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IEEE Transactions on Networking

A Nonblocking Multistage Switching Network for Distributed Quantum Computing

Yu Liu, Yingling Mao, Xu Xu, Xiaojun Shang, Fan Ye, Yuanyuan Yang

Published Feb 27, 2025• 6 citations
Publisher

Abstract

Quantum computing, utilizing the unique properties of quantum mechanics, has the potential to revolutionize various fields. However, current quantum processors face challenges in scaling the number of qubits, limiting their practical applications. In response, Distributed Quantum Computing (DQC) has emerged as a promising paradigm where multiple interconnected Quantum Processing Units (QPUs) collaborate to execute quantum circuits. In this paper, we focus on designing networks to interconnect QPUs for the implementation of DQC. We find that in real-world experiments and systems, the photon collection and coupling efficiency is low, leading to significant performance degradation in direct connection networks. To address this limitation, we propose a novel multistage switching network tailored for DQC, which has low system complexity and high entanglement generation rates. The proposed switching network comprises$\log _{2}(N)$stages and$N/2$binary switches at each stage, where N represents the number of QPUs. We prove that the proposed network is nonblocking and develop an efficient routing algorithm with a time complexity of$\mathcal {O}(N\log (N))$. Additionally, we show the success probability of entanglement generation in the proposed switching network. Extensive simulations demonstrate that our network significantly outperforms the highly efficient circuit-switching Beneš network and three direct connection networks.

DOI
10.1109/ton.2025.3544319

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Quantum computing has the potential to solve complicated problems that are impossible for classical servers. Nevertheless, the applications of current quantum processors are restricted by their limited qubit capacity. Distributed Quantum Computing (DQC) is promising to scale up the computing capability by interconnecting quantum processors and performing computing collectively. The network interconnecting quantum processors can impact the efficiency of DQC. In this paper, we analyze and compare the performance of various interconnection networks for DQC. First, we meticulously derive the success probabilities of entanglement generation and the fidelity of shared Bell states generated within three typical static networks: line, ring, and grid. In addition, we propose a switching network with a minimal number of switch stages and evaluate its performance in terms of probability and fidelity. Moreover, we conduct extensive simulations based on real-world parameters to compare the static and switching networks, and the results reveal that the switching network performs better and is more scalable.
Distributed Quantum Computing (DQC) enables the execution of quantum circuits across multiple interconnected quantum processing units (QPUs), but requiring efficient qubit allocation and network topology design to optimize computational performance. Proper qubit allocation minimizes entanglement costs across QPUs, balances computational workload, and ensures efficient execution of quantum computing tasks. Meanwhile, network topology plays a crucial role in reducing entanglement routing complexity and communication overhead for remote quantum gate operations. In this paper, we propose a joint optimization framework for network topology design and qubit allocation in DQC to minimize the communication overhead. We formulate the problem as a tractable integer nonlinear programming model that explicitly incorporates entanglement routing, thereby ensuring a more tractable optimization process. To further improve computational efficiency, we present a partially linearized version of the problem, making it solvable using any classical optimization solver. Extensive simulations on both random and real-world quantum circuits validate the effectiveness of our proposed approach, demonstrating its capability to handle complex quantum circuits while reducing communication costs in DQC.
Distributed Quantum Computing (DQC) has the potential to solve industrial large-scale problems by connecting multiple small quantum processors together to form a larger computing system. Concerning the emerging distributed paradigm, a pivotal challenge lies in crafting specialized network topologies to establish efficient connections among quantum processors while minimizing communication costs. In this paper, we propose a novel DQC topology generation algorithm (DQC-TG) to create optimal and near-optimal network topologies for homogeneous and heterogeneous quantum computers, respectively. Furthermore, for specific quantum circuits requiring diverse communication demands between each pair of qubits, we extend the original algorithm into DQC- TG- Plus to design network topologies tailored for these circuits to further enhance the performance. We perform extensive simulations to evaluate the superiority of the generated network topology designs by our algorithms to baselines.
Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One approach to scale QPUs is to connect multiple machines through quantum and classical channels to form clusters or even quantum networks. Using this paradigm, several smaller QPUs can collectively execute circuits that each would not be able on its own. However, communication between QPUs is costly as it requires generating and maintaining entanglement, and hence it should be used wisely. In this paper, we evaluate the architectures, and in particular the entanglement patterns, of variational quantum circuits in a distributed quantum computing (DQC) setting. That is, using Qiskit, we simulate the execution of an eight qubit circuit using four QPUs each with two computational and two communication qubits where non-local CX-gates are performed using the remote-CX protocol. We compare the performance of various circuits on a binary classification task where training is executed under ideal and testing under noisy conditions. The study provides initial results on suitable VQC architectures for the DQC paradigm, and indicates that a standard VQC baseline is not always the best choice, and alternative architectures that use entanglement between QPUs sparingly deliver better results under noise.
Quantum computing has the potential to outperform classical computing in solving specific problems. However, the limited qubit capacity of existing Quantum Processing Units (QPUs) poses significant barriers to the practical implementation of quantum computing. Distributed quantum computing (DQC) offers a promising approach to scaling the qubit capacity of quantum systems by interconnecting multiple QPUs and enabling collaborative computation. Nevertheless, DQC necessitates implementing remote quantum gate operations that consume entangled qubit pairs, which poses a significant challenge for DQC. In this work, we formulate and investigate the remote gate scheduling (RGS) problem, considering two approaches for remote gate operations: Telegate and Teledata. We propose a hybrid heuristic algorithm that dynamically schedules quantum gate operations within a circuit, executed on distributed QPUs, while minimizing entanglement consumption. We conducted extensive simulations using real-world quantum circuits and processors to evaluate the proposed approach. The results show that our approach reduces entanglement consumption by up to 90% and 25% compared to the two baselines, Telegate-SA and Teledata-ZS, respectively. Furthermore, the execution time of our approach is significantly shorter than that of the baselines.
Distributed quantum computing (DQC) has emerged as a promising approach to overcome the scalability limitations of monolithic quantum processors in terms of computational capability. However, realising the full potential of DQC requires effective resource management and circuit scheduling. This involves efficiently assigning each circuit to a subset of quantum processing units (QPUs), based on factors such as their computational power and connectivity. In heterogeneous DQC networks with arbitrary connectivity topologies and non-identical QPUs, this becomes a complex challenge. This paper addresses resource management and circuit scheduling in such settings, with a focus on computing resource allocation in a quantum data centre. We propose circuit scheduling algorithms based on Mixed-Integer Linear Programming (MILP). Our MILP model accounts for errors arising from inter-QPU communication. In particular, the proposed schemes consider key factors, including network topology, QPU capacities, and quantum circuit structure, to make efficient scheduling and allocation decisions. Simulation results demonstrate that our proposed algorithms significantly improve circuit execution time and scheduling efficiency (measured by makespan and throughput), while also reducing inter-QPU communication overhead, compared to baseline strategies. This work provides valuable insights into resource management strategies for scalable and heterogeneous DQC systems.