A Caltech Library Service

Preparing random states and benchmarking with many-body quantum chaos

Choi, Joonhee and Shaw, Adam L. and Madjarov, Ivaylo S. and Xie, Xin and Finkelstein, Ran and Covey, Jacob P. and Cotler, Jordan S. and Mark, Daniel K. and Huang, Hsin-Yuan and Kale, Anant and Pichler, Hannes and Brandão, Fernando G. S. L. and Choi, Soonwon and Endres, Manuel (2023) Preparing random states and benchmarking with many-body quantum chaos. Nature, 613 (7944). pp. 468-473. ISSN 0028-0836. doi:10.1038/s41586-022-05442-1.

Image (JPEG) (Extended Data Fig. 1: Experimental system and parameter feedback) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 2: Universality of moments of the projected ensemble) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 3: Emergent randomness and benchmarking in other quantum systems) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 4: Detecting errors during quantum evolution) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 5: Finite sampling analysis for F꜀) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 6: Predicting fidelity scaling) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 7: Comparison to digital quantum devices executing random circuits) - Supplemental Material
See Usage Policy.

Image (JPEG) (Extended Data Fig. 8: Applications to target state benchmarking) - Supplemental Material
See Usage Policy.

[img] PDF (Supplementary Sections 1–8 and reference) - Supplemental Material
See Usage Policy.


Use this Persistent URL to link to this item:


Producing quantum states at random has become increasingly important in modern quantum science, with applications being both theoretical and practical. In particular, ensembles of such randomly distributed, but pure, quantum states underlie our understanding of complexity in quantum circuits1 and black holes, and have been used for benchmarking quantum devices in tests of quantum advantage. However, creating random ensembles has necessitated a high degree of spatio-temporal control placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 10⁴ experimental samples. This method has broad applicability, as we demonstrate for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analogue and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics and enables applications of this concept in a much wider context.

Item Type:Article
Related URLs:
URLURL TypeDescription ReadCube access ItemDiscussion Paper InCaltech News
Choi, Joonhee0000-0002-3507-8751
Shaw, Adam L.0000-0002-8059-5950
Xie, Xin0000-0003-4575-6103
Finkelstein, Ran0000-0002-4524-5875
Covey, Jacob P.0000-0001-5104-6883
Cotler, Jordan S.0000-0003-3161-9677
Mark, Daniel K.0000-0002-5017-5218
Huang, Hsin-Yuan0000-0001-5317-2613
Kale, Anant0000-0002-7049-5630
Pichler, Hannes0000-0003-2144-536X
Brandão, Fernando G. S. L.0000-0003-3866-9378
Choi, Soonwon0000-0002-1247-062X
Endres, Manuel0000-0002-4461-224X
Alternate Title:Emergent Quantum Randomness and Benchmarking from Hamiltonian Many-body Dynamics, Emergent Randomness and Benchmarking from Many-Body Quantum Chaos
Additional Information:© 2023 Springer Natur. We acknowledge experimental help from P. Scholl during the revision of this manuscript, as well as discussions with A. Deshpande and A. Gorshkov. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF grant no. PHY-1733907), the NSF CAREER award (no. 1753386), the AFOSR YIP (no. FA9550-19-1-0044), the DARPA ONISQ programme (no. W911NF2010021), the Army Research Office MURI program (no. W911NF2010136), the NSF QLCI program (no. 2016245), the DOE (grant no. DE-SC0021951), the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator (grant no. DE-AC02-05CH11231) and F. Blum. J.C. acknowledges support from the IQIM postdoctoral fellowship. A.L.S. acknowledges support from the Eddleman Quantum graduate fellowship. R.F. acknowledges support from the Troesh postdoctoral fellowship. J.P.C. acknowledges support from the PMA Prize postdoctoral fellowship. H.P. acknowledges support by the Gordon and Betty Moore Foundation. H.-Y.H. is supported by the J. Yang & Family Foundation. A.K. acknowledges funding from the Harvard Quantum Initiative (HQI) graduate fellowship. J.S.C. is supported by a Junior Fellowship from the Harvard Society of Fellows and the US Department of Energy under grant contract no. DE-SC0012567. S.C. acknowledges support from the Miller Institute for Basic Research in Science. These authors contributed equally: Joonhee Choi, Adam L. Shaw. Contributions. J.C., A.L.S, S.C. and M.E. conceived the idea and experiment. J.C. and A.L.S. performed the experiments and data analysis. J.C., A.L.S., J.S.C., D.K.M., H.-Y.H., H.P., F.G.S.L.B., S.C. and M.E. contributed to the underlying theory. J.C., A.L.S., I.S.M., X.X., R.F., J.P.C. and A.K. contributed to building the experimental set-up and data taking. J.C., A.L.S., S.C. and M.E. wrote the manuscript with input from all authors. S.C. and M.E. supervised this project. Data availability. The data that support the findings of this study are available from the corresponding authors upon reasonable request. Code availability. The code that supports the findings of this study is available from the corresponding authors upon reasonable request. The authors declare no competing interests.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0044
Defense Advanced Research Projects Agency (DARPA)W911NF2010021
Army Research Office (ARO)W911NF2010136
Department of Energy (DOE)DE-SC0021951
Department of Energy (DOE)DE-AC02-05CH11231
Eddleman Quantum graduate fellowshipUNSPECIFIED
Troesh Family Distinguished Scholars fellowshipUNSPECIFIED
Caltech Division of Physics, Mathematics and AstronomyUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
J. Yang Family and FoundationUNSPECIFIED
Harvard Quantum InitiativeUNSPECIFIED
Harvard Society of FellowsUNSPECIFIED
Department of Energy (DOE)DE-SC0012567
Miller Institute for Basic Research in ScienceUNSPECIFIED
Issue or Number:7944
Record Number:CaltechAUTHORS:20230227-866489000.2
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119515
Deposited By: George Porter
Deposited On:28 Feb 2023 03:22
Last Modified:07 Jun 2023 20:31

Repository Staff Only: item control page