​​among the multiple values ​​indicating the options. Here, "multiple values ​​indicating the options" refers to each component that makes up the number assigned to the option. For example, if option A is assigned to (1,0,0), then "1", "0", and "0" each correspond to "multiple values ​​indicating the options".

[0043] The auxiliary bit y1 shown in Fig. 5 is a value obtained by exclusive ORing all of the multiple values ​​indicating the options. The logical operation may be exclusive OR, logical OR, or logical AND.

[0044] Even if an error occurs in which a bit inversion occurs in any of the Ising bits x1 to x3, the calculation model according to this embodiment is not easily affected by the error.

[0045] Errors occur when unintended quantum transitions or noise occur in the quantum annealing machine. For example, suppose that the quantum annealing machine would normally output option A(x1, x2, x3) = (1, 0, 0) in Figure 5 as the option with the smaller Ising energy, but noise occurs and the Ising bit x1 is inverted to "0" instead of "1." In this case, the quantum annealing machine erroneously outputs option G(x1, x2, x3) = (0, 0, 0) due to the noise.

[0046] The computation model of this embodiment detects an error using the auxiliary bit y1. An information processing method using the computation model according to this embodiment will be described below.

[0047] 6 is a process flow of the division processing method according to this embodiment. The information processing method according to this embodiment includes, for example, an optimization step S1, a comparison step S2, an extraction step S3, a calculation step S4, and a correction step S5.

[0048] In the optimization step S1, a calculation is performed to solve the optimization problem using the above-mentioned computational model. For example, in the case of QUBO, first, the options for the optimization problem are applied to the above-mentioned energy function (cost function). For example, the input variable q i , q j Next, the calculation model applies the Ising bits x1 to x3 and the auxiliary bit y1 to the input variable q i , q j Then, the input variable q i , q j From this, the values ​​of the corresponding Ising bits x1 to x3 and auxiliary bit y1 can be obtained.

[0049] The comparison step S2 is performed, for example, every time the optimization step S1 is performed. The comparison step S2 does not necessarily have to be performed every time the optimization step S1 is performed, and may be performed at an appropriately set timing.

[0050] In the optimization step S1, the computation model may output a combination of a plurality of Ising bits x1 to x3. In that case, the computation model executes the comparison step S2 and subsequent steps for the values ​​of each of the Ising bits x1 to x3.

[0051] In the comparison step S2, the value of the auxiliary bit y1 output in the optimization step S1 is compared with the result of performing the same logical operation as that used to obtain the value of the auxiliary bit y1 on the Ising bit corresponding to the value used in the logical operation of the auxiliary bit y1.

[0052] 5, the auxiliary bit y1 is calculated by the exclusive OR of three values ​​representing options in the optimization problem. The three values ​​representing options in the optimization problem correspond to the Ising bits x1 to x3, respectively.

[0053] For example, an exclusive OR is performed on the Ising bits x1 to x3. The exclusive OR is the same logical operation as that used to determine the value of the auxiliary bit y1. If no error occurs, the same logical operation is performed, so the operation result matches the value of the auxiliary bit y1. For example, in option A in FIG. 5, the exclusive OR of the Ising bits x1 to x3 is "1", which matches the value of the auxiliary bit y1.

[0054] On the other hand, if an error occurs in one bit of the Ising bits x1 to x3, the values ​​of the Ising bits x1 to x3 will be different values. For example, assume that the Ising bit x1 in the option A in FIG. 5 is erroneously recognized as "0" instead of "1" due to an error. In this case, in the case of the option A, the exclusive OR of the Ising bits x1 to x3 will be "0". The calculation result and the value of the auxiliary bit y1 will not match.

[0055] In other words, if the calculation result and the value of the ancillary bit y1 do not match, it can be said that an error has occurred.

[0056] The information processing method according to this embodiment can detect errors by repeating the optimization step S1 and the comparison step S2.

[0057] Then, an extraction step S3, a calculation step S4 and a correction step S5 are performed if an error is detected.

[0058] In the extraction step S3, combinations of variables that the Ising bits x1 to x3 can select from the value of the auxiliary bit y1 are listed.

[0059] For example, in the choice A in Fig. 5, a case where the logical operation result for the Ising bits x1 to x3 does not match the value of the auxiliary bit y1 will be described as an example. When the value of the auxiliary bit y1 is "1", the combinations of variables that the Ising bits x1 to x3 can select are (x1, x2, x3) = (1, 0, 0), (0, 1, 0), (0, 0, 1), and (1, 1, 1). In the extraction step S3, all of these possible combinations of variables are listed.

[0060] Next, in the calculation step S4, a calculation is performed using the above-mentioned calculation model for each combination of all the variables extracted in the extraction step S3. For example, each of (x1, x2, x3) = (1, 0, 0), (0, 1, 0), (0, 0, 1), and (1, 1, 1) listed in the extraction step S3 is applied to the calculation model and a calculation is performed. By performing the calculation, the Ising energy for each combination of variables is obtained.

[0061] When it is desired to perform the calculation step S4 in a short time, in the extraction step S3, the combinations of variables that the annealing bits x1 to x3 can select may be appropriately reduced. For example, as a result of the optimization step S1, when (x1, x2, x3) = (0, 0, 0) and the value of the auxiliary bit y1 is "1", the annealing bits x1 to x3 that satisfy the value of the auxiliary bit y1 being "1" and having a Hamming distance of 1 from (x1, x2, x3) = (0, 0, 0) may be extracted as the combinations of variables that can be selected, such as (x1, x2, x3) = (1, 0, 0), (0, 1, 0), and (0, 0, 1). The Hamming distance is the number of different characters at corresponding positions among two character strings having the same number of characters. In other words, the Hamming distance measures the number of replacement times required when transforming one character string into another character string.

[0062] Next, based on the result of the calculation step S4, a correction step S5 is performed. In the correction step S5, the values of the annealing bits x1 to x3 are corrected with the combination of variables that had the smallest annealing energy in the calculation step S4. For example, let the results of the calculated annealing energies for (x1, x2, x3) = (1, 0, 0), (0, 1, 0), (0, 0, 1), and (1, 1, 1) be H1, H2, H3, H4, and H5, respectively, and assume that the magnitudes of the annealing energies are H1 < H2 < H3 < H4 < H5. In this case, when an error is detected, the values of the annealing bits x1 to x3 are replaced with the combination of (x1, x2, x3) = (1, 0, 0) that has the smallest magnitude of annealing energy.

[0063] When the correction step S5 is performed, the values of the annealing bits x1 to x3 are corrected. Therefore, the information processing method according to this embodiment can correct errors by performing the extraction step S3, the calculation step S4, and the correction step S5.

[0064] The optimization step S1 is performed, for example, by an Ising machine specialized for calculation of the Ising model or QUBO. For example, a quantum annealing machine (D-wave, NEC), a coherent Ising machine (NTT), a simulated bifurcation machine (Toshiba), a digital annealer (Fujitsu), a CMOS annealer (Hitachi), and other machines are examples of Ising machines.

[0065] The Ising machine may be a quantum gate type computer. For example, by using QAOA (Quantum Approximate Optimization Algorithm), the Ising model and QUBO can be calculated by a quantum gate type computer.

[0066] The above-mentioned comparison step S2, extraction step S3, calculation step S4, and correction step S5 are performed using a general-purpose information processing device that has general-purpose properties. For example, machines such as personal computers, supercomputers, and microcomputers are examples of general-purpose information processing devices. Between the optimization step S1 and the comparison step S2, the Ising machine sends the values ​​of the Ising bits and auxiliary bits calculated in the optimization step S1 to the general-purpose information processing device, and the general-purpose information processing device executes the comparison step S2 and subsequent steps using the values ​​of the Ising bits and auxiliary bits sent from the Ising machine.

[0067] The optimization step S1 may be executed by the general-purpose information processing device.

[0068] The Ising machine and the general-purpose information processing device perform the above information processing based on calculation programs including an optimization program, a comparison program, an extraction program, a calculation program, and a correction program.

[0069] The optimization program performs an optimization step S1. The comparison program performs a comparison step S2. The extraction program performs an extraction step S3. The calculation program performs a calculation step S4. The correction program performs a correction step S5.

[0070] According to the calculation program and information processing device of this embodiment, an error can be detected using the auxiliary bit y1, and an appropriate optimal solution can be obtained.

[0071] The above describes the embodiments of the present invention in detail with reference to the drawings. However, each configuration and combination thereof in each embodiment is merely an example, and addition, omission, substitution, and other modifications of the configuration are possible without departing from the spirit of the present invention.

[0072] For example, when determining the auxiliary bit, it is not necessary to use all of the multiple values ​​indicating the options. For example, in FIG. 7, the auxiliary bit y2 is the logical product of two values ​​of the multiple values ​​indicating the options.

[0073] In the case shown in Fig. 7, when an error occurs in the Ising bits x1 to x3 whose interiors are indicated by dots, the value of the auxiliary bit y2 and the value of the logical product for the Ising bits x1 and x2 do not match. That is, in the case shown in Fig. 7, an error occurring in at least some of the Ising bits x1 to x3 can be detected.

[0074] Also, for example, the number of auxiliary bits is not limited to one, and may be multiple. Fig. 8 shows an example in which there are multiple auxiliary bits. In Fig. 8, auxiliary bit y2 is a value obtained by logically multiplying two values ​​among the multiple values ​​indicating the options, and auxiliary bit y3 is a value obtained by logically summing two values ​​among the multiple values ​​indicating the options.

[0075] In the case shown in FIG. 8, when an error occurs in the Ising bits x1 to x3 indicated by dots, the value of the auxiliary bit y2 does not match the value of the logical product for the Ising bits x1 and x2. Also, when an error occurs in the Ising bits x1 to x3 indicated by diagonal lines, the value of the auxiliary bit y3 does not match the value of the logical sum for the Ising bits x1 and x2. That is, in the case shown in FIG. 8, an error occurring in at least a part of the Ising bits x1 to x3 can be detected. The part where an error can be detected using the auxiliary bit y2 and the part where an error can be detected using the auxiliary bit y3 are different from each other, and an error in a wider part can be detected.

[0076] Furthermore, for example, the number of values ​​used in the logical operation of the auxiliary bits may be different for each auxiliary bit, as shown in Fig. 9. For example, in Fig. 9, auxiliary bit y4 is the exclusive OR of two values ​​among the multiple values ​​indicating the options, and auxiliary bit y5 is the exclusive OR of three values ​​among the multiple values ​​indicating the options. Auxiliary bit y5 is also the exclusive OR of auxiliary bit y4 and a value (x3) among the multiple values ​​indicating the options that was not used in the logical operation of auxiliary bit y4.

[0077] The Ising model and QUBO can calculate two-body problems using two variables, but cannot calculate many-body problems using two or more variables. As shown in Figure 9, by using the auxiliary bit y4, the three-body problem of Ising bits x1, x2, and x3 can be replaced with a two-body problem of auxiliary bit y4 and Ising bit x3.

[0078] The auxiliary bits can also be used to set constraints on the Ising model and QUBO.

[0079] As shown in Fig. 10, there are cases where the number of options for an optimization problem is smaller than the number of combinations of the Ising bits x1 to x3 expressed in binary. Fig. 10 shows an example in which the number of combinations of the Ising bits x1 to x3 is 8, while the number of options is five, A, B, C, F, and G.

[0080] In Fig. 10, values ​​are assigned to the options A, B, C, D, and E according to a certain rule. The certain rule here is a rule that no option is assigned to a combination in which at least one of the auxiliary bits y2 and y6 is "1".

[0081] By making such an allocation and placing restrictions on combinations in which at least one of the auxiliary bits y2 and y6 is "1", it is possible to increase the speed of information processing.

[0082] The constraint is applied to the energy function. For example, if the interaction parameters are specified so that the Ising energy is increased in the calculation for solving the optimization problem using the auxiliary bit y2 and the auxiliary bit y6, the constraint can be applied to the energy function. More specifically, k1y2+k2y6 is applied to the energy function. k1 and k2 are coefficients of the constraint term and are values ​​greater than 0.

[0083] A computer calculates combinations that a human would eliminate as equivalent to other combinations. By adding the above constraints, impossible combinations that have no assigned options can be excluded from the calculations used to solve the optimization problem. Eliminating unnecessary combinations increases the speed of information processing.

[0084] The auxiliary bits y2 and y6 provide constraints and can also be used to detect errors in the Ising bits x1 to x3. [Explanation of symbols]

[0085] b bit, x1~x3 Ising bits, y1~y6 auxiliary bits

Claims

1. A computational program executed by an Ising machine specialized for an Ising model or QUBO or a general-purpose information processing device, The calculation program includes an arithmetic program and a comparison program, The calculation program instructs the Ising machine or the general-purpose information processing device to perform a calculation using a calculation model, The computation model is an Ising model or a computation model applicable to QUBO, and has a plurality of Ising bits and a first auxiliary bit; Each of the plurality of Ising bits and the first auxiliary bit is a binary variable, The plurality of Ising bits represent each of options in a combinatorial optimization problem by a combination of the variables, the first auxiliary bit indicates a value obtained by logically operating two or more values ​​among the plurality of values ​​indicating the options, the logical operation is at least one selected from the group consisting of an exclusive OR, a logical OR, and a logical AND; The comparison program compares the value of the first auxiliary bit with a result of performing the same logical operation as when determining the value of the first auxiliary bit on an Ising bit corresponding to a value used in the logical operation of the first auxiliary bit. A calculation program.

2. The computational model further includes a second auxiliary bit, The computer program product according to claim 1 , wherein the second auxiliary bit indicates a value obtained by ORing two or more values ​​among the plurality of values ​​indicating the options.

3. The computer program product according to claim 1 , wherein the plurality of Ising bits represent the options in binary.

4. The computational model further includes a third auxiliary bit, The third auxiliary bit indicates a value obtained by logically operating the value of the first auxiliary bit and a value among a plurality of values ​​indicating the options that was not used in the logical operation to obtain the first auxiliary bit.

5. If the comparison results by the comparison program are not consistent, an extraction program that lists combinations of the variables that the mismatched options can take based on the value of the first auxiliary bit; The calculation program according to any one of claims 1 to 4, further comprising: a correction program for replacing a variable when the comparison result is a mismatch with a combination of variables that results in the smallest calculation result using the calculation program among the combinations of variables that can be selected from the options.

6. An information processing method, comprising causing an Ising machine specialized for an Ising model or QUBO, or a general-purpose information processing device with general-purpose capabilities, to execute a computational program described in any one of claims 1 to 5.

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