Quantum computer control device, quantum walk system, and quantum computer

Abstract

To provide a quantum computer control device capable of realizing node embedding with high accuracy using a quantum walk.SOLUTION: A quantum computer control device is configured with a classical computer that controls a quantum computer that performs quantum walk. The quantum walk performs a node embedding conversion processing in which a graph is read as an input and a feature amount of the graph is output as a continuous value; movement of the quantum walker that moves a node on the graph is defined by a coin operator; and the coin operator is prepared and set for each node of the graph.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a quantum computer control device, a quantum walk system, and a quantum computer for executing a quantum walk. [Background technology]

[0002] Patent Document 1 relates to a technology called DeepWalk, which is a social representation based on online learning. It is one of the efficient methods for learning nodes in a social representation represented as a graph. The DeepWalk method in Patent Document 1, commonly referred to as graph embedding or node embedding, learns node representations by utilizing the graph structure of a social network and the node adjacency relationships. First, a sequence of node labels in the social network is generated using a random walk. For example, starting from node 1, the node sequence obtained by sampling its nearest neighbors is [1, 2, 4, 5, 4, 7, ...]. Next, the generated node sequence is input into a neural network model, and the node representations are converted into continuous values ​​(vectors). Each converted node is a vector (= feature) that reflects the relationships and similarities between nodes. This method is useful in applications such as social network analysis, recommendation systems, and information retrieval, and offers higher accuracy and efficiency than some conventional techniques.

[0003] Patent Document 2 is an extension of the theory in Patent Document 1. It points out that breadth-first search (BFS) and depth-first search (DFS) are important elements in node learning representation, and proposes a random walk model with parameters that achieve both BFS and DFS. As a result, it has achieved superior performance to Patent Document 1 in some graphs. In summary, Patent Documents 1 and 2 perform node embedding based on the following procedure.

[0004] ●Sample an arbitrary walk length from the graph structure and create sequence data of node sequences (for example, the aforementioned [1, 2, 1, 3, 4, 7, 5, ...]). ●The sequence data is input into a neural network such as word2vec (which is trained as a data processor that distributes and vectorizes words), and the node and edge information is vectorized and converted into continuous values. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] PEROZZI, Bryan; AL-RFOU, Rami; SKIENA, Steven. Deepwalk: Online learning of social representations. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. 2014. p. 701-710. [Non-patent document 2] GROVER, Aditya; LESKOVEC, Jure. node2vec: Scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining. 2016. p. 855-864. Summary of the Invention [Problem to be solved by the invention]

[0006] The above conventional node embedding methods are executed on classical computers. When considering how to improve the accuracy of node embedding by newly executing them on quantum computers, the following problems 1 to 3 are found in this order.

[0007] ●Problem 1 When sequence data obtained from a random walk is vectorized using a neural network, it is difficult to embed nodes in the graph structure without losing information.

[0008] That is, with regard to Problem 1, when using a classical computer as in Non-Patent Documents 1 and 2, the cause of information loss is the procedure of inputting the node sequence obtained by random walking into a neural network and converting it into a vector with continuous values ​​as the output. Specifically, when the neural network outputs, there are parameters such as the number of dimensions of the vector, the number of words considered for learning (= window size), and the length of the sequence (= walk length). Vectorization is performed by fixing these parameters. Since the accuracy of node embedding changes depending on the values ​​of these parameters, it can be said that information loss is occurring.

[0009] On the other hand, quantum walks that run on quantum computers are called the quantum version of random walks, and nodes are expressed as probabilities. Therefore, because nodes are described by probability distributions that include information about graph interactions, detailed node embedding can be achieved as continuous values ​​without inputting them into a neural network, which is expected to reduce information loss. In other words, the advent of quantum computers makes it possible to directly express nodes in terms of quantum probabilities, which is expected to reduce the loss of information about graph structure that was unavoidable during some conversion processes when using classical computers.

[0010] ●Problem 2 However, no method has yet been proposed that is specialized for node embedding using quantum algorithms that run on this quantum computer.

[0011] ●Problem 3 Here, a simple candidate method for problem 2 is to use a quantum walk, which is a quantum version of a random walk. In other words, a quantum walk, which is a quantum algorithm, can calculate a result equivalent to a random walk faster than a random walk, which is a classical algorithm on a classical computer. However, when applying a quantum walk to a graph for node embedding, it is customary for the quantum walk on the graph to use a superposition state (a state in which the walk starts from all nodes), but simply using this state to embed nodes poses problems with accuracy.

[0012] Specifically, simply embedding nodes in a quantum superposition state only produces the effect of DFS, making it difficult to achieve both BFS and DFS, which are necessary for accurately embedding nodes.

[0013] In view of the above problems of the conventional techniques, an object of the present invention is to provide a quantum computer control device, a quantum walk system, and a quantum computer that can realize node embedding with high accuracy using a quantum walk. [Means for solving the problem]

[0014] To achieve the above object, the present invention is characterized in that it is a quantum computer control device composed of a classical computer that controls a quantum computer that executes a quantum walk, the quantum walk reading a graph as input and outputting the feature quantity of the graph as a continuous value, performing a node embedding conversion process, the movement of a quantum walker moving through nodes on the graph being determined by a coin operator, and the coin operator is prepared and set for each node of the graph. Also, the present invention is characterized in that it is a quantum walk system comprising the quantum computer control device and the quantum computer. Also, the present invention is characterized in that it is the quantum computer. [Effects of the Invention]

[0015] According to the present invention, by preparing and setting a coin operator for each node of a graph and then executing a quantum walk, node embedding can be realized with high accuracy using a quantum walk. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 is a configuration diagram of a quantum walk system according to an embodiment. [Figure 2] FIG. 1 is a functional block diagram of a quantum walk system according to an embodiment. [Figure 3] 1 is a flowchart of the operation of a quantum walk system according to an embodiment. [Figure 4] 10 is a flowchart of a quantum walk by a converter according to an embodiment. [Figure 5] This is a pseudocode representation of the same content as the flowchart in Figure 4. [Figure 6] FIG. 10 is a diagram illustrating an example of a graph showing an example of weight calculation according to the present embodiment. [Figure 7] FIG. 7 is a diagram showing a schematic example of a quantum circuit when the quantum walk according to the present embodiment is applied to the graph of FIG. 6. [Figure 8] FIG. 10 is a diagram illustrating a verification example of the effect of the present embodiment. [Figure 9] FIG. 1 is a diagram illustrating an example of the hardware configuration of a general (classical) computer. DETAILED DESCRIPTION OF THE INVENTION

[0017] FIG. 1 is a configuration diagram of a quantum walk system 100 according to one embodiment. The quantum walk system 100 comprises a quantum computer control device 10 and a quantum walk device 20 that can communicate with each other via a network such as the Internet or a LAN (local area network).

[0018] The quantum walk device 20 is realized as a quantum computer in terms of hardware, and executes the quantum walk according to this embodiment, which realizes both BFS and DFS. The quantum computer control device 10 is realized as a classical computer in terms of hardware, and performs various control processes for the quantum walk device 20, which is a quantum computer, to execute the quantum walk, such as setting the quantum walk algorithm to be executed and setting the graph data to be processed by the quantum walk to the quantum walk device 20, as well as processing to accept the quantum walk processing result in the quantum walk device 20 (as a classical bit state, which is the measurement result of the quantum walk, rather than as a quantum bit state handled inside the quantum computer) in the quantum computer control device 10, which is a classical computer, and further performing post-processing on the quantum walk processing result accepted as the classical bit state on the quantum computer control device 10.

[0019] 2 is a functional block diagram of a quantum walk system 100 according to one embodiment. As shown in the figure, in the quantum walk system 100, a quantum computer control device 10 includes an initialization unit 1, a setting unit 2, and a processing unit 4, and a quantum walk device 20 includes a conversion unit 3.

[0020] 3 is a flowchart of the operation of the quantum walk system 100 according to one embodiment. Below, the details of the processing content of each element in the functional block diagram of FIG. 2 will be described while explaining each step in FIG.

[0021] In step S1, the initialization unit 1 receives as input a labeled graph G(V,E,M) that has already been prepared externally as a data set or the like, converts it into a mathematical model that can be processed by the conversion unit 3, outputs it to the conversion unit 3 and the setting unit 2, and then proceeds to step S2.

[0022] Here, a labeled graph G(V, E, M), as generally defined in fields such as graph theory, is a graph consisting of a node set V, an edge set E, and a label set M, which is a set of labels assigned to each node in the node set V and / or each edge in the edge set E. Here, the labels may be composed of any information depending on what the nodes and edges of the original graph specifically represent. (For example, in the case of the Karate dataset shown in FIG. 8, which will be described later, the nodes represent members of the karate club, the edges represent friendships, and the labels represent the distinction between two factions A and B.) Note that, as will be described in detail later, the quantum walk algorithm of this embodiment does not require label information as input; instead, it is sufficient to use information on the node set V and the edge set E as input. In order to make this graph G processable by the conversion unit 3, which is composed of a quantum computer, the initialization unit 1 converts this graph G into a mathematical model by determining which element of the graph G each quantum bit processed in the quantum computer corresponds to. For example, conversion to a mathematical model is performed as including information such as which specific quantum bits processed by the quantum computer correspond to which individual nodes in the graph G. Details of this mathematical model will be described later when explaining the conversion unit 3, which is processing by the quantum computer.

[0023] In step S2, the setting unit 2 sets the quantum walk algorithm and its setting parameters to the conversion unit 3 in accordance with the mathematical model obtained by the initialization unit 1 (which, as mentioned above, includes information on predetermined arrangements regarding how each element of the graph G is assigned to the quantum bits of the quantum computer), and then proceeds to step S3.

[0024] Since the converter 3 executes the quantum walk according to the set quantum walk algorithm and its setting parameters, details of the setting process of the setting unit 2 will be described later as details of the quantum walk in the converter 3 according to the setting when explaining the converter 3. Specific setting parameters include the return probability, forward probability, and walk length, which will be described later.

[0025] In step S3, the conversion unit 3 executes a quantum walk algorithm based on the parameters set by the setting unit 2 in step S2 for the graph G (as an object that can be processed on a quantum computer as a mathematical model) obtained by the initialization unit 1 in step S1, thereby obtaining continuous features of the graph G, and outputs these features to the processing unit 4, before proceeding to step S4. That is, the conversion unit 3 executes the quantum walk to convert the graph G, which is discrete data, into continuous features (real-valued features).

[0026] The conversion unit 3 executes the quantum walk algorithm by performing processing as a quantum computer on the quantum bits, but the continuous features of the graph G, which is the final result of the conversion processing by the quantum walk, are given as numerical data representing the measurement results of the quantum bits, and are read by the processing unit 4 as being expressed in classical bits that can be processed by a classical computer.

[0027] 4 is a flowchart of the quantum walk by the conversion unit 3 according to an embodiment, and FIG. 5 is a so-called pseudocode representation of the same content as the flowchart in FIG. 4. In the pseudocode, the quantum walk is represented as t, w p ,w q (described later) as a parameter. p ,w q ) Hereinafter, the quantum walk according to this embodiment in the conversion unit 3 will be described in detail with reference to FIGS.

[0028] The first three lines of the pseudocode (Figure 5) are the functions QWalkVec(t,w p ,w q ) is explained by the data formats of the input data to the function and the output data from the function.

[0029] As shown, the input data is the graph G(V, E, M) mentioned above in the initialization section 1, and three parameters set in the setting section 2: the walking length t, which is the number of steps to walk on the quantum walk graph G, and the return probability 1 / w, which is a parameter that allows both BFS and DFS. p and forward probability 1 / w q where, for example, there are two parameters w, which can be specified as positive integers. q w q By using these three parameters (t, w), the return probability and forward probability can be set as their inverses. p ,w q ) can be manually prepared by a user or the like and set in the setting unit 2. For the sake of explanation, let the number of nodes in the node set V of the graph G be N. The output data is a real-valued matrix Φ of size N×t (N rows and t columns). In other words, this matrix Φ converts the graph G into continuous-valued feature quantities.

[0030] From the fourth line onwards in the pseudocode, the lines are numbered from 1 to 12, and the function QWalkVec(t,w p ,w q ) and corresponds to each step in Figure 4. Each step in Figure 4 is explained below.

[0031] Step S21 corresponds to line number 1 in the pseudocode. In step S21, the matrix Φ is initialized to a predetermined state as the quantum state to be processed, and then the process proceeds to step S22. The matrix Φ is of size N×t as described above. Similar to a general quantum walk, the quantum walk according to this embodiment has log N + log k qubits and can be executed by a quantum computer configured as a quantum walk circuit that processes these qubits with a predetermined circuit gate configuration according to the applied quantum algorithm. Here, log N qubits are used to describe the position information of the quantum walkers at each node, and log k qubits are used to describe the movement information of the quantum walkers. k is the maximum degree of the graph, that is, the maximum number among the connection numbers of the nodes constituting the graph (the number of edges of the node, the number of other nodes connected to the node).

[0032] For example, when performing a quantum walk on the network of FIG. 6 described later, N = 4, and the four states <ij| of two qubits <ij| = <00|, <01|, <10|, <11| are assigned as position information to the states where the quantum walkers exist at nodes 1, 2, 3, 4 respectively, and k = 2, and the two states of one qubit can be assigned as movement information indicating whether to move from node a to either of the two adjacent nodes b or c.

[0033] Step S22 corresponds to line number 2 in the pseudocode. It represents a process of setting each of the N nodes as a target node v o = 1, 2,..., N and repeating the processing from step S23 to step S31 for all target nodes vo. For the sake of explanation, integers are assigned as v o = 1, 2,..., N to identify each node.

[0034] Step S23 corresponds to line number 3 in the pseudocode. For the target node vo that is the processing target at that time, two parameters, the return probability 1 / w pand forward probability 1 / w q The edge weight w calculated from ij vo By using the coin operator C^ vo and the initial state |Ψ(0)> vo The edge weight w in step S23 is created and the process proceeds to step S24. ij vo Details of these will be explained later, but the probability determined by the parameters is expected to have the following effect: Return probability 1 / w p Returns the return parameter w p is used to control the likelihood of immediately revisiting a node in the walk, i.e., w p Setting a high value increases the probability of visiting an already visited node (with probability 1 / w p ) becomes lower, and w p If is low, the likelihood of revisiting (with probability 1 / w p ) is higher. Forward probability 1 / w q The forward parameter w gives q is the quantum walker's target node v o This controls whether to encourage search (forward) from the node to a distant node. q Setting to a high value will make the quantum walker reach the target node,v,. o tends to stay near 1 / w q becomes lower, and w q If ,is low, the quantum walker o It tends to move away from the q becomes higher.

[0035] Step S24 corresponds to line number 4 in the pseudo code, and means that the process from step S25 to step S30 is repeated while incrementing the walking length t set as length t by 1 from 1 the first time to t the last time. For the sake of explanation, let us assume that the walking length during the increment from 1 to t is t i (=1, 2, 3, ..., t). That is, the process from step S25 to S30 is performed for each walking length t iThe process is repeated in order for (=1, 2, 3, ..., t).

[0036] Step S25 corresponds to line number 5 in the pseudo code, and the target node vo and walking length t i In step S26, a quantum walk is performed using the following formula (A), where S is a shift operator. This quantum walk will also be described later.

[0037]

number

[0038] Step S26 corresponds to lines 6, 7, 8, and 9 in the pseudocode, and stores the measured values ​​in matrix Φ by performing measurements of the following equation (B) for i = 1, 2, ..., N. (Note that t on the first line of equations (A) and (B) and t on the seventh line of the pseudocode in Figure 5 are actually the walking length t i (=1,2,…,t), but we use t to avoid confusion with quantum state i.)

[0039]

number

[0040] The details of this measurement will be described later in the same way as for quantum walks. By this measurement, the quantum state Φ with N rows and t columns and the walking length t i t corresponding to iThe quantum state of the n-th N-dimensional column vector is determined as the measurement result. This measurement result means, as a result of proceeding with the node-to-node movement by the quantum walk starting from the walking length 1, the probability existing in each of the N nodes of the graph G at the current walking length ti, calculated as a real-valued N-dimensional column vector. For example, in the network example of FIG. 6 described later (number of nodes N = 4), the bra vector <i| in the right side of the equation in the first row of (B) is represented by the log N = log 4 = 2 qubits as four states <i| = <00|, <01|, <10|, <11|, corresponding to nodes 1, 2, 3, 4 respectively, and |Ψ(t)> is composed of a superposition of the four states (the four states corresponding to the ket vector |i> corresponding to the bra vector <i|) at time t(=t i ). Also, in the network example of FIG. 6 described later, the maximum degree k = 3, and <i|×<i→j| (× is a circled direct product) in the right side of the equation in the first row of (B) is represented as three states <i|×<i→j1| or <i|×<i→j2| or <i|×<i→j3| by the log3 qubits, representing whether to move to any of the (at most) three adjacent nodes j1, j2, j3 from node i.

[0041] Note that, as shown in Equation (B) and Equation (D) described later, the fact that the quantum walker is located at node i and can move to the adjacent node j at the next time is expressed as <i|×<i→j| in the bra vector and |i>×|i→j> in the ket vector, represented by the direct product. At the time of measurement, the probability of position i can be measured as the sum of all of the movement destinations j of i→j as in Equation (B). Multiplying <i|×<i→j| by |Ψ(t)> in Equation (B) is a process generally performed in the quantum walk in order to measure as the sum of all of the movement destinations j of i→j in this way, and can be realized by a known quantum circuit configuration.

[0042] Therefore, in the example of FIG. 6 described later, by the measurement of (B), for each walking length t iThe probability that the quantum walker's position i is in each of the four nodes |i>=|00>,|01>,|10>,|11>=1,2,3,4 is expressed as a four-dimensional column vector, e.g., (0.3, 0.4, 0.1, 0.2). T (T is transpose) o For each target node v, the sum is normalized to 1 (measurement probability based on the ratio of the number of measurements). o The final probability is obtained for each walking length t i For each target node v o For example, in the example in Figure 6, the probability of walking for a certain length t i For each target node v o If the following formulas are obtained for =1, 2, 3, and 4, the average of these can be used as the final probability. Generally, this is as shown in formula (I) below. v o =1 with probability (0.3, 0.4, 0.1, 0.2) T v o For =2, the probability is (0.4, 0.3, 0.2, 0.1) T v o =3, the probability is (0.1, 0.4, 0.3, 0.2) T v o =4, the probability is (0.2, 0.1, 0.4, 0.3) T

[0043] As is clear from the flow in Figure 4 and the pseudocode (Figure 5), the walking length t i = 1, multiplication by the operator in equation (A) (line 5 of the pseudocode) is performed for the walking length t i = 1 time (processing of the operator 1st power by a 1-stage circuit configuration) and then measure the walking length t i = 2, multiplication of equation (A) (line 5 of the pseudocode) is performed for walking length t i = 2 times (processing of the square operator by a two-stage circuit configuration) and then measure the walking length t i= 3, multiplication of equation (A) (line 5 of the pseudocode) is performed for the walking length t i = 3 times (processing of the operator cubed by a three-stage circuit configuration) before measurement. (That is, for example, walking length t i = When measuring three times, the walking length t i = 1 and walking length t i = 2 and the quantum state is not determined at some intermediate point.)

[0044] Step S30 corresponds to line number 10 in the pseudo code, and at this point, each walking length t i It is determined whether or not the processing (processing from step S24 to S30) has been completed for all of (=1, 2, 3, ..., t), and if it has been completed, the process proceeds to step S31, and if it has not been completed, the process returns to step S24, and the current walking length t i The next walking length t incremented by 1 from i Repeat the above process for +1.

[0045] Step S31 corresponds to line number 11 in the pseudocode, and currently, each of the N target nodes v o It is determined whether the processing (processing from step S22 to S31) has been completed for all of (=1, 2, 3, ..., N), and if it has been completed, the process proceeds to step S32. If it has not been completed, the process returns to step S22, and the next node for which the processing has not been completed is designated as the target node v o Then, the above process is repeated.

[0046] Step S32 corresponds to line number 12 in the pseudocode, and in step S32, a matrix Φ of size N×t is output as the result of the quantum walk, completing the processing of the flow in FIG. 4 (and the identical pseudocode in FIG. 5). The matrix Φ output in step S32 is the matrix Φ of each walk length t i (=1, 2, 3, ..., t) in step S26. o This is a list of all t N-dimensional column vectors measured as the average of the measurement results.

[0047] The quantum walk according to this embodiment has been described above in detail with reference to Figures 4 and 5. The coin operator and the like will now be described in further detail.

[0048] As explained in step S23 (the third line of the pseudocode) and the like, the quantum walk of this embodiment is executed as the following steps 1 and 2. Step 1: Target node v of the quantum walk o and assign the weight between each node to the target node v o , and the coin operator and the initial state are determined as dependent on the target node v o Create it as a dependency of . ●Step 2: Each node is set as the initial position of the quantum walk, and a quantum walk is performed for all nodes with a walking length of t, taking into account the edge weights.

[0049] In conventional quantum walks, all nodes are treated uniformly, whereas in this embodiment, the target node v o Then, this target node v o By defining the weights between nodes and the coin operator in step 1 as being dependent on , we can realize a random walk that combines BFS and DFS.

[0050] Regarding step 1, specifically, in step S23 (the third line of the pseudocode), the parameter w is calculated using the following formula (C): p ,w q Using the value of o The weight w of the edge between nodes i and j depends on ij vois calculated as corresponding to the quantum state |i→j>, which represents the movement from source node i to another destination node j, "i→j", and this weight controls the degree of diffusion of the quantum walk, resulting in both BFS and DFS. Note that in formula (C), by checking whether the conditions on lines 1 to 4 are met in order, starting from the first line, the weight setting on the line with the met condition can be used.

[0051]

number

[0052] In formula (C), l(a, b) is the shortest distance between node a and node b, and is the shortest number of hops. In the case of the shortest number of hops, the smallest unit of distance between each node is 1, which means the distance between adjacent nodes. In formula (C), the weight of the edge between nodes i and j is the edge weight w ij vo The first line is the condition that the source node i is connected to the target node v. o The second line defines the weight as 1 when the target node v o The distance from the destination node j is closer than the source node i, and moving from i to j results in the target node v o The weight of the return probability when returning to the side closer to p The larger the return probability, the higher the probability of revisiting a node that has already been visited, thereby enhancing the BFS effect. o If the distance from the source node i to the destination node j is the same, moving from i to j will reach the target node v o The weight when maintaining the same distance from the forward probability 1 / w q The larger this probability is, the more effective the DFS is. (Note that here, the target node v oEven if the distance (depth) from i to j is the same, it will move to other nodes frequently, resulting in quantum interference, which will spread the quantum to the whole, and it is expected that the DFS effect will be enhanced.) Line 4 shows that if lines 1 to 3 above do not apply, moving from i to j will reach the target node v. o The weight when moving further away from the forward probability 1 / w q The larger this probability, the more effective the DFS becomes. o ,i) <l(v o ,j), the fourth line applies.

[0053] Using Figure 6 as an example, we will explain an example of weight calculation for the target node v0=2 that is being considered when assigning weights to edges in graph G. In Figure 6, the number of nodes in graph G is N=4, with nodes 1, 2, 3, and 4, and the existence of edges between each node is defined by the relationships shown in the figure. Note that the arrows on the edges connecting nodes in Figure 6 do not represent a directed graph, but rather represent the direction of movement between nodes in a quantum walk, and indicate that the weight is calculated taking into account this direction of movement. (Graph G itself may be a directed or undirected graph.) Since the graph is configured as follows: 1 → 2 or 3 has degree 1, 2 → 1 or 3 has degree 2, 3 → 1, 2, or 3 has degree 3, and 4 → 3 has degree 1, the maximum degree k for this graph G is k=3.

[0054] ●Calculation example 1...Between edges 1 and 2, The weight when moving from i to j = 1 to 2 is 1 / w p Because l(1,2)=1 and l(2,2)=0, This is because the condition l(v0,i)>(v0,j) in the second line of equation (C) is met. Conversely, when moving from i to j = 2 to 1, the weight is 1. This is because l(v0,i) = 0, which corresponds to the first line of equation (C). ●Calculation example 2...For the area between edges 1 and 3, The weight when moving from i to j = 1 to 3 and the weight when moving from i to j = 1 to 3 are both 1 / wq This is because l(2,1)=1 and l(2,3)=1, which satisfies the condition in the third line of equation (C). ●Calculation example 3...For the area between edges 2 and 3, The weight when moving from i to j = 2 to 3 is 1. This is because l(v0,i) = 0, which corresponds to the first line of equation (C). The weight when moving from i to j = 3 to 2 is 1 / w p Because l(2,3)=1 and l(2,2)=0, This is because the condition l(v0,i)>(v0,j) in the second line of equation (C) is met. ●Calculation example 4...Between edges 3 and 4, The weight when moving from i to j = 3 to 4 is 1 / w q Because l(2,3)=1 and l(2,4)=2, This is because the conditions in lines 1 to 3 of formula (C) are not met, but the fourth line is met. The weight when moving from 4 to 3 is 1 / w p Because l(2,4)=2 and l(2,3)=1, This is because the condition l(v0,i)>(v0,j) in the second line of equation (C) is met.

[0055] In addition, w p ,w q The value of varies depending on the graph G in question, and an appropriate value can be determined experimentally through some trial and error, and the results of that quantum walk can be used. By adjusting the parameters, for example, for a certain graph G, (w p ,w q )=(0.1,1.0), we can achieve both breadth-first search (BFS) and depth-first search (DFS), but give priority to BFS. p ,w q)=(1.0,0.1), it is expected that a quantum walk in which DFS is relatively prioritized can be realized. That is, the quantum walk itself has the advantage of being able to be executed faster than a random walk on a classical computer. In addition, as shown in the experimental example of Fig. 8 described later, in this embodiment, by actually achieving both BFS and DFS using a quantum walk based on optimal parameters that can be experimentally set, it is possible to obtain results with higher accuracy than a random walk on a classical computer.

[0056] In this way, the target node v o The weight w depends on the parameter ij vo Using the above, the quantum walk according to the above equations (A) and (B) can be specifically realized as follows.

[0057] The above formula (A) is a general quantum walk framework for the target node v o Dependence weight w ij vo In other words, in a general quantum walk, a specific target node v o The quantum walk time transition is realized simultaneously from all nodes in a superposition state by quantum operations as an initial state "|Ψ(0)>" that does not give dependency, whereas the initial state "|Ψ(0)>" in equation (A) of this embodiment is vo ” is the target node v o Then, similar to the general quantum walk framework, quantum walk time transitions are performed simultaneously from all nodes (i.e., target node v o The weight w ij vo This is to reflect the movement of the quantum walker in a way that takes into account the network structure in the initial state and coin operator and makes both BFS and DFS compatible, but it does not mean the initial position where the quantum walker starts moving. As will be described later in the example of Figure 6, this weight w ij vo is the number of nodes in a particular target node v.o When we look at a quantum walker moving on a graph G from o It is set taking into consideration whether or not the distance from the o Dependence initial state |Ψ(0)> vo is as shown in the following formula (D).

[0058]

number

[0059] The meaning of this formula (D) is that for a quantum state |i> that means that it is located at node i, the weight matrix w ij vo was included in the element, k i This represents a vector of dimension equal to the length of k. i is the destination node j that can be moved to as an adjacent node from the currently located node i, where j=1,2,…,k i The quantum state |i> of the current position i and the quantum state |i→j> representing the movement from position i to position j at the next time are combined as a tensor product (direct product). In this way, the initial state is set as a superposition of the direct product of the position state and the movement state for multiple possible movement states for the position state. This setting itself is the same as a general quantum walk, but in this embodiment, in particular, when superposition is performed, the target node v o The weight of the dependency w ij vo The division term in the denominator is the whole vector |Ψ(0)> vo It serves to normalize the magnitude of

[0060] Coin Operator C vo ^ is as follows: i For each node i (walk length t i Let the quantum walker at node i be the nearest node (neighboring node) j=1,2,…,k iIn this embodiment, as will be clear from the formulas (F) and (G) described later, the coin operator C vo ^ with the weight w mentioned above ij vo (Note that in order for the coin operator to function properly and for the quantum walk to reflect the movement rate to be realized, the same weight w ij vo It is designed to reflect this.)

[0061]

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[0062] Equation (E) means that for each node i=1,2,...,N (target node v o (not of interest as such) but the target node v o This means that we have N coin operators with different dependencies. i vo is the coin operator of node i, given by the following formula (F):

[0063]

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[0064] where |s i vo > where the weight w ij vo This is reflected in the following equation (G). ij vo The role played by this weight w ij vo The larger is, the more likely it is that quantum walker transfer from i to j will occur.

[0065]

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[0066] Furthermore, the shift operator S^ in the above formula (A) can be designed as desired within the scope of quantum computation, but a simple design example is as shown in the following formula (H), which, when moving from state i to state j with the coin operator, similarly updates the state of the quantum walk from state i to state j, and has the same definition and role as those used in existing quantum walks. For example, a quantum that moves from node 1 to 4 moves to the vector element 4 → 1 of node 4.

[0067]

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[0068] The coin operator C defined above vo By multiplying ^ and the shift operator S^ by the walking length t times as shown in the above formula (A), the initial state |Ψ(0)> vo A quantum walk is performed by applying

[0069] Finally, the feature representation matrix Φ is defined as follows: The measurement in the second line of the above equation (B) is calculated as follows: o The summed state Φ i,t (In equation (B) this is performed for the state Φ[i,t]).

[0070]

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[0071] The quantum walk is executed multiple times, and the final result is obtained as the average value of the measurements taken each time. That is, in the process expressed by the flow of FIG. 4 and the pseudo code of FIG. 5, one quantum walk and one measurement are executed multiple times in step S26, and the target node v corresponding to step S26 is obtained. o , walking length t iThe expected value (average value) of the measurement results at each walking length t is obtained as the N-dimensional probability vector. i In this case, we apply this to all target nodes v o The results of averaging using equation (I) for the above can be enumerated over the total walking length t in step S32 to obtain the final measurement results of the matrix Φ (N rows, t columns).

[0072] The processing of the conversion unit 3 in step S3 of FIG. 3 has been described above.

[0073] In step S4, as post-processing for the features of graph G obtained by conversion unit 3 as described above, processing unit 4 executes a classification task by machine learning using a pre-trained model, and obtains a classification result.

[0074] If the matrix Φ is an N-by-t matrix that represents the features of graph G, each of the N rows represents the time transition of the stay probability at each of the N nodes over the walking length t as a row vector of dimension t, the same as the walking length t, thereby expressing the features of each of the N nodes. Therefore, a classification task using machine learning can be performed on these N features to obtain classification results for each node. For example, if each node in graph G is a person and human relationships are represented by graph G, it is possible to obtain classification results such as whether person i at node i and person j at node j have the same attribute or belong to the same group.

[0075] 7 is a diagram showing a schematic example of a quantization circuit when the quantum walk of this embodiment is applied to the graph G shown in FIG. 6. The leftmost circuit part PD is a part where the initial state of formula (D) is prepared for the graph G of FIG. 6 as two quantum bits of position information and two quantum bits of movement information, the next circuit part PE is a part that processes formula (E) as a coin operator, the next circuit part PH is a part that processes formula (H) as a shift operator, and the last circuit part PM is a part that measures the two quantum bits of position information in the processing result by the quantum walk circuit. Note that, for each t within the walking length t, iWhen performing a quantum walk of =1,2,...,t, as shown in Figure 7, we use the coin operator and shift operator in equation (A) as i Similarly, the corresponding circuit parts PE and PH are multiplied by t i After repeating this process only once, measurements can be made at the circuit part PM.

[0076] The quantum walk circuit in Figure 7 is o In the case of the graph G in Figure 6, the target node v o The final result can be obtained by averaging the four results of the four quantum walk circuits with =1, 2, 3, 4.

[0077] Also, for example, when the walking length is t=3, i To perform a quantum walk for t = 1, 2, 3, perform the following process for each t i By performing multiple measurements for each of =1, 2, and 3, a matrix Φ of size 4 × 3, which is the measurement result, is obtained as a probability. t i Prepare the initial state for =1, and set the circuit parts PE and PH to t i = 1 run and measure the size 4 × 3 matrix Φt i =Get the first column. t i Prepare the initial state for =2, and set the circuit parts PE and PH to t i = 2 times and measure the size 4 × 3 matrix Φt i =Get the second column. t i Prepare the initial state for =3, and set the circuit parts PE and PH to t i = 3 times and measure the size of the matrix Φt of 4 × 3. i =Get the third column.

[0078] FIG. 8 is a diagram showing an example of verification of the effects of this embodiment. The table at the top lists the datasets used and the parameters that provided the best performance for those graphs, and the table at the bottom shows the results of a comparison of the accuracy of the embodiment of the present invention with a control.

[0079] The experimental procedure follows Non-Patent Document 1. Specifically, a training set of size TR is randomly sampled from the labeled nodes, and the remaining nodes are used as test data. This process is repeated 20 times, and the average of the Micro-F1 and Macro-F1 scores is used to evaluate the performance score. For the node classification task of all methods, a one-versus-rest logistic regression model implemented by LibLinear is used. The parameters of the neural network Word2vec required in Non-Patent Documents 1 and 2 are γ = 80, w = 10, and d = 128. The results obtained by DeepWalk and node2vec are shown. p, q, w p , w q ∈{0.25,0.50,1,2,4}. (The roles of p and q are w p ,w q The optimal parameters for Node2vec and QWalkVec (as mentioned above in the pseudocode in FIG. 4, this embodiment is called QWalkVec) are listed in the table at the bottom.

[0080] The bottom table shows the experimental results for the graphs Karate, Webkb, IIPs, and DD199. The performance of Node2vec and QWalkVec is shown using the best-performing parameters listed in the top table.

[0081] For Karate results, training ratio T R We set the training ratio T R We set t between 20% and 80%, because the number of training nodes becomes too small due to the size of the graph. To determine the optimal approach, we run t = 400. QWalkVec consistently outperforms DeepWalk and node2vec.

[0082] For WebKb results, we run t=400 to determine the best performance among different walk lengths. QWalkVec consistently outperforms DeepWalk and node2vec in terms of micro-F_1 and macro-F_1 scores.

[0083] For IIPs results, we run t=400 to determine the best performance. In terms of micro F_1 scores, DeepWalk, node2vec, and QWalkVec perform almost identically, but node2vec consistently performs slightly better than DeepWalk and QWalkVec. In terms of macro F_1 scores, node2vec consistently outperforms DeepWalk and QWalkVec.

[0084] For the DD199 results, run t=100 to determine the best performance. In terms of micro F_1 score, T R ≦50%, node2vec consistently outperforms DeepWalk and QWalkVec. However, T R At 50%, 70%, QWalkVec performs as well as node2vec. R DeepWalk and node2vec outperform QWalkVec at 20% and 30%, but T R At ≤40%, QWalkVec consistently outperforms DeepWalk and node2vec.

[0085] From the trends in these data sets, w p <w q In this case (where the effect of breadth-first search BFS is strong), we confirmed that the accuracy tends to improve compared to existing methods.

[0086] As described above, the embodiments of the present invention are useful in social network analysis, recommendation systems, etc., and can contribute to improving the accuracy and efficiency of node classification. Various supplementary examples related to the embodiments of the present invention will be described below.

[0087] (1) According to an embodiment of the present invention, by effectively expanding the scope of application of quantum walks as an example of the use of quantum computers, which are a novel technology, it is possible to contribute to technological innovation and to achieving Goal 9 of the United Nations-led Sustainable Development Goals (SDGs), “Build infrastructure, promote industry, innovation and foster innovation.”

[0088] (2) FIG. 9 is a diagram showing an example of the hardware configuration of a general (classical) computer device 70. The quantum computer control device 10 as a classical computer device in the quantum walk system 100 can be realized as one or more computer devices 70 having such a configuration. When the quantum computer control device 10 is realized using two or more computer devices 70, information required for processing may be transmitted and received via a network. The computer device 70 includes a CPU (Central Processing Unit) 71 that executes predetermined instructions, a GPU (Graphics Processing Unit) 72 as a dedicated processor that executes some or all of the CPU 71's execution instructions in place of or in cooperation with the CPU 71, a RAM 73 as a main memory device that provides a work area for the CPU 71 (and GPU 72), a ROM 74 as an auxiliary memory device, a communication interface 75, a display 76 that displays and outputs images, an input interface 77 that accepts user input via a mouse, keyboard, touch panel, etc., a speaker 78 that outputs audio, and a bus BS for transmitting and receiving data among these devices.

[0089] The quantum computer control device 10 can be realized by a CPU 71 and / or a GPU 72 that reads from a ROM 74 and executes a predetermined program corresponding to the function of each unit. Both the CPU 71 and the GPU 72 are types of arithmetic devices (processors). Here, when display-related processing is performed, a display 76 also operates in conjunction with the CPU 71 and GPU 72; when communication-related processing related to data transmission and reception is performed, a communication interface 75 also operates in conjunction with the CPU 71 and GPU 72; and when audio output-related processing is performed, a speaker 78 also operates in conjunction with the CPU 71 and GPU 72. [Explanation of symbols]

[0090] 100... quantum walk system, 10... quantum computer control device, 20... quantum walk device 1...initialization unit, 2...setting unit, 3...conversion unit, 4...processing unit

Claims

1. A quantum computer control device configured by a classical computer that controls a quantum computer that executes a quantum walk, The quantum walk reads a graph as an input and outputs the feature quantity of the graph as a continuous value, and performs a node embedding conversion process, in which the movement of a quantum walker moving through nodes on the graph is determined by a coin operator; A quantum computer control device, characterized in that the coin operator is prepared and set for each node of the graph.

2. The quantum computer control device according to claim 1, characterized in that it controls the feature of the graph to be output as a continuous value as a measurement result of the result of executing the quantum walk on the sum of the quantum states for each coin operator.

3. The quantum computer control device described in claim 1, characterized in that in order to prepare and set the coin operator for each node of the graph, with the node of interest as the target node, the weight with which the quantum walker moves between nodes to determine the coin operator is set as a weight according to the positional relationship between the source node and destination node between the nodes and the target node.

4. The quantum walk is executed by applying at least the coin operator to an initial state, the initial state being defined as a superposition of a Cartesian product of a position state and a movement state; The quantum computer control device according to claim 1, characterized in that the node of interest is set as a target node, the initial state is determined for each target node, and weights used for the superposition are weights according to the positional relationship between the source node and destination node in the movement state and the target node.

5. 2. The quantum computer control device according to claim 1, further comprising: classifying each node in the graph represented in the result of the quantum walk executed by the quantum computer by machine learning based on the feature quantities of each node.

6. A quantum walk system comprising: the quantum computer control device according to claim 1; and the quantum computer according to claim 1.

7. A quantum computer device that performs a quantum walk, The quantum walk reads a graph as an input and outputs the feature quantity of the graph as a continuous value, and performs a node embedding conversion process, in which the movement of a quantum walker moving through nodes on the graph is determined by a coin operator; A quantum computer device characterized in that the coin operator is prepared and set for each node of the graph and then the quantum walk is executed.

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