Enhanced Estimation of Quantum Properties with Common Randomized Measurements

Creators: Vermersch, Benoît; Rath, Aniket; Sundar, Bharathan; Branciard, Cyril; Preskill, John¹; Elben, Andreas

1. California Institute of Technology

Abstract

We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state. This consists in performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multicopy observables and present performance guarantees in terms of variance bounds that depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through experimental and numerical examples detecting mixed-state entanglement, and estimating polynomial approximations of the von Neumann entropy and state fidelities.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Acknowledgement

We thank Daniel K. Mark and Steve Flammia for helpful discussions and Richard Kueng and Hsin-Yuan (Robert) Huang for their valuable comments on the manuscript. Work in Grenoble is funded by the French National Research Agency via the JCJC project QRand (Grant No. ANR-20-CE47-0005) and via the research programs EPIQ (Gran No. ANR-22-PETQ-0007, Plan France 2030), and QUBITAF (Grant No. ANR-22-PETQ-0004, Plan France 2030). B.V. acknowledges funding from the Austrian Science Fund (Grant No. P 32597 N). A.R. acknowledges support from the Laboratoire d’excellence LANEF in Grenoble (Grant No. ANR-10-LABX-51-01) and from the Grenoble Nanoscience Foundation. B.S. is supported by the Caltech Summer Undergraduate Research Fellowship. J.P. acknowledges funding from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (Grants No. DE-NA0003525 and No DE-SC0020290), the U.S. Department of Energy Quantum Systems Accelerator, and the National Science Foundation (Grant No. PHY-1733907). The Institute for Quantum Information and Matter is a National Science Foundation Physics Frontiers Center. A.E. acknowledges funding by the German National Academy of Sciences Leopoldina under Grant No. LPDS 2021-02 and by the Walter Burke Institute for Theoretical Physics at Caltech. Our julia code uses ITensor [68] and PastaQ [57], and is available from Ref. [69].

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