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Physics-Informed Bayesian Optimization of Variational Quantum Circuits

Kim Nicoli · Christopher J. Anders · Lena Funcke · Tobias Hartung · Karl Jansen · Stefan Kühn · Klaus-Robert Müller · Paolo Stornati · Pan Kessel · Shinichi Nakajima

Great Hall & Hall B1+B2 (level 1) #1308


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.

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