Physics-Informed Bayesian Optimization of Variational Quantum Circuits
<|reference_start|>Physics-Informed Bayesian Optimization of Variational Quantum Circuits: 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.<|reference_end|>
@article{nicoli2024physics-informed,
    title={Physics-Informed Bayesian Optimization of Variational Quantum Circuits},
    author={Kim A. Nicoli and Christopher J. Anders and Lena Funcke and Tobias
  Hartung and Karl Jansen and Stefan K"uhn and Klaus-Robert M"uller and Paolo
  Stornati and Pan Kessel and Shinichi Nakajima},
    journal={arXiv preprint arXiv:2406.06150},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06150},
    primaryClass={cs.LG quant-ph}
}