Stochastic noise can be helpful for variational quantum algorithms

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.

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Publication Details

Journal
Physical review. A/Physical review, A
Published
2025-05-22
DOI
https://doi.org/10.1103/physreva.111.052441
Citations
11
Primary Topic
Quantum Computing Algorithms and Architecture
Type
article
Field-Weighted Citation Impact
27.29

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article

Stochastic noise can be helpful for variational quantum algorithms

Xin Jin, Jens Eisert, Liang Jiang, Antonio Anna Mele et al.
11 citations
Physical review. A/Physical review, A
Quantum Computing Algorithms and Architecture
27.29
article

Stochastic noise can be helpful for variational quantum algorithms

Xin Jin, Jens Eisert, Liang Jiang, Antonio Anna Mele, Frederik Wilde, Junyu Liu
article en
11 citations

Abstract

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.

Physical review. A/Physical review, AVol. 111(5)
University of Pittsburgh (US), Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute (DE), Helmholtz-Zentrum Berlin für Materialien und Energie (DE), University of Chicago (US), Science Exchange (United States) (US), Technische Universität Berlin (DE), Freie Universität Berlin (DE)
National Science Foundation, David and Lucile Packard Foundation, U.S. Department of Energy, National Aeronautics and Space Administration, International Business Machines Corporation, University of Chicago, University of Pittsburgh, Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, Nuclear Safety and Security Commission, Einstein Stiftung Berlin, QuantERA, Office of Science, Multidisciplinary University Research Initiative, European Research Council, Air Force Office of Scientific Research, Army Research Office
Openalex Percentile: Top 1%
Quantum Computing Algorithms and Architecture
27.29
DOIOpen Access PDFOpenAlex
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