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...

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Bibliographic Details
Published inarXiv.org
Main Authors Liu, Junyu, Wilde, Frederik, Mele, Antonio Anna, Jiang, Liang, Eisert, Jens
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.06.2023
Subjects
Algorithms
Eigenvalues
Machine learning
Noise levels
Saddle points
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Summary: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.
ISSN:2331-8422