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arXiv:2301.08269 · IEEE/ACM Transactions on Networking

FENDI: Toward High-Fidelity Entanglement Distribution in the Quantum Internet

Huayue Gu, Zhouyu Li, Ruozhou Yu, Xiaojian Wang, Fangtong Zhou, Jianqing Liu, Guoliang Xue

Published Sep 13, 2024• 28 citations
arXivHTMLPDF

Abstract

A quantum network distributes quantum entanglements between remote nodes, and is key to many applications in secure communication, quantum sensing and distributed quantum computing. This paper explores the fundamental trade-off between the throughput and the quality of entanglement distribution in a multi-hop quantum repeater network. Compared to existing work which aims to heuristically maximize the entanglement distribution rate (EDR) and/or entanglement fidelity, our goal is to characterize the maximum achievable worst-case fidelity, while satisfying a bound on the maximum achievable expected EDR between an arbitrary pair of quantum nodes. This characterization will provide fundamental bounds on the achievable performance region of a quantum network, which can assist with the design of quantum network topology, protocols and applications. However, the task is highly non-trivial and is NP-hard as we shall prove. Our main contribution is a fully polynomial-time approximation scheme to approximate the achievable worst-case fidelity subject to a strict expected EDR bound, combining an optimal fidelity-agnostic EDR-maximizing formulation and a worst-case isotropic noise model. The EDR and fidelity guarantees can be implemented by a post-selection-and-storage protocol with quantum memories. By developing a discrete-time quantum network simulator, we conduct simulations to show the characterized performance region (the approximate Pareto frontier) of a network, and demonstrate that the designed protocol can achieve the performance region while existing protocols exhibit a substantial gap.

DOI
10.1109/tnet.2024.3450271

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A quantum network distributes quantum entanglements between remote nodes, and is key to many applications in secure communication, quantum sensing and distributed quantum computing. This paper explores the fundamental trade-off between the throughput and the quality of entanglement distribution in a multi-hop quantum repeater network. Compared to existing work which aims to heuristically maximize the entanglement distribution rate (EDR) and/or entanglement fidelity, our goal is to characterize the maximum achievable worst-case fidelity, while satisfying a bound on the maximum achievable expected EDR between an arbitrary pair of quantum nodes. This characterization will provide fundamental bounds on the achievable performance region of a quantum network, which can assist with the design of quantum network topology, protocols and applications. However, the task is highly non-trivial and is NP-hard as we shall prove. Our main contribution is a fully polynomial-time approximation scheme to approximate the achievable worst-case fidelity subject to a strict expected EDR bound, combining an optimal fidelity-agnostic EDR-maximizing formulation and a worst-case isotropic noise model. The EDR and fidelity guarantees can be implemented by a post-selection-and-storage protocol with quantum memories. By developing a discrete-time quantum network simulator, we conduct simulations to show the characterized performance region (the approximate Pareto frontier) of a network, and demonstrate that the designed protocol can achieve the performance region while existing protocols exhibit a substantial gap.
Operating a quantum network incurs high capital and operational expenditures, which are expected to be compensated by the high value of enabled quantum applications. However, existing mechanisms mainly focus on maximizing the entanglement distribution rate and neglect the cost incurred on users. This paper aims to address how to utilize quantum network resources in a cost-efficient manner while sustaining high-quantity and high-quality entanglement distribution. We first consider how to establish a steady stream of entanglements between remote nodes with the minimum cost. Utilizing a recent flow-based abstraction and a novel graph representation, we design an optimal algorithm for min-cost remote entanglement distribution. Next, we consider distributing entanglements with the highest fidelity subject to a cost bound and prove its NP-hardness. To explore the cost-fidelity trade-off due to swapping and purification, we propose an approximation scheme for maximizing fidelity while satisfying an arbitrary cost bound. Our algorithms provide rigorous tools for supporting high-performance quantum network applications with financial consideration and offer strong theoretical guarantees. Extensive simulation results validate the advantageous performance in cost efficiency and/or fidelity compared to existing solutions and heuristics.
We consider the problem of optimizing the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum Internet, where the repeaters may perform a probabilistic Bell-state measurement and we may impose a minimum end-to-end fidelity as a requirement. We construct an efficient linear programming (LP) formulation that computes the maximum total achievable entanglement distribution rate, satisfying the end-to-end fidelity constraint in polynomial time (in the number of nodes in the network). Our LP formulation gives the optimal rate for a class of entanglement generation protocols where the repeaters have very short-lived quantum memories. We also propose an efficient algorithm that takes the output of the LP solver as an input and runs in polynomial time (in the number of nodes) to produce the set of paths to be used to achieve the entanglement distribution rate. Moreover, we point out a practical entanglement generation protocol that can achieve those rates.
Entanglement distribution rate (EDR) is a fundamental performance metric for quantum networks. Existing EDR models often focus on expected throughput, but expectation alone is insufficient for Quality-of-Service (QoS)-aware provisioning, where a network must satisfy user demands with a specified probability rather than only on average. This paper studies the distribution of end-to-end EDR over linear quantum repeater chains. Existing works for exact distribution calculation becomes computationally expensive as chain width and length increase. To overcome this, we develop a moment-based analytical approximation that represents each intermediate segment throughput as a Gaussian distribution with matched mean and variance. The algorithm runs in O(L) time for a chain of length L while retaining the accuracy of cumulative distribution information needed for QoS probability queries. Evaluations against exact recursive computation show that the approximation preserves the main throughput trends, achieves speedups up to 6,000×, and maintains modest distributional error in the tested regimes. These results demonstrate that the proposed approximation provides an efficient analytical foundation for QoS-aware EDR analysis and future optimization of quantum repeater chains.
Quantum entanglement distribution between remote nodes is key to many promising quantum applications. Existing mechanisms have mainly focused on improving throughput and fidelity via entanglement routing or single-node scheduling. This paper considers entanglement scheduling and distribution among many source-destination pairs with different requests over an entire quantum network topology. Two practical scenarios are considered. When requests do not have deadlines, we seek to minimize the average completion time of the communication requests. If deadlines are specified, we seek to maximize the number of requests whose deadlines are met. Inspired by optimal scheduling disciplines in conventional single-queue scenarios, we design a general optimization framework for entanglement scheduling and distribution called ESDI, and develop a probabilistic protocol to implement the optimized solutions in a general buffered quantum network. We develop a discrete-time quantum network simulator for evaluation. Results show the superior performance of ESDI compared to existing solutions.
Abstract We address the problem of efficiently distributing high-fidelity entangled states across the nodes of a quantum network—a fundamental requirement for quantum communication, distributed quantum computing, and emerging quantum internet applications. We consider a repeater-based architecture that combines entanglement swapping (or fusion) with purification operations, which enhance fidelity by consuming additional entangled pairs. While prior work has explored routing and limited purification strategies, we present the first algorithms for fidelity-constrained entanglement distribution that are near-optimal and compatible with arbitrary purification models. Our approach introduces the notion of purification-augmented entanglement trees, and we develop dynamic programming (DP) algorithms to construct such trees that maximize the generation rate of entangled pairs (EPs) under fidelity constraints. We further extend our framework to a linear programming (LP)–based flow model that enables simultaneous generation of EPs across multiple source-destination pairs. For multipartite entanglement, we generalize our methods to GHZ and arbitrary graph states, supported by novel analytical models for fidelity evolution under fusion and purification. We evaluate our techniques using the NetSquid quantum network simulator and observe consistent performance improvements over prior approaches—achieving an average 50\% increase in generation rate, and up to 100-150\% in some scenarios.
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.