Distributed Quantum Simulation

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.