JP2022055125A - Calculation method, calculation device, calculation program, and recording medium - Google Patents

Abstract

To increase a probability that a solution satisfying all constraint expressions of a mathematical model is obtained through quantum search.SOLUTION: A calculation method includes a quantum search step (S4), a solution determination step (S6), and correction steps (S8, S10). In the quantum search step, quantum search is executed for the Hamiltonian obtained through the formulation of a mathematical model. In the solution determination step, it is determined whether a solution obtained in the quantum search step satisfies at least one constraint of constraints in the mathematical model. In the correction steps, when, of the constraints for which determination is made in the solution determination step, one or more constraints not satisfied by the solution obtained in the quantum search step are present, the corrected Hamiltonian is generated which is obtained by fixing the value of a partial variable in the Hamiltonian.SELECTED DRAWING: Figure 1

Description

The present disclosure relates to a calculation method for generating a Hamiltonian representing the energy of a system of a mathematical model and calculating by quantum search, a calculation device for executing the calculation method, and a calculation program.

Non-Patent Document 1 discloses a method for formulating and calculating a mathematical model into a QUABO (quadratic optimization problem) model using an annealing machine.

Quantum Bridge Analytics I: A Tutorial on Formulating and Using QUBO Models (Fred Glover, Gary Kochenberger, Yu Du, Quantum Bridge Analytics 1 Qubo for Oct 31)

When formulating a mathematical model, correction of the formula, such as approximating a part of the formula obtained from the mathematical model, in order to make it a formula that can be calculated by a computing device that executes a quantum search algorithm, including an annealing machine. May be done. In this case, the corrected equation may not be able to express the constraints of the mathematical model exactly, and the execution of the quantum search based on the equation may obtain a solution that does not satisfy some of the constraints. ..

In order to solve the above problems, the calculation method according to one aspect of the present disclosure includes a quantum search step for executing a quantum search for the Hamiltonian obtained by formulating a mathematical model, and a solution obtained by the quantum search step. However, the constraint that the solution determination step of determining whether or not at least one of the constraint conditions in the mathematical model satisfies the constraint condition and the solution obtained by the quantum search step are determined in the solution determination step. If at least one of the conditions is not satisfied, a correction step of generating a corrected Hamiltonian in which the values of some variables in the Hamiltonian are fixed is included.

Further, in the computing device according to one aspect of the present disclosure, an execution unit that executes a quantum search for the Hamiltonian obtained by formulating the mathematical model and a solution obtained by the quantum search are at least one in the mathematical model. When the solution determination unit for determining whether or not the constraint condition is satisfied and the solution obtained by the quantum search do not satisfy at least one of the constraint conditions determined by the solution determination unit, one in the Hamiltonian. It is provided with a correction unit that generates a correction Hamiltonian with a fixed variable of the unit.

The arithmetic unit according to each aspect of the present disclosure may be realized by a computer. In this case, the computer may be operated as each part (software element) included in the arithmetic unit. In this case, a calculation program for realizing the calculation device by a computer and a computer-readable recording medium on which the calculation device is recorded are also included in the scope of the present disclosure.

According to one aspect of the present disclosure, the probability that a solution satisfying all the constraint conditions of the mathematical model can be obtained by quantum search is improved.

It is a flowchart for demonstrating the calculation method which concerns on embodiment of this disclosure. It is a block diagram of the arithmetic unit which concerns on embodiment of this disclosure.

[Embodiment]
<Overview of arithmetic unit>
Hereinafter, one embodiment of the present disclosure will be described in detail.

The calculation method according to the present embodiment is a method of calculating a combination of variables in the mathematical model by an annealing machine, which minimizes the energy of the entire system of the mathematical model. In the present embodiment, a Hamiltonian representing the energy of the mathematical model is generated, a QUATBO matrix is generated from the Hamiltonian, and the calculation is performed by solving the QUATBO matrix with an annealing machine.

The calculation method of the mathematical model according to the present embodiment will be described in more detail with reference to FIGS. 1 and 2. FIG. 1 is a flowchart for explaining a calculation method of a mathematical model according to the present embodiment. FIG. 2 is a block diagram of a calculation device 2 for executing the calculation method shown in the flowchart of FIG.

As shown in FIG. 2, the calculation device 2 according to the present embodiment is a device for generating data for executing a calculation by the annealing machine 4 and accumulating and displaying the calculation result. The calculation device 2 includes an operation unit 6, a memory 8, a control unit 10, a communication unit 12, and a display unit 14. Further, the control unit 10 includes a Hamiltonian generation unit 16, a QUABO matrix generation unit 18, a solution determination unit 20, and a correction unit 22. Further, the correction unit 22 includes a fixed variable determination unit 24, a correction Hamiltonian generation unit 26, a correction Hamiltonian evaluation unit 28, and a variable fixation release unit 30.

The operation unit 6 is operated by, for example, the user of the arithmetic unit 2. For example, the operation unit 6 may include a keyboard or the like used for inputting data for calculation by the calculation device 2 from the outside. For example, the operation unit 6 may be used to input data for setting each parameter of the mathematical model or setting when calculating the mathematical model.

The memory 8 stores data input from each unit included in the calculation device 2 at least temporarily. The data stored in the memory 8 is appropriately read from each unit included in the calculation device 2.

The control unit 10 generates data for executing the calculation by the annealing machine 4 based on the parameters of the mathematical model and the calculation settings input to the calculation device 2. The detailed operation of each part of the control unit 10 will be described in more detail later together with the description of the calculation method according to the present embodiment.

The communication unit 12 is a communication device for transmitting at least a part of the data read from the memory 8 to the external device of the computing device 2, receiving the data transmitted from the external device, and recording the data in the memory 8. .. In the present embodiment, the communication unit 12 is capable of mutual communication of data with the annealing machine 4.

The display unit 14 is a device for displaying at least a part of the data read from the memory 8 to the user or the like of the calculation device 2. For example, the display unit 14 may be a monitor that displays the data input to the calculation device 2, the calculation setting of the calculation device 2, the calculation result by the annealing machine 4, and the like.

<Formulation of mathematical model>
In the calculation method of the mathematical model according to the present embodiment, first, the mathematical model is formulated to generate Hamiltonian H expressing the energy of the entire system of the mathematical model (step S2). In step S2, for example, first, the user of the calculation device 2 inputs each parameter of the mathematical model to be calculated to the calculation device 2 by the operation unit 6. Each parameter of the input mathematical model may be temporarily recorded in the memory 8. Each parameter of the input mathematical model is then read out by the Hamiltonian generation unit 16 of the control unit 10.

The Hamiltonian generation unit 16 analyzes the data read from the memory 8, generates a formula representing a mathematical model, and converts the formula into a formula formulated according to the QUABO model. As a result, the Hamiltonian generation unit 16 generates, for example, the objective function _HO and the constraint condition equation _HL in which the constraint conditions in the mathematical model are formulated. Next, the Hamiltonian generation unit 16 synthesizes the generated objective function _HO and the constraint equation _HL to generate the Hamiltonian H. For example, Hamiltonian H is expressed as H _{= HO} + HL.

When the objective function HO is a formulation of the _QUABO model, the objective function _HO is expressed by, for example, the following equation (1).

In equation (1), x _i is a binary variable that takes a value of 0 or 1. Further, _ai and _bij are coefficients of the first-order term and the second-order term, respectively. Also, i, j, and h are natural numbers. Also, h corresponds to the total number of possible combinations of each variable in the mathematical model. Since the spin variable s _i = ± 1 can be expressed as x _i = (s _i +1) / 2, the objective function _HO is equivalent to the energy function of the Ising model.

The constraint condition equation _HL can be expressed as the following equation (2) by using, for example, a coefficient _Cl or the like.

Here, L _l is a constraint condition term in which the constraint condition is formulated, respectively. The constraint term L _l is a term that increases in the case of a combination that does not satisfy the constraint condition in the original mathematical model. This makes it possible to increase the energy of the entire system so that it is not adopted as a solution when the constraints in the original mathematical model are not satisfied. In addition, k in the equation (2) is a natural number and corresponds to the number of constraint conditions in the mathematical model.

<Annealing process>
Next, as a quantum search step, a quantum annealing step is executed for the Hamiltonian H (step S4), and an annealing step is executed. In step S4, first, data regarding the Hamiltonian H is input from the Hamiltonian generation unit 16 to the QUATBO matrix generation unit 18, so that a QUABO matrix for the Hamiltonian H is generated.

The QUAD matrix is an upper triangular matrix that expresses the corresponding Hamiltonian by the matrix of the QUABO model. For the generation of a QUATBO matrix from a Hamiltonian, a commonly used method of converting a Hamiltonian to a QUABO matrix can be adopted. This produces a QUAD matrix that can be calculated by the annealing machine. The generated QUAD matrix is recorded in memory 8 at least temporarily, for example.

Next, the QUAD matrix generated from Hamiltonian H is input to the annealing machine 4 and calculated using the annealing machine 4. For example, the communication unit 12 reads the QUAD matrix data from the memory 8 and transmits it to the annealing machine 4. The annealing machine 4 that has received the data of the QUABO matrix receives the data of the QUABO matrix and executes quantum annealing for the QUABO matrix. The communication unit 12 may receive data related to the QUABO matrix directly from the QUABO matrix generation unit 18 and transmit the data to the annealing machine 4.

From the above, at least the communication unit 12 and the QUAO matrix generation unit 18 in the calculation device 2 function as execution units for executing quantum annealing with respect to the Hamiltonian H.

As a result, a combination of variables that optimizes the energy of Hamiltonian H is obtained as a solution. The result of the calculation by the annealing machine 4 is transmitted to the communication unit 12. The communication unit 12 that has received the result of the calculation by the annealing machine 4 records the result in the memory 8. The result of the calculation by the annealing machine 4 may be read out from the memory 8 by the display unit 14 and displayed on the display unit 14.

<Hamiltonian correction>
The Hamiltonian H generated in step S2 needs to be an expression capable of generating computable data by the annealing machine 4 used. For example, in the present embodiment, the calculation is performed using the annealing machine 4 for calculating the problem of the QUABO model. Therefore, in the present embodiment, when the mathematical model is formulated to generate the Hamiltonian H, it is necessary to generate the Hamiltonian H capable of generating the QUATO matrix described later.

Therefore, when the Hamiltonian H is generated from the mathematical model, some terms of the Hamiltonian H may be corrected by approximation or the like. However, when the Hamiltonian H is corrected, the corrected objective function _HO or constraint expression _HL of the corrected Hamiltonian H may not be an exact representation of the objective function and constraints of the original mathematical model. There is. As described above, when Hamiltonian H cannot accurately represent a mathematical model, an inappropriate solution may be obtained as a result of quantum annealing.

In particular, the QUAO model is equivalent to the Ising model and is a model that considers up to the two-body interaction of each qubit. However, in general, in a mathematical model, it may be necessary to consider the interaction of three or more elements. In this case, it is necessary to consider many-body interactions of three or more bodies in the calculation process of the mathematical model.

In order to formulate such a mathematical model along the QUAO model, it is necessary to approximate the many-body interaction term to the two-body interaction term. Specifically, for the approximation from the multi-body interaction term to the two-body interaction term, a method such as reduction of the Hamiltonian order using an additional auxiliary variable can be considered.

However, when the multi-body interaction term is approximated to the two-body interaction term, in step S4, the optimal combination of variables in the original mathematical model becomes a combination in which the energy increases in the Hamiltonian after approximation, and the solution is as follows. It may not be selected. In particular, in accordance with the above, in step S4, a combination of variables that does not satisfy the constraint conditions in the original mathematical model may be determined to have optimality in the Hamiltonian after approximation and may be selected as a solution.

In addition, in the present embodiment, for the convenience of converting a mathematical model into a QUA model and executing a calculation, when the mathematical model is formulated, one of the objective function and the constraint condition expression is cubic or higher. If the term is included, it is necessary to approximate the term to the terms up to the second order. Even in this case, in step S4, the combination of variables having the optimum in the original mathematical model is not adopted as the solution, and in particular, the combination of the variables that does not satisfy the constraints in the mathematical model is adopted as the solution. Problems arise.

<Solution determination process and correction process>
In the calculation method according to the present embodiment, when a solution that does not satisfy the constraint conditions in the mathematical model is obtained, the Hamiltonian H is corrected to improve the probability that a solution that satisfies the constraint conditions in the mathematical model can be obtained. In order to realize the object, in the calculation method according to the present embodiment, it is necessary to determine whether or not the solution obtained in step S4 satisfies the constraint condition of the mathematical model.

Specifically, in the present embodiment, the solution obtained by quantum annealing in step S4 is analyzed to determine whether or not the solution satisfies at least one of the constraints included in the mathematical model. The determination (step S6) and the solution determination step are executed. The solution determination step is executed by the solution determination unit 20 reading the solution data obtained by quantum annealing in step S4 from the memory 8 and analyzing the solution.

In step S6, it may be determined whether or not the solution obtained in step S4 satisfies the constraint condition for each of all the constraint conditions in the mathematical model. On the other hand, in step S6, it is determined whether or not the solution obtained in step S4 satisfies the constraint condition only for one or more specific constraint conditions among all the constraint conditions in the mathematical model. You may.

If the solution obtained by quantum annealing in step S4 does not satisfy at least one of the constraints determined in step S6, a correction step of correcting Hamiltonian H is executed. Specifically, in the correction step, the Hamiltonian H is corrected by fixing the values of some variables in the Hamiltonian H.

More specifically, in the correction step, first, among the variables included in the Hamiltonian H, which variable value is fixed is determined (step S8).

In step S8, for example, the solution determination unit 20 sends data to the fixed variable determination unit 24 of the correction unit 22 indicating that the solution obtained in step S4 does not satisfy any of the constraints of the mathematical model. Will be sent. At the same time, the solution determination unit 20 transmits data regarding each of the solution obtained in step S4, the constraint condition of the mathematical model, and the Hamiltonian H to the fixed variable determination unit 24 of the correction unit 22. In response to this, the fixed variable determination unit 24 analyzes the data to determine which of the variables included in the Hamiltonian H is fixed.

In step S8, for example, among the variables included in Hamiltonian H, the variables included in the constraint condition term L _l corresponding to the constraint condition satisfied by the solution obtained in step S4 are given priority over the variables whose values are fixed. To decide. Further, in step S8, for example, among the variables included in Hamiltonian H, the variables that are factors that affect the increase in the energy of Hamiltonian H due to the fluctuation of the value are preferentially determined as the variables whose values are fixed. do.

Next, a corrected Hamiltonian H'with fixed values of some of the Hamiltonian H is generated based on the data of the variable having a fixed value determined in step S8 (step S10).

In step S10, the fixed variable determination unit 24 transmits the variable data for fixing the value, the solution data obtained in step S4, and the data regarding the Hamiltonian H to the corrected Hamiltonian generation unit 26. In response to this, the corrected Hamiltonian generation unit 26 analyzes these data and generates data related to the corrected Hamiltonian H'.

The corrected Hamiltonian _H'can be expressed as H' _{= H'O} + H'L using the correction objective function _H'O and the correction constraint equation H'L. Here, the correction objective function _H'O is a term obtained by transforming the objective function _HO with respect to the variable for which the value is fixed, which is determined in step S8, by fixing the value. The correction constraint condition formula _{H'L can be expressed by the formula shown in the following formula (3) using the correction constraint condition term L'l .}

Here, each of the correction constraint condition terms L' _l is a term in which each of the constraint condition terms L _l is modified by fixing the value with respect to the variable for fixing the value determined in step S8. Here, a part of the solution obtained in step S4 is applied to each value of the variable whose value is fixed in the correction objective function _H'O and the correction constraint condition expression _H'L .

In addition, the variable included in some of the correction constraint condition terms L' _l may be only the variable whose value is fixed, which is determined in step S8. In this case, the correction constraint condition term L' _l is a constant term that takes a constant value regardless of the values of other variables whose values are not fixed. The fact that a part of the correction constraint term L' _l becomes a constant term means that the number of constraints to be considered among the constraints in the mathematical model is reduced.

Further, it is conceivable that some of the objective function _HO and the constraint term L _l do not include the variable whose value is fixed, which is determined in step S8. Each of the objective function _HO and the constraint condition term L _l , which is determined in step S8 and does not include a variable for fixing the value, is equal to each of the corresponding correction objective function _H'O and the correction constraint condition term L' _l . Is.

<Evaluation of corrected Hamiltonian and defixation of variables>
Next, the generated corrected Hamiltonian H'is evaluated (step S12), and the corrected Hamiltonian evaluation step is executed. Step S12 is executed by transmitting data related to the corrected Hamiltonian H'from the corrected Hamiltonian generation unit 26 to the corrected Hamiltonian evaluation unit 28 and analyzing the data by the corrected Hamiltonian evaluation unit 28.

In step S12, it is determined whether or not the solution obtained by performing quantum annealing for the corrected Hamiltonian H'may satisfy at least one constraint condition in the mathematical model. The determination can be easily performed by analyzing the parameters of the generated corrected Hamiltonian H'.

It is assumed that it is determined in step S12 that the solution obtained when quantum annealing for the corrected Hamiltonian H'is unlikely to exist that satisfies all of the constraints determined in step S12. In this case, following step S12, at least some of the variables whose values were fixed in the corrected Hamiltonian H'are released from the fixed values (step S14), and the variable fixing release step is performed.

In step S14, the corrected Hamiltonian evaluation unit 28 sends the data of the corrected Hamiltonian H'and the variable whose value is fixed as the result of the determination in step S12 to the variable fixing release unit 30. In response to this, the variable defixation unit 30 analyzes the data and releases a new Hamiltonian whose value is defixed for at least some of the variables whose values were fixed in the corrected Hamiltonian H'. Generate.

In step S14, among the variables whose values were fixed in the corrected Hamiltonian H', only some of the variables may be released from the fixed values. In this case, the Hamiltonian generated by the variable fixing release unit 30 becomes a new corrected Hamiltonian H'' in which the value is fixed only for some of the variables whose values are fixed in the corrected Hamiltonian H'. ..

On the other hand, in step S14, the fixed value may be released for all the variables whose values were fixed in the corrected Hamiltonian H'. In this case, the Hamiltonian generated by the variable fixing release unit 30 is equal to the Hamiltonian H generated by the Hamiltonian generation unit 16 in step S2.

By executing steps S12 and S14, it is possible to reduce the probability that quantum annealing for the corrected Hamiltonian H'that does not satisfy at least one constraint condition will be executed. Therefore, the calculation method according to the present embodiment including step S12 and step S14 executes the algorithm for finding the solution of the mathematical model more efficiently.

<Re-execution of quantum annealing>
If step S14 is not executed, the corrected Hamiltonian evaluation unit 28 transmits data regarding the corrected Hamiltonian H'to the QUABO matrix generation unit 18, and a QUABO matrix corresponding to the corrected Hamiltonian H'is generated. Further, when step S14 is executed, the data regarding the corrected Hamiltonian H'' or Hamiltonian H generated by the variable fixing release unit 30 is transmitted to the QUABO matrix generation unit 18, and the corresponding QUAT matrix is generated.

After that, quantum annealing for the QUAD matrix generated by the QUABO matrix generation unit 18 is executed by the same method as in step S4 described above. Subsequently, step S6 is executed again to determine whether or not the solution obtained by the quantum annealing satisfies at least one of the constraints of the mathematical model.

If the solution obtained by the quantum annealing is determined by step S6 to satisfy the constraint condition in the mathematical model, the solution is adopted as the optimum solution in the mathematical model (step S16), and the calculation of the mathematical model is performed. Complete. The solution adopted in step S16 may be displayed on the display unit 14, for example, by transmitting data related to the solution from the memory 8 to the display unit 14.

On the other hand, if it is determined again in step S6 that the solution obtained by the quantum annealing does not satisfy the constraint condition in the mathematical model, step S8 is executed again.

For example, it is assumed that the solution obtained by quantum annealing for the corrected Hamiltonian H'does not satisfy at least one of the constraints determined in step S6. In this case, in the subsequent step S8, the value of the variable whose value has already been fixed in the corrected Hamiltonian H'may be kept as it is, and a variable whose value is newly fixed may be determined and the value may be fixed. Alternatively, in step S8, for the variable whose value is already fixed in the corrected Hamiltonian H', the fixed value may be released and a new variable whose value is fixed may be set. Here, as the value of the variable whose value is newly fixed, a part of the solution obtained by quantum annealing for the corrected Hamiltonian H'may be adopted.

After that, steps S10 and S12 are executed, and in some cases, step S14 is additionally executed. As a result, a new corrected Hamiltonian is obtained, and by executing step S4 again, quantum annealing for the new corrected Hamiltonian is executed. Steps S4 to S14 are repeatedly executed in step S6 until the solution obtained by quantum annealing is determined to satisfy at least one constraint condition of the mathematical model.

<Effects of calculation method and calculation device>
In the corrected Hamiltonian H', the values of some variables are fixed as compared with the Hamiltonian H. Therefore, the corrected Hamiltonian H'is limited in the combination of possible values of each variable in the solution search by quantum annealing as compared with the Hamiltonian H. In other words, the corrected Hamiltonian H'has a lower probability that the value of each variable will not satisfy the constraint condition in the solution search by quantum annealing as compared with the Hamiltonian H. Therefore, the solution obtained as a result of quantum annealing for the corrected Hamiltonian H'is more likely to satisfy the constraint condition than the solution obtained as a result of quantum annealing for Hamiltonian H.

Further, the value of the variable is a value that satisfies all the constraints of the mathematical model determined in step S6. Therefore, quantum annealing for the corrected Hamiltonian H'is performed in a state where at least a part of the variables is already fixed to a value that satisfies at least a part of the constraints of the mathematical model. Therefore, the solution obtained as a result of quantum annealing for the corrected Hamiltonian H'is more likely to satisfy the constraint condition than the solution obtained as a result of quantum annealing for Hamiltonian H.

In addition, the variable whose value is fixed in the corrected Hamiltonian H'is fixed in value so as to match the solution obtained in step S4. It can be said that the solution obtained in step S4 has the optimum in Hamiltonian H, although some of them do not satisfy the constraints. Therefore, quantum annealing for the corrected Hamiltonian H'is performed with at least some of the variables fixed to at least locally optimal values in the mathematical model. Therefore, the solution obtained as a result of quantum annealing for the corrected Hamiltonian H'has optimality in the mathematical model, at least locally.

As described above, according to the calculation method according to the present embodiment, it is possible to obtain a solution that has at least local optimum in the mathematical model and satisfies the constraint condition in the mathematical model.

Further, as the variable whose value is fixed in the corrected Hamiltonian H', a variable that causes an increase in energy is selected in the process of quantum annealing in step S4. Therefore, in the corrected Hamiltonian H', the increase in energy in the process of solution search by quantum annealing is suppressed as compared with the Hamiltonian H, and a more optimal solution is searched more efficiently. Therefore, the solution obtained as a result of quantum annealing for the corrected Hamiltonian H ″ is more likely to be more optimal than the solution obtained as a result of the quantum annealing for the corrected Hamiltonian H ′.

In step S14, among the variables whose values are fixed in the corrected Hamiltonian H ′, the fixed values may be released from some variables to generate the corrected Hamiltonian H ″. In this case, the solution obtained as a result of quantum annealing for the corrected Hamiltonian H ″ is more likely to satisfy the constraint condition than the solution obtained as a result of quantum annealing for Hamiltonian H.

In addition, the number of variables with fixed values in the corrected Hamiltonian H ″ is smaller than the number of variables with fixed values in the corrected Hamiltonian H ′. Therefore, the corrected Hamiltonian H ″ has an improved degree of freedom of variables as compared with the corrected Hamiltonian H ′, and the range of the solution search becomes wider. Therefore, the solution obtained as a result of quantum annealing for the corrected Hamiltonian H ″ is more likely to have more global optimization than the solution obtained as a result of quantum annealing for the corrected Hamiltonian H ′.

Further, as described above, when the fixed values are released for all the variables whose values are fixed in the corrected Hamiltonian H'in step S14, the quantum annealing for the Hamiltonian H is executed again in the following step S4. Will be. However, quantum annealing is a metaheuristic calculation algorithm, and even if the calculation is based on the same calculation parameters, the solution obtained may differ each time the calculation is performed. Therefore, for example, even if quantum annealing for Hamiltonian H is executed again in step S4, a different solution may be obtained and a solution satisfying the constraint condition may be obtained. Therefore, even in the above-mentioned case, according to the calculation method according to the present embodiment, the probability of obtaining a solution satisfying the constraint condition in the mathematical model is improved.

<Supplementary note>
The mathematical model according to the present embodiment is a model that can search for the optimum combination of variable values by quantum annealing, and it is possible to apply a model that needs to be corrected such as approximation at the time of formulation. can. For example, in the mathematical model according to the present embodiment, a labor scheduling model, which is a model for determining a combination of which work is assigned to each worker on which day and at which time zone, may be applied. .. In this case, for example, the objective function _HO is a combination of the total value of the product of the working hours of each worker and the function whose value increases when the holiday desired by each worker is not realized. It may be adopted. Further, as the constraint condition of the labor scheduling model, the number of workers required for each work, the daily working time limit of each worker, the number of holiday days required to be assigned to each worker, and the like may be set. ..

In this embodiment, as an algorithm for quantum search, an algorithm for executing quantum annealing using an annealing machine has been described. However, the calculation method according to the present embodiment is not limited to this, and can be applied to an algorithm for executing a quantum search for a Hamiltonian obtained by formulating an Ising model. For example, in the calculation method according to the present embodiment, the Hamiltonian obtained by formulating a mathematical model may be applied to a quantum search algorithm using a simulated branch.

<Examples using software and programs>
Each unit included in the control unit 10 according to each of the above-described embodiments may be realized by an integrated circuit included in the arithmetic unit 2, in other words, a logic circuit formed in an IC chip or the like, in other words, by hardware. Alternatively, each unit included in the control unit 10 may be realized by software.

When each of the above parts is software, the processing in each part of the control unit 10 may be executed by executing the instruction of the program which is the software which realizes the function of each part in the terminal which can communicate with the annealing machine 4. The terminal includes, for example, one or more processors and a terminal-readable recording medium that stores the program. In the terminal, the processor reads the program from the recording medium and executes it, thereby achieving the object of the present disclosure. Therefore, the above program functions as a calculation program that executes processing in each unit of the control unit 10.

As the processor, for example, a CPU (Central Processing Unit) can be used. As the recording medium, a "non-temporary tangible medium", for example, a ROM (Read Only Memory) or the like, a tape, a disk, a card, a semiconductor memory, a programmable logic circuit, or the like can be used. Further, a RAM (Random Access Memory) for expanding the above program may be further provided.

The program may be supplied to the terminal via any transmission medium (communication network, broadcast wave, etc.) capable of transmitting the program. It should be noted that one aspect of the present disclosure can also be realized in the form of a data signal embedded in a carrier wave, in which the above program is embodied by electronic transmission.

The present disclosure is not limited to the above-described embodiments, and various modifications can be made within the scope of the claims, and the embodiments obtained by appropriately combining the technical means disclosed in the different embodiments. Is also included in the technical scope of the present disclosure.

2 Arithmetic logic unit 10 Control unit 12 Communication unit 16 Hamiltonian generation unit 18 QUABO matrix generation unit 20 Solution judgment unit 22 Correction unit 24 Fixed variable determination unit 26 Correction Hamiltonian generation unit 28 Correction Hamiltonian evaluation unit 30 Variable fixation release unit

Claims (8)

A quantum search process that executes a quantum search for the Hamiltonian obtained by formulating a mathematical model, and
A solution determination step for determining whether or not the solution obtained by the quantum search step satisfies at least one constraint condition among the constraint conditions in the mathematical model.
If the solution obtained by the quantum search step does not satisfy at least one of the constraints determined in the solution determination step, a correction to generate a corrected Hamiltonian in which the values of some variables in the Hamiltonian are fixed is generated. Calculation method including process. The calculation method according to claim 1, wherein in the correction step, the values of at least a part of the variables included in the constraint condition satisfied by the solution obtained in the quantum search step among the constraint conditions are fixed. The calculation method according to claim 1 or 2, wherein in the correction step, a variable that is a factor that increases the energy of the mathematical model in the quantum search step is determined as a variable whose value is preferentially fixed. From claim 1, further including a corrected Hamiltonian evaluation step, which determines whether or not the solution obtained by the quantum search for the corrected Hamiltonian may satisfy at least one constraint condition in the mathematical model. The calculation method according to any one of 3. When it is determined in the corrected Hamiltonian evaluation step that there is no possibility that a solution satisfying all of the constraint conditions determined in the corrected Hamiltonian evaluation step can be obtained by the quantum search for the corrected Hamiltonian, the value in the corrected Hamiltonian is determined. The calculation method according to claim 4, further comprising a variable fixing release step of releasing the fixed value of at least a part of the variables fixed to. An execution unit that executes a quantum search for the Hamiltonian obtained by formulating a mathematical model,
A solution determination unit for determining whether or not the solution obtained by the quantum search satisfies at least one constraint condition among the constraint conditions in the mathematical model.
When the solution obtained by the quantum search does not satisfy at least one of the constraint conditions determined by the solution determination unit, the correction unit that generates a corrected Hamiltonian with fixed values of some variables in the Hamiltonian. A computing device equipped with. A calculation program for operating a computer as the calculation device according to claim 6, wherein the computer functions as the execution unit, the solution determination unit, and the correction unit. A computer-readable recording medium on which the calculation program according to claim 7 is recorded.

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