Physics-Informed Bayesian Optimization of Variational Quantum Circuits

Kim Andrea Nicoli, Christopher J. Anders, Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kuhn, Klaus Robert Muller, Paolo Stornati, Pan Kessel, Shinichi Nakajima

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.

Submission Number: 13767