Physics-Informed Bayesian Optimization of Variational Quantum Circuits

• URL: http://arxiv.org/abs/2406.06150v1
• Date: Mon, 10 Jun 2024 10:17:06 GMT
• Title: Physics-Informed Bayesian Optimization of Variational Quantum Circuits
• Authors: Kim A. Nicoli, Christopher J. Anders, Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kühn, Klaus-Robert Müller, Paolo Stornati, Pan Kessel, Shinichi Nakajima,
• Abstract summary: We propose a novel and powerful method to harness Bayesian optimization for Variational Quantum Eigensolvers (VQEs) We derive a VQE- Kernel which incorporates important prior information about quantum circuits. We also propose a novel acquisition function for Bayesian optimization called Maximum Improvement over Confident Regions (EMICoRe)
• Score: 13.530592183149661
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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