Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Liu, Junyu, Wilde, Frederik, Mele, Antonio Anna, Jin, Xin, Jiang, Liang, Eisert, Jens
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Bundesministerium für Wirtschaft und Klimaschutz, David and Lucile Packard Foundation, National Aeronautics and Space Administration, International Business Machines Corporation, University of Chicago, University of Pittsburgh, Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, Einstein Stiftung Berlin, QuantERA, Multidisciplinary University Research Initiative, Air Force Office of Scientific Research, Army Research Office
OpenAlex ID: W4306295172