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arXiv:2411.02881 · Physical Review Letters

Distributed Quantum Simulation

Anonymous, Jue Xu, Wenjun Yu, Zekun Ye, Penghui Yao, Qi Zhao

Published Sep 14, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum simulation is a promising pathway toward practical quantum advantage by simulating large-scale quantum systems. In this Letter, we propose communication-efficient distributed quantum simulation protocols by exploring three quantum simulation algorithms, including the product formula, the truncated Taylor series, and quantum signal processing over a quantum network. Crucially, our protocols significantly reduce the local hardware requirements of individual quantum processing units while ensuring the overall gate complexity does not exceed that of standard monolithic architectures. Our protocols are further shown to be optimal by deriving a lower bound on the quantum communication complexity for distributed quantum simulations with respect to evolution time and the number of distributed quantum processing units. Additionally, our distributed techniques go beyond quantum simulation and are applied to distributed versions of Grover's algorithm and quantum phase estimation. Our work not only paves the way for achieving a practical quantum advantage by scalable quantum simulation but also enlightens the design of more general distributed architectures across various physical systems for quantum computation.

DOI
10.1103/zh7p-f7tc

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Quantum simulation is a promising pathway toward practical quantum advantage by simulating large-scale quantum systems. In this Letter, we propose communication-efficient distributed quantum simulation protocols by exploring three quantum simulation algorithms, including the product formula, the truncated Taylor series, and quantum signal processing over a quantum network. Crucially, our protocols significantly reduce the local hardware requirements of individual quantum processing units while ensuring the overall gate complexity does not exceed that of standard monolithic architectures. Our protocols are further shown to be optimal by deriving a lower bound on the quantum communication complexity for distributed quantum simulations with respect to evolution time and the number of distributed quantum processing units. Additionally, our distributed techniques go beyond quantum simulation and are applied to distributed versions of Grover's algorithm and quantum phase estimation. Our work not only paves the way for achieving a practical quantum advantage by scalable quantum simulation but also enlightens the design of more general distributed architectures across various physical systems for quantum computation.
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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, andRzz(θ)R_{zz}(\theta)Rzz​(θ)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.