Stochastic noise can be helpful for variational quantum algorithms

Liu, Junyu; Wilde, Frederik; Mele, Antonio Anna; Jin, Xin; Jiang, Liang; Eisert, Jens

doi:10.1103/PhysRevA.111.052441

Stochastic noise can be helpful for variational quantum algorithms

Journal Article · Thu May 22 04:00:00 EDT 2025 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.111.052441· OSTI ID:2568191

Liu, Junyu; ; ; Jin, Xin; ;

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms.

Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2568191

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 5 Vol. 111; ISSN PLRAAN; ISSN 2469-9926

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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