Noise-induced barren plateaus in variational quantum algorithms

Wang, Samson; Fontana, Enrico; Cerezo, M.; Sharma, Kunal; Sone, Akira; Cincio, Lukasz; Coles, Patrick J.

doi:10.1038/s41467-021-27045-6

Noise-induced barren plateaus in variational quantum algorithms

Journal Article · Sun Nov 28 23:00:00 EST 2021 · Nature Communications

DOI:https://doi.org/10.1038/s41467-021-27045-6· OSTI ID:1832931

; Fontana, Enrico; ; Sharma, Kunal; ; Cincio, Lukasz;

Abstract

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n . These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

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Sponsoring Organization:: USDOE

OSTI ID:: 1832931

Alternate ID(s):: OSTI ID: 1846141

Journal Information:: Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 12; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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