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arXiv:2502.19118 · IEEE Transactions on Quantum Engineering

Network-Assisted Collective Operations for Efficient Distributed Quantum Computing

Iago F. Llovo, Guillermo Díaz-Camacho, Natalia Costas, Andrés Gómez Tato

Published Jan 1, 2025• 1 citation
arXivHTMLPDF

Abstract

Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, and$R_{zz}(\theta)$gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.

DOI
10.1109/tqe.2025.3619387

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This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. As quantum circuits grow in complexity, efficiently managing the entanglement resources required for communication between quantum processing units (QPUs) becomes increasingly critical. We propose novel methods to optimize entanglement consumption while accounting for network constraints. Our approach leverages graph partitioning techniques to optimize both qubit teleportation and gate teleportation, minimizing the number of Einstein-Podolsky-Rosen (EPR) pairs required to execute general quantum circuits. Additionally, we formulate an integer linear program (ILP) to further reduce entanglement requirements by mapping the logical resources of partitioned circuits to the physical constraints of the underlying quantum network. Finally, we analyze the entanglement cost for implementing the Quantum Fourier Transform (QFT) across multiple QPUs, employing an approach that exploits the circuit's structure to minimize total entanglement consumption. These contributions provide a pathway to scalable and resource-efficient distributed quantum computing.
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 computers face inherent scaling challenges, a fact that necessitates investigation of distributed quantum computing systems, whereby scaling is achieved through interconnection of smaller quantum processing units. However, connecting large numbers of QPUs will eventually result in connectivity constraints at the network level, where the difficulty of entanglement sharing increases with network path lengths. This increases the complexity of the quantum circuit partitioning problem, since the cost of generating entanglement between end nodes varies with network topologies and existing links. We address this challenge using a simple modification to existing partitioning schemes designed for all-to-all connected networks, that efficiently accounts for both of these factors. We investigate the performance in terms of entanglement requirements and optimisation time of various quantum circuits over different network topologies, achieving lower entanglement costs in the majority of cases than state-of-the-art methods. We provide techniques for scaling to large-scale quantum networks employing both network and problem coarsening. We show that coarsened methods can achieve improved solution quality in most cases with significantly lower run-times than direct partitioning methods.
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.
Abstract Distributed quantum computing (DQC) combines the computing power of multiple networked quantum processing modules, ideally enabling the execution of large quantum circuits without compromising performance or qubit connectivity 1,2 . Photonic networks are well suited as a versatile and reconfigurable interconnect layer for DQC; remote entanglement shared between matter qubits across the network enables all-to-all logical connectivity through quantum gate teleportation (QGT) 3,4 . For a scalable DQC architecture, the QGT implementation must be deterministic and repeatable; until now, no demonstration has satisfied these requirements. Here we experimentally demonstrate the distribution of quantum computations between two photonically interconnected trapped-ion modules. The modules, separated by about two metres, each contain dedicated network and circuit qubits. By using heralded remote entanglement between the network qubits, we deterministically teleport a controlled-Z (CZ) gate between two circuit qubits in separate modules, achieving 86% fidelity. We then execute Grover’s search algorithm 5 —to our knowledge, the first implementation of a distributed quantum algorithm comprising several non-local two-qubit gates—and measure a 71% success rate. Furthermore, we implement distributed iSWAP and SWAP circuits, compiled with two and three instances of QGT, respectively, demonstrating the ability to distribute arbitrary two-qubit operations 6 . As photons can be interfaced with a variety of systems, the versatile DQC architecture demonstrated here provides a viable pathway towards large-scale quantum computing for a range of physical platforms.
Quantum computers offer computational advantages for specific problems over classical systems [8], but today's devices are limited by qubit counts and susceptibility to noise. Distributed quantum computing (DQC) addresses these constraints by interconnecting quantum processors via quantum networks to enable cooperative execution of quantum algorithms [4]. DQC can be realized either through quantum teleportation [3], which transfers qubit states across nodes, or through remote gates [7], which enact quantum operations between spatially separated qubits while preserving their physical allocation. Both approaches depend on pre-shared entanglement, which must be distributed across potentially multi-hop quantum networks via entanglement swapping [11]. In realistic settings, DQC performance is influenced by factors such as entanglement fidelity, quantum memory coherence time, and routing path length, yet the impact of these parameters on computational fidelity remains insufficiently understood. This work investigates these effects through simulation of distributed Grover circuits executed over quantum networks with 1-4 routers, incorporating entanglement swapping, network delays, and varying physical constraints to assess how network-level properties affect circuit-level performance.