发表机构
University of Toronto; University of Toronto Scarborough（多伦多大学; 多伦多大学士嘉堡校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
CASH-QSE方法在经典层面保留CASSCF参考态，构造严格正交的量子态，通过厄米本征值问题获得能量，无需重叠测量，在H2O和N2键伸缩基准上达到化学精度，并显著降低采样成本。
AI 中文摘要
变分量子本征求解器（VQE）制备的波函数可能包含大量经典可处理的分量，然而其能量贡献却在量子设备上进行采样。将波函数表示为经典参考态与单独制备的量子态的组合，可以在无需量子采样的条件下评估参考态能量。然而，这些分量之间的近线性相关会放大测量误差，并使最终的能量估计失稳。我们引入了经典活性空间混合量子子空间扩展（CASH-QSE），该方法在经典层面保留完全活性空间自洽场（CASSCF）参考态，并利用占据结构构造与参考态及彼此之间严格正交的量子态。能量通过一个普通的厄米本征值问题获得，无需重叠测量，同时相同的占据约束简化了被测量的算符。利用完全组态相互作用来指导组分选择，我们沿H$_2$O和N$_2$键伸缩坐标测试了CASH-QSE，这些坐标跨越了从弱关联到强关联的区域。基准测试对两种分子均使用STO--3G基组，对H$_2$O使用受限的cc-pVDZ轨道空间。CASH-QSE达到了化学精度，同时将最大的完整测量电路限制在数百个全连接逻辑受控非门以内。在有利的情况下，与采用自适应导数组装拟Trotter拟设（ADAPT-VQE）的VQE相比，它还将理想化的最终能量采样成本降低了几个数量级。
英文摘要
The wave function prepared by a variational quantum eigensolver (VQE) can contain a substantial classically tractable component, yet its energy contribution is sampled on the quantum device. Representing the wave function as a combination of a classical reference and separately prepared quantum states allows the reference energy to be evaluated without quantum sampling. However, near-linear dependence among these components can amplify measurement errors and destabilize the resulting energy estimate. We introduce Classical Active-Space Hybrid Quantum Subspace Expansion (CASH-QSE), which retains a complete-active-space self-consistent field (CASSCF) reference classically and uses occupation structure to construct quantum states exactly orthogonal to the reference and to one another. The energy follows from an ordinary Hermitian eigenvalue problem without overlap measurements, while the same occupation constraints simplify the measured operators. Using full configuration interaction to guide component selection, we test CASH-QSE along H$_2$O and N$_2$ bond-stretching coordinates spanning weakly to strongly correlated regimes. The benchmarks use STO--3G for both molecules and a restricted cc-pVDZ orbital space for H$_2$O. CASH-QSE reaches chemical accuracy while limiting the largest complete measurement circuits to a few hundred all-to-all logical controlled-NOT gates. In favorable cases, it also reduces the idealized final-energy sampling cost by several orders of magnitude relative to VQE with an adaptive derivative-assembled pseudo-Trotter ansatz (ADAPT-VQE).
