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Published March 20, 2024 | in press
Journal Article Open

Benchmarking highly entangled states on a 60-atom analogue quantum simulator


Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2,3,4,5, and it remains unsolved how to estimate the actual entanglement content of experiments6. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2,3,4,5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Copyright and License

© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.


We thank J. Preskill, G. Chan, H.-Y. Huang, M. Stoudenmire, A. Baumgärtner, G. Nomura, E. Bataille, K. Leung and R. Tsai for their feedback on this work. We acknowledge support from the National Science Foundation (NSF) QLCI program (grant no. 2016245), the Department of Energy (grant no. DE-SC0021951), the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NSF grant no. PHY-1733907), the Defense Advanced Research Projects Agency (DARPA) ONISQ program (grant no. W911NF2010021), the Air Force Office of Scientific Research (AFOSR) YIP (grant no. FA9550-19-1-0044), Army Research Office MURI program (grant no. W911NF2010136), NSF CAREER award no. 2237244 and NSF CAREER award no. 1753386. Support is also acknowledged from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. Z.C. acknowledges the DARPA grant no. 134371-5113608 award and NSF 10434. J.C. acknowledges support from the IQIM postdoctoral fellowship. P.S. acknowledges support from the IQIM postdoctoral fellowship. R.F. acknowledges support from the Troesh postdoctoral fellowship. A.E. acknowledges funding by the German National Academy of Sciences Leopoldina under the grant number LPDS 2021-02 and by the Walter Burke Institute for Theoretical Physics at Caltech.


These authors contributed equally: Adam L. Shaw, Zhuo Chen, Joonhee Choi, Daniel K. Mark.

A.L.S., P.S. and R.F. performed the experiments. A.L.S., Z.C. and J.C. performed the data analysis. A.L.S., Z.C., J.C., D.K.M. and A.E. contributed to underlying theory and associated numerics. A.L.S. and M.E. wrote the manuscript with contributions and input from all authors. S.C. and M.E. supervised this project.

Data Availability

The data supporting this study are available from the corresponding author upon request.

Code Availability

The codes supporting this study are available from the corresponding author upon request.

Conflict of Interest

The authors declare no competing interests.


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Additional details

March 21, 2024
March 21, 2024