Learning to learn with an evolutionary strategy applied to variational quantum algorithms

Variational Quantum Algorithms (VQAs) employ parameterized quantum circuits optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing "parameter shift rule" mandates a double evaluation of the cost function for each parameter. In this article, we introduce a novel optimization approach named "Learning to Learn with an Evolutionary Strategy" (LLES). LLES unifies "Learning to Learn" and "Evolutionary Strategy" methods. "Learning to Learn" treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, "Evolutionary Strategy" employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. The obtained results underscore the efficacy of this novel approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the "Evolutionary Strategy" method.