AI 中文总结
本研究针对H₂解离问题优化虚拟量子子空间扩展（VQSE），明确参考态与FCI波函数的重叠度、算子池表达能力的协同影响，通过算子与正则化实现化学精度，为VQSE实用部署提供协同设计依据。
AI 中文摘要
虚拟量子子空间扩展（VQSE）通过对参考态进行额外测量以捕获被排除的虚拟轨道的影响，从而扩展了变分量子本征求解器（VQE），这使得VQSE在化学应用中颇具吸引力，这类应用中势能面上的精确能量差对反应速率与动力学建模至关重要。本研究分析了VQSE在H₂解离问题上的性能，其中参考态采用了破缺自旋对称性的Hartree-Fock分子轨道。我们识别出两种影响精度的机制：参考态与精确全组态相互作用（FCI）波函数的重叠程度，以及算子池的表达能力，且这两种机制存在强依赖关系。当算子被限制为仅在活性空间到虚拟空间之间作用时，结果对参考态高度敏感，增大活性空间并不能保证精度提升，此时优先考虑参考态重叠而非能量最小化至关重要。在活性空间内添加单激发和粒子数算子，无论参考态如何，都能恢复多参考组态相互作用单双激发（MR-CISD）的精度。在含噪声的硬件实验中，我们通过添加额外算子并采用严格正则化达到了化学精度。这些发现为实用VQSE部署中参考态保真度、算子池表达能力与硬件约束的协同设计提供了依据。
英文摘要
The Virtual Quantum Subspace Expansion (VQSE) extends the Variational Quantum Eigensolver (VQE) by leveraging additional measurements on the reference state to capture the influence of excluded virtual orbitals. This makes VQSE attractive for chemical applications where accurate energy differences along potential energy surfaces are crucial for modeling reaction rates and kinetics. In this work, we analyze VQSE performance on H$_2$ dissociation including references that use Hartree--Fock molecular orbitals with broken spin symmetry. We identify two mechanisms which affect accuracy: overlap of the reference state with the exact full configuration interaction (FCI) wavefunction and operator pool expressivity. We show these mechanisms are strongly co-dependent. When operators are restricted to act only from the active to the virtual space, results become highly sensitive to the reference, and enlarging the active space does not guarantee improved accuracy. In this case, prioritizing reference overlap over energy minimization is therefore essential. Adding single excitations and number operators within the active space recovers the accuracy of MR-CISD (multi-reference configuration interaction singles and doubles) regardless of the reference. In our noisy hardware experiments, we achieve chemical accuracy by adding additional operators and using strict regularization. These findings motivate careful co-design of reference fidelity, pool expressivity, and hardware constraints for practical VQSE deployment.
