A quantum network congestion-aware dynamic entanglement purification method for improving throughput

Abstract

The application discloses a quantum network congestion-aware dynamic entanglement purification method for improving throughput, and belongs to the technical field of quantum network communication. The method comprises the following steps: constructing a quantum network model comprising the number of nodes, the number of links and the node exchange success rate, initializing network global variables and network parameters; generating communication requests between different node pairs and setting a fidelity threshold; selecting a low-cost entanglement path based on a weighted priority formula combining path length and entanglement exchange success rate; determining the purification position through the hop-by-hop degradation characteristic of fidelity, determining the purification times by using the probability purification characteristic, and introducing a link congestion factor to dynamically adjust the purification strategy to relieve network congestion. The application effectively reduces the time and resource cost of establishing entanglement between non-adjacent nodes, significantly improves the network throughput meeting the fidelity requirement, and realizes efficient utilization of entanglement resources and good support for multiple concurrent requests.

Description

Technical Field

[0001] This invention relates to the field of quantum network communication technology, and in particular to a method for improving throughput through dynamic entanglement purification for congestion awareness in quantum networks. Background Technology

[0002] In recent years, quantum networks composed of quantum nodes and quantum links have effectively overcome the limitations of traditional internet systems by utilizing the properties of quantum entanglement, and may be able to solve specific problems that classical computers struggle to handle in the future. Quantum communication networks can transmit information across long distances using quantum teleportation. Leveraging the properties of quantum entanglement, they support key applications such as quantum computing, clock synchronization, enhanced sensing, and metrology, and provide unparalleled security and efficiency in information transmission, solving critical data and information security issues. However, establishing entanglement between distant quantum nodes faces significant challenges. First, each quantum node can only store a limited number of qubits, and network resources are limited and costly, making quantum networks extremely sensitive to resource congestion caused by concurrent requests. Second, due to the no-cloning theorem for qubits, classical network communication methods cannot be used for the allocation of entangled pairs between remote quantum nodes in quantum networks; therefore, technologies such as quantum teleportation and entanglement swapping must be relied upon to establish long-distance connections. Due to the inherent limitations of quantum hardware, entanglement swapping and entanglement purification are probabilistic operations. This characteristic directly affects the reliability, latency, and resource consumption of entanglement establishment, thus constituting a core problem that must be solved in the design of quantum network routing.

[0003] Choosing an entangled path to establish end-to-end entanglement in a quantum network is a crucial step in transmitting quantum information between non-adjacent nodes. However, establishing end-to-end entanglement in multi-hop quantum networks faces two major challenges: fidelity degradation and inefficient use of entanglement resources. Specifically, due to the imperfections of entanglement swaps and factors such as entanglement decoherence, a pair of qubits may not be in an ideal entangled state, meaning the fidelity of the entangled pair decays hop by hop. Secondly, a low entanglement swap success rate not only prolongs the delay in entanglement establishment but also wastes valuable resources such as quantum memory and entangled pairs. Existing path selection strategies often prioritize path length or single-link capacity in isolation, failing to capture the combined cost of the impact of entanglement swap success rate and entanglement hop count on subsequent operations (such as entanglement purification). Here, we define the combined cost as the expected consumption of quantum resources (such as entangled pairs used for trials) and time overhead for establishing an end-to-end entanglement path that meets fidelity requirements.

[0004] Furthermore, to ensure the accuracy of end-to-end quantum information transmission, entanglement purification techniques must be used to improve link fidelity to meet specific threshold requirements. However, the strategy for determining the optimal number of purification operations and link locations still needs further optimization. Insufficient purification cannot meet the required fidelity, while excessive purification wastes scarce entanglement resources and exacerbates network congestion. Existing purification schemes mainly target link-level entanglement purification to maximize link entanglement fidelity, lacking consideration for the link load of multi-request concurrent networks and resource contention among multiple requests. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this invention provides a congestion-aware dynamic entanglement purification method for improving throughput in quantum networks. This invention selects the optimal entanglement path by designing a comprehensive cost-priority function based on path length and entanglement swap success rate. Furthermore, it introduces a link congestion factor to dynamically adjust the purification location and number of purification cycles, achieving efficient utilization of entanglement resources and a significant increase in network throughput that meets fidelity requirements.

[0006] The specific technical solution of the present invention is as follows: This invention provides a method for improving throughput through congestion-aware dynamic entanglement purification in quantum networks, comprising the following steps: Step S1: Build the basic operating environment for the quantum network: Construct a quantum network model based on the physical topology of quantum nodes and quantum links, read parameters from the quantum hardware configuration or network controller, and initialize the network global variables and network parameters. Step S2: Generate communication requests and set fidelity requirements: Based on the basic operating environment of the quantum network, generate network communication requests between different quantum node pairs, and set an end-to-end request fidelity threshold for each network communication request to obtain a set of communication requests to be processed; Step S3: Selecting entangled paths based on weighted priority: Based on quantum properties and their impact on entanglement purification operations, for each network communication request in the set of communication requests to be processed, candidate path generation and priority selection are performed to select a low-cost entangled path; wherein, the candidate path generation is to limit the number of path hops to generate a set of candidate paths, and the priority selection is to calculate the priority using a weighted priority formula and select the entangled path with higher priority; Step S4: Congestion-aware dynamic adjustment of purification parameters: Based on the initial entanglement fidelity of the quantum network's operating environment, the end-to-end request fidelity threshold of the network communication request, and the entanglement path, the initial purification link position is determined through the hop-by-hop degradation characteristic of fidelity, and the number of purification attempts required to meet the fidelity requirement is determined through the probabilistic purification characteristic; a link congestion factor is set, and the load status of each link is evaluated through the link congestion factor to dynamically adjust the link position of the entanglement purification operation, thereby alleviating network congestion caused by multiple concurrent network requests.

[0007] Preferably, the network global variables and network parameters mentioned in step S1 include: the number of network nodes, the number of network links, the node entanglement switching success rate, the maximum entanglement capacity of the links, and the initial entanglement fidelity of adjacent nodes; The quantum network model includes A quantum node, A random quantum network topology connected graph structure composed of quantum links, wherein there is at least one communicable path between any two nodes in the connected graph structure; each quantum node Configured with random entanglement swap success rate Each quantum link The maximum capacity of the configured link is The initial fidelity for entanglement between adjacent nodes is .

[0008] Preferably, the network communication request in step S2 is: simulating the communication needs between different nodes in the network, and generating different quantum node pairs. Network communication requests between Each of the aforementioned network communication requests There are corresponding end-to-end request fidelity threshold requirements. .

[0009] Preferably, the weighted priority formula in step S3 is: ; in, and Let represent the influence of path length and path entanglement swap success rate on entanglement path selection, respectively, and satisfy ... ; Indicates a request The The length of the communication path; Indicates a request The The probability of successful entanglement swapping along a communication path; Indicates a request The The priority level of each communication path candidate.

[0010] Preferably, the candidate path generation in step S3 specifically involves: limiting the number of path hops between different quantum nodes and initializing the candidate path set; The priority selection specifically involves: for each request R's candidate path set, calculating the priority of each path using the weighted priority formula. And through the priority level By comprehensively balancing path length and entanglement swap success rate, and avoiding network traffic load imbalance caused by simply pursuing a high swap success rate, the ultimate goal is to optimize the request... Select the entanglement path with higher priority to establish end-to-end entanglement and conduct network communication.

[0011] Preferably, the fidelity degradation characteristic described in step S4 is characterized by the following formula: ; in, Indicates the initial fidelity. Indicates from Down to The maximum number of hops traversed; this formula is used to determine the fidelity threshold when fidelity degrades to the end-to-end request fidelity threshold. The previous target purification path, For the process End-to-end entanglement fidelity after jump entanglement swap.

[0012] Preferably, the probabilistic purification characteristic described in step S4 is characterized by the following formula: ; in, To maintain the fidelity of the entangled pairs to be purified, N represents the fidelity of the sacrificial entangled pairs used for purification, and N is the number of purification attempts. This represents the fidelity of entanglement pairs when purification is successful after N attempts.

[0013] Preferably, the specific method for determining the number of purification cycles that meet the fidelity requirements in step S4 is as follows: For each network request and its communication path Link entanglement fidelity from initial fidelity As the number of relay entanglement exchanges increases, it gradually degenerates; the required fidelity threshold is used. As a condition, the degradation to the threshold is calculated. The longest path before degradation and the fidelity after degradation are used to perform multiple probabilistic purification operations on the degraded fidelity to ensure that the request always meets the fidelity threshold. Under the condition of completing network communication, the number of purification times The following constraints must be met: ; in, This represents the fidelity of entangled pairs reaching the current link after entanglement swap degradation. This represents the fidelity of entangled pairs initially on the current link without any entanglement swapping operations. For the current link The maximum entanglement capacity, For the current link The situation regarding the use of entangled resources.

[0014] Preferably, the link congestion factor mentioned in step S4 The calculation formula is: ; when When, it indicates a link When the load approaches saturation, adjusting the link position of the entanglement purification operation avoids consuming too much entanglement resources on a single link, thus achieving a load balancing optimization effect.

[0015] Furthermore, the end-to-end entangled connections output by the method are directly used as resource inputs to the execution unit of at least one of the following quantum information tasks: distributed quantum computing, quantum network clock synchronization, quantum enhanced sensing, and quantum metrology. In this case, by establishing end-to-end entangled connections between different quantum nodes that meet the fidelity threshold requirements, entanglement resource support is provided for the quantum information task, improving the efficiency and reliability of remote entanglement establishment, thereby increasing the success rate of task execution and overall performance.

[0016] The beneficial technical effects of this invention are as follows: 1. The entanglement path selection method proposed in this invention selects a more efficient communication path for each network request by comprehensively considering the path hop count and entanglement swap success rate. Specifically, this invention designs a priority function for each candidate path. This function integrates the path-level entanglement swap success rate and hop count to quantify the overall cost, where the overall cost is defined as the expected quantum resources and time overhead required to establish an end-to-end entanglement that meets fidelity requirements. This function can select the most cost-effective entangled communication path for each network request. Compared to existing strategies that consider path length, entanglement success rate, and link capacity in isolation, this comprehensive metric method can guarantee a high entanglement establishment success rate and effectively reduce the waste of quantum resources and time due to the reallocation of entanglement resources in the link caused by swap failures, thereby significantly improving the overall quality and cost-effectiveness of path selection. 2. The network congestion-aware dynamic entanglement purification decision mechanism proposed in this invention can adaptively determine the purification location and number of iterations based on the request's fidelity threshold and the real-time link load. Specifically, this mechanism evaluates the fidelity decay and link load status along the entire path for each request in real time, thereby dynamically deciding where and how many rounds of purification operations to perform. Its goal is to minimize the additional resource overhead caused by purification operations while ensuring end-to-end fidelity is met throughout the process, and to proactively avoid congested links to balance network load. Compared to traditional fixed or local purification strategies, this mechanism, while ensuring end-to-end fidelity is met throughout the process, accurately avoids distortion caused by "insufficient purification" and resource waste and network congestion caused by "over-purification," achieving an optimal balance between resource consumption and fidelity assurance. 3. This invention synergistically optimizes entanglement path selection and entanglement purification strategies. Existing solutions often separate routing and purification, leading to suboptimal decisions. This invention implements dynamic purification on high-quality paths, enabling both to mutually reinforce each other and jointly reduce the overall cost of establishing end-to-end entanglement. By synergistically optimizing entanglement path selection and entanglement purification strategies, multi-hop end-to-end entangled connections that meet requirements can be efficiently established, mitigating network congestion caused by improper purification operations. This systematically improves network throughput that meets fidelity requirements and provides excellent support for multiple concurrent requests. 4. This invention addresses the varying fidelity requirements of different quantum applications by performing appropriate operations on the entangled communication path for each request. This transforms the previously uniform, coarse-grained resource allocation model into a precise, dynamic optimization process based on the specific fidelity requirements of each request. Consequently, it achieves higher resource efficiency, better service quality, and stronger overall performance at the system level. 5. The algorithm framework proposed in this invention provides a feasible solution for the efficient and reliable operation of quantum networks. This invention improves the efficiency and reliability of long-range entanglement establishment, supports core applications such as distributed quantum computing and clock synchronization, and provides feasible support for the operation of quantum networks. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for improving throughput through dynamic entanglement purification in a quantum network based on congestion awareness, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the establishment of entanglement between non-adjacent nodes in a quantum network congestion-aware dynamic entanglement purification method to improve throughput in an embodiment of the present invention. Figure 3 This is a schematic diagram of entanglement purification and purification of entangled pairs in a quantum network congestion-aware dynamic entanglement purification method to improve throughput in an embodiment of the present invention; Figure 4This is a schematic diagram of the quantum network entanglement path selection and entanglement purification strategy in a quantum network congestion-aware dynamic entanglement purification method to improve throughput in an embodiment of the present invention; Figure 5 This is a schematic diagram comparing the experimental results of the quantum network purification strategy (HESPCAP) of the quantum network congestion-aware dynamic entanglement purification method for improving throughput in an embodiment of the present invention with the greedy congestion mitigation entanglement purification algorithm (GPCAP) and the shortest path first congestion mitigation entanglement purification algorithm (MPCAP). In the diagram, (a) is a schematic diagram of the impact of the number of network nodes on entanglement success, (b) is a schematic diagram of the impact of the number of network links on entanglement success, and (c) is a schematic diagram of the impact of the average entanglement swap success rate of nodes on entanglement success. Figure 6 This is a comparative diagram of experimental results of the purification strategy (HESPCAP) of a quantum network congestion-aware dynamic entanglement purification method to improve throughput in an embodiment of the present invention, and the congestion mitigation entanglement purification algorithm (GPCAP), the traditional hop-by-hop entanglement purification algorithm (HESPP) based on path selection based on comprehensive path length and path entanglement exchange success rate, and the traditional hop-by-hop entanglement purification algorithm (GPP) based on greed. In the diagram, (a), (b), and (c) are schematic diagrams of the impact of link average capacity on network throughput, end-to-end average fidelity, and network resource utilization, respectively. Figure 7 This is a comparative diagram of experimental results for the purification strategy (HESPCAP) of a quantum network congestion-aware dynamic entanglement purification method to improve throughput in an embodiment of the present invention, and the congestion mitigation entanglement purification algorithm (GPCAP), the traditional hop-by-hop entanglement purification algorithm (HESPP) based on path selection based on comprehensive path length and path entanglement exchange success rate, and the traditional hop-by-hop entanglement purification algorithm (GPP) based on greed. In the diagram, (a), (b), and (c) are schematic diagrams of the impact of the number of network requests on network throughput, end-to-end average fidelity, and network resource utilization, respectively. Figure 8 This is a comparative diagram of experimental results for the purification strategy (HESPCAP) of a quantum network congestion-aware dynamic entanglement purification method to improve throughput in an embodiment of the present invention, compared with the greedy congestion mitigation entanglement purification algorithm (GPCAP), the traditional hop-by-hop entanglement purification algorithm (HESPP) based on path selection with comprehensive path length and path entanglement exchange success rate, and the greedy traditional hop-by-hop entanglement purification algorithm (GPP). In the diagram, (a), (b), and (c) are schematic diagrams showing the impact of the average request fidelity threshold on network throughput, end-to-end average fidelity, and network resource utilization, respectively. Detailed Implementation

[0018] The step numbers used in this invention are only for distinguishing different steps or objects and are not necessarily for describing a specific order or sequence. It should be understood that these numbers may correspond to different execution sequences where appropriate, so that embodiments of the invention can be implemented in a different order than that illustrated or described. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover non-exclusive inclusion; for example, a process, method, apparatus, or product that includes a series of steps or units is not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, apparatus, or products. The invention will now be described in detail with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0019] Example 1: Method Example This embodiment provides a method for improving throughput through dynamic entanglement purification in a congestion-aware quantum network. The specific process is as follows: Figure 1 As shown, it includes the following steps: Step S1: Construct a quantum network model and initialize global network variables and network parameters, including but not limited to the number of network nodes, the number of network links, and the node exchange success rate.

[0020] Read parameters from the quantum hardware configuration or network controller, and initialize the network global variables and network parameters accordingly; construct a system based on... A quantum node, A random quantum network topology consisting of quantum links ensures that there is at least one communicable path between any two nodes in the network. For each quantum node... Set the success rate of random entanglement swaps For each quantum link Set the maximum link capacity to And set the initial fidelity of entanglement directly generated between adjacent nodes to be 0. .

[0021] Step S2: Generate communication requests for different network nodes and set the request fidelity threshold.

[0022] Simulate the communication needs between different nodes in a network, and generate different quantum node pairs. Network communication requests between This ensures communication between different quantum network nodes, while also providing support for each request. Set fidelity threshold requirements .

[0023] Step S3: Based on quantum properties and their impact on entanglement purification operations, design an entanglement path selection algorithm to select a low-cost entanglement path for network requests.

[0024] Limit the path hop count between different quantum nodes and initialize the candidate path set for network requests; for each request The priority of each path in the candidate path set is calculated by combining the path hop count and the probability of successful path entanglement swaps, as shown in the following formula: ; in and Let represent the influence of path length and path entanglement swap success rate on entanglement path selection, respectively, and satisfy ... , Indicates a request The The length of the communication path, Indicates a request The The probability of successful entanglement swapping of communication paths. Indicates a request The The priority of candidate communication paths is also an indicator of communication cost savings. This metric allows for a comprehensive consideration of path length and entanglement switching success rate, avoiding network traffic load imbalance caused by solely pursuing a high switching success rate, and preventing increased entanglement switching costs due to a low success rate in pursuing the shortest path. The proposed routing algorithm is used for requests... Select the entanglement path with higher priority to establish end-to-end entanglement and conduct network communication.

[0025] like Figure 2 As shown, the process of establishing entanglement between non-adjacent nodes is as follows: Alice (the first communicator) shares a pair of entangled qubits labeled "1" and "2" with the quantum repeater, while the quantum repeater shares another pair of entangled qubits labeled "3" and "4" with Bob (the second communicator). The quantum repeater performs Bell state measurements on qubits "2" and "3". Based on the measurement results, corresponding quantum operations are applied to qubits "1" and "4", ultimately causing entanglement between qubits "1" and "4". This process makes long-distance quantum information transmission possible.

[0026] The following is combined with Figure 4 The path selection process is illustrated with an example.

[0027] Figure 4 (a) shows the initial network topology, with two requests. and In the picture Indicates a relay node. and The numbers above the end nodes and relay nodes indicate the entanglement swap success rate of that node. The lines connecting nodes indicate entangled connections between them. The number on each link represents the entanglement capacity of that link, i.e., the maximum number of network requests that link can support. For example, a link... The number 3 indicates the link capacity. That is, link A maximum of three entanglements are allowed, which can be used for a maximum of three network requests.

[0028] exist Figure 4 In (b), for the request First, select the k paths with the fewest hops, i.e., the paths... , as well as its path length Success rate of path entanglement swap The values ​​are 2 and 0.61, 3 and 0.96, and 5 and 0.97, respectively. Assuming that path length and path entanglement swap success rate are equally important when selecting a path, therefore the values ​​are set... Then, the utility function is calculated based on the data for each path to obtain the path. The utility function is ,path The utility function is ,path The utility function is The path can be obtained through calculation. The result is the highest, meaning this path has the highest priority and will ultimately be the one requested. Choose the path for end-to-end communication. The path selected through weighted optimization can achieve a high probability of successfully establishing an end-to-end entangled path while reducing the consumption of valuable quantum resources when entanglement establishment fails.

[0029] The routing algorithm of this invention is used for requests. Select the entanglement path with higher priority to establish end-to-end entanglement and conduct network communication.

[0030] Step S4: Based on fidelity-based hop-by-hop degradation and probabilistic purification, dynamically adjust the purification link position and purification count to alleviate network congestion caused by multiple concurrent network requests.

[0031] Fidelity decreases exponentially with path size. The formula relating fidelity to path hop count is as follows: ; in Indicates the initial fidelity. Indicates from Down to The maximum hop path that can be traversed. This formula is used to determine the point at which fidelity degrades to the requested fidelity threshold. The previous optimal purification path.

[0032] After determining the optimal purification location, when performing entanglement purification at that location, since entanglement purification is probabilistic, it is necessary to further determine how many rounds of purification operations to perform at that location.

[0033] The process of entanglement purification to improve fidelity is as follows: Figure 3 As shown, in this basic entanglement purification process, the first communicating party (Alice) and the second communicating party (Bob) share two Bell pairs, where Bell pair 1 is the entangled pair to be retained, and Bell pair 2 is the sacrifice pair. Both parties execute a controlled NOT gate (CNOT gate, with the control bit being Bell pair 1 and the target bit being Bell pair 2) on their respective two qubits, and then measure Bell pair 2. If the measurements are consistent, Bell pair 1 is retained; otherwise, it is discarded. Bell pair 2 is consumed immediately after measurement; its function is to purify the retained pair through entanglement correlation testing. After successful purification, the fidelity of Bell pair 1 is improved, while Bell pair 2 is consumed.

[0034] The formula for calculating the entanglement fidelity after probabilistic purification is as follows: ; in, and These represent the fidelity of two entangled pairs on the same quantum link: For entangled pairs to be purified (i.e., entangled pairs for which we want to retain and improve fidelity). This refers to the entangled pair (also known as the sacrificial pair) used for purifying the entangled pair to be purified. During the entanglement purification operation, the entanglement resources of the sacrificial pair are consumed, i.e., through a fidelity of [missing value]. The entanglement pairs are used to purify the fidelity. The fidelity of the purified entangled pairs is calculated using the formula above; N represents the number of purification attempts. This indicates that the entanglement fidelity is and Entanglement between pairs of attempts Fidelity after successful entanglement purification operation.

[0035] For each network request and its communication path Link entanglement fidelity from initial fidelity As the number of relay entanglement swaps increases, it gradually degrades. (The request is based on a fidelity threshold.) As a condition, the degradation to the threshold is calculated. The longest path before degradation and the fidelity after degradation are used to perform a probabilistic purification operation on the degraded fidelity through multiple attempts, so that the request always meets the fidelity threshold. Network communication is completed under the given conditions. Number of purification cycles. The following constraints must be met: ; in , These represent the fidelity of the current link after entanglement-swapping degradation and the fidelity of the current link during the purification operation, respectively. This represents the fidelity of entangled pairs established between non-adjacent nodes through entanglement swaps. The fidelity degrades due to the entanglement swap operation, meaning that entanglement purification operations are needed to improve its fidelity. Is with The initial fidelity of entangled pairs in the same quantum link that have not undergone entanglement swapping operations, i.e., the initial fidelity of entangled pairs that have not degenerated in the current purified link; Indicates the current link The maximum entanglement capacity, Indicates the current link The entanglement resource usage, in the formula The rounding sign ensures that the number of purification cycles is a positive integer.

[0036] Setting a link congestion factor to adjust the link location for entanglement purification operations can alleviate network congestion. congestion factor The calculation formula is as follows: ; when If a purification operation is performed on the current link, all remaining entanglement resources on that link will be consumed. This will prevent subsequent network requests from performing entanglement swapping operations through that link, indicating that the link is in a state of flux. The link congestion factor is approaching saturation. This invention uses 1 as the threshold for determining the link congestion factor. When the value approaches 1, purification operations should be avoided on that link. This is to prevent purification operations from consuming all remaining entanglement resources on the current link, ensuring that subsequent network requests can use the current link's resources for entanglement swapping. By adjusting the link location for entanglement purification operations, excessive entanglement resource consumption on a single link is avoided, achieving load balancing optimization.

[0037] It should be noted that the above probability purification formula and the purification number constraint formula are different. , They are identical in symbolism and have the same essential meaning. Both refer to the fidelity of entangled pairs that need to be purified (i.e., entangled pairs that have degenerated after entanglement exchange). Both refer to the fidelity of sacrificial entangled pairs used as purification resources (i.e., entangled pairs initially without entanglement swapping operations on the same link). The former formula is defined from the general perspective of purification operations, while the latter formula, based on the former formula, determines the purification number constraint in combination with the specific scenario. There is no definitional conflict between the two.

[0038] The following is combined with Figure 4 An example is provided to illustrate the purification decision-making process.

[0039] The request is obtained through the entanglement path selection in step S3. and The entanglement path is and Assuming initial fidelity ,ask fidelity threshold According to the fidelity degradation formula Calculation yields That is, the fidelity will degrade to [a certain value] after the second entanglement swap operation. Therefore, the optimal purification location is the link. To ensure that the end-to-end entanglement fidelity always meets the requested threshold, it is necessary to... Execution Secondary purification.

[0040] like Figure 4 As shown in (c), the link Only three entangled pairs are available. Performing a purification operation on this link will result in a request. It cannot be completed within the current time slot, i.e. This means that in the link Performing purification will consume all remaining entanglement resources in that link, making the request... Entanglement cannot be established between non-adjacent nodes by performing entanglement switching over this link, thus reducing network throughput within a time slot.

[0041] To address the problem of excessive resource usage in a single link entanglement, the purification strategy of this invention, due to the link... Execution The second purification step would cause a decrease in throughput, so we avoid performing entangled purification on this link and instead perform it on the previous hop link. implement Secondary purification. This is because, on this link, the fidelity of the entangled pairs has not yet fallen below the requested fidelity threshold, and entanglement resources are sufficient, while purification... This can further improve the fidelity of entanglement pairs, enabling higher fidelity at nodes. After performing the entanglement swap operation, the link The fidelity on the link always meets the request fidelity threshold requirement, so there is no need to continue to perform purification operations on the link and consume too much entanglement resources, ensuring that the request can pass through the link safely.

[0042] Specifically, Substitute into the probability purification formula: ; Calculations show that, for the requested... The fidelity of the assigned entanglement pairs is improved to 0.956. Substituting this into the fidelity degradation formula... ,in , Calculations yielded This ensures that in the link implement This purification operation allows non-adjacent nodes to satisfy the request. Under the fidelity threshold requirement, entanglement is established and information transmission is completed through entanglement swapping operations, while simultaneously enabling the request... It is also possible to have enough entanglement resources within the time slot to complete end-to-end entanglement requests, thereby achieving the goal of increasing network throughput within a time slot when network requests compete for resources and cause congestion.

[0043] Example 2: Experimental Verification

[0044] This embodiment verifies the effectiveness of the entanglement path selection and entanglement purification method in Embodiment 1 through quantum network simulation. By changing the network size and the probability of successful node entanglement exchange, the effectiveness of the routing algorithm is evaluated using the link entanglement success probability as an indicator. By changing the number of requests, link capacity, and request fidelity threshold, the effectiveness of the entanglement purification algorithm is evaluated using network throughput, end-to-end fidelity of successful entanglement establishment, and network resource utilization as indicators.

[0045] 1. Experimental setup Extensive simulations were performed using a custom quantum network simulator to evaluate the performance of the proposed entanglement routing method; The simulated entangled communication network is generated based on the following given parameters: a certain number of quantum nodes, quantum links randomly connecting these nodes, the success rate of quantum node entanglement swapping, the capacity of the quantum links, and the initial fidelity of the quantum links; By default, the quantum network topology has 100 quantum nodes and 200 quantum links, and the entanglement fidelity of the generated links is [value missing]. ; In the experimental verification, the parameters varied as follows: number of nodes 100-500, number of quantum links 200-800, node entanglement swap success rate 0.5-0.9, average request fidelity threshold 0.7-0.9, average link capacity 4-12 entangled pairs, and number of network requests 100-500. Each experiment was run 100 times, and the average value was taken.

[0046] 2. Comparison of Algorithms and Evaluation Metrics The algorithm proposed in this invention is called HESPCAP, which is an abbreviation of the first letters of the words Hop-count and EntanglementSwapping success Probability-based Congestion Alleviation Purification, meaning a congestion relief purification algorithm based on path hop count and entanglement swap success rate. To verify the performance of the proposed algorithm HESPCAP in selecting entangled paths under different network conditions, it is first compared with the following two routing algorithms: Greedy Congestion Relief Entanglement Purification Algorithm (GPCAP) and Shortest Path First Congestion Relief Entanglement Purification Algorithm (MPCAP). Then, to verify the performance of finally establishing entanglement between non-adjacent nodes, it is evaluated with the following three comparison algorithms: Greedy Congestion Relief Entanglement Purification Algorithm (GPCAP), Traditional Hop-by-Hop Entanglement Purification Algorithm (HESPP) based on path selection combining path length and path entanglement exchange success rate, and Greedy Traditional Hop-by-Hop Entanglement Purification Algorithm (GPP). The evaluation modifies the average quantum link capacity, the average end-to-end network request fidelity threshold, and the number of end-to-end network requests. The network throughput is evaluated based on the number of successful end-to-end entanglement establishment requests where the end-to-end entanglement link entanglement exchange success rate reaches a certain value and the entanglement fidelity meets the network request fidelity threshold. Specifically, three indicators are used for comprehensive evaluation: average network throughput (the maximum number of successful end-to-end source-destination entanglement establishment requests that can be satisfied within a time slot), the average end-to-end entanglement fidelity, and average quantum network resource utilization (the amount of entanglement resources allocated to all successful end-to-end entanglement requests within a time slot).

[0047] 3. Verification of the effectiveness of the routing algorithm Figure 5(a)-(c) illustrate the impact of changes in the number of network nodes, the number of network links, and the average entanglement swap success rate on entanglement success. When the number of quantum nodes is small or the number of quantum links is large, there are multiple paths between two non-adjacent quantum nodes; as the number of nodes increases, the number of paths between non-adjacent nodes decreases, the number of path hops increases, and the probability of successful path entanglement gradually decreases. Among the changes in the number of selectable links ( Figure 5 (a)(b)) The algorithm HESPCAP of this invention takes into account the quantum characteristics of the link more comprehensively, and its entanglement success rate in selecting entangled paths is always higher than that of the traditional algorithms GPCAP and MPCAP. In the experiment on the success rate of entanglement swapping at relay nodes ( Figure 5 (c) When the success probability of a swap is low, GPCAP always selects the quantum node with the highest success probability among its current neighbors, which can easily lead to an excessive number of nodes in the selected path, resulting in a significant difference in the success probability of entanglement selection compared to HESPCAP and MPCAP. As the average entanglement swap probability of nodes increases, the differences among the three algorithms gradually narrow. Within the range of 100-500 nodes, 200-800 edges, and a node entanglement swap success rate of 0.5-0.9, the algorithm of this invention achieves average performance improvements of 11.86%, 11.13%, and 5.36% respectively in entanglement swap success rate compared to Min_Hop (minimum number of hops) in selecting entangled paths, and average performance improvements of 22.19%, 22.55%, and 45.48% respectively compared to Greedy.

[0048] 4. Performance comparison when link capacity changes Figure 6 (a)-(c) demonstrate the performance of each algorithm as the quantum link capacity varies in the quantum network. When the link capacity is small (i.e., there are fewer entangled resources available in the network), the throughput of all four purification algorithms is low; as the quantum link capacity increases, the network throughput also increases steadily. The algorithm of this invention, HESPCAP, takes request congestion into account, and the paths selected by the Greedy routing algorithm generally contain more quantum nodes (i.e., consume more entangled resources) than the entangled paths selected by the algorithm of this invention for network requests. Therefore, the throughput of the purification algorithm of this invention, HESPCAP, is consistently higher than that of the traditional hop-by-hop purification algorithm and the Greedy-based hop-by-hop purification algorithm. Figure 6 (b) shows that the entanglement fidelity established by the algorithm of the present invention achieves a 100% satisfaction rate; Within the range of link capacity from 4 to 12, the network throughput of the algorithm HESPCAP of this invention is improved by 44.15%, 10.14% and 66.38% respectively compared with the comparative methods GPCAP, HESPP and GPP; the request fidelity satisfaction rate reaches 100%; and the resource consumption rate is reduced by 14.32%, increased by 15.03% (i.e. higher than HESPP) and reduced by 1.19% respectively.

[0049] 5. Performance comparison when the number of requests changes Figure 7 (a)-(c) demonstrate the performance of each algorithm in terms of network throughput, average end-to-end entanglement fidelity, and average network entanglement resource utilization under different numbers of end-to-end entanglement requests. The network throughput of all four algorithms increases with the number of end-to-end entanglement requests, but the increase gradually decreases due to the decrease in entanglement resources in the quantum network caused by the increase in the number of requests. The algorithm of this invention exhibits superior network throughput performance. Figure 7 (b) shows that the algorithm of the present invention achieves a 100% entanglement fidelity satisfaction rate; As the number of end-to-end requests increases, more end-to-end entanglements can be established (i.e., network throughput increases). Therefore, the resource consumption of the four algorithms also increases. The Greedy routing algorithm selects a longer path, consuming more entanglement resources than the Hepcap routing algorithm. Congestion mitigation also consumes resources; therefore, purification algorithms with congestion mitigation consume more resources than traditional purification algorithms. Within the request quantity range of 100-500, compared to GPCAP, HESPP, and GPP, the proposed algorithm Hepcap achieves an average network throughput increase of 37.92%, 7.71%, and 55.31%, respectively, with a request fidelity satisfaction rate of 100%. Resource consumption is reduced by an average of 15.65% (GPCAP), increased by 10.91% (HESPP), and decreased by 5.00% (GPP).

[0050] 6. Performance comparison when fidelity threshold changes Figure 8(a)-(c) illustrate the impact of varying end-to-end entanglement request fidelity thresholds on the performance of each algorithm in three aspects: network throughput, average end-to-end entanglement fidelity, and average network resource utilization in quantum networks. The increase in the request fidelity threshold is directly related to network resource utilization: as the request fidelity threshold increases, more entanglement resources in the quantum network are used to improve entanglement request fidelity, resulting in more requests failing to successfully establish end-to-end entanglement, thus reducing network throughput. The Greedy routing algorithm selects longer entanglement paths, consuming more entanglement resources needed by other requests. Therefore, as the fidelity threshold increases, the paths selected by Greedy can only satisfy a limited number of requests, resulting in a smaller change in throughput. In contrast, the path selected by the Hesscap routing algorithm avoids both network traffic load imbalance and reduced network throughput caused by simply pursuing a high exchange success rate, and low entanglement exchange success rates and increased resource costs for path attempts to establish entanglement caused by simply pursuing the shortest path. This makes it easier to successfully establish end-to-end entanglement, resulting in higher throughput. As the request fidelity threshold increases, network throughput will change more significantly. Figure 8 (b) shows that as the average fidelity threshold of the request increases, the end-to-end entanglement average fidelity achieved by the four algorithms also gradually increases, and all of them meet the fidelity threshold of the request. Figure 8 (c) shows that as the fidelity threshold increases, more entanglement resources are used for entanglement purification to improve entanglement fidelity, thus gradually increasing the utilization rate of network entanglement resources. When a certain threshold is reached, the number of requests satisfied decreases, but purification ceases as long as the path entanglement fidelity exceeds the request fidelity threshold. Therefore, when the request fidelity threshold is high, the change in network entanglement resource utilization tends to level off. Within the fidelity threshold range of 0.7-0.9, the algorithm HESPCAP of this invention, compared to GPCAP, HESPP, and GPP, achieves an average increase in network throughput of 50.48%, 7.23%, and 71.77%, respectively, with a request fidelity satisfaction rate of 100%, and an average decrease in resource consumption of 19.21%, an increase of 13.58%, and a decrease of 9.84%.

[0051] 7. Experimental Conclusions The experimental results above show that the Entangled Routing and Entangled Purification Method (HESPCAP) proposed in this invention can effectively improve the success rate of entanglement establishment and network throughput under different network scales, link capacities, number of requests and fidelity thresholds, while ensuring that the end-to-end fidelity meets the requirements, thus achieving efficient utilization of entanglement resources.

[0052] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, and for those of ordinary skill in the art, various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. Therefore, the present invention is not limited to the specific details without departing from the general concept defined by the claims and their equivalents.

Claims

1. A method for improving throughput through congestion-aware dynamic entanglement purification in quantum networks, characterized in that, Includes the following steps: Step S1: Build the basic environment for quantum network operation: Construct a quantum network model based on the physical topology of quantum nodes and quantum links, read parameters from quantum hardware configuration or network controller, and initialize network global variables and network parameters. Step S2: Generate communication requests and set fidelity requirements: Based on the basic operating environment of the quantum network, generate network communication requests between different quantum node pairs, and set an end-to-end request fidelity threshold for each network communication request to obtain a set of communication requests to be processed; Step S3: Selecting entangled paths based on weighted priority: Based on quantum properties and their impact on entanglement purification operations, for each network communication request in the set of communication requests to be processed, candidate path generation and priority selection are performed to select a low-cost entangled path; wherein, the candidate path generation is to limit the number of path hops to generate a set of candidate paths, and the priority selection is to calculate the priority using a weighted priority formula and select the entangled path with higher priority; Step S4: Congestion-aware dynamic adjustment of purification parameters: Based on the initial entanglement fidelity of the quantum network's operating environment, the end-to-end request fidelity threshold of the network communication request, and the entanglement path, the initial purification link position is determined through the hop-by-hop degradation characteristic of fidelity, and the number of purification attempts required to meet the fidelity requirement is determined through the probabilistic purification characteristic; a link congestion factor is set, and the load status of each link is evaluated through the link congestion factor to dynamically adjust the link position of the entanglement purification operation, thereby alleviating network congestion caused by multiple concurrent network requests.

2. The method according to claim 1, characterized in that, The network global variables and network parameters mentioned in step S1 include: number of network nodes, number of network links, node entanglement switching success rate, maximum entanglement capacity of links, and initial entanglement fidelity of adjacent nodes; The quantum network model includes A quantum node, A random quantum network topology connected graph structure composed of quantum links, wherein there is at least one communicable path between any two nodes in the connected graph structure; each quantum node Configured with random entanglement swap success rate Each quantum link The maximum capacity of the configured link is The initial fidelity for entanglement between adjacent nodes is .

3. The method according to claim 1, characterized in that, The network communication request mentioned in step S2 is: to simulate the communication needs between different nodes in the network and generate different quantum node pairs. Network communication requests between Each of the aforementioned network communication requests There are corresponding end-to-end request fidelity threshold requirements. .

4. The method according to claim 1, characterized in that, The weighted priority formula mentioned in step S3 is: ； in, and Let represent the influence of path length and path entanglement swap success rate on entanglement path selection, respectively, and satisfy ... ; Indicates a request The The length of the communication path; Indicates a request The The probability of successful entanglement swapping of communication paths; Indicates a request The The priority level of each communication path candidate.

5. The method according to claim 4, characterized in that, The candidate path generation in step S3 specifically involves: limiting the number of hops between different quantum nodes and initializing the candidate path set; The priority selection specifically involves: for each request R's candidate path set, calculating the priority of each path using the weighted priority formula. And through the priority level By comprehensively balancing path length and entanglement swap success rate, and avoiding network traffic load imbalance caused by simply pursuing a high swap success rate, the ultimate goal is to optimize the request... Select the entanglement path with higher priority to establish end-to-end entanglement and conduct network communication.

6. The method according to claim 1, characterized in that, The fidelity jump-by-jump degradation characteristic mentioned in step S4 is characterized by the following formula: ； in, Indicates the initial fidelity. Indicates from Down to The maximum number of hops traversed; this formula is used to determine the fidelity threshold when fidelity degrades to the end-to-end request fidelity threshold. The previous target purification path, For the process End-to-end entanglement fidelity after jump entanglement swap.

7. The method according to claim 6, characterized in that, The probabilistic purification characteristic described in step S4 is characterized by the following formula: ； in, To maintain the fidelity of the entangled pairs to be purified, N represents the fidelity of the sacrificial entangled pairs used for purification, and N is the number of purification attempts. This represents the fidelity of entanglement pairs when purification is successful after N attempts.

8. The method according to claim 1, characterized in that, The specific method for determining the number of purification cycles required to meet the fidelity requirement in step S4 is as follows: For each network request and its communication path Link entanglement fidelity from initial fidelity As the number of relay entanglement exchanges increases, it gradually degenerates; the required fidelity threshold is used. As a condition, the degradation to the threshold is calculated. The longest path before degradation and the fidelity after degradation are used to perform multiple probabilistic purification operations on the degraded fidelity to ensure that the request always meets the fidelity threshold. Under the condition of completing network communication, the number of purification times The following constraints must be met: ； in, This represents the fidelity of entangled pairs reaching the current link after entanglement swap degradation. This represents the fidelity of entangled pairs initially on the current link without any entanglement swapping operations. For the current link The maximum entanglement capacity, For the current link The situation regarding the use of entangled resources.

9. The method according to claim 1, characterized in that, The link congestion factor mentioned in step S4 The calculation formula is: ； when When, it indicates a link When the load approaches saturation, adjusting the link position of the entanglement purification operation avoids consuming too much entanglement resources on a single link, thus achieving a load balancing optimization effect.

10. The method according to any one of claims 1 to 9, characterized in that, The end-to-end entangled connections output by the method are directly used as resource inputs to the execution unit of at least one of the following quantum information tasks: distributed quantum computing, quantum network clock synchronization, quantum enhanced sensing, and quantum metrology. In particular, by establishing end-to-end entangled connections between different quantum nodes that meet the fidelity threshold requirements, entanglement resource support is provided for the quantum information tasks, improving the efficiency and reliability of remote entanglement establishment, thereby improving the success rate and overall performance of task execution.

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