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.

提出了一种利用贝叶斯优化来优化变分量子本征解算器（VQE）的新方法，包括推导出一个 VQE-kernel 来匹配 VQE 的目标函数的已知函数形式，通过减少后验不确定性来显著优化系统，以及提出了一种名为 EMICoRe 的新的贝叶斯优化获取函数，能够通过将低预测不确定性的区域间接视为 “已观察到” 的方式来主动利用 VQE-kernel 的归纳偏好，实验证明该方法相比于现有的基线方法具有改进效果。