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Efficient Estimation of Pauli Observables by Derandomization

Huang, Hsin-Yuan and Kueng, Richard and Preskill, John (2021) Efficient Estimation of Pauli Observables by Derandomization. Physical Review Letters, 127 (3). Art. No. 030503. ISSN 0031-9007. doi:10.1103/PhysRevLett.127.030503.

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We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper ItemCode
Huang, Hsin-Yuan0000-0001-5317-2613
Kueng, Richard0000-0002-8291-648X
Preskill, John0000-0002-2421-4762
Additional Information:© 2021 American Physical Society. Received 19 March 2021; accepted 14 June 2021; published 16 July 2021. The authors thank Andreas Elben, Stefan Hillmich, Steven T. Flammia, Jarrod McClean, and Lorenzo Pastori for valuable input and inspiring discussions. H. H. is supported by the J. Yang and Family Foundation. J. P. acknowledges funding from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, (DE-NA0003525, DE-SC0020290), and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is a NSF Physics Frontiers Center.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics, AWS Center for Quantum Computing
Funding AgencyGrant Number
J. Yang Family and FoundationUNSPECIFIED
Department of Energy (DOE)DE-NA0003525
Department of Energy (DOE)DE-SC0020290
Issue or Number:3
Record Number:CaltechAUTHORS:20210512-104041014
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109097
Deposited By: George Porter
Deposited On:12 May 2021 19:38
Last Modified:02 Aug 2021 16:56

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