2022/10/13 by Junyu Liu, Frederik Wilde, Liu, Junyu +8 · 5 citations
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Neural Networks and Applications #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2210.06723
openalex publication_date 2022/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.