AI 中文总结
该研究以氢链为对象，对比CMO与LMO两种分子轨道，发现结合算符定域性截断的LMO波函数展开可使哈密顿量模拟的量子门数量呈多对数增长，为量子化学模拟选轨道与截断策略提供了指导。
AI 中文摘要
我们以一维氢链系统为研究对象，探究作为波函数展开基的分子轨道，以及基于算符系数和基于定域性的哈密顿量截断对基于Trotter分解的哈密顿量模拟计算成本的影响。分析采用Hartree-Fock正则分子轨道（CMOs）和基于Pipek-Mezey的定域分子轨道（LMOs）两种轨道。对于短氢链，我们评估了基态能量和保真度，发现基于CMO的波函数展开中，对哈密顿量系数设置阈值可在保持计算精度的同时有效降低门成本；而在基于LMO的波函数展开中，基于算符定域性的哈密顿量截断效果更优。我们通过经验公式拟合截断阈值与基态能量、保真度的关系，估算了实现基态波函数高保真度（F≥0.99）所需的阈值。利用估算的阈值，我们对最长达H₁₀₀的长氢链进行了量子门资源估算。结果表明，结合哈密顿量截断的基于LMO的波函数展开具有指数级优势：采用基于算符系数的哈密顿量截断的基于CMO的波函数展开时，哈密顿量模拟所需量子门数量呈多项式增长；而采用基于算符定域性的哈密顿量截断的基于LMO的波函数展开时，该数量呈多对数增长。这些结果为大规模量子化学模拟中轨道表示与哈密顿量截断策略的选择提供了有用指导。
英文摘要
We investigate how molecular orbitals used as the basis of wave function expansion and how operator coefficient-based and locality-based Hamiltonian truncation affects the computational cost of Trotter decomposition-based Hamiltonian simulation in one-dimensional hydrogen chain systems. The analysis is performed using both Hartree--Fock canonical molecular orbitals (CMOs) and Pipek--Mezey-based localized molecular orbitals (LMOs). For short hydrogen chains, we evaluate the ground-state energy and fidelity and find that, in the CMO-based wave function expansion, introducing a threshold on Hamiltonian coefficients is effective in reducing the gate cost while maintaining computational accuracy. In contrast, in the LMO-based wave function expansion, operator locality-based Hamiltonian truncation is found to be more effective. By fitting the relationship between the truncation threshold and the ground-state energies and fidelities with empirical formulas, we estimate the threshold values required to achieve high fidelity ($F \ge 0.99$) in the ground-state wave function. Using the estimated thresholds, we then perform quantum gate resource estimation for longer hydrogen chains up to H$_{100}$. The results suggest an exponential advantage of the LMO-based wave function expansion with Hamiltonian truncation: the number of quantum gates required for Hamiltonian simulation grows polynomially when the CMO-based wave function expansion with operator coefficient-based Hamiltonian truncation is adopted, whereas it grows polylogarithmically when the LMO-based wave function expansion is combined with operator locality-based Hamiltonian truncation. These results provide useful guidelines for choosing orbital representations and Hamiltonian truncation strategies in large-scale quantum chemical simulations.
Comments12+3 pages, 6+1 figures, 3+4 tables
