  Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era
algorithms for harnessing quantum computing in diverse fields. However, the
underlying optimization processes within these algorithms usually deal with
local minima and barren plateau problems, preventing them from scaling
efficiently. Our goal in this paper is to study alternative optimization
methods that can avoid or reduce the effect of these problems. To this end, we
propose to apply the Differential Evolution (DE) algorithm to VQAs
optimizations. Our hypothesis is that DE is resilient to vanishing gradients
and local minima for two main reasons: (i) it does not depend on gradients, and
(ii) its mutation and recombination schemes allow DE to continue evolving even
in these cases. To demonstrate the performance of our approach, first, we use a
robust local minima problem to compare state-of-the-art local optimizers
(SLSQP, COBYLA, L-BFGS-B and SPSA) against DE using the Variational Quantum
Eigensolver algorithm. Our results show that DE always outperforms local
optimizers. In particular, in exact simulations of a 1D Ising chain with 14
qubits, DE achieves the ground state with a 100\% success rate, while local
optimizers only exhibit around 40\%. We also show that combining DE with local
optimizers increases the accuracy of the energy estimation once avoiding local
minima. Finally, we demonstrate how our results can be extended to more complex
problems by studying DE performance in a 1D Hubbard model.

Quantum Physics