Physics-Informed Bayesian Optimization of Variational Quantum Circuits

TL;DR

This paper introduces a Bayesian optimization method tailored for Variational Quantum Eigensolvers, leveraging a specialized kernel and a new acquisition function to efficiently find ground states of quantum Hamiltonians.

Contribution

It develops a VQE-specific kernel and a novel acquisition function, EMICoRe, to enhance Bayesian optimization for quantum circuit parameter tuning.

Findings

Significantly reduces the number of evaluations needed to optimize VQEs.

Outperforms existing optimization methods in numerical experiments.

Achieves accurate objective function reconstruction with minimal data.

Abstract

In this paper, we propose a novel and powerful method to harness Bayesian optimization for Variational Quantum Eigensolvers (VQEs) -- a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a VQE-kernel which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty. Moreover, we propose a novel acquisition function for Bayesian optimization called Expected Maximum Improvement over Confident Regions (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly ``observed''. As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.