A Caltech Library Service

Random quantum circuits transform local noise into global white noise

Dalzell, Alexander M. and Hunter-Jones, Nicholas and Brandão, Fernando G. S. L. (2021) Random quantum circuits transform local noise into global white noise. . (Unpublished)

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution p_(noisy) of a generic noisy circuit instance and the output distribution pideal of the corresponding noiseless instance shrink exponentially with the expected number of gate-level errors, as F = exp(−2sϵ ± O(sϵ²)), where ϵ is the probability of error per circuit location and s is the number of two-qubit gates. Furthermore, if the noise is incoherent, the output distribution approaches the uniform distribution p_(unif) at precisely the same rate and can be approximated as p_(noisy) ≈ F_(p_(ideal)) + (1−F)p_(unif), that is, local errors are scrambled by the random quantum circuit and contribute only white noise (uniform output). Importantly, we upper bound the total variation error (averaged over random circuit instance) in this approximation as O(Fϵ√s), so the "white-noise approximation" is meaningful when ϵ√s ≪ 1, a quadratically weaker condition than the ϵs≪1 requirement to maintain high fidelity. The bound applies when the circuit size satisfies s ≥ Ω(nlog(n)) and the inverse error rate satisfies ϵ⁻¹ ≥ Ω̃ (n). The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; it was an underlying assumption in complexity-theoretic arguments that low-fidelity random quantum circuits cannot be efficiently sampled classically. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Dalzell, Alexander M.0000-0002-3756-8500
Hunter-Jones, Nicholas0000-0001-8578-1958
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:We thank Adam Bouland, Bill Fefferman, Zeph Landau, Yunchao Liu, Oskar Painter, John Preskill, and Thomas Vidick for helpful feedback about this work. AD and FB acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907). This material is also based upon work supported by the NSF Graduate Research Fellowship under Grant No. DGE-1745301. NHJ is supported in part by the Stanford Q-FARM Bloch Fellowship in Quantum Science and Engineering. NHJ would like to thank the Aspen Center for Physics for its hospitality during the completion of part of this work. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
Group:AWS Center for Quantum Computing, Institute for Quantum Information and Matter
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1745301
Stanford UniversityUNSPECIFIED
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Colleges and UniversitiesUNSPECIFIED
Record Number:CaltechAUTHORS:20211213-224949608
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112385
Deposited By: George Porter
Deposited On:14 Dec 2021 02:50
Last Modified:14 Dec 2021 02:50

Repository Staff Only: item control page