We analytical prove two results for parametrized quantum circuits (PQCs): (1) We find an exponentially large symmetry, which leads to an exponentially large degeneracy in the cost landscape minima. (2) We show that this degeneracy is broken by noise. We propose a novel optimizer called Symmetry-based minima hopping (SYMH), that exploits these results to enhance the optimization of PQCs by allowing one to hop between non-degenerate local minima.
For details see “Optimizing parametrized quantum circuits via noise-induced breaking of symmetries”, E. Fontana, M. Cerezo, A. Arrasmith, I. Rungger, P.J. Coles. arXiv:2011.08763.