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

TL;DR

This paper introduces LLES, a novel optimization method combining learning-to-learn and evolutionary strategies to improve parameter optimization in variational quantum algorithms, reducing computational costs.

Contribution

The paper presents a new hybrid optimization approach for VQAs that unifies learning-to-learn and evolutionary strategies, demonstrating improved efficiency and effectiveness.

Findings

LLES effectively optimizes VQAs for quantum tasks.

Identifies a key hyperparameter influencing gradient estimation.

Demonstrates success on Ising Hamiltonian and quantum neural network tasks.

Abstract

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.