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Entanglement accelerates quantum simulation

Nature Physics volume 21, pages 1338–1345 (2025)Cite this article

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Abstract

Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. Classical simulation methods can efficiently simulate many-body states with low entanglement, but struggle as the degree of entanglement grows. Here we investigate the relationship between quantum entanglement and quantum simulation, and show that product formula approximations for simulating many-body systems can perform better for entangled systems. We establish an upper bound for algorithmic error in terms of entanglement entropy that is tighter than previous results, and develop an adaptive simulation algorithm that incorporates measurement gadgets to estimate the algorithmic error. This shows that entanglement is not only an obstacle to classical simulation, but also a feature that can accelerate quantum algorithms.

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Fig. 1: Entanglement entropy and Trotter error in one segment.
Fig. 2: Comparison of theoretical bounds.
Fig. 3: Cost of different simulation methods and Trotter error terms in the light-cone structure.
Fig. 4: Number of Trotter steps determined with different error bounds for PF2.

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Code availability

The code used in this study is available via GitHub at https://github.com/zhaoqthu/Entanglement-accelerates-quantum-simulation.

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Acknowledgements

We thank W. Yu, F. Shi and J. Xu for helpful discussions. Q.Z. acknowledges funding from the Innovation Program for Quantum Science and Technology via Project No. 2024ZD0301900, the National Natural Science Foundation of China (NSFC) via Project Nos 12347104 and 12305030, the Guangdong Basic and Applied Basic Research Foundation via Project No. 2023A1515012185, the Hong Kong Research Grant Council (RGC) via Grant Nos 27300823, N_HKU718/23 and R6010-23, Guangdong Provincial Quantum Science Strategic Initiative No. GDZX2303007 and the HKU Seed Fund for Basic Research for New Staff via Project No. 2201100596. Y.Z. acknowledges the support of the Innovation Program for Quantum Science and Technology under Grant Nos 2024ZD0301900 and 2021ZD0302000, the NSFC under Grant No. 12205048, the Shanghai Science and Technology Innovation Action Plan under Grant No. 24LZ1400200, the Shanghai Municipal Science and Technology Grant No. 25TQ003 and start-up funding from Fudan University. A.M.C. acknowledges support from the United States Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing programme (Award No. DE-SC0020312) and from the National Science Foundation (QLCI Grant No. OMA-2120757).

Author information

Authors and Affiliations

  1. QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong, Hong Kong, China

    Qi Zhao

  2. Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education), Fudan University, Shanghai, China

    You Zhou

  3. Hefei National Laboratory, Hefei, China

    You Zhou

  4. Department of Computer Science, Institute for Advanced Computer Studies, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA

    Andrew M. Childs

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  1. Qi Zhao
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  2. You Zhou
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Contributions

Q.Z., Y.Z. and A.M.C. collaboratively initialized the research ideas, derived the mathematical proofs and wrote the manuscript. Q.Z. performed the numerical simulations.

Corresponding authors

Correspondence to Qi Zhao, You Zhou or Andrew M. Childs.

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Nature Physics thanks Burak Şahinoğlu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections I–VII and Figs. 1 and 2.

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Zhao, Q., Zhou, Y. & Childs, A.M. Entanglement accelerates quantum simulation. Nat. Phys. 21, 1338–1345 (2025). https://doi.org/10.1038/s41567-025-02945-2

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