Physics-Informed Bayesian Optimization of Variational Quantum Circuits
This addresses the challenge of efficiently optimizing quantum circuits for quantum computing applications, representing an incremental advance in hybrid quantum-classical methods.
The paper tackles the optimization of Variational Quantum Eigensolvers (VQEs) by proposing a physics-informed Bayesian optimization method, which reduces the number of required observations to as few as three points to determine the objective function along a one-dimensional subspace and improves over state-of-the-art baselines.
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.