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IEEE Transactions on Network Science and Engineering

An Efficient Scheduling Scheme of Swapping and Purification Operations for End-to-End Entanglement Distribution in Quantum Networks

Zhaoying Wang, Jian Li, Kaiping Xue, David S. L. Wei, Ruidong Li, Nenghai Yu, Qibin Sun, Jun Lu

Published Jul 26, 2023• 31 citations
Publisher

Abstract

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.

DOI
10.1109/tnse.2023.3299177

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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.
Swapping and purification are the two fundamental building blocks for high-fidelity entanglement distribution in multi-hop quantum networks. Unfortunately, it is still a mystery how they intertwine with each other to affect the fidelity and cost of end-to-end entanglements. Current scheduling algorithms consider this problem under relatively limited assumptions and a critical yet unjustified conjecture. In this work, we first consider more general assumptions with operation failures and, accordingly, extend a tree-based modeling for joint swapping and purification. Then, we analytically prove the previous conjecture that the optimal strategy underBinary systemis always to purify the entanglements before any swapping. This sheds light on the protocol and device design for quantum networks. We then further propose a tree-based algorithm, which can efficiently schedule swapping and purification along a path for bothBinaryandWerner systems. Extensive simulations of the proposed method against state-of-the-art solutions show that our method uses fewer entanglements to establish qualified end-to-end entanglements, and thus achieves higher network throughput.
Swapping and purification are the two fundamental building blocks for multi-hop quantum networks. However, their interplay and its impact on end-to-end fidelity and cost are not yet fully explored. Existing scheduling algorithms address this problem under certain simplified assumptions and models that may not fully capture the complexities of real scenarios. In this work, we first consider more general assumptions that account for operation failures and extend a tree-based modeling approach for joint swapping and purification. Then, for the first time, we analytically prove the previous conjecture that the optimal strategy under Binary system is always to purify the entanglements before any swapping. This sheds light on the protocol and device design for entanglement distribution in quantum networks. We then further propose a tree-based algorithm, which can efficiently schedule swapping and purification along a path for both Binary and Werner systems. Extensive simulations have been conducted to evaluate the proposed method against the existing solutions, and the results show that our method uses fewer entanglements to establish qualified end-to-end entanglements and thus achieves higher network throughput.
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.
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, 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 communication technology provides an absolute security guarantee for information transmitted between quantum applications. To establish practical quantum networks, providing entangled pairs of stable quality, suitable for varying distances, is crucial. However, due to the inherent losses and imperfections of the operations during the entanglement distribution process, the fidelity of end-to-end entangled pairs will be greatly reduced. Consequently, establishing fidelity-guaranteed entangled pairs will be challenging. In this work, we introduce an entanglement distribution method that ensures the fidelity requirements of applications across different distances, while maintaining high efficiency. The method first decomposes the end-to-end fidelity requirements to target fidelity for purification at each link, based on the worst-case consumption. Then it performs multiple-round symmetrical entanglement purification based on the backup scheme to purify each entangled pair to the target value. The experimental results indicate that the scheme has acceptable performance in resource consumption and great feasibility while ensuring high efficiency.