In this study, we propose a resource allocation model for end-to-end (E2E) fidelity-guaranteed entanglement distribution considering novel path-based entanglement purification (PEP) model for online quantum networks. The proposed PEP model is developed by extending the existing link-based entanglement purification (LEP) model. A heuristic framework is designed for both the PEP and LEP models, consisting of two stages: (i) an E2E entanglement purification stage based on the PEP (or LEP) model, and (ii) a resource allocation stage. The resource allocation stage employs an integer linear programming (ILP) formulation for small-scale quantum networks with a limited number of requests, and a greedy-based heuristic for large-scale networks with higher request volumes. This heuristic algorithm incorporates entanglement distribution probability (EDP), entanglement swapping probability (ESP), and fidelity metrics to ensure feasibility under noisy intermediate-scale quantum (NISQ) constraints. An online traffic model is considered, where requests arrive according to a Poisson process, each with a fixed execution time and a variable deadline. A time-slotted operation framework is adopted for the quantum network. In each Bell-pair generation window, Bell pairs are generated and distributed between adjacent nodes. The duration of these windows is constrained by the decoherence time of the Bell pairs. Extensive simulations are conducted on the square-grid quantum networks of varying dimensions and parameter ranges, including different ranges of EDP, ESP, and fidelity values. The number of requests and capacity of edges (in terms of quantum channels) are also varied. Across all simulation setups, the proposed PEP model consistently outperforms the LEP model in terms of the blocking ratio (BR).
In this study, we propose a resource allocation model for end-to-end (E2E) fidelity-guaranteed entanglement distribution considering novel path-based entanglement purification (PEP) model for online quantum networks. The proposed PEP model is developed by extending the existing link-based entanglement purification (LEP) model. A heuristic framework is designed for both the PEP and LEP models, consisting of two stages: (i) an E2E entanglement purification stage based on the PEP (or LEP) model, and (ii) a resource allocation stage. The resource allocation stage employs an integer linear programming (ILP) formulation for small-scale quantum networks with a limited number of requests, and a greedy-based heuristic for large-scale networks with higher request volumes. This heuristic algorithm incorporates entanglement distribution probability (EDP), entanglement swapping probability (ESP), and fidelity metrics to ensure feasibility under noisy intermediate-scale quantum (NISQ) constraints. An online traffic model is considered, where requests arrive according to a Poisson process, each with a fixed execution time and a variable deadline. A time-slotted operation framework is adopted for the quantum network. In each Bell-pair generation window, Bell pairs are generated and distributed between adjacent nodes. The duration of these windows is constrained by the decoherence time of the Bell pairs. Extensive simulations are conducted on the square-grid quantum networks of varying dimensions and parameter ranges, including different ranges of EDP, ESP, and fidelity values. The number of requests and capacity of edges (in terms of quantum channels) are also varied. Across all simulation setups, the proposed PEP model consistently outperforms the LEP model in terms of the blocking ratio (BR).
In this paper, we consider the problem of concurrent multipath routing and end-to-end entanglement distribution for online resource allocation in quantum networks. We propose a heuristic algorithm to solve this problem, considering quantum memory, decoherence time, entanglement distribution probability, and fidelity. A time-slotted quantum network operation model is considered based on the cut-off decoherence time of quantum memories. The proposed heuristic is designed for a quantum network with noisy intermediate scale quantum (NISQ) constraints, including fixed quantum memory decoherence time, and probabilistic entanglement generation and swapping. It considers integer linear programming (ILP)-based and heuristic approaches to select multiple paths and resource allocation in the network. Simulations are performed to evaluate the performance of ILP and heuristic based approaches in terms of requests using multipath approach, blocking ratio, and computation time in a small sized quantum network with few requests. Next, the performance of heuristic based approaches are evaluated for a large problem size. The obtained results ensure that performance of ILP and heuristic based approaches are comparable, and multipath routing outperforms single path routing in terms of blocking ratio.
Quantum networks must deliver end-to-end entanglement whose fidelity meets application requirements, which typically requires entanglement purification along multi-hop paths. Existing scheduling approaches either purify at the link level or optimize end-to-end fidelity for a static set of requests, and do not capture concurrent requests competing for network resources over time. This paper studies concurrent entanglement purification scheduling in a time-slotted quantum network with heterogeneous links, in which requests compete for link capacity and quantum memories, and each request may be served by multiple parallel paths for increased reliability. We formulate a mixed-integer linear programming (MILP) scheduler that maximizes the number of scheduled requests, with max-min path allocation as a fairness criterion, and develop reinforcement learning (RL) schedulers based on DQN, PPO, and SAC, whose rewards balance request success against Bell-pair consumption. Simulations under varying network load, topologies and target fidelity thresholds show that the RL schedulers achieve the highest success rates, improving on MILP by up to 6% and on Progressive Filling and Greedy heuristics by 16.5% and 19.5% respectively, at the cost of higher Bell pair consumption and the deferral of a small fraction of requests. MILP, in contrast, achieves the highest fairness and the lowest Bell pair consumption in most scenarios.
Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.
Many quantum-network applications require end-to-end Bell pairs whose fidelity exceeds a request-specific threshold, but existing entanglement routing algorithms either optimize only throughput without regard for fidelity or enforce fidelity guarantees using centralized controllers with global link-state knowledge. We present Q-GUARD, an online entanglement routing algorithm that enforces per-request fidelity thresholds within a distributed protocol model in which nodes exchange link-state information only with their k-hop neighbors. After link outcomes are realized in each slot, Q-GUARD builds per-link purification cost tables from realized Bell pairs, allocates per-hop fidelity targets using a Werner-state equal-split rule, and selects between candidate path segments using a segment-local expected-goodput (EXG) metric that jointly accounts for swap success, purification overhead, and resource availability. We also introduce Q-GUARD-WS, an extension that exploits per-link hardware quality estimates to allocate purification effort non-uniformly across hops. On synthetic 100-node topologies with heterogeneous link fidelity and stochastic BBPSSW purification, Q-GUARD raises the qualified success rate from under 20\% to over 85\% on 4-hop paths and nearly doubles the qualified service radius in Euclidean distance relative to throughput-only and naive-purification baselines, while Q-GUARD-WS provides additional throughput gains under high hardware heterogeneity.
Entanglement routing establishes remote entanglement connection between two arbitrary nodes, which is one of the most important functions in quantum networks. The existing routing mechanisms mainly improve the robustness and throughput facing the failure of entanglement generations, which, however, rarely include the considerations on the most important metric to evaluate the quality of connection, entanglement fidelity. To solve this problem, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (SD) pairs in quantum networks. In our proposal, we first consider the single S-D pair scenario and design an iterative routing algorithm, Q-PATH, to find the optimal purification decisions along the routing path with minimum entangled pair cost. Further, a low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP, is designed to reduce the computational complexity by using a simple but effective purification decision method. Then we consider the common scenario with multiple S-D pairs and design a greedy-based algorithm considering resource allocation and rerouting process for multiple routing requests. To verify the effectiveness and superiority of the proposed algorithms, extensive simulations are conducted, and the simulation results show that the proposed algorithms not only can provide fidelity-guarantee routing solutions, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio, compared with the existing routing scheme.
Entanglement routing establishes remote entanglement connection between two arbitrary nodes, which is one of the most important functions in quantum networks. The existing routing mechanisms mainly improve the robustness and throughput facing the failure of entanglement generations, which, however, rarely include the considerations on the most important metric to evaluate the quality of connection, entanglement fidelity. To solve this problem, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (S-D) pairs in quantum networks. In our proposal, we first consider the single S-D pair scenario and design an iterative routing algorithm, Q-PATH, to find the optimal purification decisions along the routing path with minimum entangled pair cost. Further, a low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP, is designed to reduce the computational complexity by using a simple but effective purification decision method. Finally, we consider the common scenario with multiple S-D pairs and design a greedy-based algorithm considering resource allocation and re-routing process for multiple routing requests. Simulation results show that the proposed algorithms not only can provide fidelity-guaranteed routing solutions, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio, compared with the existing routing scheme.