KR102219374B1 - A method and an apparatus for solving traveling salesman problem using a grover operator - Google Patents

Abstract

The present invention provides a method for solving a travel salesman problem, which comprises the steps of: setting eigenvectors corresponding to each of a plurality of cycles passing through all nodes to overlap each other; determining a database corresponding to all cyclic lengths of the traveling salesman problem by applying quantum phase estimation using a unitary matrix to a state in which the eigenvectors are superimposed; and determining the shortest path through all nodes by comparing the cycle length of the database with a preset reference value.

Description

A method and device for solving the problem of a salesman using a Grover operator {A METHOD AND AN APPARATUS FOR SOLVING TRAVELING SALESMAN PROBLEM USING A GROVER OPERATOR}

The present invention provides a method and apparatus for solving a salesman problem using a Grover operator.

The traveling salesman problem (TSP) is a problem of finding the shortest cycle to visit every city and return to the original city. The traveling salesman problem belongs to the NP-difficulty problem in the combinatorial optimization problem, and it may take exponential time when the brute-force method is applied. Solving the salesman problem is important because it is possible to directly solve the problem corresponding to the salesman problem by solving the problem of the salesman, and the solution can be practically widely applied.

The classic approach to solving the salesman problem can be divided into two. The first is an exact solution approach, such as branch and bound. The correct answer approach can find the optimal solution, but it takes a long time to calculate. The second is an approximate approach, such as a heuristic. Although the approximation approach has a short computation time, there is no guarantee that the solution obtained by the approximation approach is an optimal solution.

Meanwhile, research was conducted to solve the problem of traveling salesman by introducing quantum physics. Martonak applied quantum annealing and simulated annealing to the traveling salesman problem. As a result, it was shown that the quantum quenching technique could be better than the quenching technique.

The present invention provides a method and apparatus for solving a salesman problem using a Grover operator. More specifically, the present invention provides a method of finding the shortest path state in a salesman database in consideration of a quantum counting algorithm.

According to an embodiment, a method for solving a traveling salesman problem for a plurality of nodes includes setting eigenvectors corresponding to each of a plurality of cycles through all nodes to overlap each other, and a unitary matrix in a state in which the eigenvectors are overlapped. It may include determining a database corresponding to all the circulation lengths of the traveling salesman problem by applying the used quantum phase estimation, and determining the shortest path through all nodes by comparing the circulation length of the database with a preset reference value. .

According to an embodiment, the determining of the shortest path includes determining a rotation angle of a Grover operator corresponding to the database by applying a quantum counting algorithm to the database, and rotation of the Grover operator. When the angle is 0, determining that there is no circulation length shorter than the reference value, and when the Grover operator rotation angle is not 0, determining that there is a circulation length shorter than the reference value.

According to an embodiment, the method for solving the salesman problem includes determining a weight based on the size of the Grover operator rotation angle when the rotation angle of the Grover operator is not 0, and determining the size of the reference value by applying the weight to the reference value. It may further include the step of decrementing and determining the shortest path through all the nodes by comparing the reference value of which the circular length and the size of the database have been reduced.

According to an embodiment, the unitary matrix is determined based on Equation 1 below, and a phase corresponding to an eigenvector of the unitary matrix may be a sum of distances between nodes.

[Equation 1]

U: unitary matrix

Um:

According to an embodiment, in determining the database, quantum phase estimation may be applied based on Equation 2 below.

[Equation 2]

N: number of nodes, |Cj>: eigenvector corresponding to specific cycle, QPE: quantum phase estimation, |Dj>: data state corresponding to specific cycle

According to an embodiment, a method for solving the salesman problem includes the steps of configuring the database in a detachable state by applying an inverse-quantum phase estimation to the database, unitary converting the database configured in the detachable state, and It may further include determining the shortest path through all the nodes based on the converted result value.

According to an embodiment, in an electronic device including a control unit for solving the salesman problem, the control unit is a data setting unit configured to set eigenvectors corresponding to each of a plurality of cycles passing through all nodes to overlap each other, the eigenvector A database determination unit that determines a database corresponding to all the circulation lengths of the traveling salesman problem by applying quantum phase estimation using a unitary matrix in the state of the overlapping state, and passes through all nodes by comparing the circulation length of the database with a preset reference value. It may include a salesman problem solving unit to determine the shortest route.

According to an embodiment, the traveling salesman problem solving unit determines a Grover operator rotation angle corresponding to the database by applying a quantum counting algorithm to the database, and the Grover operator rotation angle is 0. In this case, it is determined that there is no circulation length shorter than the reference value, and when the Grover operator rotation angle is not 0, it may be determined that there is a circulation length shorter than the reference value.

According to an embodiment, the traveling salesman problem solving unit determines a weight based on the size of the Grover operator rotation angle, when the Grover operator rotation angle is not 0, and reduces the size of the reference value by applying the weight to the reference value. , It is possible to determine the shortest path through all nodes by comparing the circulating length of the database and a reference value of which the size is reduced.

According to an embodiment, the unitary matrix is determined based on Equation 3 below, and a phase corresponding to an eigenvector of the unitary matrix may be a sum of distances between nodes.

[Equation 3]

U: unitary matrix

Um:

According to an embodiment, the database determiner may apply quantum phase estimation based on Equation 4 below.

[Equation 4]

N: number of nodes, |Cj>: eigenvector corresponding to specific cycle, QPE: quantum phase estimation, |Dj>: data state corresponding to specific cycle

According to an embodiment, the salesman problem solving unit configures the database in a detachable state by applying inverse-quantum phase estimation to the database, unitary converts the database configured in the detachable state, and unitary conversion results Based on the value, the shortest path through all nodes can be determined.

According to an embodiment disclosed in the present invention, it is possible to prepare a state in which all circulations are overlapped to form a salesman database, and an optimum solution to the salesman problem may be obtained by finding the shortest circulation state in the salesman database with a Grover search algorithm.

In addition, even if the distance between cities is not symmetric (that is, if the number of cities is asymmetric) or the number of cities increases, an optimal solution to the problem of the salesman can be obtained through the method for solving the problem of the salesman disclosed in the present invention.

1 is a view showing the problem of a salesman in a case of four cities according to an embodiment of the present invention.
2 is a diagram showing a circuit diagram for solving the problem of a traveling salesman when there are four cities according to an embodiment of the present invention.
3A and 3B are diagrams showing the configuration of an MC-Z gate for solving a traveling salesman problem according to an embodiment of the present invention.
4A and 4B are diagrams showing the configuration of an MC-Z gate for solving a traveling salesman problem according to an embodiment of the present invention.
5 is a flowchart of a method for solving a salesman problem according to an embodiment of the present invention.
6 is a flowchart of a method for determining a shortest path according to an embodiment of the present invention.
7 is a block diagram of an electronic device according to an embodiment of the present invention.

In the present invention, various modifications may be made and various embodiments may be provided, and specific embodiments will be illustrated in the drawings and described in detail in the detailed description. However, this is not intended to limit the present invention to a specific embodiment, it is to be understood to include all changes, equivalents, and substitutes included in the spirit and scope of the present invention. In describing each drawing, similar reference numerals have been used for similar elements.

Terms such as first, second, A, and B may be used to describe various elements, but the elements should not be limited by the terms. These terms are used only for the purpose of distinguishing one component from another component. For example, without departing from the scope of the present invention, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element. The term and/or includes a combination of a plurality of related listed items or any of a plurality of related listed items.

When a component is referred to as being "connected" or "connected" to another component, it is understood that it may be directly connected or connected to the other component, but other components may exist in the middle. Should be. On the other hand, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there is no other component in the middle.

The terms used in the present application are only used to describe specific embodiments, and are not intended to limit the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In the present application, terms such as "comprise" or "have" are intended to designate the presence of features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, but one or more other features. It is to be understood that the presence or addition of elements or numbers, steps, actions, components, parts, or combinations thereof, does not preclude in advance.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs. Terms as defined in a commonly used dictionary should be interpreted as having a meaning consistent with the meaning in the context of the related technology, and should not be interpreted as an ideal or excessively formal meaning unless explicitly defined in this application. Does not.

According to an embodiment, the problem of a salesman having n cities from city 0 to city n-1 may be considered. According to various embodiments, assuming a distance from city x to city y is φ _xy , the unitary matrix U may be as follows.

U _m :

According to an embodiment, a phase corresponding to the eigenvector |l> of _{U m may be φ lm} , which is a distance from city l to city m. That is, _{the phases corresponding to each eigenvector of U m} may be a distance from each city to the m city. According to various embodiments, since the unitary matrix U is a _{tensor product of U m} , a phase corresponding to an eigenvector of U may be a sum of distances between cities.

According to one example, the circulation length of the salesman problem may be expressed as a sum of distances between cities. According to various embodiments, since the phase corresponding to the eigenvector of U is the sum of distances between cities, any of these phases may be a circular length. That is, a certain eigenvector of U may correspond to a specific cycle of the traveling salesman problem, and a phase of a certain coherence vector may correspond to a specific cycle length.

According to an embodiment, if an eigenvector |C _{j > corresponding to a specific cycle is prepared, a state |D j} > corresponding to the cycle length can be obtained by quantum phase estimation using a unitary matrix U as follows.

According to an embodiment, when a state in which eigenvectors corresponding to all cycles are superimposed is prepared, states corresponding to all cycle lengths can be obtained by quantum phase estimation using the unitary matrix U as follows.

According to an embodiment, the state before quantum phase estimation may not have a state corresponding to the cycle length. According to various embodiments, a state after quantum phase estimation may be considered to determine whether there is a cycle shorter than a specific length (eg, L). For example, in the salesman database, a sign having a circulating length shorter than L can be changed by properly configuring the MC-Z gate, and inverse quantum phase estimation can be performed as follows.

Meanwhile, in the following, for the convenience of expression, the notation definition is defined as follows.

In the above equation, M is the number of cycles shorter than L. Using the above definition, if unitary conversion D is performed in the aforementioned cyclic state, it may be as follows.

로 고려될 수 있다. 결국 본 발명에 따를 경우 그로버 연산자 G가 정의되었으므로, 회전각 θ를 양자 카운팅 알고리즘으로 알아낼 수 있다. 일 실시예에 따르면, θ가 0이면 L보다 짧은 순환은 존재하지 않을 수 있으며, θ가 0이 아니면 L보다 짧은 순환이 존재할 수 있다.In other words,

Can be considered as In the end, in the case of the present invention, since the Grover operator G is defined, the rotation angle θ can be found using a quantum counting algorithm. According to an embodiment, if θ is 0, there may not be a cycle shorter than L, and if θ is not 0, there may be a cycle shorter than L.

According to an embodiment, when the rotation angle θ obtained by the quantum counting algorithm is not 0, the weight of the cycle state shorter than L may be maximized by appropriately repeating G. In other words, a cyclic state shorter than L can be found with the Grover search algorithm. In the following, in order to help understanding the present invention, the solution proposed by the present invention will be applied to the actual salesman problem.

1 is a view showing the problem of a salesman in a case of four cities according to an embodiment of the present invention.

According to an embodiment, the traveling salesman problem illustrated in FIG. 1 may be a symmetric case. _{For example, the length of φ 01} , which is a path from city 0 to city 1, in FIG. 1, _{and φ 10} , which is a path from city 1 to city 0, may be the same.

According to an embodiment, the unitary matrix in the traveling salesman problem illustrated in FIG. 1 may be as follows.

According to an embodiment, since the phase corresponding to the eigenvector of U is the sum of the distances between cities, any of these phases may be a circular length. That is, any eigenvector of U can correspond to a specific cycle of the traveling salesman problem. According to various embodiments, in the problem of a salesman with four cities, a total of six possible ring cycles, and corresponding eigenvectors may also be six as shown in Table 1 below.

Circular number Circulation path Eigenvector One

2

3

4

5

6

According to an embodiment, it is possible to prepare a state in which cyclic number 1, circulating number 3, circulating number 4, and circulating number 6 are overlapped. For example, the overlapping state can include all cycles of the problem of a salesman in which there are 4 cities and the distances between cities are symmetric. According to various embodiments, it is possible to solve the traveling salesman problem by finding the shortest cycle in all the cycles. On the other hand, as an example, the distance between cities was set as follows, and accordingly, the vector and the length of the cycle number 1, the cycle number 3, the cycle number 4, and the cycle number 6 are shown in Table 2 below.

Circular number Circulation path Eigenvector Circulation length One

3

4

6

According to an embodiment, in Table 2, it may be considered whether there is a cycle having a cycle length shorter than π. In Table 2, since there are four total cycles and one cycle shorter than π (6 cycles), the rotation angle θ estimated by the quantum counting algorithm may be 60°. In other words, the shortest cycle can be found with a Grover search algorithm that performs Grover operator G once.

2 is a diagram showing a circuit diagram for solving the problem of a traveling salesman when there are four cities according to an embodiment of the present invention.

According to an embodiment, the U _state may be applied to prepare a state in which cyclic number 1, circulating number 3, circulating number 4, and circulating number 6 are overlapped. According to various embodiments, quantum phase estimation may be performed in a prepared state to obtain a circulation length corresponding to a circulation state. Quoting the previous example, since the minimum unit of the circular length is π/8, there may be 4 qubits used for quantum phase estimation.

According to an embodiment, a qubit may be a basic unit of quantum information used in a quantum computer. The qubit is a two-dimensional quantum system, and can be described as follows. In the following equation, |0> and |1> may be the basis state of the qubit. If a given qubit is measured, the classical bit value 0 with the probability of p and the classical bit value 1 with the probability of 1-p can be obtained.

According to one embodiment, “Is there a cycle with a cycle length shorter than π?” Whether or not can be considered in solving the salesman problem. Referring to the previous example, since the cycle length state with the cycle length π may be |1000>, if the cycle length is shorter than π, the first qubit may be |0>. Therefore, the MC-Z gate can be configured to change the sign of the state where the first qubit is |0>.

3A and 3B are diagrams showing the configuration of an MC-Z gate for solving a traveling salesman problem according to an embodiment of the present invention. More specifically, FIGS. 3A and 3B are diagrams showing the configuration of an MC-Z gate that changes the sign of a circulating state shorter than π.

행렬을 의미하는 게이트일 수 있다. 다양한 실시예에 따르면, 도 3a에서 도시하고 있는 MC-Z 게이트와 도 3b에서 도시하고 있는 MC-Z 게이트는 동일한 동작을 수행할 수 있다.According to an embodiment, the X gate may be a “NOT” gate, and the Z gate is

It may be a gate meaning a matrix. According to various embodiments, the MC-Z gate illustrated in FIG. 3A and the MC-Z gate illustrated in FIG. 3B may perform the same operation.

According to an embodiment, the weight of the target state may be increased by applying the unitary transformation D to the circulating state. However, since the circulating state and the circulating length state are entangled, D may not act on the circulating state. Therefore, by performing inverse-quantum phase estimation, it is possible to make it separable and act on D.

On the other hand, in the above-described example, the problem of determining the salesman is constructed based on a cycle shorter than π, but the problem of determining the salesman may be constructed based on a different circulation length. According to the present invention, the problem of determining the traveling salesman for a certain circulation length can be solved by changing only the configuration of the MC-Z gate.

According to an embodiment, detailed calculations by the circuit shown in FIG. 2 may be summarized as follows.

According to an embodiment, the classical bit 10110100 may be obtained by finally measuring |C6> = |10110100> with a 100% probability. By citing the previous example, it can be seen that the state measured by the obtained result corresponds to the path 0→3→1→2→0. That is, according to the present invention, there is one cycle shorter than π, and the cycle is 0→3→1→2→0, so it can be seen that 0→3→1→2→0 is the shortest cycle.

Meanwhile, in the above-mentioned embodiment, the case where the distance between cities is symmetric is mentioned, but the scope of the present invention is not limited to the case where the distance between cities is symmetric. Therefore, hereinafter, a method for solving the problem of a salesman when the distance between cities is asymmetric is disclosed.

As previously mentioned in the description of FIG. 1, assume that there are four cities. However, assuming that the distance between cities is asymmetric, and specifically, the distance between cities is as follows, the eigenvectors and circulation lengths of all circulations may be as shown in Table 3 below.

Circular number Circulation path Eigenvector Circulation length One

2

3

4

5

6

According to an embodiment, it is possible to prepare a state in which all the cycles of the cycle numbers 1 to 6 are overlapped. According to various embodiments, this overlapping state may include all cycles of the four-city salesman problem. On the other hand, when the city distance is asymmetric, the weights of all cycle states may not be the same, unlike the case where the city distance is symmetric. Looking at whether there is a cycle with a circulation length shorter than 7π/8 based on Table 2 above. , Since there is one cycle (6 cycles) shorter than 7π/8, and its weight is approximately 0.353, the rotation angle θ estimated by the quantum counting algorithm may be about 41°. Therefore, in this embodiment, the shortest cycle can be found with a Grover search algorithm that performs Grover operator G twice. Hereinafter, the process of finding the shortest cycle will be described in detail.

According to an embodiment, a cycle length corresponding to each state may be obtained through quantum phase estimation. According to various embodiments, since the minimum unit of the circular length is π/8, the number of qubits used for quantum phase estimation may be four. In this situation, in order to consider whether there is a cycle with a cycle length shorter than 7π/8, it is necessary to change the sign of a cycle length shorter than 7π/8. For this purpose, the sign of the state where the first qubit is |0> can be changed. In this case, the sign of the state of the circulation length of which the circulation length is 7π/8 may also be changed.

4A and 4B are diagrams showing the configuration of an MC-Z gate for solving a traveling salesman problem according to an embodiment of the present invention. More specifically, FIGS. 4A and 4B are diagrams showing the configuration of an MC-Z gate that changes the sign of a circulating state shorter than 7π/8. According to an embodiment, the MC-Z gate illustrated in FIG. 4A and the MC-Z gate illustrated in FIG. 4B may perform the same operation.

According to an embodiment, afterwards, inverse-quantum phase estimation is performed to make the state separable, and D is applied to increase the weight of the target state. According to various embodiments, the weight of the target state may be maximized by repeating the Grover operator G twice as described in the case where the city distance is symmetrical. That is, from the quantum phase estimation, a series of processes can be repeated once more.

According to an embodiment, when the results of Table 3 mentioned above are applied to the circuit diagram shown in FIG. 2, the classical bit 11100001 can be obtained by finally measuring |C5> = |11100001> with a probability of about 0.95. According to various embodiments, a state measured as a measurement result may correspond to a path 0→2→1→3→0. More specifically, there is one cycle shorter than 7π/8, and the cycle is 0→2→1→3→0, so it can be seen that the 0→2→1→3→0 cycle is the shortest cycle.

5 is a flowchart of a method for solving a salesman problem according to an embodiment of the present invention. The flowchart shown in FIG. 5 may be performed by the electronic device shown in FIG. 7.

According to an embodiment, in step S510, eigenvectors corresponding to each of a plurality of cycles passing through all nodes may be set to overlap each other. According to various embodiments, the step of setting an initial value for solving the salesman problem may be included before step S510. For example, the initial value for solving the salesman problem may be set differently depending on whether the salesman problem is symmetrical or asymmetrical.

According to an embodiment, in step S520, a database corresponding to all circulation lengths of the salesman problem may be determined by applying a quantum phase estimation using a unitary matrix to a state in which the eigenvectors are overlapped. According to various embodiments, the phase corresponding to the eigenvector of the unitary matrix may be a sum of distances between nodes constituting the traveling salesman problem.

According to an embodiment, the quantum phase estimation may be applied based on the following equation.

N: number of nodes, |C _j >: eigenvector corresponding to a specific cycle, QPE: quantum phase estimation, |D _j >: data state corresponding to a specific cycle

According to an embodiment, in step S530, the shortest path through all nodes may be determined by comparing the circulation length of the database with a preset reference value. A detailed description of step S530 will be described later with reference to FIG. 6.

On the other hand, although not shown, the method for solving the salesman problem according to the present invention includes the steps of configuring the database in a detachable state by applying inverse-quantum phase estimation to the database, and unitary converting the database configured in the detachable state. , And determining a shortest path through all nodes based on the unitary-transformed result value.

6 is a flowchart of a method for determining a shortest path according to an embodiment of the present invention.

According to an embodiment, a rotation angle of a Grover operator corresponding to the database may be determined by applying a quantum counting algorithm to the database determined in step S520 in step S610. According to various embodiments, in step S620, it may be checked whether the rotation angle of the Grover operator is 0°.

According to an embodiment, when it is determined in step S620 that the rotation angle of the Grover operator is 0°, it may be determined that there is no circulation length shorter than a preset reference value. That is, it may be determined that the circulation length corresponding to the rotation angle of the Grover operator determined in step S630 is the shortest path.

According to an embodiment, when it is determined in step S620 that the rotation angle of the grover operator is not 0°, the weight may be determined based on the size of the rotation angle of the grover operator through step S640. According to various embodiments, the size of the reference value may be reduced by applying the weight determined in step S650 to a preset reference value.

According to an embodiment, in step S660, the shortest path through all nodes may be determined by comparing a reference value with a reduced circulating length and a size of the database. That is, according to the present invention, the shortest path may be determined through steps S640 to S660 even if the circulation length corresponding to the rotation angle of the Grover operator determined through step S610 is not the shortest path.

7 is a block diagram of an electronic device according to an embodiment of the present invention.

According to an embodiment, the electronic device may include a control unit 700 for solving the problem of a salesman. According to various embodiments, the control unit 700 includes a data setting unit 710 that sets eigenvectors corresponding to each of a plurality of cycles through all nodes to overlap each other, and a unitary matrix in a state in which the eigenvectors are overlapped. A database determination unit 720 that determines a database corresponding to all circulation lengths of the salesman problem by applying the used quantum phase estimation, and a salesman who determines the shortest path through all nodes by comparing the circulation length of the database with a preset reference value It may include a problem solving unit 730.

According to an embodiment, the traveling salesman problem solving unit 730 determines a rotation angle of a Grover operator corresponding to the database by applying a quantum counting algorithm to the database, and the Grover operator rotation When the angle is 0, it is determined that there is no circulation length shorter than the reference value, and when the Grover operator rotation angle is not 0, it may be determined that there is a circulation length shorter than the reference value. According to various embodiments, the traveling salesman problem solving unit 730 determines a weight based on the size of the glover operator rotation angle, and applies the weight to the reference value when the glover operator rotation angle is not 0. The size is reduced, and the shortest path through all nodes may be determined by comparing the circular length of the database with a reference value whose size is reduced.

According to an embodiment, the salesman problem solving unit 730 configures the database in a detachable state by applying an inverse-quantum phase estimation to the database, and converts the database configured in the detachable state into a unitary conversion. The shortest path through all the nodes can be determined based on the result of the transformation.

So far, the present invention has been looked at around its preferred embodiments. Those of ordinary skill in the art to which the present invention pertains will be able to understand that the present invention can be implemented in a modified form without departing from the essential characteristics of the present invention. Therefore, the disclosed embodiments should be considered from an illustrative point of view rather than a limiting point of view. The scope of the present invention is shown in the claims rather than the above description, and all differences within the scope equivalent thereto should be construed as being included in the present invention.

Claims (12)

In a method for solving a salesman problem for a plurality of nodes,
Setting eigenvectors corresponding to each of the plurality of cycles through all nodes to overlap each other;
Determining a path database of a traveling salesman corresponding to all circulation lengths of the salesman problem by applying a quantum phase estimation using a unitary matrix to the state in which the eigenvectors are overlapped;
Determining a shortest route through all nodes by comparing a circulation length of the salesman's route database with a preset reference value;
Applying an inverse-quantum phase estimation to the salesman’s route database to configure the salesman’s route database in a detachable state;
Unitary conversion of the route database of the salesman configured in the detachable state; And
Including the step of determining the shortest path through all the nodes based on the unitary transformed result,
How to solve the salesman problem. In a method for solving a salesman problem for a plurality of nodes,
Setting eigenvectors corresponding to each of the plurality of cycles through all nodes to overlap each other;
Determining a path database of a traveling salesman corresponding to all circulation lengths of the salesman problem by applying a quantum phase estimation using a unitary matrix to the state in which the eigenvectors are overlapped; And
Comprising the step of determining the shortest path through all the nodes by comparing the circulation length of the path database of the salesman and a preset reference value,
The step of determining the shortest path,
Determining a rotation angle of a Grover operator corresponding to the salesman’s route database by applying a quantum counting algorithm to the salesman’s route database; And
If the Grover operator rotation angle is 0, determining that there is no circulation length shorter than the reference value, and when the Grover operator rotation angle is not 0, determining that there is a circulation length shorter than the reference value. Characterized by,
How to solve the salesman problem. The method of claim 2,
If the Grover operator rotation angle is not 0, determining a weight based on the Grover operator rotation angle size;
Reducing the size of the reference value by applying the weight to the reference value; And
The step of determining the shortest path through all the nodes by comparing the reference value of the reduced size and the circulation length of the path database of the salesman,
How to solve the salesman problem. The method of claim 2,
The unitary matrix is determined based on Equation 1 below, and a phase corresponding to the eigenvector of the unitary matrix is a sum of distances between nodes,
How to solve the salesman problem.
[Equation 1]

U: unitary matrix
U _m :

The method of claim 2,
The step of determining the path database of the traveling salesman is characterized by applying a quantum phase estimation based on Equation 2 below,
How to solve the salesman problem.
[Equation 2]

N: number of nodes, |C _j >: eigenvector corresponding to a specific cycle, QPE: quantum phase estimation, |D _j >: data state corresponding to a specific cycle delete In the electronic device including a control unit for solving the problem of the salesman,
The control unit,
A data setting unit for setting eigenvectors corresponding to each of a plurality of cycles passing through all nodes to overlap each other;
A database determining unit for determining a path database of a salesman corresponding to all circulating lengths of the salesman problem by applying a quantum phase estimation using a unitary matrix to the state in which the eigenvectors are overlapped; And
A salesman problem solving unit for determining a shortest route through all nodes by comparing the circulation length of the salesman’s route database with a preset reference value,
The salesman problem solving unit configures the salesman's route database in a detachable state by applying an inverse-quantum phase estimation to the salesman’s route database, unitary converts the salesman’s route database configured in the detachable condition, and unitary Characterized in that, based on the converted result value, the shortest path through all nodes is determined,
Electronic device. In the electronic device including a control unit for solving the problem of the salesman,
The control unit,
A data setting unit for setting eigenvectors corresponding to each of a plurality of cycles passing through all nodes to overlap each other;
A database determining unit for determining a path database of a salesman corresponding to all circulating lengths of the salesman problem by applying a quantum phase estimation using a unitary matrix to the state in which the eigenvectors are overlapped; And
A salesman problem solving unit for determining a shortest route through all nodes by comparing the circulation length of the salesman’s route database with a preset reference value,
The salesman problem solving unit determines a Grover operator rotation angle corresponding to the salesman’s route database by applying a quantum counting algorithm to the salesman’s route database, and the Grover operator’s rotation angle is zero. In case, it is determined that there is no circulation length shorter than the reference value, and when the rotation angle of the Grover operator is not 0, it is determined that there is a circulation length shorter than the reference value,
Electronic device. The method of claim 8,
The traveling salesman problem solving unit determines a weight based on the size of the Grover operator rotation angle, when the Grover operator rotation angle is not 0, applies the weight to the reference value to reduce the size of the reference value, and reduces the size of the reference value, and the traveling salesman's path database Characterized in that the shortest path through all nodes is determined by comparing the reference value of which the circulation length of is reduced and the size of,
Electronic device. The method of claim 8,
The unitary matrix is determined based on Equation 3 below, and a phase corresponding to the eigenvector of the unitary matrix is a sum of distances between nodes,
Electronic device.
[Equation 3]

U: unitary matrix
Um:

The method of claim 8,
The database determining unit is characterized in that applying a quantum phase estimation based on Equation 4 below,
Electronic device.
[Equation 4]

N: number of nodes, |Cj>: eigenvector corresponding to specific cycle, QPE: quantum phase estimation, |Dj>: data state corresponding to specific cycle delete

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