JP2022167230A - Closed path generation apparatus, closed path generation method, and program - Google Patents

Abstract

To provide a closed path generation apparatus, a closed path generation method, and a program for reducing the time for generating a closed path.SOLUTION: A closed path generation apparatus 50 includes a solution unit 54 which selects a first closed path and a second closed path out of a plurality of closed paths, and causes a quantum annealing machine to solve a problem based on a first Ising model formed by setting a first spin that represents whether to connect two nodes of an edge included in the first closed path to the second closed path and a second spin that represents whether to connect two nodes of an edge included in the second closed path to the first closed path.SELECTED DRAWING: Figure 3

Description

The present invention relates to a circuit generation device, a circuit generation method, and a program for generating a circuit.

When solving the traveling salesman problem (hereinafter sometimes referred to as TSP), which is one of combinatorial optimization problems, using quantum annealing, the number of cities and the order of arrival are used as variables ( In the method defined as spin), it takes time to find a solution because n2 variables (spins) are required for the number of cities ⁿ (=an integer equal to or greater than 1).

As a related technique, the technique disclosed in Patent Document 1 is proposed. In the technique disclosed in Patent Document 1, first, for each point (node) of a graph given in the Hamiltonian cycle problem, a group of edges (paths between two points) connected to the node is generated. Next, for each edge group, a binary variable is generated that indicates whether an edge included in the edge group was selected as a path. Next, an Ising model is generated in which the binary variable is the spin. Next, based on the solution of the Ising model calculated by the Ising machine, the solution of the Hamiltonian circuit problem is obtained.

WO2020/170410

However, even when the technique of Patent Document 1 is used, it takes time to find a solution depending on the graph given in the traveling salesman problem because the solution is repeatedly found until one cycle is found.

An object of one aspect is to provide a circuit generation device, a circuit generation method, and a program that shorten the time to generate a circuit.

In order to achieve the above object, the circuit generation device in one aspect is
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. The feature is that it has a solution-finding unit that causes a quantum annealing machine to solve based on

Also, in order to achieve the above object, a closed path generation method in one aspect includes:
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. a solution step that causes a quantum annealing machine to solve based on
characterized by having

Furthermore, in order to achieve the above objectives, the program in one aspect is
to the computer,
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. a solution step that causes a quantum annealing machine to solve based on
is characterized by executing

As one aspect, the time to generate a cycle can be shortened.

FIG. 1 is a diagram illustrating an example of a system having a quantum annealing machine. FIG. 2 is a diagram for explaining the traveling salesman problem. FIG. 3 is a diagram for explaining an example of a circuit generation device. FIG. 4 is a diagram for explaining exclusion of unnecessary routes. FIG. 5 is a diagram for explaining a closed circuit. FIG. 6 is a diagram for explaining a plurality of closed paths. FIG. 7 is a diagram for explaining a method of making a plurality of closed circuits into one closed circuit. FIG. 8 is a diagram for explaining auxiliary processing. FIG. 9 is a diagram for explaining quantum annealing for making a plurality of cycles into one. FIG. 10 is a diagram for explaining quantum annealing for making a plurality of cycles into one. FIG. 11 is a diagram for explaining an example of the operation of the circuit generators (A) and (B). FIG. 12 is a diagram for explaining an example of the operation of the circuit generators (A) and (C). FIG. 13 is a diagram showing an example of a computer that implements the circuit generation device.

First, an overview of the quantum annealing machine is provided to facilitate understanding of the embodiments.

Quantum annealing is an approximate solution method for solving combinatorial optimization problems. Specifically, quantum annealing is a technique for solving the problem of finding the minimum value of an objective function by controlling quantum effects.

Quantum annealing machines are specialized hardware for solving combinatorial optimization problems, for example. FIG. 1 is a diagram illustrating an example of a system having a quantum annealing machine.

The system 1 is configured using, for example, a quantum annealing machine 10, an information processing device 20, a terminal device 30, a network 40, and the like.

The quantum annealing machine 10 is hardware having a quantum processing unit 11 (QPU: Quantum processing unit), a control unit 12, a reading unit 13, and the like.

The quantum processing unit 11 is a circuit in which a plurality of quantum bits are interconnected. The circuit (or device) of the quantum processing unit 11 uses, for example, a plurality of unit cells configured by connecting a predetermined number of quantum bits, and a coupler for connecting the quantum bits between different unit cells. A superconducting quantum circuit constructed by

The control unit 12 is a circuit (or device) that controls the quantum processing unit 11 . If the quantum processing unit 11 is a superconducting quantum circuit, the control unit 12 controls the local magnetic field applied to the quantum processing unit 11 based on the control signal transmitted from the information processing device 20 . The local magnetic field is controlled using, for example, microwaves.

The reading unit 13 is a circuit (or device) that reads the state (spin) of the quantum bit of the quantum processing unit 11 . The reading unit 13 reads the state of the quantum bit each time quantum annealing ends, and transmits state information representing the state of the quantum bit to the information processing device 20 .

The information processing device 20 is connected to the terminal device 30 via the network 40 . The information processing device 20 is also connected to the quantum annealing machine 10 .

Specifically, the information processing device 20 transmits a control signal for controlling the local magnetic field to the control unit 12 . The information processing device 20 receives state information representing the state of the quantum bit from the reading unit 13 .

Note that FIG. 1 shows a configuration in which the user operates the information processing device 20 using the terminal device 30 via the network 40, but the user may directly operate the information processing device 20. .

The information processing device 20 is, for example, a CPU (Central Processing Unit), a programmable device such as an FPGA (Field-Programmable Gate Array), a GPU (Graphics Processing Unit), or one or more of them. or a server computer.

The terminal device 30 is connected to the information processing device 20 via the network 40 . The terminal device 30 is, for example, a programmable device such as a CPU or FPGA, or a GPU, or a circuit equipped with one or more of them, or an information processing device such as a personal computer or a mobile terminal.

The network 40 is constructed using communication lines such as the Internet, a LAN (Local Area Network), a dedicated line, a telephone line, an in-house network, a mobile communication network, Bluetooth (registered trademark), and WiFi (Wireless Fidelity). general network.

Next, a method of solving a combinatorial optimization problem by a quantum annealing machine will be explained. To solve a combinatorial optimization problem with a quantum annealing machine, first, the target combinatorial optimization problem is represented by an Ising model, QUBO (Quadratic Unconstrained Binary Optimization), or the like.

The Ising model can be represented by the Hamiltonian H(σ) shown in Equation 1, for example. The Hamiltonian H(σ) represents the energy of the entire system.

J _ij represents the coupling strength between adjacent qubits. The coupling strength is controlled, for example, by externally applying magnetic flux to the couplers coupling adjacent qubits.

h _i represents the local magnetic field externally applied to the qubit. Application of the local magnetic field is achieved, for example, by injecting microwaves from the outside.

Next, we put the combinatorial optimization problem into a quantum annealing machine. Specifically, the Ising model or QUBO is minor-embedded into the quantum bit topology configured in the quantum processing unit 11 . Minor embedding is the process of mapping Ising spins (variables) to qubits.

The quantum annealing machine then begins quantum annealing. Specifically, the control unit 12 of the quantum annealing machine applies a local magnetic field to the quantum processing unit 11 and then weakens the local magnetic field over time. As a result, the Hamiltonian finally converges to the minimum state.

Next, the reading unit 13 of the quantum annealing machine reads the states of the quantum bits of the quantum processing unit 11 .

However, since the Hamiltonian may not converge to the minimum state, it is preferable to obtain the solution by repeating the above-described annealing multiple times. The reason why the Hamiltonian does not converge to the minimum state is that the circuit of the quantum processing unit 11 is susceptible to noise and is not stable.

Next, a method of solving the TSP (Traveling Salesman Problem) with a quantum annealing machine will be described. TSP is the problem of finding the route that minimizes the distance traveled if the salesman visits every city only once and returns to the starting point (the starting city).

A case where the spin (variable: Ising spin) is defined as shown in (1) and (2) will be described with reference to FIG. FIG. 2 is a diagram for explaining the traveling salesman problem. In the example of FIG. 2, when traveling through five cities (city 1 to city 5: five nodes), a travel cost is given to the route (edge) between the two cities, and a travel that tours all five cities Find the path that minimizes the distance.

(1) Define a spin (variable) for each city in the question of what order to visit a certain city. In that case, when a city is visited in a certain order, it is 1, and otherwise it is 0. Therefore, if the number of cities is ⁿ , the number of spins is n2. Therefore, in the example of FIG. 2, since the number of cities is 5, the number of spins is 25.

Thus, in example (1), the number of spins required is the square of the number of cities, so the number of spins increases exponentially as the number of cities visited increases. Therefore, it takes time to find the approximate solution. Therefore, a method of defining spin as shown in (2) has been proposed.

(2) Define a spin (variable) as each route between two cities as a combinatorial problem of what kind of route should be selected in order to visit all cities only once. In that case, when the number of cities is n, the number of spins is _n C ₂ . Therefore, in the example of FIG. 2, since the number of cities is 5, the number of spins is 10.

Thus, in the example (2), the path is defined as a spin and the number of spins is reduced, so the solution-seeking time of (2) can be shortened from the solution-seeking time of (1).

(embodiment)
Next, an embodiment in which the solution-seeking time is further shortened from the solution-seeking time of (2) will be described. Specifically, in order to shorten the solution-finding time, the quantum annealing machine 10 is caused to perform quantum annealing after excluding unnecessary paths in advance.

Embodiments will be described with reference to the drawings. In the drawings described below, elements having the same or corresponding functions are denoted by the same reference numerals, and repeated description thereof may be omitted.

[Device configuration]
A cycle generating device for shortening the solution-finding time will be described. The circuit generation device 50 is built in the information processing device 20 or the terminal device 30 . Alternatively, the functions of the circuit generation device 50 may be distributed between the information processing device 20 and the terminal device 30 .

The cycle generation device 50 includes an acquisition unit 51, an extraction unit 52, an Ising model generation unit 53, a solution determination unit 54, and a route generation unit 55, as shown in FIG. FIG. 3 is a diagram for explaining an example of a circuit generation device.

The acquisition unit 51 acquires graph information representing a graph provided by the TSP. Graph information (graph) is associated with node information (node) representing a city (point), edge information (edge) representing a route between two nodes, and cost information (cost) assigned to each route. information.

Cost information is information representing the cost of traveling between two nodes. The movement cost is, for example, the distance. However, movement costs are not limited to distance.

The extraction unit 52 sequentially selects the nodes included in the graph given in the TSP, and for each selected node, refers to the cost associated with the edge represented by the selected node and other nodes, and presets Extract the edge corresponding to the cost less than or equal to the given rank.

Specifically, first, the extraction unit 52 acquires the graph from the acquisition unit 51 . Next, the extraction unit 52 selects nodes included in the obtained graph. Next, the extraction unit 52 extracts edges represented by the selected node and nodes other than the selected node.

Next, the extracting unit 52 extracts edges whose costs associated with the edges are lower than or equal to a preset rank among the extracted edges. That is, the extraction unit 52 extracts a predetermined number of edges with small cost values.

The extraction unit 52 executes the above-described processing for all nodes included in the graph, and extracts a predetermined number of edges for each node.

The ranking is determined by experiments and simulations. For example, it is conceivable to obtain the lowest 25[%] cost value.

However, the rank is not limited to 25[%]. Also, the order may be changed as needed. A change in ranking will be described later.

Specifically, with reference to FIG. 4, extraction processing (processing for excluding unnecessary routes) will be described. FIG. 4 is a diagram for explaining exclusion of unnecessary routes.

The example of FIG. 4 shows that a cities (nodes) are extracted for each of cities 1 to n. That is, a routes (edges) are extracted for each of cities 1 to n. For example, in the case of city 1, a paths (edges) represented by cities 1 and 2, cities 1 and 4, . there is

The Ising model generation unit 53 generates an Ising model (second Ising model) or QUBO using the extracted edge as a spin (variable). Specifically, the Ising model generation unit 53 generates an Ising model as shown in Equation (2). Note that the Ising model may be generated manually.

The solving unit 54 causes the quantum annealing machine 10 to solve based on the generated Ising model.

Specifically, first, the solution obtaining unit 54 acquires the Ising model shown in Equation 2 from the Ising model generating unit 53 . Next, the solution finding unit 54 generates control information for controlling the quantum processing unit 11 of the quantum annealing machine 10 based on the acquired Ising model. After that, the solution seeking unit 54 transmits a control signal including control information to the control unit 12 .

When the quantum processing unit 11 is a superconducting quantum circuit, the control unit 12 controls the local magnetic field applied to the quantum processing unit 11 based on the received control signal.

Specifically, the solution-finding unit 54 first issues an instruction for minor embedding to the quantum bit topology configured in the quantum processing unit 11 of the quantum annealing machine 10 based on the Ising model shown in Equation 2. , to the controller 12 of the quantum annealing machine 10 .

In order to instruct the quantum annealing machine 10, the solving unit 54 expands the Hamiltonian equation of Equation 2, and among the terms obtained after expansion, the coefficients of the first-order term or the second-order term composed of the same spin are set to the bias related to the spin. , the coefficient of the quadratic term consisting of separate spins is the interaction between the spins. At this time, if the Hamiltonian is QUBO, conversion to the Ising model is performed, and parameters are set for the quantum annealing machine. It has been proved that QUBO can be converted to the Ising model.

Next, the solution-seeking unit 54 instructs the control unit 12 to apply a local magnetic field to the quantum processing unit 11, and then instructs the control unit 12 to weaken the local magnetic field over time. As a result, the Hamiltonian H of Equation 2 finally converges to the minimum state.

The path generation unit 55 generates a cycle using state information representing the state of the quantum bit. Specifically, first, the path generation unit 55 acquires state information from the reading unit 13 of the quantum annealing machine. Next, the route generator 55 generates closed path information representing closed paths based on the state information.

For example, the path generator 55 generates a closed path as shown in FIG. FIG. 5 is a diagram for explaining a closed circuit. The example in FIG. 5 represents a cycle that circulates 17 cities (nodes) in the shortest distance.

The circuit information is information representing the connection state between cities included in the circuit. In the example of FIG. 5, the circuit information is information indicating that the route between cities 1 and 2, the route between cities 2 and 3, . . . , the routes between cities 17 and 1 are connected.

As described above, in the embodiment, an edge with a low cost is extracted in advance, the extracted edge is defined as a spin, and quantum annealing is performed using the quantum annealing machine 10. Therefore, the solution-finding time can be shortened. .

In other words, edges estimated to be unnecessary are excluded to reduce the number of spins, thereby shortening the solution-finding time.

However, in the above-described embodiment, the following events (A), (B), and (C) occur.

(A) The quantum annealing machine 10 may not be able to find a solution when the spin is the edge extracted according to the order set in advance.

Therefore, the extraction unit 52 changes the preset order when the solution cannot be obtained. Specifically, first, the extracting unit 52 acquires error information indicating that the solution could not be obtained from the solution obtaining unit 54 . Next, the extraction unit 52 changes the order so that the number of edges to be extracted increases. For example, if the number of nodes is n, at least 1/n*100[%] is increased.

Next, after changing the ranking, the extraction unit 52 extracts edges again for each node. Next, the Ising model generation unit 53 generates a new Ising model using the newly extracted edge as a spin. After that, the solving unit 54 causes the quantum annealing machine 10 to solve based on the generated new Ising model.

(B) Since the Hamiltonian H shown in Equation 2 does not include a constraint expression for obtaining a combination of edges that makes one cycle, multiple cycles may be solved. For example, multiple cycles may be generated as shown in FIG. FIG. 6 is a diagram for explaining a plurality of closed paths.

Therefore, when a plurality of closed paths are obtained, the path generation unit 55 uses the plurality of closed paths to generate one closed path that minimizes the total cost. Specifically, the path generation unit 55 sequentially connects minor cycles other than the major cycle to the cycle (major cycle) that includes the most nodes among the plurality of cycles. For example, the path generation unit 55 converts the plurality of closed paths shown in FIG. 6 into one closed path shown in FIG.

First, the path generation unit 55 selects a minor cycle, and obtains the distance between each node of the selected minor cycle and each node of the major cycle. Next, the route generator 55 connects the nodes based on the obtained distance.

FIG. 7 is a diagram for explaining a method of making a plurality of closed circuits into one closed circuit. In the example of FIG. 7A, first, the route generator 55 selects a minor cycle having cities 10, 11, and 12. In the example of FIG. Next, the route generation unit 55 makes the selected minor cycle and the major cycle having cities 5 to 9 and cities 13 to 17 into one cycle.

For example, the route generation unit 55 obtains the distances from the cities 5 to 9 and from the cities 13 to 17 in the major cycle for each of the cities 10, 11, and 12 in the minor cycles. As a result, since the distance between cities 10 and 9 and the distance between cities 12 and 13 are shorter than the other distances obtained, the route generation unit 55 determines that the distances between cities 10 and 9, as shown in FIG. 7B. Connect the city 12 and the city 13 to generate a new great cycle.

Next, the route generator 55 selects the minor cycles having cities 1, 2, 3, and 4, and combines the selected minor cycles and the major cycles having cities 5 to 17 into one cycle.

For example, the route generation unit 55 obtains the distances from the cities 5 to 17 of the major cycle for each of the cities 1, 2, 3, and 4 of the minor cycles. As a result, since the distance between city 1 and city 17 and the distance between city 4 and city 5 are shorter than the other distances obtained, the route generation unit 55 generates the distance between city 1 and city 17, and the distance between city 1 and city 17, as shown in FIG. 7C. Connect city 4 and city 5 to generate a new great cycle.

However, although the distance between cities 3 and 5 is shorter than the distance between cities 1 and 17, cities 3 and 5 are not selected because city 5 has already been selected.

Note that the path generation unit 55 obtains a cycle that minimizes the cost due to the constraints of the Hamiltonian H already shown in Equation 2, and it is not necessary to change the order within each cycle. Therefore, by reducing the problem of finding a combination that minimizes the additional cost when connecting a minor cycle to a major cycle, the amount of calculation required for the above-described process of combining a plurality of cycles into one cycle is small and short. can be obtained in time.

However, when a great cycle is generated by the method described above, it may not be the shortest path. Therefore, in order to further improve accuracy, the route generation unit 55 executes auxiliary processing using the 2-opt method. The auxiliary process sequentially selects two paths, reconnects the connections of the two selected paths (edges), and if the great cycle becomes shorter, adopts the reconnected cycle.

Further, the auxiliary processing is ended when the great cycle is not shortened even by reconnecting.

FIG. 8 is a diagram for explaining auxiliary processing. For example, as shown in FIG. 8A, when the route (arrow) between cities 16 and 14 and the route (arrow) between cities 13 and 15 are selected, as shown in FIG. The route is switched to the route of city 16 and city 15. Also, the route between cities 13 and 15 is replaced with the route between cities 13 and 14 .

If the great cycle becomes shorter as a result of this replacement, the replaced great cycle is adopted. In this way, the replacement process described above is repeated, and the auxiliary process is stopped when the great cycle is not shortened (when there is no improvement). As a result, a large cycle is obtained as shown in FIG. 8C.

By executing the auxiliary process in this way, even when the plurality of cycles described above are converted into one cycle (great cycle), it is possible to obtain a route that provides a better approximate solution to the great cycle.

(C) Method (B) described above (processing using exhaustive search) is effective when the number of nodes is small. However, when the number of nodes increases, the time required to generate a cycle increases when exhaustive search is performed as in method (B).

Therefore, in the problem of combining multiple cycles into one, if the number of nodes to be handled is large, the optimal connection point (node) is solved by quantum annealing from among the combinations that connect the cycles, and based on the result of solving Make multiple cycles into one cycle. After that, similar to the method (B), auxiliary processing (2-opt method) is used to improve the cycle to a shorter path.

In the method (C), first, the Ising model generation unit 53 generates a large cycle (first cycle) including the largest number of nodes among a plurality of cycles, and small cycles other than the large cycle connected to the large cycle (second two cycles) and .

Next, the Ising model generation unit 53 generates a spin (variable: first spin) representing whether or not to connect two nodes of the edge included in the major cycle to the minor cycle, and the edge included in the minor cycle. An Ising model (first Ising model) or QUBO, which is set with a spin (variable: second spin) indicating whether or not to connect two nodes having a large cycle, is generated.

Specifically, the Ising model generation unit 53 generates an Ising model as shown in Equation (3). Note that the Ising model may be generated manually.

The solving unit 54 causes the quantum annealing machine 10 to solve based on the generated Ising model.

Specifically, first, the solution obtaining unit 54 acquires the Ising model shown in Equation 3 from the Ising model generating unit 53 . Next, the solution finding unit 54 generates control information for controlling the quantum processing unit 11 of the quantum annealing machine 10 based on the acquired Ising model. After that, the solution seeking unit 54 transmits a control signal including control information to the control unit 12 .

When the quantum processing unit 11 is a superconducting quantum circuit, the control unit 12 controls the local magnetic field applied to the quantum processing unit 11 based on the received control signal.

Specifically, the solution-finding unit 54 first issues an instruction for minor embedding to the quantum bit topology configured in the quantum processing unit 11 of the quantum annealing machine 10 based on the Ising model shown in Equation 3. , to the controller 12 of the quantum annealing machine 10 .

In order to instruct the quantum annealing machine 10, the solving unit 54 expands the Hamiltonian equation of Equation 3, and among the terms obtained after expansion, the coefficients of the first-order term or the second-order term consisting of the same spin are set to the bias related to the spin. , the coefficient of the quadratic term consisting of separate spins is the interaction between the spins. At this time, if the Hamiltonian is QUBO, conversion to the Ising model is performed, and parameters are set for the quantum annealing machine.

Next, the solution-seeking unit 54 instructs the control unit 12 to apply a local magnetic field to the quantum processing unit 11, and then instructs the control unit 12 to weaken the local magnetic field over time. As a result, the Hamiltonian H of Equation 2 finally converges to the minimum state.

Next, the path generation unit 55 generates a closed path using the state information representing the state of the quantum bit. Specifically, first, the path generation unit 55 acquires state information from the reading unit 13 of the quantum annealing machine. Next, the route generator 55 generates closed path information representing closed paths based on the state information.

Generation of a closed path will be described with reference to FIGS. 9 and 10. FIG. 9 and 10 are diagrams for explaining quantum annealing for making a plurality of cycles into one.

First, it is assumed that the three cycles shown in FIG. 9 are generated. In the example of FIG. 9, it is assumed that a major cycle including the largest number of nodes and two minor cycles other than the major cycle are generated from among the three cycles.

A great cycle has 10 nodes (node 1 to node 10) and 10 edges. Small cycle 1 (i=1) has 3 nodes (node 1 to node 3) and 3 edges. Small cycle 2 (i=2) has 4 nodes (node 1 to node 4) and 4 edges. Also, the nodes and edges of the major cycle and minor cycle are expressed as shown in the table 91 of FIG.

Next, the solving unit 54 causes the quantum annealing machine 10 to solve based on the Ising model shown in Equation 3 in order to make the major cycle and minor cycles 1 and 2 shown in FIG. 9 into one cycle. Then, the result as shown in FIG. 10 is obtained.

That is, as shown in the table 101 of FIG. 10, the results of connecting the edge 6-7 of the major cycle and the minor cycle 1 and connecting the edge 1-2 of the major cycle and the minor cycle 2 are obtained. Also, as shown in the table 102 of FIG. 10, the result of connecting the edge 1-2 of the minor cycle 1 and the major cycle is obtained. Also, as shown in the table 103 of FIG. 10, the result of connecting the edge 4-1 of the minor cycle 2 and the major cycle is obtained.

Next, the path generator 55 connects the major cycle and the two minor cycles 1 and 2 based on the above results. As a result, a closed circuit is generated as shown in FIG. 7C.

However, when a cycle is generated by the quantum annealing described above, the generated cycle may not be the shortest path. Therefore, in order to further improve the accuracy, the route generation unit 55 executes auxiliary processing using the 2-opt method to make the closed route a more approximate solution route.

In this way, quantum annealing requires overhead (additional processing), so exhaustive search may be able to search for the optimal connection node in a short time, but the number of nodes is large. In this case, the large cycle can be generated in a shorter time than the method (B).

[Device operation]
Next, the operation of the circuit generation device according to the embodiment will be described with reference to FIGS. 11 and 12. FIG. 11 and 12 are diagrams for explaining an example of the operation of the circuit generator. In the following description, the drawings will be referred to as appropriate. Also, in the embodiment, the cycle generation method is implemented by operating the cycle generation device. Therefore, the description of the cycle generation method in the embodiment is replaced with the description of the operation of the cycle generation device below.

First, with reference to FIG. 11, the operation of the cycle generator employing the method described in (B) will be described. The acquiring unit 51 first acquires graph information representing a graph provided by the TSP (step A1).

Next, the extraction unit 52 sequentially selects nodes included in the graph given in the TSP, and refers to the cost associated with the edge represented by the selected node and other nodes for each selected node. , edges corresponding to costs below a preset rank are extracted (step A2).

Next, the Ising model generator 53 generates an Ising model or QUBO with the extracted edge as a spin (variable) (step A3). Specifically, the Ising model generation unit 53 generates an Ising model (second Ising model) as shown in Equation 2. Note that the Ising model may be generated manually.

Next, the solving unit 54 causes the quantum annealing machine 10 to solve based on the generated Ising model (step A4). If the quantum annealing machine 10 can find the solution (step A5: Yes), the path generation unit 55 generates a closed path using the state information representing the state of the quantum bit (step A6).

Moreover, when the quantum annealing machine 10 cannot solve (step A5: No), the extraction unit 52 determines whether the rank is the highest (step A7). If the order is the highest (step A7: Yes), the extraction unit 52 terminates the processing assuming that the quantum annealing machine 10 cannot solve. The maximum rank is, for example, a state in which an increase of 1/n*100[%] is not possible when there are n nodes.

If the ranking is not the highest (step A7: No), the extraction unit 52 changes the preset ranking (step A8). Specifically, in step A8, the extracting unit 52 acquires error information from the solution obtaining unit 54 indicating that the solution could not be obtained. Next, at step A8, the extraction unit 52 changes the order so that the number of edges to be extracted increases. For example, if the number of nodes is n, at least 1/n*100[%] is increased.

Next, in step A8, after the extraction unit 52 changes the order, the process proceeds to step A2 to extract edges again. Then, in step A3, the Ising model generating unit 53 generates a new Ising model using the newly extracted edge as a spin. After that, in step A4, the solution finding unit 54 causes the quantum annealing machine 10 to find a solution based on the generated new Ising model.

When a plurality of cycles are generated (step A9: Yes), the path generation unit 55 sequentially connects minor cycles other than the major cycle to the cycle (major cycle) containing the most nodes among the plurality of cycles (step A10). If there is one closed path (step A9: No), the process is terminated. It should be noted that auxiliary processing may be performed even when there is only one closed path.

Specifically, in step A10, the path generation unit 55 selects a minor cycle, and obtains the distance between each node of the selected minor cycle and each node of the major cycle. Next, in step A10, the route generator 55 connects the nodes based on the obtained distance.

The route generator 55 executes auxiliary processing (step A11). Auxiliary processing is, for example, processing such as the 2-opt method. Two paths are selected in sequence, the connections of the two selected paths (edges) are reconnected, and if the great cycle becomes shorter, the reconnected cycle is adopted.

Further, the auxiliary processing is ended when the great cycle is not shortened even by reconnecting.

Next, using FIG. 12, the operation of the circuit generation device employing the method described in (C) will be described. Since the processing of steps A1 to A11 has already been explained, the explanation of the processing of steps A1 to A11 will be omitted.

In step B1, the Ising model generation unit 53 generates a large cycle (first cycle) including the largest number of nodes among a plurality of cycles, and a small cycle other than the large cycle connected to the large cycle (second cycle). to select.

Next, in step B1, the Ising model generation unit 53 generates a spin (variable: first spin) representing whether or not to connect two nodes of an edge included in the major cycle to the minor cycle, and An Ising model (first Ising model) or QUBO is generated in which a spin (variable: second spin) representing whether or not to connect two nodes of included edges to a great cycle is set.

Specifically, the Ising model generation unit 53 generates an Ising model as shown in Equation (3). Note that the Ising model may be generated manually.

At step B2, the solution finding unit 54 causes the quantum annealing machine 10 to find a solution based on the generated Ising model.

Specifically, in step B<b>2 , first, the solution obtaining unit 54 acquires the Ising model shown in Equation 3 from the Ising model generating unit 53 . Next, in step B2, the solution-finding unit 54 generates control information for controlling the quantum processing unit 11 of the quantum annealing machine 10 based on the acquired Ising model. After that, the solution seeking unit 54 transmits a control signal including control information to the control unit 12 .

Next, in step B2, the solution-seeking section 54 instructs the control section 12 to apply a local magnetic field to the quantum processing section 11, and then to weaken the local magnetic field over time. As a result, the Hamiltonian H of Equation 2 finally converges to the minimum state.

At step B3, the path generator 55 generates a closed path using state information representing the state of the quantum bit. Specifically, in step B3, first, the path generation unit 55 acquires state information from the reading unit 13 of the quantum annealing machine. Next, in step B3, the route generator 55 generates closed path information representing closed paths based on the state information.

However, when a great cycle is generated by quantum annealing, it may not be the shortest path. Therefore, in order to further improve the accuracy, in step B3, the route generation unit 55 executes auxiliary processing using the 2-opt method.

[Effect of this embodiment]
As described above, according to the embodiment, in the traveling salesman problem, the quantum annealing machine 10 is caused to execute quantum annealing after excluding unnecessary paths in advance, so that the solution-finding time for generating a cycle can be shortened.

Also, even when a plurality of cycles are generated, the plurality of cycles are combined into one cycle, and auxiliary processing is further executed, so that a cycle with a more approximate solution can be generated.

Furthermore, when the number of nodes is large, it is possible to generate a large cycle in a shorter time than the method (B) by solving the optimum connection points (nodes) using quantum annealing.

In the embodiment, the method (C) is applied when there are a plurality of cycles generated based on the result of quantum annealing. However, the method (C) may be applied to a plurality of cycles generated based on methods other than quantum annealing.

[program]
The program in the embodiment may be any program that causes a computer to execute steps A1 to A11 and B1 to B3 shown in FIGS. 11 and 12 . By installing this program in a computer and executing it, the circuit generation device and the circuit generation method in the embodiments can be realized. In this case, the processor of the computer functions as an acquisition unit 51, an extraction unit 52, an Ising model generation unit 53, a solution determination unit 54, and a route generation unit 55, and performs processing.

Also, the programs in the embodiments may be executed by a computer system constructed by a plurality of computers. In this case, for example, each computer may function as one of the acquiring unit 51, the extracting unit 52, the Ising model generating unit 53, the solution obtaining unit 54, and the route generating unit 55, respectively.

[Physical configuration]
Here, a computer that implements the circuit generation device by executing the program in the embodiment will be described with reference to FIG. 13 . FIG. 13 is a block diagram showing an example of a computer (for example, the information processing device 20, the terminal device 30, etc.) that implements the circuit generation device in the embodiment.

As shown in FIG. 13, a computer 110 includes a CPU (Central Processing Unit) 111, a main memory 112, a storage device 113, an input interface 114, a display controller 115, a data reader/writer 116, and a communication interface 117. and These units are connected to each other via a bus 121 so as to be able to communicate with each other. Note that the computer 110 may include a GPU or FPGA in addition to or instead of the CPU 111 .

The CPU 111 expands the programs (codes) in the present embodiment stored in the storage device 113 into the main memory 112 and executes them in a predetermined order to perform various calculations. The main memory 112 is typically a volatile storage device such as a DRAM (Dynamic Random Access Memory). Also, the program in this embodiment is provided in a state stored in a computer-readable recording medium 120 . Note that the program in this embodiment may be distributed on the Internet connected via the communication interface 117 . Note that the recording medium 120 is a non-volatile recording medium.

Further, as a specific example of the storage device 113, in addition to a hard disk drive, a semiconductor storage device such as a flash memory can be mentioned. Input interface 114 mediates data transmission between CPU 111 and input devices 118 such as a keyboard and mouse. The display controller 115 is connected to the display device 119 and controls display on the display device 119 .

Data reader/writer 116 mediates data transmission between CPU 111 and recording medium 120 , reads programs from recording medium 120 , and writes processing results in computer 110 to recording medium 120 . Communication interface 117 mediates data transmission between CPU 111 and other computers.

Specific examples of the recording medium 120 include general-purpose semiconductor storage devices such as CF (Compact Flash (registered trademark)) and SD (Secure Digital); magnetic recording media such as flexible disks; An optical recording medium such as a ROM (Compact Disk Read Only Memory) can be mentioned.

It should be noted that the circuit generation device in the embodiment can also be realized by using hardware corresponding to each part instead of a computer in which a program is installed. Furthermore, the circuit generator may be partly implemented by a program and the rest by hardware.

[Appendix]
The following additional remarks are disclosed regarding the above embodiments. Some or all of the embodiments described above can be expressed by the following (Appendix 1) to (Appendix 9), but are not limited to the following description.

(Appendix 1)
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. A circuit generation device having a solution-producing unit for causing a quantum annealing machine to solve the problem based on the basis.

(Appendix 2)
The circuit generation device according to Appendix 1,
In the traveling salesman problem, nodes included in a given graph are sequentially selected, and for each selected node, the cost associated with the edge represented by the selected node and other nodes is referred to, and the preset having an extraction unit that extracts edges corresponding to costs below the rank;
The solving unit causes the quantum annealing machine to solve based on a second Ising model in which the extracted edge is set to the spin,
Cycle generator.

(Appendix 3)
The circuit generation device according to appendix 2,
If the solution cannot be obtained, the extraction unit changes the order and extracts a new edge based on the changed order.
The solution-finding unit causes the quantum annealing machine to solve based on the second Ising model in which the newly extracted edge is the spin.

(Appendix 4)
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. a solution step that causes a quantum annealing machine to solve based on
A cycle generation method with

(Appendix 5)
The cycle generating method according to appendix 4,
In the traveling salesman problem, nodes included in a given graph are sequentially selected, and for each selected node, the cost associated with the edge represented by the selected node and other nodes is referred to, and the preset an extraction step of extracting edges corresponding to costs below the rank;
In the solution-finding step, the quantum annealing machine solves based on a second Ising model in which the extracted edge is set to the spin,
Cycle generation method.

(Appendix 6)
The cycle generation method according to appendix 5,
In the extracting step, if the solution cannot be obtained, changing the order and extracting a new edge based on the changed order;
In the solution finding step, the quantum annealing machine is caused to find a solution based on an Ising model in which the newly extracted edge is a spin.

(Appendix 7)
to the computer,
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. a solution step that causes a quantum annealing machine to solve based on
A program containing instructions that causes a

(Appendix 8)
The program according to Supplementary Note 7,
The program causes the computer to:
In the traveling salesman problem, nodes included in a given graph are sequentially selected, and for each selected node, the cost associated with the edge represented by the selected node and other nodes is referred to, and the preset including instructions to perform an extraction step of extracting edges corresponding to costs below rank;
In the solution-finding step, the quantum annealing machine solves based on a second Ising model in which the extracted edge is set to the spin,
A program containing instructions.

(Appendix 9)
The program according to Appendix 8,
In the extracting step, if the solution cannot be obtained, changing the order and extracting a new edge based on the changed order;
A program comprising instructions for causing the quantum annealing machine to solve based on the Ising model in which the newly extracted edges are spins in the solution-finding step.

Although the present invention has been described with reference to the embodiments, the present invention is not limited to the above embodiments. Various changes that can be understood by those skilled in the art can be made to the configuration and details of the present invention within the scope of the present invention.

As described above, according to the present invention, it is possible to shorten the time required to generate a closed path. INDUSTRIAL APPLICABILITY The present invention is useful in the field of generating a cycle by quantum annealing the traveling salesman problem.

1 System 10 Quantum Annealing Machine 11 Quantum Processing Unit 12 Control Unit 13 Reading Unit 20 Information Processing Device 30 Terminal Device 40 Network 50 Circuit Generation Device 51 Acquisition Unit 52 Extraction Unit 53 Ising Model Generation Unit 54 Solving Unit 55 Path Generation Unit 110 Computer 111 CPU
112 Main memory 113 Storage device 114 Input interface 115 Display controller 116 Data reader/writer 117 Communication interface 118 Input device 119 Display device 120 Recording medium 121 Bus

Claims (9)

A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. A cycle generating device having a solution-producing means for causing a quantum annealing machine to solve a solution based on the basis. The circuit generation device according to claim 1,
In the traveling salesman problem, nodes included in a given graph are sequentially selected, and for each selected node, the cost associated with the edge represented by the selected node and other nodes is referred to, and the preset having extraction means for extracting edges corresponding to costs below rank;
The solution-finding means causes the quantum annealing machine to solve based on a second Ising model in which the extracted edges are set to spins.
Cycle generator. The circuit generation device according to claim 2,
When the solution cannot be obtained, the extraction means changes the order and extracts a new edge based on the changed order.
The solution finding means causes the quantum annealing machine to find a solution based on the second Ising model in which the newly extracted edge is the spin. A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. Let the quantum annealing machine solve based on
Cycle generation method. A cycle generation method according to claim 4,
In the traveling salesman problem, nodes included in a given graph are sequentially selected, and for each selected node, the cost associated with the edge represented by the selected node and other nodes is referred to, and the preset Extract edges corresponding to costs below rank,
Let the quantum annealing machine solve based on a second Ising model in which the extracted edge is set to spin,
Cycle generation method. A cycle generation method according to claim 5,
In the extraction, if the solution cannot be obtained, the order is changed, and a new edge is extracted based on the changed order;
The method of generating a cycle in which the quantum annealing machine is caused to solve based on an Ising model in which the newly extracted edges are spins in the solving. to the computer,
A first cycle and a second cycle connected to the first cycle are selected from among a plurality of cycles, and two nodes of edges included in the first cycle are connected to the second cycle. and a second spin representing whether to connect the two nodes of the edge included in the second cycle to the first cycle. Let the quantum annealing machine solve based on
A program containing instructions. The program according to claim 7,
The program causes the computer to:
In the traveling salesman problem, nodes included in a given graph are sequentially selected, and for each selected node, the cost associated with the edge represented by the selected node and other nodes is referred to, and the preset Extract the edge corresponding to the cost below the rank,
Let the quantum annealing machine solve based on a second Ising model in which the extracted edge is set to spin,
A program containing instructions. The program according to claim 8,
In the extraction, if the solution cannot be obtained, the order is changed, and a new edge is extracted based on the changed order;
A program comprising instructions for causing said quantum annealing machine to solve based on an Ising model in which said newly extracted edges are spins in said solving.

Images