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IEEE International Conference on Quantum Computing and Engineering (QCE)

Generation and Distribution of GHZ States in Quantum Networks

Mohammad Ghaderibaneh, Himanshu Gupta, C. R. Ramakrishnan

Published Sep 17, 2023• 14 citations
Publisher

Abstract

In quantum networks, multipartite entangled states distributed over the network are useful in implementing and supporting many quantum network applications for communications, sensing, and computing. The focus of our work is to de-velop techniques to efficiently generate distributed Greenberger-Horne-Zeilinger (GHZ) states, a special class of multipartite entanglement states. Prior works on generating GHZ states have focused on the objective of minimizing the number of maximally entangled (bipartite) pairs (EPs), while ignoring the stochastic nature of quantum processes and assuming uniform network links for generating EPs. In contrast, in our work, we take into consideration the stochastic nature of quantum networks, and focus on maximizing the expected generated rate of the GHZ states under given fidelity constraints. In this context, we develop two efficient generation schemes, viz., Fusion - Retain - only and General Fusion, comprised of optimal or near-optimal sub-steps. Both schemes, at a high-level, first determine a way to “connect” the nodes over which the GHZ state is to distributed, and then, determine a sequence of fusion operations on the EPs created over the connections. Using extensive simulations over a quantum network simulator (NetSquid), we demonstrate the effectiveness of our developed techniques and show that our schemes outperform prior work as well as a simple centralized approach by up to orders of magnitude while generating GHZ states of tolerable fidelity.

DOI
10.1109/qce57702.2023.00127

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In quantum networks, multipartite entangled states distributed over the network are useful in implementing and supporting many quantum network applications for communications, sensing, and computing. The focus of our work is to de-velop techniques to efficiently generate distributed Greenberger-Horne-Zeilinger (GHZ) states, a special class of multipartite entanglement states. Prior works on generating GHZ states have focused on the objective of minimizing the number of maximally entangled (bipartite) pairs (EPs), while ignoring the stochastic nature of quantum processes and assuming uniform network links for generating EPs. In contrast, in our work, we take into consideration the stochastic nature of quantum networks, and focus on maximizing the expected generated rate of the GHZ states under given fidelity constraints. In this context, we develop two efficient generation schemes, viz., Fusion - Retain - only and General Fusion, comprised of optimal or near-optimal sub-steps. Both schemes, at a high-level, first determine a way to “connect” the nodes over which the GHZ state is to distributed, and then, determine a sequence of fusion operations on the EPs created over the connections. Using extensive simulations over a quantum network simulator (NetSquid), we demonstrate the effectiveness of our developed techniques and show that our schemes outperform prior work as well as a simple centralized approach by up to orders of magnitude while generating GHZ states of tolerable fidelity.
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, quantum networks can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph-based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
Abstract Multipartite entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states, are important resources in multiparty quantum networking tasks. We consider protocols for generating such states from networks of Bell pairs and local operations and classical communication. We present a computationally-efficient protocol for generating GHZ states that is also efficient with respect to the number of consumed Bell pairs, (local) gates, and Bell-pair sources. Our protocol: (1) requires O ( N ) gates in a network with N nodes, independent of the network topology; (2) has time complexity O ( N 2 ), avoiding the Steiner tree and any other computationally-hard problem; (3) maintains a near-optimal number of consumed Bell pairs. Numerically, our protocol outperforms those based on (approximate) Steiner trees with respect to the number of gates and Bell-pair sources. We prove that the minimal Bell-pair source cost is given by solving the graph-theoretic dominating set problem, and we demonstrate numerically that our protocol is nearly optimal for this quantity. Finally, we analytically characterize the impact of noisy Bell pairs and gates on the fidelity of the distributed GHZ states.
We study the performance (rate and fidelity) of distributing multipartite entangled states in a quantum network through the use of a central node. Specifically, we consider the scenario where the multipartite entangled state is first prepared locally at a central node and then transmitted to the end nodes of the network through quantum teleportation. As our first result, we present leading-order analytical expressions and lower bounds for both the rate and fidelity at which a specific class of multipartite entangled states, namely, Greenberger-Horne-Zeilinger (GHZ) states, are distributed. Our analytical expressions for the fidelity accurately account for time-dependent depolarizing noise encountered by individual quantum bits while stored in quantum memory, as verified using Monte Carlo simulations. As our second result, we compare the performance to the case where the central node is an entanglement switch and the GHZ state is created by the end nodes in a distributed fashion. Apart from these two results, we outline how the teleportation-based scheme could be physically implemented using trapped ions or nitrogen-vacancy centers in diamond.
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.
A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.
We consider problems of distributing high-fidelity entangled states across nodes of a quantum network. We consider a repeater-based network architecture with entanglement swapping (fusion) operations for generating long-distance entanglements, and purification operations that produce high-fidelity states from several lower-fidelity states. The contributions of this paper are two-fold: First, while there have been several works on fidelity-aware routing and incorporating purification into routing for generating EPs, this paper presents the first algorithms for optimal solutions to the high-fidelity EP distribution problem. We provide a dynamic programming algorithm for generating the optimal tree of operations to produce a high-fidelity EP, and an LP-based algorithm for generating an optimal collection of trees. Second, following the EP algorithms, this paper presents the first algorithms for the high-fidelity GHZ-state distribution problem and characterizes its optimality. We evaluate our techniques via simulations over NetSquid, a quantum network simulator.