Physics-Informed Bayesian Optimization of Variational Quantum Circuits

Published: 21 Sept 2023, Last Modified: 15 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Bayesian optimization, Expected improvement, Quantum computing, Variational Quantum Eigensolvers
TL;DR: We propose a novel physics-informed kernel and a new acquisition function for the optimization of variational quantum eigensolvers (VQEs).
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 \emph{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.
Supplementary Material: pdf
Submission Number: 13767