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.
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.
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.
Entanglement purification is a fundamental operation to combat against quantum decoherence and improve the fidelity of the entanglement. When multiple rounds of entanglement purification are performed, the fidelity of the final entanglement depends on the way how we schedule entanglement purification operations at each round. In this paper, we formulate and analyze the optimal entanglement purification scheduling problem arising from this context. Our main results include an optimal link-level purification scheduling algorithm and a joint entanglement purification scheduling and routing algorithm to establish fidelity-guaranteed end-to-end entanglements with quasi-optimal throughput in quantum networks. Our algorithmic framework developed in this paper can serve as functional building blocks for entanglement provisioning to support high-fidelity quantum information transfer by exploiting the limited quantum resources in a cost-effective way in order to fully realize the unrivalled capabilities offered by quantum networks.
Quantum networks, as a pivotal platform to support numerous quantum applications, have the potential to far exceed traditional communication networks. Establishing end-to-end entanglement connections with guaranteed fidelity is a key prerequisite for realizing the functionality of quantum networks. Entanglement purification techniques are commonly used in the entanglement distribution process to provide end-to-end entanglement connections that meet the fidelity requirements. Since the purification operation sacrifices a certain amount of entanglement resources, it is critical and challenging to efficiently utilize the scarce entanglement resources in quantum networks with concurrent competing requests. To address this problem, we propose a novel demand-oriented resource scheduling (DRS) algorithm. Considering the overall network demand, DRS introduces a congestion factor to evaluate the resource demand of each link, and performs purification operations sequentially based on the congestion level of the links, thus avoiding the excessive consumption of entanglement resources of bottleneck links. Extensive simulation results show that the DRS algorithm can achieve higher network throughput with similar resource conversion rates compared to traditional resource allocation schemes. Our work provides a new scheme for the resource scheduling problem under concurrent competing requests, which can promote the further development of existing entanglement routing techniques.
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.
Entanglement-based quantum networks provide unconditionally secure quantum communication by distributing end-to-end entangled pairs. To reach such goal, entanglement swapping and purification are two necessary operations, which can expand the entanglement distance and improve the fidelity of entangled pairs, respectively. During the end-to-end entanglement distribution process, the execution sequence of these two operations has a significant impact on the final performance, such as throughput and fidelity. Thus, how to schedule the sequence of swapping and purification becomes a critical problem in quantum networks. Our work focuses on such scheduling problem and we devise an efficient solution with fidelity maintenance. In our article, we first propose a concurrent swapping method for any-length path to reduce delay. Secondly, by modeling the scheduling sequence as a permutation problem, we obtain an optimal scheduling principle called “prioritized purification (PP)”. Finally, to meet the fidelity requirement of the end-to-end entangled pairs, we propose a fidelity maintenance scheme based on PP (FMSPP). The simulation results show that the proposed FMSPP can achieve higher distribution rates and less resource overhead than other scheduling solutions, and the advantages are more significant when there are more hops on the path.
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.