Stochastic noise can be helpful for variational quantum algorithms
This provides a new perspective for near-term variational quantum algorithms by leveraging inherent stochasticity to overcome optimization challenges.
The paper tackles the problem of saddle points in variational quantum algorithms by showing that stochastic noise can naturally help avoid them, proving convergence guarantees and demonstrating practical examples on quantum hardware.
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.