Global optimization in variational quantum algorithms via dynamic tunneling method

TL;DR

This paper introduces a novel global optimization method for variational quantum algorithms that uses dynamic tunneling based on quantum state distance, improving upon traditional parameter space approaches.

Contribution

The authors adapt the dynamic tunneling flow to utilize quantum state distance, addressing degeneracy issues and enhancing optimization in variational quantum algorithms.

Findings

Improved optimization performance on the transverse-field Ising model

Effective resolution of degeneracy issues in quantum state parametrization

Demonstrated advantages over conventional Euclidean distance-based methods

Abstract

We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the conventional dynamic tunneling flow to exploit the distance measure of quantum states, resolving issues of extrinsic degeneracy arising from the parametrization of quantum states. Our global optimization algorithm is applied to the variational quantum eigensolver for the transverse-field Ising model to demonstrate the performance of our routine while comparing it with the conventional dynamic tunneling method, which is based on the Euclidean distance measure on the parameter space.