基于采样的量子对角化方法估算HeH$^{+}$、ArH$^{+}$和H$_2$O的基态能量
Ground-State Energy Estimation of HeH$^{+}$, ArH$^{+}$, and H$_2$O via Sample-Based Quantum Diagonalization
AI总结：
本研究采用混合量子-经典框架SQD，结合IBM量子硬件计算HeH$^+$、ArH$^+$和H$_2$O的基态能量，结果与同基组CCSD能量吻合，验证了SQD用于基准系统的可行性。
AI中文摘要：
精确的基态能量是量子化学中理解分子结构、化学键合及反应能量学的关键。本研究采用适用于近期量子器件的混合量子-经典框架——基于采样的量子对角化（Sample-Based Quantum Diagonalization, SQD），探究HeH$^+$、ArH$^+$和H$_2$O分子系统的基态性质。与需要深度参数化电路及重复期望值测量的变分方法（如VQE）不同，SQD可直接从测量的比特串重构低能量行列式子空间。本计算中，比特串通过IBM量子硬件生成，采用浅局域幺正Jastrow（local unitary cluster Jastrow, LUCJ）电路，其参数由基于限制性哈特利-福克（restricted Hartree--Fock, RHF）参考的耦合簇单双激发（coupled-cluster singles and doubles, CCSD）计算的$t_1$和$t_2$振幅构建。从这些样本中，我们使用6-31G和cc-pVDZ基组计算HeH$^+$、ArH$^+$和H$_2$O的基态势能曲线。对于所有三个系统，采用cc-pVDZ基组的SQD结果与同基组的CCSD能量高度吻合，并再现了势能曲线平衡区域的趋势。HeH$^+$和ArH$^+$被选为简单但具有天体物理重要性的分子离子基准，而H$_2$O作为代表性多原子分子被纳入，以评估SQD在双原子离子系统之外的适用性。在采用的平衡几何结构下，与同活性空间CASCI基准的偏差分别为HeH$^+$ 0.00 mHa、ArH$^+$ 2.51 mHa、H$_2$O 6.34 mHa。这些结果证明了硬件辅助SQD用于当前基准系统的可行性，并为其在更大分子活性空间中的准确性和计算规模的进一步研究提供了动力。
英文摘要：
Accurate ground-state energies are essential for understanding molecular structure, chemical bonding, and reaction energetics in quantum chemistry. In this work, we investigate the ground-state properties of the molecular systems HeH$^+$, ArH$^+$, and H$_2$O using Sample-Based Quantum Diagonalization (SQD), a hybrid quantum-classical framework designed for near-term quantum devices. Unlike variational approaches such as VQE, which require deep parameterized circuits and repeated expectation-value measurements, SQD reconstructs a low-energy determinant subspace directly from measured bitstrings. For the present calculations, bitstrings were generated on IBM quantum hardware using shallow local unitary cluster Jastrow (LUCJ) circuits whose parameters were constructed from the $t_1$ and $t_2$ amplitudes of coupled-cluster singles and doubles (CCSD) calculations based on restricted Hartree--Fock (RHF) references. From these samples, we compute ground-state potential-energy curves of HeH$^+$, ArH$^+$, and H$_2$O with the 6-31G and cc-pVDZ basis sets. For all three systems, the SQD results obtained with the cc-pVDZ basis closely follow the corresponding same-basis CCSD energies and reproduce the equilibrium-region trends of the potential-energy curves. HeH$^+$ and ArH$^+$ were chosen as simple yet astrophysically important molecular-ion benchmarks, while H$_2$O was included as a representative polyatomic molecule to assess the applicability of SQD beyond diatomic ionic systems. At the adopted equilibrium geometries, the deviations from the same-active-space CASCI references are 0.00, 2.51, and 6.34 mHa for HeH$^+$, ArH$^+$, and H$_2$O, respectively. These results demonstrate the feasibility of hardware-assisted SQD for the present benchmark systems and motivate further studies of its accuracy and computational scaling for larger molecular active spaces.
