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IEEE Transactions on Communications

A Heuristic Remote Entanglement Distribution Algorithm on Memory-Limited Quantum Paths

Lutong Chen, Kaiping Xue, Jian Li, Nenghai Yu, Ruidong Li, Jianqing Liu, Qibin Sun, Jun Lu

Published Sep 12, 2022• 34 citations
Publisher

Abstract

Remote entanglement distribution plays a crucial role in large-scale quantum networks, and the key enabler for entanglement distribution is quantum routers (or repeaters) that can extend the entanglement transmission distance. However, the performance of quantum routers is far from perfect yet. Amongst the causes, the limited quantum memories in quantum routers largely affect the rate and efficiency of entanglement distribution. To overcome this challenge, this paper presents a new modeling for the maximization of entanglement distribution rate (EDR) on a memory-limited path, which is then transformed into entanglement generation and swapping sub-problems. We propose a greedy algorithm for short-distance entanglement generation so that the quantum memories can be efficiently used. As for the entanglement swapping sub-problem, we model it using an Entanglement Graph (EG), whose solution is yet found to be at least NP-complete. In light of it, we propose a heuristic algorithm by dividing the original EG into several sub-problems, each of which can be solved using dynamic programming (DP) in polynomial time. By conducting simulations, the results show that our proposed scheme can achieve a high EDR, and the developed algorithm has a polynomial-time upper bound and reasonable average runtime complexity.

DOI
10.1109/tcomm.2022.3205683

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Remote entanglement distribution plays a crucial role in large-scale quantum networks, and the key enabler for entanglement distribution is quantum routers (or repeaters) that can extend the entanglement transmission distance. However, the performance of quantum routers is far from perfect yet. Amongst the causes, the limited quantum memories in quantum routers largely affect the rate and efficiency of entanglement distribution. To overcome this challenge, this paper presents a new modeling for the maximization of entanglement distribution rate (EDR) on a memory-limited path, which is then transformed into entanglement generation and swapping sub-problems. We propose a greedy algorithm for short-distance entanglement generation so that the quantum memories can be efficiently used. As for the entanglement swapping sub-problem, we model it using an Entanglement Graph (EG), whose solution is yet found to be at least NP-complete. In light of it, we propose a heuristic algorithm by dividing the original EG into several sub-problems, each of which can be solved using dynamic programming (DP) in polynomial time. By conducting simulations, the results show that our proposed scheme can achieve a high EDR, and the developed algorithm has a polynomial-time upper bound and reasonable average runtime complexity.
This paper considers the problem of finding an optimal order for entanglement swapping in a heterogeneous path of quantum repeaters so as to maximize the path throughput defined as the delivery rate of end-to-end entanglements. The primary difficulty in addressing this problem lies in the vast array of possible swapping orders for large paths and the complexity of the expected throughput, which depends on the attributes of each node and edge along the path, as well as the order of swapping. To cope with these issues, we first propose simple approximations in estimating the swapping outcome between two entanglement distributions that can run in constant time, thereby providing an efficient approach for evaluating and comparing different swapping orders, allowing us to solve the problem exactly for small paths. Second, as the number of possible orders grows exponentially with the number of repeaters in the path, we develop an efficient heuristic based on the greedy selection of nodes to sequentially perform swaps according to their swapping scores, defined as the expected number of entanglements resulting from their swaps. The scores are local but dynamic in the sense that they depend not just on the entanglement distributions available on the path but also on prior swapping decisions. Finally, we illustrate the efficiency and effectiveness of our proposed model and approach through extensive experimentation conducted using a general quantum network simulator.
Entanglement swapping enables entanglement distribution between distant nodes in quantum networks. This paper aims at designing remote entanglement distribution (RED) protocols to schedule entanglement swapping for maximizing the entanglement distribution rate (EDR). The concept of Enodes is introduced to represent the entangled quantum bit pairs in the network. With such a concept, we can transform the design of the optimal RED protocols into solving certain linear programming problems. In addition, we study RED in the homogeneous repeater chain, which is a basic and critical quantum network. Specifically, we determine the closed-form expression for the maximum EDR in such a setting. Our results will enable the distribution of long-distance entanglement with noisy intermediate-scale quantum (NISQ) technologies.
Distributing entanglement between distant nodes is an essential task in quantum networks. To achieve this task, quantum repeaters have been introduced to perform entanglement swapping. This paper offers a design of remote entanglement distribution (RED) protocols that maximize the entanglement distribution rate (EDR). We introduce the concept of enodes, representing the entangled quantum bit (qubit) pairs in the network. This concept enables us to design the optimal RED protocols based on the solutions of some linear programming problems. Moreover, we investigate RED in a homogeneous repeater chain, which is a building block for many quantum networks. In particular, we determine the maximum EDR for homogeneous repeater chains in a closed form. Our results enable the distribution of long-distance entanglement with noisy intermediate-scale quantum (NISQ) technologies and provide insights into the design and implementation of general quantum networks.
Entanglement distribution via probabilistic entanglement swapping across a quantum repeater chain connecting two quantum nodes is a challenging problem. The difficulty lies in the exponential number of possible swapping structures within the repeater chain, necessitating efficient search algorithms, especially as the chain length increases. In this paper, we first explore the algorithmic design to facilitate the search for the optimal swapping structure along a repeater chain, aiming to maximize the entanglement distribution rate. Second, we examine the computational complexities of various algorithms and find that prior approaches exhibit excessively high complexities. Thus, we propose an efficient dynamic programming-based algorithm, FastHED, that leverages heuristics to expedite the search for the optimal swapping structure. Our theoretical analysis reveals that the upper bound of the proposed algorithm’s computational complexity isO(n(log⁡n)3)O(n(\log n)^{3})O(n(logn)3)(more precisely,O(n(log⁡n)2log⁡log⁡n)O(n(\log n)^{2} \log \log n)O(n(logn)2loglogn)whenn≤229n\le 2^{29}n≤229), a significant improvement over the existing algorithm with a complexity ofO(n2log⁡n)O(n^{2} \log n)O(n2logn), where n denotes the repeater chain’s length. Additionally, we design a best-first framework to evaluate the performance of different algorithms. Numerical results show that our algorithm achieves a higher average entanglement distribution rate than existing algorithms.
Entanglement distribution between distant quantum nodes plays an essential role in realizing quantum networks’ capabilities. In addition to path selection, remote entanglement distribution involves two pivotal quantum operations, i.e., entanglement generation and entanglement swapping. The existing studies mainly adopt two methods, i.e., Tell-and-Generation (TAG) and Tell-and-Swapping (TAS), to manage these two quantum operations on a selected path. However, both methods fatally introduce redundant stop-and-wait processes, which are detrimental to the performance of remote entanglement distribution in terms of latency and fidelity. To achieve low-latency and high-fidelity entanglement distribution between far-off quantum nodes, we propose a segment-based method consisting of an entanglement generation algorithm and a segment design to diminish the unnecessary stop-and-wait processes. The entanglement generation algorithm adopts a concurrent design to establish entanglement links using the one-demand generation model, thus effectively reducing waiting time compared to hop-by-hop and parallel designs. The segment design is proposed to split a long-distance path into multiple short-haul segments with the similar ability to swap entanglement, and these segments build multi-hop entanglement connections in parallel. Extensive simulations show that the segment-based method significantly outperforms the existing methods, including TAG and TAS, in entanglement distribution latency and effectively mitigates fidelity attenuation.
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.