Graph state segmentation and distribution method and system based on quantum communication network

Abstract

The invention discloses a graph state segmentation and distribution method and system based on a quantum communication network, comprehensively considers finiteness of node quantum resources and quality of distributed graph states, provides a feasible solution for effectively distributing any graph state in a large-scale quantum communication network, and provides a graph state segmentation scheme based on segmentation-integration. According to the method, a large-scale graph state is divided into a plurality of sub-graph states to be prepared and distributed respectively, graph state related operation is executed on part of nodes, so that the nodes are restored to the required complete graph state, quantum resources required by a single node can be effectively reduced when the large-scale graph state is generated, the smoothness of a whole quantum communication network is kept, and the generation efficiency of the large-scale graph state is improved. Congestion caused by a certain node is avoided; meanwhile, a reliable transmission strategy and conflict-free multi-destination routing are adopted, so that the success rate of graph state distribution is improved.

Description

Technical Field

[0001] The present invention relates to the field of quantum communication technology, and in particular to a graph segmentation and distribution method and system based on a quantum communication network. Background Art

[0002] Quantum communication technology is a research direction with great application value in quantum information research. It can provide an absolutely secure communication method from a physical level. By utilizing quantum superposition and entanglement effects, based on uncertainty, measurement collapse and the principle of no cloning, it provides security guarantees that cannot be eavesdropped or cracked by calculation. It is mainly divided into two directions: quantum teleportation and quantum key distribution. Quantum teleportation is based on the distribution of entangled pairs and joint measurement of Bell states, with the assistance of classical channels, to achieve the transmission of quantum states; quantum key distribution uses the transmission measurement of quantum superposition states to achieve quantum key sharing between the two communicating parties to achieve unconditional and absolutely secure confidential communication. Because lossy quantum channels cause great difficulties for the transmission of quantum states over long distances, their fidelity will decrease as the transmission distance increases, but due to the principle of no cloning, they cannot be copied or amplified and retransmitted. Therefore, only quantum teleportation is used for communication, and its transmission distance is very limited. To this end, entanglement swapping technology provides a method to achieve long-distance quantum state transmission: adding repeaters and performing entanglement swapping technology at the repeaters can shorten the distance that quantum bits are transmitted in lossy channels and utilize more quantum bit resources to achieve quantum teleportation over longer distances. This technology is also the main means of realizing long-distance quantum communication and large-scale quantum communication networks.

[0003] Graph states are a special type of multi-particle entangled quantum state, that is, the entanglement relationship between quantum bits is represented in the form of a graph, including GHZ (Greenberger-Horne-Zeilinger, multi-particle maximum entanglement) state and cluster state are all a type of graph state. Compared with the network that uses Bell state for quantum communication, the network constructed between nodes using this more complex entangled state can realize some unique functions, such as quantum secret sharing, measurement-based quantum computing, quantum error correction coding, quantum multi-party secure computing, etc., and is a very important type of quantum resource. However, due to the complex entanglement relationship of graph states, operating on graph states also requires more complex quantum gates, so how to effectively prepare and distribute graph states is the primary challenge faced in utilizing this important quantum resource. Summary of the invention

[0004] The purpose of the present invention is to provide a graph segmentation and distribution method and system based on a quantum communication network, which comprehensively considers the limited node quantum resources and the quality of the distributed graph, and provides a feasible solution for effectively distributing arbitrary graphs in large-scale quantum communication networks.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A graph segmentation and distribution method based on a quantum communication network, comprising:

[0007] According to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link, a corresponding weight is assigned to each link;

[0008] Receive a graph state distribution request, which carries the complete graph state to be distributed and the node position of each node in the graph state in the quantum communication network; for the complete graph state to be distributed, if the resource consumption required for distribution exceeds the set requirements, divide the complete graph state into several sub-graph states so that the resource consumption required for distribution of each sub-graph state does not exceed the set requirements;

[0009] Each sub-graph state obtained by segmentation is placed in the quantum communication network respectively, and the multi-destination conflict-free routing discovery is performed based on the minimum spanning tree algorithm in combination with the weights of each link in the quantum communication network, so as to obtain multiple non-conflicting paths corresponding to all sub-graph states, calculate the success probability of the multiple non-conflicting paths, and distribute the corresponding sub-graph state through the obtained path pair if the path meets the set reliable transmission requirements;

[0010] Each sub-graph state is restored to the complete graph state through the graph state integration technology.

[0011] A graph segmentation and distribution system based on a quantum communication network, used to implement the above method, the system comprising:

[0012] A link weight assignment unit is used to assign corresponding weights to each link according to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link;

[0013] A graph state segmentation unit is used to receive a graph state distribution request, which carries a complete graph state to be distributed and the node position of each node in the graph state in the quantum communication network; for the complete graph state to be distributed, if the resource consumption required for distribution exceeds the set requirements, the complete graph state is segmented into a plurality of sub-graph states so that the resource consumption required for distribution of each sub-graph state does not exceed the set requirements;

[0014] A graph distribution unit based on a quantum communication network is used to place each sub-graph obtained by segmentation into the quantum communication network, perform multi-destination conflict-free routing discovery based on a minimum spanning tree algorithm in combination with the weights of each link in the quantum communication network, obtain multiple non-conflicting paths corresponding to all sub-graphs, calculate the success probabilities of the multiple non-conflicting paths, and distribute the corresponding sub-graph through the obtained path pair if the path meets the set reliable transmission requirements;

[0015] The graph state integration unit is used to restore each sub-graph state to the complete graph state through the graph state integration technology.

[0016] It can be seen from the technical solution provided by the present invention that a graph segmentation scheme based on segmentation-integration is proposed, in which a large-scale graph is segmented into several sub-graphs which are prepared and distributed separately, and then restored to the required complete graph by performing graph-related operations on some nodes. This can effectively reduce the quantum resources required for a single node when generating a large-scale graph, help maintain the smooth flow of the entire quantum communication network, and avoid congestion caused by a certain node; at the same time, the present invention also adopts a reliable transmission strategy and conflict-free multi-destination routing to improve the success rate of graph distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0018] Figure 1 A flowchart of a method for graph segmentation and distribution based on a quantum communication network provided by an embodiment of the present invention;

[0019] Figure 2 A schematic diagram of the preparation of a pattern provided in an embodiment of the present invention;

[0020] Figure 3 A schematic diagram of the topology of a quantum communication network provided by an embodiment of the present invention;

[0021] Figure 4 A schematic diagram of distributing using graphical copies provided by an embodiment of the present invention;

[0022] Figure 5 A schematic diagram of segmentation and integration of graphs provided in an embodiment of the present invention;

[0023] Figure 6 A schematic diagram of a graph segmentation and distribution system based on a quantum communication network provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the protection scope of the present invention.

[0025] First, the terms that may be used in this article are explained as follows:

[0026] The terms "include", "comprises", "contains", "has" or other descriptions with similar semantics should be interpreted as non-exclusive inclusion. For example, including certain technical feature elements (such as raw materials, components, ingredients, carriers, dosage forms, materials, dimensions, parts, components, mechanisms, devices, steps, procedures, methods, reaction conditions, processing conditions, parameters, algorithms, signals, data, products or products, etc.) should be interpreted as including not only certain technical feature elements explicitly listed, but also other technical feature elements known in the art that are not explicitly listed.

[0027] The term "consisting of..." means excluding any technical feature elements not explicitly listed. If this term is used in a claim, it will make the claim closed, so that it does not contain technical feature elements other than the technical feature elements explicitly listed, except for the conventional impurities related to them. If this term only appears in a clause of a claim, it only limits the elements explicitly listed in the clause, and the elements recorded in other clauses are not excluded from the overall claim.

[0028] The following is a detailed description of a method and system for graph segmentation and distribution based on a quantum communication network provided by the present invention. The contents not described in detail in the embodiments of the present invention belong to the prior art known to professionals in the field. If no specific conditions are specified in the embodiments of the present invention, the conditions are carried out according to the conventional conditions in the field or the conditions recommended by the manufacturer. The reagents or instruments used in the embodiments of the present invention, if the manufacturer is not specified, are all conventional products that can be purchased commercially.

[0029] Embodiment 1

[0030] The embodiment of the present invention provides a method for graph segmentation and distribution based on a quantum communication network, such as Figure 1 As shown, it mainly includes the following steps:

[0031] Step 1: Assign weights to the links of the quantum communication network.

[0032] In the embodiment of the present invention, a corresponding weight is assigned to each link according to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link.

[0033] In one embodiment, the method of assigning corresponding weights to each link can be described as follows:

[0034] The network topology of the quantum communication network is denoted as G net , for each of its links Assign weight It is expressed as:

[0035]

[0036] in, Indicates link The entanglement pair fidelity, Indicates link Communication delay; Indicates link The available bandwidth of the link The minimum number of available qubits in the last two nodes; E net Represents the network topology G net The link set in , k1, k2, k3 are the setting coefficients.

[0037] Step 2: Image segmentation.

[0038] In an embodiment of the present invention, a graph distribution request is received, which carries the complete graph to be distributed and the node position of each node in the graph in the quantum communication network; for the complete graph to be distributed, if the resource consumption required for distribution exceeds the set requirements, the complete graph is divided into several sub-graphs so that the resource consumption required for distribution of each sub-graph does not exceed the set requirements.

[0039] In one embodiment, the graph segmentation scheme can be described as:

[0040] (1) Assign a weight to each edge in the complete graph to obtain a weight matrix W of the complete graph, and calculate a Laplace matrix in combination with the degree matrix of the complete graph.

[0041] (2) Calculate the eigenvector of the Laplacian matrix and use it for K-means clustering to segment the graph into different regions. Each segmentation method obtains two regions, and the node sets in the two regions are recorded as A and B respectively.

[0042] (3) For each segmentation method, the normalized cut value of each region is calculated separately Among them, cut(A,B) represents the sum of the weights of the edges between A and B, V represents the intersection of A and B, assoc(A,V) is the sum of the weights of all nodes in A to V, and assoc(B,V) is the sum of the weights of all nodes in B to V.

[0043] (4) Select the segmentation result corresponding to the segmentation method with the minimum normalized cutting value, and determine whether the resource consumption required for the distribution of each sub-graph state in the segmentation result does not exceed the set requirements. If so, the segmentation is completed; if not, the segmentation is continued until the resource consumption required for the distribution of each sub-graph state in the segmentation result does not exceed the set requirements.

[0044] Step 3: Graph distribution based on multi-destination routing and reliable transmission strategy.

[0045] In an embodiment of the present invention, each sub-graph state obtained by segmentation is placed in the quantum communication network according to the node position of each node in the sub-graph state in the quantum communication network. Combined with the weight of each link in the quantum communication network, multi-destination conflict-free routing discovery is performed based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all sub-graph states, calculate the success probability of the multiple non-conflicting paths, and if the path meets the set reliable transmission requirements, the corresponding sub-graph state is distributed through the obtained path pair.

[0046] In one embodiment, the multi-destination routing scheme can be described as:

[0047] Each subgraph state obtained by segmentation is placed in the quantum communication network according to the node position of each node in the quantum communication network; for each subgraph state, a source node is selected to construct a copy of the subgraph state to be sent, and its node is the destination node. A priority queue is created to store the links to be added to the minimum spanning tree, and the links are links in the quantum communication network. A node set is initialized to store the nodes that have been added to the minimum spanning tree; the source node is added to the visited node set, and all its adjacent links are added to the priority queue. Repeat the following steps until all destination nodes are visited:

[0048] Take the link with the smallest weight from the priority queue and check whether the two nodes of the link are in the visited node set; if both nodes are in the node set, skip the link and continue to take the next link (that is, the link with the second smallest weight); if only one node is in the node set, add the other node to the visited node set and add the link to the minimum spanning tree;

[0049] Add all adjacent links of the newly added node to the priority queue;

[0050] Traverse the links in the minimum spanning tree, visit all nodes in turn in a path manner, and obtain an optimal route covering all destination nodes, that is, a path corresponding to a subgraph state; all subgraph states use the same process, and finally obtain multiple non-conflicting paths corresponding to all subgraph states.

[0051] Those skilled in the art can understand that, in common graph generation requests, the position overlap of the sub-graphs obtained after segmentation in the grid network is not large, and the probability of conflict between the routes of each sub-graph is low. Since the routing algorithms of each sub-graph are executed in sequence, the consumed quantum resources will be deducted before the routing of the subsequent sub-graph, so there will be no situation where the routes of two sub-graphs overlap.

[0052] In one embodiment, the source node can be selected in the following manner: cluster the nodes according to the weight of the links, select a central node so that the routing cost from the central node to the remaining nodes is minimal, and use the central node as the source node.

[0053] In one embodiment, the reliable transmission strategy can be described as: calculating the success probability of the multiple non-conflicting paths, and if the path meets the set reliable transmission requirements, optimizing the redundant quantum bits in the corresponding path so that the success probability of the optimized path is equal to the set value, and then distributing the sub-graph state.

[0054] Step 4: Restore each sub-graph state to the complete graph state through the graph state integration technology.

[0055] The solution provided by the embodiment of the present invention mainly achieves the following beneficial effects: In the existing graph distribution method, there is a lack of judgment on node resources, and in the actual quantum communication network, the limited quantum resources in the node is one of the key factors restricting the communication efficiency. Therefore, the graph distribution method is proposed based on the limited quantum resources of the integrated node, which is the only way for the graph to move towards practical application. The present invention proposes a graph segmentation method based on segmentation-integration, which divides a large-scale graph into several sub-graphs and prepares and distributes them separately, and finally restores them to the required complete graph by performing graph-related operations on some nodes. It can effectively reduce the quantum resources required for a single node when generating a large-scale graph, which helps to keep the entire quantum communication network unobstructed and avoid congestion caused by a certain node. The reliable transmission strategy and conflict-free multi-destination routing adopted by the present invention can improve the success rate of graph distribution.

[0056] In order to more clearly demonstrate the technical solution and technical effects provided by the present invention, the method provided by the embodiment of the present invention is described in detail with reference to specific embodiments below.

[0057] 1. Overall overview of the plan.

[0058] The present invention focuses on the preparation and distribution process of the special multi-particle entangled state of graph in the quantum communication network, comprehensively considers the limited node quantum resources and the quality of the distributed graph, and provides a feasible solution for effectively distributing arbitrary graphs in large-scale quantum communication networks. The present invention mainly includes two parts. The first is a graph distribution method based on a quantum communication network, that is, a method for distributing graphs on a quantum communication network, which includes a series of communication protocols related to graph storage and processing: quantum gates and quantum measurements for graph operations, management of graph distribution requests, allocation of quantum resources required for graphs, etc., combined with entanglement exchange and teleportation, multi-destination routing and reliable transmission strategies for graph distribution are designed; and a graph segmentation method under limited node resources, that is, using the idea of ​​segmentation-integration, a partial sub-graph is distributed first, and then restored to the complete graph required by the request through graph-related operations. The method of segmenting the graph will combine the resource conditions of each node, the expected transmission quality, and the additional quantum resource consumption of the integrated sub-graph to provide a strategy for segmenting the complete graph into several sub-graphs.

[0059] The solution provided by the present invention can solve the following technical problems encountered in the process of graph distribution:

[0060] (1) Existing quantum communication networks designed for single-bit transmission tasks are difficult to transmit multi-particle entangled states such as graph states.

[0061] The current quantum communication network is built based on the Bell state, a special two-qubit entangled state, and quantum teleportation technology. Entanglement exchange technology can solve the problem of long-distance quantum communication, and entanglement purification technology can solve the problem of low initial fidelity. However, when faced with entangled states of more bits, the existing network architecture and communication protocols are insufficient to support their transmission and processing due to the lack of quantum gates for processing multi-particle entangled states. Therefore, it is necessary to expand the existing network architecture and communication protocols in a targeted manner so that they have the function of processing quantum states such as graph states.

[0062] (2) Existing graph distribution methods fail to take into account the node quantum resources.

[0063] Distributing graph states between different nodes in a quantum network is limited by quantum bit resources. Existing methods lack discussion on the node quantum resource status. In actual scenarios, we often encounter situations where node resources cannot meet distribution requests. This problem needs to be avoided when designing quantum communication protocols. Therefore, it is necessary to propose a new graph state distribution and segmentation method for this situation, taking factors such as node resources into consideration to improve the success rate and quality of the distribution method.

[0064] 2. Detailed introduction of the plan.

[0065] As mentioned above, the present invention mainly includes two parts: graph distribution and graph segmentation. The following describes these two parts in detail.

[0066] 1. Graph distribution scheme based on quantum communication network.

[0067] A graph state is a general term for a type of multi-particle entangled state. The entanglement relationship between its particles can be represented by a graph G = (V, E), so it is called a graph state, denoted by |ψ G >, GHZ state and cluster state are both types of graph states; where V is the node set and E is the edge set.

[0068] (1) Preparation of graphics.

[0069] To prepare the image state, a common single quantum bit state is required. As the initial resource. To entangle multiple |+>, a controlled Z gate (CZ gate) is needed. This is a controlled gate acting on two quantum bits. When the control quantum bit is set to |0>, the target quantum bit is not operated; when the control quantum bit is set to |1>, the Z gate is executed on the target quantum bit, which has the effect of keeping |0> unchanged and changing the phase of |1>, so that |1> becomes -|1>.

[0070]

[0071] To prepare the graph state, it is necessary to apply a CZ gate once on both nodes involved in all edges. The present invention does not restrict the order of the control qubits and the target qubits, and the order of executing the CZ gates on different edges.

[0072] Therefore, the process of preparing the graph can be expressed by the following formula

[0073]

[0074] Among them, |V| represents the number of nodes in the node set V, It means taking a tensor product of all vertices in the graph and transforming all single-qubit states into a composite system, that is, a multi-qubit state. As the number of bits increases, the state space will also increase.

[0075] Other graphical operations include:

[0076] Deleting a vertex: Removing a vertex v∈V and its associated edges can be achieved by performing a Z-based Pauli measurement on the qubit of the vertex.

[0077] Local complement: After performing local complement on a vertex a, the graph structure of the resulting graph becomes That is, the neighbors of a, N a The complete graph of Overlay with the original graph G, delete the repeated edges, and keep the non-repeated ones. This can be achieved using a special operator:

[0078]

[0079] Add or delete an edge: For the edge that needs to be added or deleted, perform a CZ gate on the two qubits to which the edge belongs.

[0080] Locally fill a and then remove the vertex: This can be achieved by performing a Y-based Pauli measurement on a.

[0081] like Figure 2 The figure shows a schematic diagram of the preparation of the graph.

[0082] (2) Distribution of graphics.

[0083] In order to distribute graphs between different nodes in a quantum communication network, the present invention constructs a copy of the graph to be distributed in a certain node (called the source node), shares entangled pairs over long distances through the entanglement exchange technology, and uses quantum teleportation to send the graph quantum bits to be distributed to the corresponding nodes.

[0084] In order to ensure the success rate of quantum teleportation, the present invention needs to share high-fidelity entangled pairs between the source node that prepares the replica and multiple target nodes, so multi-destination routing and reliable transmission strategies are adopted.

[0085] like Figure 3 As shown, this is a topological diagram of a quantum communication network. Figure 4 A schematic diagram of distribution using graphical copies.

[0086] (2.1) Multi-destination routing.

[0087] In the process of graph distribution, it is necessary to establish an entanglement relationship between the preparation node and multiple destination nodes. If each source-end node is routed separately, there is a high probability of route conflicts and quantum resource grabbing. Therefore, a conflict-free multi-destination routing method is required. The present invention combines the basic parameters of quantum communication networks such as channel parameters and network topology, and performs multi-destination conflict-free routing discovery based on the minimum spanning tree algorithm to avoid route conflicts and quantum resource grabbing during the routing process.

[0088] The present invention is a quantum communication network topology G net The edges in the net (E net ) to reflect its routing cost, specific to each link Its weight It is determined by the following factors:

[0089] Link entanglement pair fidelity Since the higher the fidelity, the higher the routing quality, and the composite fidelity of multi-hop links can be approximated by the product, this metric takes the negative logarithm of the fidelity, that is,

[0090] Classical communication delay of a link That is, the delay of the link to perform classic communication. The lower the delay, the higher the routing quality. Therefore, this metric is its communication delay, that is,

[0091] Link available bandwidth Link The minimum number of available qubits between the two nodes. The larger the bandwidth, the higher the routing quality, so this metric uses an inverse function, that is,

[0092] Its weight can be expressed as follows according to the above cost:

[0093]

[0094] By modifying the coefficients k1, k2, and k3 as required, routing effects with different emphases can be achieved.

[0095] After obtaining the above weights, we can get a weighted graph G net =(V net ,E net ,W net ), the minimum spanning tree can be obtained by using Prim's algorithm. Each sub-graph obtained by segmentation is placed in the quantum communication network, so that the nodes in each sub-graph correspond to the nodes in the quantum communication network; the following is an introduction using a single sub-graph as an example.

[0096] The nodes of the prepared copies in the subgraph state are taken as the source nodes, a priority queue is created to store the links to be added to the minimum spanning tree, and a node set is initialized to store the nodes that have already been added to the minimum spanning tree. The links involved here refer to the two links of the quantum communication network, and after the subgraph state is placed in the quantum communication network, the nodes in the subgraph state correspond to the nodes in the quantum communication network. Therefore, there is no need to distinguish the nodes in the following description.

[0097] Add the source node to the set of visited nodes, add all its adjacent links to the priority queue, and repeat the following steps until all destination nodes have been visited:

[0098] Take the link with the smallest weight from the priority queue and check whether the two nodes of the link are in the visited node set; if both nodes are in the node set, skip the edge and continue to take the next link; if only one node is in the node set, add the other node to the visited node set and add the link to the minimum spanning tree;

[0099] Add all adjacent links of the newly added node to the priority queue; traverse the links in the minimum spanning tree and visit all nodes in turn in a path manner to obtain an optimal route (path) covering all destination nodes.

[0100] (2.2) Reliable transmission strategy.

[0101] For a graph distribution task, after meeting the minimum fidelity requirement F G Under the premise of G ≥ the set value (for example, 0.95), it is said that reliable transmission has been achieved. In this transmission process, the failure probability of the distribution task is mainly caused by the entanglement exchange operations of each link, so establishing a probability model of the transmission process can well implement a reliable transmission strategy.

[0102] The probability model of the present invention adopts a layer-by-layer decomposition form to decompose the success rate of the entire task into the success rate on each source-end path:

[0103]

[0104] in, represents the probability of the mth path successfully delivering n entangled pairs, and M is the number of non-conflicting paths. By traversing and summing all the cases where at least one entangled pair is successfully delivered, the success probability that meets the transmission requirements can be obtained.

[0105] Said It can be further decomposed into each single-bit link and calculated by the entanglement pair delivery status of each link in the path, which is expressed as:

[0106]

[0107] Among them, whether each path can be successfully delivered is affected by each entanglement exchange operation, p represents the success rate of a single entanglement exchange operation; k m -1 represents the number of relay nodes on the mth path, and also represents the number of times the entanglement exchange operation is performed; b m represents the minimum number of available entangled pairs on the m-th path, i.e., the bottleneck capacity of the m-th path; Then the bottleneck capacity of the mth path is exactly equal to b m probability.

[0108] The bottleneck capacity of the path is b m In the case of , the success probability is decomposed into each hop and expressed as:

[0109]

[0110] in, Indicates link The probability that the entanglement capacity is exactly i is that the entanglement capacity of each hop link is not less than b m The probability of minus the entanglement capacity of each hop link is not less than b m +1, the link bottleneck capacity is exactly b m Probability

[0111] Considering that the initial fidelity of the distributed entangled pairs may not meet the transmission requirements, the success probability of the entanglement purification operation is involved, and the decomposition can be obtained The calculation is as follows:

[0112]

[0113] Among them, q m,k Indicates link The purification success rate is the equivalent link bandwidth under purification conditions, based on the number of entangled pairs required to purify a pair that meets the fidelity requirements and the link capacity allocated by the bandwidth scheduling strategy The comprehensive calculation results are: That is, round down the integer part after division.

[0114] Therefore, according to the above decomposition model, the present invention can allocate the link capacity of the scheduling strategy Adjustments are made to meet reliable transmission requirements with minimal resource consumption.

[0115] Based on the above introduction, the main process of this part can be described as follows: First, the graph state transmission success probability P is calculated based on the maximum link capacity. G Calculation, when the success probability P G When the reliable transmission requirement is exceeded, the allocated link capacity is reduced accordingly. Until its success probability just meets the reliable transmission requirements, that is, reliable transmission can be achieved with minimal resource consumption.

[0116] 2. Graph partitioning scheme under limited node resources.

[0117] If faced with a larger graph, a single node needs to consume more quantum bit resources to prepare and distribute the graph copy. Therefore, the present invention divides the larger graph G = (V, E) into several sub-graphs G i =(V i ,E i ) to distribute the graph states respectively, and then use the graph state operation to integrate the sub-graph states and restore the complete graph state required by the request. The edge that needs to be integrated can be regarded as a cut E of the original graph G cut =E-∑E i The present invention also provides each edge e according to the network parameters i ∈E gives weight W(e i ), to reflect the cost of its distribution graph, the network parameters involved here are:

[0118] Link available bandwidth Link e i The minimum number of available quantum bits between the two nodes. The smaller the bandwidth, the greater the cost of distributing the graph state, so this metric uses an inverse function, that is,

[0119] Those skilled in the art will understand that the nodes (i.e., quantum bits) of the graph state are associated with their positions in the entire quantum communication network, so the nodes in the graph state ultimately need to be actually distributed to the nodes in the quantum communication network, thereby being associated with the number of available quantum bits of the nodes in the quantum communication network. Generally speaking, in addition to the graph structure containing the graph state, the graph state distribution request also includes the positions of the nodes in the graph state in the entire quantum communication network. For example, in the graph structure storing the graph state, there is a node numbered 3, which corresponds to the node at position (3, 4) in the quantum communication network at the same time, and the remaining nodes in the graph state will also correspond to a node in an actual quantum communication network.

[0120] Link entanglement pair fidelity Since the higher the fidelity, the higher the quality of graph distribution, and the composite fidelity of multi-hop links can be approximated by the product, this metric takes the negative logarithm of the fidelity, that is,

[0121] Classic communication delay of the link That is, the delay of the link to perform classical communication. The lower the delay, the higher the efficiency of graph distribution. Therefore, this metric is its communication delay, that is,

[0122] Based on the above introduction, each e i ∈E assigned weight W(e i ), expressed as:

[0123]

[0124] in, Represents edge e i The entanglement pair fidelity, Represents edge e i Communication delay; Represents edge e i The available bandwidth of edge e i The minimum number of available quantum bits between the two nodes above; E represents the edge set in the network topology G, and k1, k2, k3 are set coefficients.

[0125] The segmentation is then calculated using the Normalized cut method:

[0126] (1) Calculate the degree matrix D and weight matrix W of the graph, and then calculate the Laplacian matrix L = DW of the graph.

[0127] (2) Calculate the eigenvector of the Laplacian matrix and use it for K-means clustering to segment the graph into different regions. Each segmentation method obtains two regions, and the node sets in the two regions are recorded as A and B respectively.

[0128] (3) For each segmentation method, the normalized cut value of each region is calculated separately Among them, cut(A,B) represents the sum of the weights of the edges between A and B, V represents the intersection of A and B, assoc(A,V) is the sum of the weights of all nodes in A to V, and assoc(B,V) is the sum of the weights of all nodes in B to V.

[0129] (4) Select the segmentation result corresponding to the segmentation method with the minimum normalized cut value.

[0130] (5) After the segmentation is obtained, the maximum number of bits consumed by a single node under the current segmentation is calculated. node ), the estimated time required to perform the distribution operation is T estimate And the number of quantum gates N expected to be used to distribute the graph gate , ensure that the node has enough resources to complete the distribution and the operation time does not exceed the quantum bit decoherence time, otherwise, cut the graph again according to the above method.

[0131] After segmentation, use the scheme described above to distribute them by subgraph state, then distribute the entangled pairs at the positions where the subgraph states need to be integrated, and use graph state operations to integrate them:

[0132] (1) Use CZ gates to connect each sub-graph state with the entangled pair to form a larger graph state.

[0133] (2) By performing a Y-based Pauli measurement on the quantum bit at the position that originally belonged to the entangled pair, the state can be restored to the state required by the request.

[0134] like Figure 5 As shown, this is a schematic diagram of the segmentation and integration of graph states.

[0135] 3. Example introduction.

[0136] 1. Graphic segmentation.

[0137] After receiving a request to distribute a graph state, the quantum communication network will generate a network topology G according to the remaining quantum bit resources of each node in the current network and the parameters of each quantum channel. net Each edge in the After obtaining the edge weights of the quantum communication network topology, firstly, according to the graph state required by the request, the edge E in the graph state topology G is also assigned a corresponding weight W (e i ′ ),e i ′ ∈E, then the graph segmentation algorithm can be performed.

[0138] First, the weight matrix W and degree matrix D are calculated based on the graph topology G. Then, the Laplacian matrix is ​​calculated based on the weight matrix and degree matrix, and K-means clustering is performed. The normalized cut value Ncut(A,B) of each region is calculated. The segmentation with the minimum normalized cut value is selected as the result, and the maximum number of bits consumed by a single node (max(Cost)) is calculated. node ) to determine whether the current segmentation can meet the requirements. If not, continue to segment the sub-graph until the requirements are met.

[0139] 2. Graphic distribution.

[0140] For each sub-graph state that has been divided, it is placed in the quantum communication network. The node with the most abundant node resources and the shortest comprehensive distance to the remaining nodes in the sub-graph state is used as the source node, and the rest are used as the target nodes. The minimum spanning tree algorithm is used for multi-destination routing to find multiple non-conflicting paths.

[0141] Then calculate the success probability P according to the obtained path G , if P G Meet the requirements of reliable transmission, that is, P G ≥0.95, that is, the redundant quantum bits can be appropriately optimized so that their success probability just meets the requirements of reliable transmission, thereby saving quantum bit resources.

[0142] According to the above distribution strategy, the source node first uses the graph-state-related quantum gates to prepare the sub-graph state copies to be distributed, and then each relay node and the target node distributes the entangled pairs over long distances using the entanglement exchange technology according to the distribution strategy, and finally distributes the sub-graph state copies to each node through quantum teleportation technology; among them, the relay nodes here are the nodes in the path belonging to the quantum communication network, and they are mainly used to perform entanglement exchange operations.

[0143] In an embodiment of the present invention, the distribution of subgraph states uses the technology of quantum teleportation, which requires the sender and the receiver to share a pair of entangled pairs. However, in a multi-hop link, the entangled pair cannot be directly shared through a physical channel, so it is necessary to perform entanglement exchange at the relay node to share the entangled relationship with nodes that are not directly connected by a physical channel. The work done by the present invention is to first prepare a shared entangled pair between all adjacent relay nodes (connected by physical channels), and perform entanglement exchange operations on all relay nodes, so that the nodes at both ends can share a pair of entangled pairs. After the source node and the destination node share a pair of entangled pairs, the Bell state joint measurement is performed on the quantum bit to be sent of the source node and one of the shared entangled pairs held by the source node, and the measurement result is sent to the receiving node through a classical channel. The receiving node can restore the quantum bit to be sent using the X gate and the Z gate based on the information obtained by the measurement. What the present invention does is to use a bit in the graph state held by the source node and the entangled pair used for teleportation to transmit its state to the receiving node. This operation will not destroy the entanglement relationship of the original graph state. Therefore, the present invention performs this operation on the quantum bits that need to be distributed in the graph state copy, and distributes them to each destination node.

[0144] 3. Graphic integration.

[0145] After obtaining each sub-graph state, the graph state integration technology can be used to restore each sub-graph state to the complete graph state required by the request.

[0146] In an embodiment of the present invention, in the aforementioned graph splitting operation, the nodes to which the edges cut off between the sub-graphs belong, for example, a complete connected graph is split into two unconnected sub-graphs, then at least one edge in the middle is abandoned, and therefore, integration requires the edges cut off due to the splitting operation (that is, the entanglement relationship of the quantum bits in the graph) to be reestablished, and here it is necessary to share a pair of entangled pairs between the two nodes to which this edge belongs, and then connect the quantum bits of the two sub-graphs at their respective nodes with one of the entangled pairs at the node using a CZ gate, so that the entangled pair also becomes part of the graph, and then perform Y-based Pauli measurements on the two quantum bits that originally belonged to the entangled pair, respectively, so that the edges discarded when the graph is cut can be reestablished, and after all the edges that need to be restored are restored through the graph operation, the integration of the sub-graphs is completed.

[0147] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by means of software plus necessary general hardware platforms. Based on such understanding, the technical solutions of the above embodiments can be embodied in the form of software products, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.), including several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0148] Embodiment 2

[0149] The present invention also provides a graph segmentation and distribution system based on a quantum communication network, which is mainly used to implement the method provided in the above embodiment, such as Figure 6 As shown, the system mainly includes:

[0150] A link weight assignment unit is used to assign corresponding weights to each link according to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link;

[0151] A graph state segmentation unit is used to receive a graph state distribution request, which carries a complete graph state to be distributed and the node position of each node in the graph state in the quantum communication network; for the complete graph state to be distributed, if the resource consumption required for distribution exceeds the set requirements, the complete graph state is segmented into a plurality of sub-graph states so that the resource consumption required for distribution of each sub-graph state does not exceed the set requirements;

[0152] A graph distribution unit based on a quantum communication network is used to place each sub-graph obtained by segmentation into the quantum communication network, perform multi-destination conflict-free routing discovery based on a minimum spanning tree algorithm in combination with the weights of each link in the quantum communication network, obtain multiple non-conflicting paths corresponding to all sub-graphs, calculate the success probabilities of the multiple non-conflicting paths, and distribute the corresponding sub-graph through the obtained path pair if the path meets the set reliable transmission requirements;

[0153] The graph state integration unit is used to restore each sub-graph state to the complete graph state through the graph state integration technology.

[0154] Considering that the main technical details involved in the above system have been introduced in detail in the previous embodiments, they will not be repeated here.

[0155] Technical personnel in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional modules is used as an example. In actual applications, the above-mentioned functions can be assigned to different functional modules as needed, that is, the internal structure of the system can be divided into different functional modules to complete all or part of the functions described above.

[0156] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A graph segmentation and distribution method based on quantum communication network, characterized in that: include: According to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link, a corresponding weight is assigned to each link; Receive a graph state distribution request, which carries the complete graph state to be distributed and the node position of each node in the graph state in the quantum communication network; for the complete graph state to be distributed, if the resource consumption required for distribution exceeds the set requirements, divide the complete graph state into several sub-graph states so that the resource consumption required for distribution of each sub-graph state does not exceed the set requirements; Each sub-graph state obtained by segmentation is placed in the quantum communication network respectively, and the multi-destination conflict-free routing discovery is performed based on the minimum spanning tree algorithm in combination with the weights of each link in the quantum communication network, so as to obtain multiple non-conflicting paths corresponding to all sub-graph states, calculate the success probability of the multiple non-conflicting paths, and distribute the corresponding sub-graph state through the obtained path pair if the path meets the set reliable transmission requirements; Each sub-graph state is restored to the complete graph state through the graph state integration technology.

2. According to claim 1, a graph segmentation and distribution method based on a quantum communication network is characterized in that: The step of assigning corresponding weights to each link according to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link includes: The network topology of the quantum communication network is denoted as G net , for each of its links Assign weight It is expressed as: in, Indicates link The entanglement pair fidelity, Indicates link Communication delay; Indicates link The available bandwidth of the link The minimum number of available qubits in the last two nodes; E net Represents the network topology G net The link set in , k1, k2, k3 are the setting coefficients.

3. According to claim 1, a graph segmentation and distribution method based on a quantum communication network is characterized in that: The step of dividing the complete graph state into a plurality of sub-graph states so that the resource consumption required for distributing each sub-graph state does not exceed the set requirement comprises: Assign a weight to each edge in the complete graph to obtain a weight matrix W of the complete graph, and calculate a Laplace matrix in combination with the degree matrix of the complete graph; Calculate the eigenvector of the Laplacian matrix and use it for K-means clustering to divide the graph into different regions. Each division method obtains two regions, and the node sets in the two regions are recorded as A and B respectively. For each segmentation method, the normalized cut value of each region is calculated separately Among them, cut(A,B) represents the sum of the weights of the edges between A and B, V represents the intersection of A and B, assoc(A,V) is the sum of the weights of all nodes in A to V, and assoc(B,V) is the sum of the weights of all nodes in B to V; Select the segmentation result corresponding to the segmentation method with the minimum normalized cutting value, and determine whether the resource consumption required for the distribution of each sub-graph state in the segmentation result does not exceed the set requirements. If so, the segmentation is completed; if not, continue the segmentation until the resource consumption required for the distribution of each sub-graph state in the segmentation result does not exceed the set requirements.

4. According to claim 1, a graph segmentation and distribution method based on a quantum communication network is characterized in that: The step of assigning a weight to each edge in the complete graph comprises: The network topology of the complete graph is denoted as G, and each edge e i ∈E gives weight W(e i ), expressed as: in, Represents edge e i The entanglement pair fidelity, Represents edge e i Communication delay; Represents edge e i The available bandwidth of edge e i The minimum number of available quantum bits between the two nodes above; E represents the edge set in the network topology G, and k1, k2, k3 are set coefficients.

5. According to claim 1, a graph segmentation and distribution method based on a quantum communication network is characterized in that: Each sub-graph state obtained by segmentation is placed in the quantum communication network respectively, and the weight of each link in the quantum communication network is combined to perform conflict-free routing discovery for multi-destination nodes based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths, including: Each subgraph state obtained by segmentation is placed in the quantum communication network respectively; for each subgraph state, a source node is selected to construct a copy of the subgraph state to be sent, and its node is the destination node. A priority queue is created to store the links to be added to the minimum spanning tree, and the links are links in the quantum communication network. A node set is initialized to store the nodes that have been added to the minimum spanning tree; the source node is added to the visited node set, and all its adjacent links are added to the priority queue. Repeat the following steps until all destination nodes are visited: Take the link with the smallest weight from the priority queue and check whether the two nodes of the link are in the visited node set; if both nodes are in the node set, skip the link and continue to take the next link; if only one node is in the node set, add the other node to the visited node set and add the link to the minimum spanning tree; Add all adjacent links of the newly added node to the priority queue; Traverse the edges in the minimum spanning tree, visit all nodes in turn according to the path, and get an optimal route covering all destination nodes, that is, a path corresponding to a subgraph state; All sub-graph states adopt the same process, and finally obtain multiple non-conflicting paths corresponding to all sub-graph states.

6. The method for graph segmentation and distribution based on a quantum communication network according to claim 1, characterized in that: The success probability of calculating the multiple non-conflicting paths is expressed as: in, represents the probability that the mth path successfully delivers n entangled pairs, and M is the number of the multiple non-conflicting paths.

7. The method for graph segmentation and distribution based on a quantum communication network according to claim 8, characterized in that: Said It is calculated by the entanglement pair delivery of each link in the path, expressed as: Where p represents the success rate of a single entanglement swap operation; k m -1 represents the number of relay nodes on the mth path, and also represents the number of times the entanglement exchange operation is performed; b m represents the minimum number of available entangled pairs on the m-th path, i.e., the bottleneck capacity of the m-th path; Then the bottleneck capacity of the mth path is exactly equal to b m probability; The bottleneck capacity of the path is b m In the case of , the success probability is decomposed into each hop and expressed as: in, Indicates link The probability that the entanglement capacity is exactly i is that the entanglement capacity of each hop link is not less than b m The probability of minus the entanglement capacity of each hop link is not less than b m +1, the link bottleneck capacity is exactly b m Probability The calculation is as follows: Among them, q m,k Indicates link The purification success rate is the equivalent link bandwidth under purified conditions.

8. The method for graph segmentation and distribution based on a quantum communication network according to claim 7, characterized in that: Also includes: If the path meets the set reliable transmission requirements, the redundant quantum bits in the corresponding path are optimized so that the success probability of the optimized path is equal to the set value; The optimization of the redundant quantum bits in the corresponding path includes: reducing the link capacity allocated in the corresponding path The link capacity Used to calculate the equivalent link bandwidth under purification conditions in, Represents the number of entangled pairs required to purify a pair of entangled pairs with the required fidelity.

9. The method for graph segmentation and distribution based on a quantum communication network according to claim 1, characterized in that: The distributing corresponding sub-graph states through the obtained path pair includes: The source node in the path uses graph-state-related quantum gates to prepare sub-graph state copies to be distributed, and then each relay node and target node distributes entangled pairs using entanglement exchange technology according to the distribution strategy, and distributes the sub-graph state copies to each node through quantum teleportation technology; among them, the relay node is a node in the path that belongs to the quantum communication network.

10. A graph segmentation and distribution system based on quantum communication network, characterized in that: For implementing the method described in any one of claims 1 to 9, the system comprises: A link weight assignment unit is used to assign corresponding weights to each link according to the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link; A graph state segmentation unit is used to receive a graph state distribution request, which carries a complete graph state to be distributed and the node position of each node in the graph state in the quantum communication network; for the complete graph state to be distributed, if the resource consumption required for distribution exceeds the set requirements, the complete graph state is segmented into a plurality of sub-graph states so that the resource consumption required for distribution of each sub-graph state does not exceed the set requirements; A graph distribution unit based on a quantum communication network is used to place each sub-graph obtained by segmentation into the quantum communication network, perform multi-destination conflict-free routing discovery based on a minimum spanning tree algorithm in combination with the weights of each link in the quantum communication network, obtain multiple non-conflicting paths corresponding to all sub-graphs, calculate the success probabilities of the multiple non-conflicting paths, and distribute the corresponding sub-graph through the obtained path pair if the path meets the set reliable transmission requirements; The graph state integration unit is used to restore each sub-graph state to the complete graph state through the graph state integration technology.

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