Provable bounds for noise-free expectation values computed from noisy samples

Barron, Samantha V.; Egger, Daniel J.; Pelofske, Elijah; Bärtschi, Andreas; Eidenbenz, Stephan; Lehmkuehler, Matthis; Woerner, Stefan

doi:10.1038/s43588-024-00709-1

Title: Provable bounds for noise-free expectation values computed from noisy samples

Journal Article · 01 November 2024 · Nature Computational Science

DOI: https://doi.org/10.1038/s43588-024-00709-1 · OSTI ID:2476042

Barron, Samantha V. ^[1];

^[2];

^[3];

^[3]; Lehmkuehler, Matthis ^[4];

^[2]

IBM Thomas J. Watson Research Center, Yorktown Heights, NY (United States)
IBM Research Europe—Zurich, Rueschlikon (Switzerland)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
University of Basel (Switzerland)

Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers. However, today’s quantum computers are noisy, posing challenges to obtaining accurate results. Here, we explore the impact of noise on quantum computing, focusing on the challenges in sampling bit strings from noisy quantum computers and the implications for optimization and machine learning. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the conditional value at risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on real quantum computers involving up to 127 qubits. The results show strong alignment with theoretical predictions.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Swiss National Science Foundation; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2476042

Report Number(s):: LA-UR--23-33295

Journal Information:: Nature Computational Science, Journal Name: Nature Computational Science Journal Issue: 11 Vol. 4; ISSN 2662-8457

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Provable bounds for noise-free expectation values computed from noisy samples

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