This paper studies reliable teleportation of quantum bits (called qubits) in a quantum data network with multiple sources (S) and destinations (D) as well as repeaters. To teleport qubits for a SD pair reliably, not only an entanglement path for the SD pair, but also appropriate purification of the links along the path is required to ensure that the end-to-end (E2E) fidelity of the established entanglement connections is high enough.This is the first work on quantifying the E2E fidelity, and also using this E2E fidelity to determine critical links to achieve the most resource efficient purification. A novel approach called E2E Fidelity aware Routing and Purification (EFiRAP) is proposed to maximize network throughput, i.e., the number of entanglement connections among multiple SD pairs, with each connection having an E2E fidelity above a given required threshold. EFiRAP accomplishes this goal by first preparing multiple candidate entanglement paths and determining optimal purification schemes, and then selecting the final set of entanglement paths that can maximize network throughput under the given quantum resource constraints. Existing works only ensured the fidelity of individual links, rather than the E2E fidelity is above a given threshold. Extensive simulations show that the proposed EFiRAP can enhance network throughput by about 50% when compared with the state-of-the-art approach.
This paper studies reliable teleportation of quantum bits (called qubits) in a quantum data network with multiple sources (S) and destinations (D) as well as repeaters. To teleport qubits for a SD pair reliably, not only an entanglement path for the SD pair, but also appropriate purification of the links along the path is required to ensure that the end-to-end (E2E) fidelity of the established entanglement connections is high enough.This is the first work on quantifying the E2E fidelity, and also using this E2E fidelity to determine critical links to achieve the most resource efficient purification. A novel approach called E2E Fidelity aware Routing and Purification (EFiRAP) is proposed to maximize network throughput, i.e., the number of entanglement connections among multiple SD pairs, with each connection having an E2E fidelity above a given required threshold. EFiRAP accomplishes this goal by first preparing multiple candidate entanglement paths and determining optimal purification schemes, and then selecting the final set of entanglement paths that can maximize network throughput under the given quantum resource constraints. Existing works only ensured the fidelity of individual links, rather than the E2E fidelity is above a given threshold. Extensive simulations show that the proposed EFiRAP can enhance network throughput by about 50% when compared with the state-of-the-art approach.
The core function of quantum networks is to establish high-fidelity quantum entanglement for long-distance communication. However, the main challenge is to efficiently allocate resources under limited conditions, maximize throughput, satisfy end-to-end (E2E) fidelity requirements, and prevent quantum decoherence caused by inefficient routing algorithms. Current research focuses on optimizing either throughput or fidelity, with a lack of approaches that optimize both simultaneously; furthermore, existing algorithms suffer from high computational complexity. To tackle these challenges, this study proposes a Satisfying Fidelity Threshold Routing and Adaptive Purification Strategy (SFTRAP). SFTRAP maximizes throughput for each request by selecting multiple paths and dynamically choosing links for entanglement purification based on the current state of link resources, thus minimizing throughput loss while satisfying fidelity threshold. The strategy also adaptively adjusts the number of purification rounds according to the fidelity threshold, thereby optimizing the time required for deep purification and enhancing algorithmic efficiency. For multi-request scenarios, SFTRAP employs a priority sorting mechanism that takes into account both path cost and path freedom, which refines request scheduling and path selection to create more efficient request combinations, thus further boosting the overall network throughput. Simulation results indicate that SFTRAP surpasses state-of-the-art methods in terms of both throughput and algorithmic efficiency, highlighting its potential for optimizing resources in quantum networks.
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.
Abstract Quantum networks can establish End-to-End (E2E) entanglement connections between two arbitrary nodes for various quantum applications through entanglement swapping. To support quantum applications reliably, quantum networks should establish E2E entanglement connections with desired entanglement fidelity by performing entanglement purification. The existing works provide mechanisms for link-level purification, which, however, leads to low throughput because of lacking consideration on purifications at network-level. (That is, efficiently allocating scarce resources to jointly purify entanglements under the situation with multiple concurrent requests in a network remains a critical but unsolved problem.) To address this problem, we analyze the cost of purification, design the E2E fidelity calculation method in detail, and propose a novel approach called Purification Scheduling Control (PSC). The basic idea of PSC is to determine the appropriate purification through jointly optimizing purification and resource allocation processes based on conflict avoidance. We conduct extensive experiments showing that PSC can maximize throughput under the fidelity requirement. This solution should spur the development of more applied reliable routing designs for quantum networks, combining quantum error correction, quantum applications, and computer network theory.
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.
Complex quantum networks can support a diverse set of long-range entanglement distribution schemes ranging from linear repeater protocols to multipath entanglement purification strategies. As a result, a network's resourcefulness, that is its ability to facilitate quantum communication, depends on the deployed distribution scheme. In this work, we analyse and compare the resourcefulness of quantum networks across a broad range of network topologies, including both regular and random networks, under two distinct entanglement distribution schemes. The first relies on entanglement swapping along a single path connecting a source-target pair, while the second exploits entanglement purification using multiple paths between the same source and target nodes. The resourcefulness of the network is quantified using a recently described metric [1] that averages over the maximum teleportation fidelity between arbitrary source-target pairs in the network. We present algorithms for estimating this metric under constraints of edge-usage and ordering of paths. Our results not only demonstrate the sensitivity of the average maximum teleportation fidelity metric to the choice of entanglement distribution protocol, but also highlight the significant improvements enabled by network purification schemes. In particular, purification-based approaches can substantially enhance average teleportation fidelity, thereby improving the overall teleportation capability of quantum networks.
Quantum Networks (QNs) typically leverage teleportation to send quantum bits (called qubits) to their destinations. To teleport a data qubit from Alice to Bob, one Entanglement Connection (EC) between Alice and Bob needs to be established. Accordingly, we have to concurrently establish as many requested ECs as possible in order to maximize the network throughput. Conventional methods either assumed a known traffic matrix and calculated the Entanglement Paths (EPs) for all requests in one batch or maximized the number of ECs established between all Source-Destination (SD) pairs without considering the amount of data qubits to be teleported. These methods are not scalable in large scale QNs since it is time consuming to calculate the EPs for a batch of requests. In addition, there may be only very few data qubits to be teleported between some SD pairs. Accordingly, the latter method may establish many useless ECs. To address these issues, we propose a Dynamic Entanglement Routing (DER) scheme which determines the EPs based on stream processing. By introducing a method to derive an appropriate purification scheme along each EP, we further extend DER to Dynamic Entanglement Routing with Purification (DERP) that provides fidelity guarantee to the established ECs. Through extensive simulations, we demonstrate that DER outperforms two representative heuristics by up to 52.79% and 61.27%, respectively, in terms of average request completion time and when we have to ensure the fidelity of the established ECs, this performance improvement will become 21.05% and 48.67%, respectively, if DERP is adopted.