Preparing random states and benchmarking with many-body quantum chaos

Joonhee Choi, Adam L. Shaw, Ivaylo S. Madjarov, Xin Xie, Ran Finkelstein, Jacob P. Covey, Jordan S. Cotler, Daniel K. Mark, Hsin-Yuan Huang, Anant Kale, Hannes Pichler, Fernando G. S. L. Brandão, Soonwon Choi () and Manuel Endres ()
Additional contact information
Joonhee Choi: California Institute of Technology
Adam L. Shaw: California Institute of Technology
Ivaylo S. Madjarov: California Institute of Technology
Xin Xie: California Institute of Technology
Ran Finkelstein: California Institute of Technology
Jacob P. Covey: California Institute of Technology
Jordan S. Cotler: Harvard University
Daniel K. Mark: Massachusetts Institute of Technology
Hsin-Yuan Huang: California Institute of Technology
Anant Kale: Harvard University
Hannes Pichler: University of Innsbruck
Fernando G. S. L. Brandão: California Institute of Technology
Soonwon Choi: Massachusetts Institute of Technology
Manuel Endres: California Institute of Technology

Nature, 2023, vol. 613, issue 7944, 468-473

Abstract: Abstract 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 holes2, and have been used for benchmarking quantum devices3,4 in tests of quantum advantage5,6. However, creating random ensembles has necessitated a high degree of spatio-temporal control7–12 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 thermalization13. 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 dynamics14 and enables applications of this concept in a much wider context4,5,9,10,15–20.

Date: 2023
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DOI: 10.1038/s41586-022-05442-1

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