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

Stochastic noise can be helpful for variational quantum algorithms