A method and system for graph segmentation and distribution based on quantum communication networks

Abstract

This invention discloses a graph segmentation and distribution method and system based on quantum communication networks. Taking into account the limited quantum resources of nodes and the quality of distributed graphs, it provides a feasible solution for effectively distributing arbitrary graphs in large-scale quantum communication networks. A segmentation-integration-based graph segmentation scheme is proposed, which divides a large-scale graph into several sub-graphs for separate preparation and distribution. Then, by performing graph-related operations on some nodes, the desired complete graph is restored. This effectively reduces the quantum resources required by a single node when generating large-scale graphs, helping to maintain the smooth operation of the entire quantum communication network and avoiding congestion caused by a single node. Furthermore, this invention employs a reliable transmission strategy and conflict-free multi-destination routing, thereby improving the success rate of graph distribution.

Description

Technical Field

[0001] This invention relates to the field of quantum communication technology, and in particular to a graph segmentation and distribution method and system based on quantum communication networks. Background Technology

[0002] Quantum communication technology is a highly valuable research area in quantum information research, providing an absolutely secure communication method at the physical level. Utilizing quantum superposition and entanglement effects, and based on the principles of uncertainty, measurement collapse, and no-cloning, it offers security guarantees that cannot be eavesdropped on or computationally cracked. It mainly focuses on two directions: quantum teleportation and quantum key distribution. Quantum teleportation is based on the distribution of entangled pairs and joint measurement of Bell states, supplemented by classical channels, to achieve the transmission of quantum states. Quantum key distribution, on the other hand, uses the transmission measurement of quantum superposition states to achieve quantum key sharing between communicating parties, thus realizing unconditionally and absolutely secure confidential communication. However, at long distances, lossy quantum channels pose significant challenges to the transmission of quantum states; the fidelity decreases with increasing distance. Due to the no-cloning principle, quantum states cannot be copied or amplified for retransmission. Therefore, communication using only quantum teleportation has a very limited transmission distance. To address this, entanglement swapping technology offers a method for achieving long-distance quantum state transmission: by adding a repeater and performing entanglement swapping at the repeater, the transmission distance of qubits in lossy channels can be shortened, and more qubit resources can be used to achieve longer-distance quantum teleportation. This technology is also the main means to achieve long-distance quantum communication and large-scale quantum communication networks.

[0003] Graph states are a special class of multi-particle entangled quantum states, representing the entanglement relationships between qubits in the form of a graph. GHZ (Greenberger-Horne-Zeilinger, multi-particle maximum entanglement) states and cluster states are both types of graph states. Networks built using these more complex entangled states between nodes can achieve unique functionalities compared to networks using Bell states for quantum communication, such as quantum secret sharing, measurement-based quantum computing, quantum error correction coding, and quantum multi-party secure computation, making them a very important quantum resource. However, due to the complexity of entanglement relationships, manipulating graph states requires more complex quantum gates. Therefore, effectively preparing and distributing graph states is the primary challenge in utilizing this important quantum resource. Summary of the Invention

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

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A graph state segmentation and distribution method based on quantum communication networks includes:

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

[0008] Receive a graph distribution request, which carries the complete graph to be distributed and the node positions 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 the distribution of each sub-graph does not exceed the set requirements.

[0009] Each subgraph obtained from the segmentation is placed into the quantum communication network. Combining the weights of each link in the quantum communication network, a multi-destination conflict-free route discovery is performed based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all subgraphs. The success probability of the multiple non-conflicting paths is calculated. If a path meets the set reliable transmission requirements, the corresponding subgraph is distributed through the obtained path pair.

[0010] The graph integration technique is used to restore each sub-graph to the complete graph.

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

[0012] The link weighting unit is used to assign corresponding weights to each link based on the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link.

[0013] The graph segmentation unit is used to receive a graph distribution request, which carries the complete graph to be distributed and the node positions of each node in the graph in the quantum communication network. If the resource consumption required for the distribution of the complete graph exceeds the set requirements, the complete graph is segmented into several sub-graphs so that the resource consumption required for the distribution of each sub-graph does not exceed the set requirements.

[0014] The graph distribution unit based on the quantum communication network is used to put each subgraph obtained by segmentation into the quantum communication network. Combining the weights of each link in the quantum communication network, it performs multi-destination conflict-free route discovery based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all subgraphs. It calculates the success probability of the multiple non-conflicting paths. If a path meets the set reliable transmission requirements, it distributes the corresponding subgraph through the obtained path.

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

[0016] As can be seen from the technical solution provided by the present invention, a graph segmentation scheme based on segmentation-integration is proposed. This scheme divides a large-scale graph into several sub-graphs, prepares and distributes them separately, and then restores the desired complete graph by performing graph-related operations on some nodes. This effectively reduces the quantum resources required by a single node when generating a large-scale graph, helps maintain the smooth operation of the entire quantum communication network, and avoids congestion caused by a single node. At the same time, the present invention also adopts a reliable transmission strategy and conflict-free multi-destination routing, thereby improving the success rate of graph distribution. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

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

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

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

[0021] Figure 4 This is a schematic diagram illustrating the distribution using graph replicas provided in an embodiment of the present invention;

[0022] Figure 5 This is a schematic diagram of the segmentation and integration of graph states provided in an embodiment of the present invention;

[0023] Figure 6 This is a schematic diagram of a graph state segmentation and distribution system based on a quantum communication network, provided as an embodiment of the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0025] First, the following explanations are provided for the terms that may be used in this article:

[0026] The terms “including,” “comprising,” “containing,” “having,” or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, “including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.)” should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0027] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0028] The following is a detailed description of a graph state segmentation and distribution method and system based on a quantum communication network provided by this invention. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Where specific conditions are not specified in the embodiments of this invention, they shall be performed according to conventional conditions in the art or conditions recommended by the manufacturer. Reagents or instruments used in the embodiments of this invention, unless otherwise specified by the manufacturer, are all conventional products that can be purchased commercially.

[0029] Example 1

[0030] This invention provides a graph state segmentation and distribution method 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 in the quantum communication network.

[0032] In this embodiment of the invention, each link is assigned a corresponding weight based on 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] Let the network topology of the quantum communication network be denoted as G. net For each of its links Assign weights Represented as:

[0035]

[0036] in, Indicates link Entanglement affects fidelity. Indicates link Communication latency; Indicates link Available bandwidth, i.e., link bandwidth The minimum number of usable qubits between the two nodes; E net Represents the network topology G net The set of links in the equation, where k1, k2, and k3 are set coefficients.

[0037] Step 2, graph segmentation.

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

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

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

[0041] (2) Calculate the eigenvectors of the Laplacian matrix and use the eigenvectors for K-means clustering to divide the graph into different regions. Each division method yields two regions, and the node sets in the two regions are denoted as A and B, respectively.

[0042] (3) For each segmentation method, calculate the normalized cut value for each region separately. Here, 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 cut value, and determine whether the resource consumption required for the distribution of each sub-graph in the segmentation result does not exceed the set requirements. If yes, the segmentation is completed; if no, continue the segmentation until the resource consumption required for the distribution of each sub-graph in the segmentation result does not exceed the set requirements.

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

[0045] In this embodiment of the invention, each sub-graph obtained by segmentation is placed into the quantum communication network according to the node positions of each node in the sub-graph in the quantum communication network. Combining the weights of each link in the quantum communication network, a multi-destination conflict-free route discovery is performed based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all sub-graphs. The success probability of the multiple non-conflicting paths is calculated. If a path meets the set reliable transmission requirements, the corresponding sub-graph is distributed through the obtained path pair.

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

[0047] Each subgraph obtained from the segmentation is placed into the quantum communication network according to the node positions of each node in the quantum communication network. For each subgraph, a source node is selected to construct a copy of the subgraph 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, which are the 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 set of visited nodes, and all its adjacent links are added to the priority queue. The following steps are repeated until all destination nodes have been visited:

[0048] Take the link with the smallest weight from the priority queue and check if both nodes of the link are in the set of visited nodes. If both nodes are in the set, skip the link and continue to the next link (i.e., the link with the second smallest weight). If only one node is in the set, add the other node to the set of visited nodes 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 sequence according to the path, and obtain an optimal route that covers all destination nodes, which is the path corresponding to a subgraph. All subgraphs adopt the same process, and finally obtain multiple non-conflicting paths corresponding to all subgraphs.

[0051] Those skilled in the art will understand that in common graph generation requests, the subgraphs obtained after segmentation have little overlap in their positions within the lattice network, and the probability of conflict between the routes of each subgraph is low. Since the routing algorithms of each subgraph are executed sequentially, the quantum resources already consumed will be deducted before the routing of subsequent subgraphs, so there will be no situation where the routes of two subgraphs overlap.

[0052] In one embodiment, the source node can be selected by clustering the nodes according to the link weights and selecting a central node, so that the routing cost from the central node to the other nodes is minimized, and the central node is selected as the source node.

[0053] In one embodiment, the reliable transmission strategy can be described as follows: calculate the success probability of the plurality of non-conflicting paths; if a path meets the set reliable transmission requirements, optimize the redundant qubits in the corresponding path so that the success probability of the optimized path is equal to the set value, and then distribute the sub-graph state.

[0054] Step 4: Use graph integration technology to restore each sub-graph to the complete graph.

[0055] The solution provided by this invention mainly achieves the following beneficial effects: Existing graph distribution methods lack assessment of node resources, while in practical quantum communication networks, the limited quantum resources within nodes are one of the key factors restricting communication efficiency. Therefore, proposing a graph distribution method that integrates the limited quantum resources of nodes is an essential path for graphs to become practical. This invention proposes a graph segmentation method based on segmentation-integration, which divides a large-scale graph into several sub-graphs for separate preparation and distribution. Finally, by performing graph-related operations on some nodes, it restores the desired complete graph. This effectively reduces the quantum resources required by a single node when generating a large-scale graph, helping to maintain the smooth operation of the entire quantum communication network and avoiding congestion caused by a single node. Furthermore, the reliable transmission strategy and conflict-free multi-destination routing adopted in this invention can improve the success rate of graph distribution.

[0056] To more clearly demonstrate the technical solution and its effects provided by the present invention, the method provided by the embodiments of the present invention will be described in detail below with reference to specific examples.

[0057] I. Overall Overview of the Plan

[0058] This invention focuses on the preparation and distribution process of graph states—a special type of multi-particle entangled state—in quantum communication networks. Taking into account the limited quantum resources of nodes and the quality of distributed graph states, it provides a feasible solution for the efficient distribution of arbitrary graph states in large-scale quantum communication networks. The invention mainly comprises two parts: first, a graph state distribution method based on quantum communication networks, which includes a series of communication protocols related to graph state storage and processing: quantum gates and quantum measurements for graph state operations, management of graph state distribution requests, allocation of quantum resources required for graph states, etc., and designs multi-destination routing and reliable transmission strategies for graph state distribution by combining entanglement swapping and teleportation; second, a graph state partitioning method under the condition of limited node resources, which adopts the partition-integration approach, designing a method to first distribute partial sub-graph states, and then recover the requested complete graph state through graph-related operations. The graph state partitioning method considers factors such as the resource situation of each node, the expected transmission quality, and the additional quantum resource consumption of integrating sub-graph states, providing a strategy to partition the complete graph state into several sub-graph states.

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

[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] Current quantum communication networks are built upon Bell states—a special type of two-qubit entangled state—and quantum teleportation technology. Entanglement swapping can solve the problem of long-distance quantum communication, while entanglement purification can address the issue of low initial fidelity. However, when faced with entangled states involving more qubits, existing network architectures and communication protocols lack quantum gates for handling multi-particle entangled states, making them insufficient for transmission and processing. Therefore, it is necessary to specifically extend existing network architectures and communication protocols to enable them to handle graph states and similar quantum states.

[0062] (2) Existing graph distribution methods fail because they do not adequately consider the quantum resources of nodes.

[0063] In quantum networks, the distribution of graph states between different nodes is limited by the availability of qubits. Current methods lack consideration of node quantum resource states, frequently leading to situations where node resources cannot meet distribution requests. This is a problem that must be avoided when designing quantum communication protocols. Therefore, new graph state distribution and partitioning methods are needed to address this issue, incorporating factors such as node resources to improve the success rate and quality of distribution.

[0064] II. Detailed introduction of the plan.

[0065] As previously mentioned, this invention mainly comprises two parts: graph distribution and graph segmentation. The following sections will provide a detailed description of each part.

[0066] 1. A graph distribution scheme based on quantum communication networks.

[0067] A graph state is a general term for a class of multi-particle entangled states, in which the entanglement relationship between particles can be represented by a graph G = (V, E), hence the name graph state, denoted as |ψ G > GHZ state and cluster state are both types of graph states; where V is the set of nodes and E is the set of edges.

[0068] (1) Preparation of graph states.

[0069] Preparing a pattern state requires the use of a common single-qubit state. As the initial resource, to entangle multiple |+>, a controlled Z-gate (CZ gate) is needed. This is a controlled gate that operates on two qubits. When the control qubit is set to |0>, no operation is performed on the target qubit; when the control qubit is set to |1>, the Z-gate is executed on the target qubit, which keeps |0> unchanged and changes the phase of |1>, making |1> become -|1>.

[0070]

[0071] To prepare the graph state, a CZ gate needs to be applied once to both nodes involved in every edge. This invention does not restrict the order of the control qubit and the target qubit, nor the order in which the CZ gates are applied to different edges.

[0072] Therefore, the process of preparing a pattern can be represented by the following formula.

[0073]

[0074] Where |V| represents the number of nodes in the node set V. This means that by performing a tensor product on all vertices in the graph, all single-qubit states are transformed into composite systems, or multi-qubit states. As the number of qubits increases, the state space also increases.

[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-basis Pauli measurement on the qubits of that vertex.

[0077] Local Completion: After performing local completion on a vertex 'a', the graph structure of the resulting graph becomes... That is, the neighbor N of a a Complete map Overlay the graph G onto the original graph, removing duplicate edges and retaining unique edges. This can be achieved using a special operator:

[0078]

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

[0080] To perform local patching on a and then remove the vertex, you can perform Y-based Pauli measurement on a.

[0081] like Figure 2 The diagram shown is a schematic diagram of pattern preparation.

[0082] (2) Distribution of graph states.

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

[0084] To ensure the success rate of quantum teleportation, this invention requires sharing high-fidelity entangled pairs between the source node that prepares the replica and multiple target nodes. Therefore, multi-destination routing and reliable transmission strategies are adopted.

[0085] like Figure 3 The diagram shown is a topological schematic of a quantum communication network. Figure 4 This is a schematic diagram illustrating the distribution using graph replicas.

[0086] (2.1) Multi-destination routing.

[0087] In the graph distribution process, entanglement needs to be established between the preparation node and multiple destination nodes. If each source-end node routes separately, there is a high probability of route conflicts and quantum resource contention. Therefore, a conflict-free multi-destination routing method is needed. This invention combines basic quantum communication network parameters such as channel parameters and network topology, and uses the minimum spanning tree algorithm to discover conflict-free multi-destination routes to avoid route conflicts and quantum resource contention during the routing process.

[0088] This invention relates to quantum communication network topology G. net The edges in the middle are assigned weights W. net (E net This reflects the routing cost, down to each individual link. Its weight It is determined by the following factors:

[0089] Link entanglement affects fidelity Since higher fidelity corresponds to higher routing quality, and the composite fidelity of multi-hop links can be approximated by a product, this metric is calculated by taking the negative logarithm of the fidelity.

[0090] Classical communication delay of a link This refers to the latency of classic communication on this link. The lower the latency, the higher the routing quality; therefore, this metric represents its communication latency.

[0091] Link available bandwidth i.e., link The minimum number of available qubits between the two nodes. Higher bandwidth generally equates to higher routing quality; therefore, this metric uses an inverse proportionality function.

[0092] Its weights, based on the aforementioned costs, can be expressed as:

[0093]

[0094] By modifying the undetermined coefficients k1, k2, and k3 according to requirements, different routing effects with different emphases can be achieved.

[0095] After obtaining the above weights, a weighted graph G can be obtained. net =(V net E net W net The minimum spanning tree can be obtained using Prim's algorithm. Each subgraph obtained from the partitioning is then placed into the quantum communication network, so that the nodes in each subgraph correspond to the nodes in the quantum communication network; the following description uses a single subgraph as an example.

[0096] The node that makes a copy in the subgraph is taken as the source node. A priority queue is created to store the links to be added to the minimum spanning tree. A node set is initialized to store the nodes that have been added to the minimum spanning tree. The links involved here refer to the two types of links in the quantum communication network. After the subgraph is put into the quantum communication network, the nodes in the subgraph correspond to the nodes in the quantum communication network. Therefore, the following description of the nodes does not need to be distinguished.

[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 if both nodes of the link are in the set of visited nodes. If both nodes are in the set, skip the edge and continue to the next link. If only one node is in the set, add the other node to the set of visited nodes 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 sequence according to the path to obtain an optimal route (path) that covers all destination nodes.

[0100] (2.2) Reliable transmission strategy.

[0101] For a graph distribution task, the minimum fidelity requirement F after distribution must be met. G Under the premise that its distribution scheme has a success rate P G A value ≥ a set threshold (e.g., 0.95) indicates that reliable transmission has been achieved. In this transmission process, the failure probability of task distribution is mainly due to the entanglement and switching operations of each link; therefore, establishing a probabilistic model of the transmission process can effectively implement a reliable transmission strategy.

[0102] The probability model of this invention adopts a layer-by-layer decomposition approach, breaking down the success rate of the entire task into the success rates of each source-end path:

[0103]

[0104] in, Let represent the probability that the m-th path successfully delivers n entangled pairs, where M is the number of non-conflicting paths. The success probability of satisfying the transmission requirements can be obtained by summing the probabilities of all cases where at least one entangled pair is successfully delivered.

[0105] The To further decompose this into each single-bit link, the delivery status of the entanglement pairs of each link in the path is calculated, as follows:

[0106]

[0107] Whether each path can be successfully delivered depends on each entanglement swap operation, where p represents the success rate of a single entanglement swap operation; k m -1 represents the number of relay nodes on the m-th path, and also represents the number of entanglement swap operations performed; b m This represents the minimum number of entangled pairs available on the m-th path, which is the bottleneck capacity of the m-th path. Then the bottleneck capacity of the m-th path is exactly equal to b. m The probability of.

[0108] The bottleneck capacity of the path is b m In this case, 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 given by the fact that the entanglement capacity of each hop link is no less than b. m The probability minus the entanglement capacity per hop is no less than b. m With a probability of +1, the bottleneck capacity of the link is exactly b. m probability

[0111] Considering that the initial fidelity of distributing entangled pairs may not meet the transmission requirements, the success probability of the entanglement purification operation can be decomposed into... The calculation is as follows:

[0112]

[0113] Where, q m,k Indicates link The purification success rate, It is the equivalent link bandwidth under purification conditions, based on the number of entangled pairs required to purify a pair of entangled pairs that meet the fidelity requirements. and the link capacity allocated by the bandwidth scheduling strategy. Based on comprehensive calculations, That is, after dividing, take the integer part downwards.

[0114] Therefore, based on the above decomposition model, the present invention can allocate link capacity according to 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, calculate the probability P of successful graph transmission based on the maximum link capacity. G The calculation, when the success probability P G When the reliable transmission requirements are exceeded, the allocated link capacity will be reduced accordingly. Until its success probability just meets the requirements for reliable transmission, that is, reliable transmission can be achieved with minimal resource consumption.

[0116] 2. Graph segmentation scheme under conditions of limited node resources.

[0117] If a large graph state is encountered, preparing and distributing a copy of the graph state by a single node would consume a significant amount of qubit resources. Therefore, this invention divides the large graph state G = (V, E) into several sub-graph states G. i =(V i E i The graph states are distributed separately, and then graph operations are used to integrate the various subgraphs to restore the complete graph state required by the request. Edges requiring integration operations can be viewed as cuts E of the original graph G. cut =E-∑E i This invention also assigns each edge e based on network parameters. i Assign weight W(e) to ∈E i To reflect the cost of its distribution graph, the network parameters involved here are:

[0118] Link available bandwidth That is, link e i The minimum number of usable qubits between the two nodes. The smaller the bandwidth, the greater the cost of distributing graphical states; therefore, this metric uses an inverse proportional function, i.e.

[0119] Those skilled in the art will understand that a node (i.e., a qubit) in a graph is associated with its position within the entire quantum communication network. Therefore, nodes in a graph ultimately need to be actually distributed to nodes in the quantum communication network, thus relating to the number of available qubits in the network. Typically, a graph distribution request includes not only the graph structure containing the graph but also the position of the node in the graph within the entire quantum communication network. For example, in the graph structure storing the graph, there is a node numbered 3, which also corresponds to the node at position (3, 4) in the quantum communication network. The other nodes in the graph also correspond to nodes in an actual quantum communication network.

[0120] Link entanglement affects fidelity Since higher fidelity corresponds to higher graph distribution quality, and the composite fidelity of multi-hop links can be approximated by a product, this metric is calculated by taking the negative logarithm of the fidelity.

[0121] Classical communication delay of a link This refers to the latency of the link performing classic communication. The lower the latency, the higher the efficiency of graph state distribution. Therefore, this metric represents its communication latency.

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

[0123]

[0124] in, Representing edge e i Entanglement affects fidelity. Representing edge e i Communication latency; Representing edge e i Available bandwidth, i.e., edge e i The minimum number of available qubits between the two nodes; E represents the set of edges in the network topology G, and k1, k2, k3 are set coefficients.

[0125] The segmentation was then calculated using a normalized cut method:

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

[0127] (2) Calculate the eigenvectors of the Laplacian matrix and use the eigenvectors for K-means clustering to divide the graph into different regions. Each division method yields two regions, and the node sets in the two regions are denoted as A and B, respectively.

[0128] (3) For each segmentation method, calculate the normalized cut value for each region separately. Where 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 obtaining the segmentation, calculate the maximum number of bits consumed by a single node under the current segmentation, max(Cost). node The estimated time T required to perform the distribution operation is [not specified]. estimate And the number of quantum gates N expected to be used in the distribution graph. gate Ensure that the nodes have sufficient resources to complete the distribution and that the operation time does not exceed the decoherence time of the qubits; otherwise, cut the graph state again according to the above method.

[0131] After segmentation, the entangled pairs are distributed according to sub-graph states using the scheme described above. Then, entangled pairs are distributed at the locations where the sub-graph states need to be integrated, and graph state operations are used for integration.

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

[0133] (2) Performing a Y-basis Pauli measurement on the qubit at the position that was originally an entangled pair can restore the graph to the requested graph.

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

[0135] III. Example Introduction.

[0136] 1. Graph segmentation.

[0137] After receiving a request to distribute a graph state, the quantum communication network will, based on the remaining qubit resources of each node in the current network and the parameters of each quantum channel, assign a graph state to the network topology G. net Each side is assigned a weight. After obtaining the edge weights of the quantum communication network topology, the edges E in the graph topology G are first assigned weights W(e) according to the requested graph state. i ′ ),e i ′ ∈E, thus a graph segmentation algorithm can be performed.

[0138] First, calculate the weight matrix W and degree matrix D based on the graph topology G; then, calculate the Laplacian matrix based on the weight and degree matrices, and perform K-means clustering; calculate the normalized cut value Ncut(A,B) for each region; select the segment with the minimum normalized cut value as the result, and calculate the maximum bit consumption max(Cost) of a single node. node The algorithm determines whether the current segmentation meets the requirements. If not, it continues to segment the subgraph until the requirements are met.

[0139] 2. Graph distribution.

[0140] For each segmented subgraph, place it in the quantum communication network. Select the node with the most abundant node resources and the shortest combined distance from the other nodes as the source node, and the rest as the target nodes. Use the minimum spanning tree algorithm to perform multi-destination routing and find multiple non-conflicting paths.

[0141] Then, the success probability P is calculated based on the obtained path. G , if P G To meet the requirements of reliable transmission, i.e., P G A value of ≥0.95 means that redundant qubits can be appropriately optimized so that their success probability just meets the requirements for reliable transmission, thereby saving qubit resources.

[0142] According to the above allocation strategy, the source node first prepares a copy of the subgraph to be distributed using graph-related quantum gates. Then, each relay node and the target node distribute entangled pairs over long distances using entanglement swapping technology according to the allocation strategy. Finally, the copy of the subgraph is distributed to each node using quantum teleportation technology. Here, the relay nodes are nodes in the path that belong to the quantum communication network, and they are mainly used to perform entanglement swapping operations.

[0143] In this embodiment of the invention, the distribution of the qubit graph uses quantum teleportation technology. This technology requires the sender and receiver to share an entangled pair. However, in multi-hop links, this entangled pair cannot be directly shared through a physical channel. Therefore, entanglement swapping needs to be performed at relay nodes to share the entanglement relationship with nodes not directly connected by a physical channel. The present invention first prepares a shared entangled pair between all adjacent (physically connected) relay nodes, and then performs entanglement swapping at all relay nodes, enabling the nodes at both ends to share an entangled pair. After the source and destination nodes share an entangled pair, a Bell state joint measurement is performed on the qubit to be transmitted at the source node and one of the shared entangled pairs held by the source node. The measurement result is sent to the receiving node through a classical channel. The receiving node can recover the qubit to be transmitted using X and Z gates based on the measurement information. What this invention does is to use a bit in the graph state held by the source node and an entangled pair used for teleportation to transmit its state to the receiving node. This operation does not destroy the original entanglement relationship of the graph state. Therefore, this invention performs this operation on all the qubits that need to be distributed in the graph state replica, and can then distribute them to each destination node.

[0144] 3. Graphical integration.

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

[0146] In this embodiment of the invention, during the aforementioned graph state segmentation operation, the nodes to which the edges cut off between the sub-graph states belong, for example, when a complete connected graph state is divided into two disconnected sub-graph states, at least one edge is discarded. Therefore, for integration, it is necessary to re-establish the edges cut off due to the segmentation operation (i.e., the entanglement relationship of the qubits in the graph state). Here, it is necessary to share an entangled pair between the two nodes to which this edge belongs. Then, the qubits of the two sub-graph states at their respective nodes are connected to one of the entangled pairs at that node using CZ gates. In this way, the entangled pair also becomes part of the graph state. Then, Y-basis Pauli measurements are performed on the two qubits that originally belonged to the entangled pair, and the edges discarded when the graph was cut off can be re-established. After all the edges that need to be restored are restored through graph state operations, the integration of the sub-graph states is completed.

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

[0148] Example 2

[0149] This invention also provides a graph state segmentation and distribution system based on a quantum communication network, which is mainly used to implement the methods provided in the foregoing embodiments, such as... Figure 6 As shown, the system mainly includes:

[0150] The link weighting unit is used to assign corresponding weights to each link based on the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link.

[0151] The graph segmentation unit is used to receive a graph distribution request, which carries the complete graph to be distributed and the node positions of each node in the graph in the quantum communication network. If the resource consumption required for the distribution of the complete graph exceeds the set requirements, the complete graph is segmented into several sub-graphs so that the resource consumption required for the distribution of each sub-graph does not exceed the set requirements.

[0152] The graph distribution unit based on the quantum communication network is used to put each subgraph obtained by segmentation into the quantum communication network. Combining the weights of each link in the quantum communication network, it performs multi-destination conflict-free route discovery based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all subgraphs. It calculates the success probability of the multiple non-conflicting paths. If a path meets the set reliable transmission requirements, it distributes the corresponding subgraph through the obtained path.

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

[0154] Since the main technical details of the above system have been described in detail in the previous embodiments, they will not be repeated here.

[0155] Those skilled in the art will understand that, for the sake of convenience and brevity, the above-described division of functional modules is used as an example. In practical applications, the above 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 description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A graph segmentation and distribution method based on quantum communication networks, characterized in that, include: Based on the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link, each link is assigned a corresponding weight. Receive a graph distribution request, which carries the complete graph to be distributed and the node positions 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 the distribution of each sub-graph does not exceed the set requirements. Each subgraph obtained from the segmentation is placed into the quantum communication network. Combining the weights of each link in the quantum communication network, a multi-destination conflict-free route discovery is performed based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all subgraphs. The success probability of the multiple non-conflicting paths is calculated. If a path meets the set reliable transmission requirements, the corresponding subgraph is distributed through the obtained path pair. The graph integration technique is used to restore each sub-graph to the complete graph.

2. The graph segmentation and distribution method based on quantum communication networks according to claim 1, characterized in that, Assigning corresponding weights to each link based on the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link includes: Let the network topology of the quantum communication network be denoted as G. net For each of its links Assign weights Expressed as: in, Indicates link Entanglement affects fidelity. Indicates link Communication latency; Indicates link Available bandwidth, i.e., link bandwidth The minimum number of usable qubits between the two nodes; E net Represents the network topology G net The set of links in the equation, where k1, k2, and k3 are set coefficients.

3. The graph segmentation and distribution method based on quantum communication networks according to claim 1, characterized in that, The step of dividing the complete graph into several sub-graphs, ensuring that the resource consumption required for distributing each sub-graph does not exceed the set requirements, includes: Assign a weight to each edge in the complete graph to obtain the weight matrix W of the complete graph, and calculate the Laplacian matrix by combining it with the degree matrix of the complete graph. Calculate the eigenvectors of the Laplacian matrix and use the eigenvectors for K-means clustering to divide the graph into different regions. Each division method yields two regions, and the node sets in the two regions are denoted as A and B, respectively. For each segmentation method, the normalized cut value for each region is calculated separately. Where 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 cut value, and determine whether the resource consumption required for the distribution of each subgraph in the segmentation result does not exceed the set requirements. If yes, the segmentation is complete; otherwise, continue the segmentation until the resource consumption required for the distribution of each subgraph in the segmentation result does not exceed the set requirements.

4. The graph segmentation and distribution method based on quantum communication networks according to claim 1, characterized in that, Assigning a weight to each edge in the complete graph includes: Let G be the network topology of the complete graph, and let e be the edge of each edge. i Assign weight W(e) to ∈E i ), represented as: in, Representing edge e i Entanglement affects fidelity. Representing edge e i Communication latency; Representing edge e i Available bandwidth, i.e., edge e i The minimum number of available qubits between the two nodes; E represents the set of edges in the network topology G, and k1, k2, k3 are set coefficients.

5. A graph segmentation and distribution method based on a quantum communication network according to claim 1, characterized in that, Each sub-graph obtained from the segmentation is placed into the quantum communication network, and combined with the weights of each link in the quantum communication network, a multi-destination node conflict-free route discovery is performed based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths, including: Each subgraph obtained from the segmentation is placed into the quantum communication network. For each subgraph, a source node is selected to construct a copy of the subgraph 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, which are links in the quantum communication network. A node set is initialized to store the nodes that have already been added to the minimum spanning tree. The source node is added to the set of visited nodes, and all its adjacent links are added to the priority queue. The following steps are repeated until all destination nodes have been visited: Take the link with the smallest weight from the priority queue and check if both nodes of the link are in the set of visited nodes. If both nodes are in the set, skip the link and continue to the next link. If only one node is in the set, add the other node to the set of visited nodes 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 sequence according to the path, and obtain an optimal route that covers all destination nodes, which is the path corresponding to a subgraph. All subgraphs follow the same process, ultimately resulting in multiple non-conflicting paths for each subgraph.

6. The graph segmentation and distribution method based on quantum communication networks according to claim 1, characterized in that, The success probability of calculating the multiple non-conflicting paths is expressed as: in, Let M represent the probability that the m-th path successfully delivers n entangled pairs, where M is the number of the plurality of non-conflicting paths.

7. A graph segmentation and distribution method based on a quantum communication network according to claim 6, characterized in that, The The delivery status is calculated based on the entanglement of each link in the path, and is expressed as follows: Where p represents the success rate of a single entanglement swap operation; k m -1 represents the number of relay nodes on the m-th path, and also represents the number of entanglement swap operations performed; b m This represents the minimum number of entangled pairs available on the m-th path, which is the bottleneck capacity of the m-th path. Then the bottleneck capacity of the m-th path is exactly equal to b. m The probability of; The bottleneck capacity of the path is b m In this case, the success probability is decomposed into each hop, and expressed as: in, Indicates link The probability that the entanglement capacity is exactly i is given by the fact that the entanglement capacity of each hop link is no less than b. m The probability minus the entanglement capacity per hop is no less than b. m With a probability of +1, the bottleneck capacity of the link is exactly b. m probability The calculation method is as follows: Where, q m,k Indicates link The purification success rate, It is the equivalent link bandwidth under purified conditions.

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

9. A graph state segmentation and distribution method based on a quantum communication network according to claim 1, characterized in that, The distribution of the corresponding sub-graph state through the obtained path includes: The source node in the path prepares a copy of the subgraph to be distributed using graph-related quantum gates. Then, each relay node and the target node distribute entangled pairs according to the allocation strategy using entanglement swapping technology. The copy of the subgraph is then distributed to each node using quantum teleportation technology. 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 a quantum communication network, characterized in that, For implementing the method according to any one of claims 1 to 9, the system comprises: The link weighting unit is used to assign corresponding weights to each link based on the channel parameters of each link in the quantum communication network and the resource status of the nodes on the link. The graph segmentation unit is used to receive a graph distribution request, which carries the complete graph to be distributed and the node positions of each node in the graph in the quantum communication network. If the resource consumption required for the distribution of the complete graph exceeds the set requirements, the complete graph is segmented into several sub-graphs so that the resource consumption required for the distribution of each sub-graph does not exceed the set requirements. The graph distribution unit based on the quantum communication network is used to put each subgraph obtained by segmentation into the quantum communication network. Combining the weights of each link in the quantum communication network, it performs multi-destination conflict-free route discovery based on the minimum spanning tree algorithm to obtain multiple non-conflicting paths corresponding to all subgraphs. It calculates the success probability of the multiple non-conflicting paths. If a path meets the set reliable transmission requirements, it distributes the corresponding subgraph through the obtained path. The graph integration unit is used to restore each sub-graph to the complete graph using graph integration technology.

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