标题： 利用破缺对称波函数通过量子虚时间演化确定分子基态 显示英文标题

标题： Determining Molecular Ground State with Quantum Imaginary Time Evolution using Broken-Symmetry Wave Function

摘要： Hartree-Fock（HF）波函数通常用于近似分子基态，但由于波函数固有的多组态性质，在开壳层系统中变得不理想，限制了量子imaginary时间演化（QITE）的精度。 我们建议用一个自旋和空间对称性破缺的波函数代替HF波函数，并通过向原始分子哈密顿量添加自旋算符 $S^2$ 作为惩罚项来增强收敛性。 我们验证了这种方法通过直接矩阵指数化进行imaginary时间演化（ITE）时，能够提供良好的收敛行为至最低能量本征态。 我们在氢分子和四方氢簇上使用QITE中的测量辅助幺正逼近进行了数值模拟。 与HF相比，QITE在分子表现出双自由基特征为0.56时，展示了更快收敛至破缺对称性（BS）基态的能力，尤其是在氢分子的情况下。 在此之前，HF仍然更有效，表明了波函数选择的双自由基特征过渡阈值。 此外，与完全活性空间构型相互作用（CAS-CI）波函数的重叠分析显示，在氮分子三键解离等高自旋、多组态系统中，BS的初始重叠比HF更大。 此方法为开壳层系统中的改进能量模拟提供了途径，其中波函数的准确性对下游量子算法以及量子化学的实际应用具有重要意义。 显示英文摘要

摘要： The Hartree-Fock (HF) wave function, commonly used for approximating molecular ground states, becomes nonideal in open shell systems due to the inherent multi-configurational nature of the wave function, limiting accuracy in Quantum Imaginary Time Evolution (QITE). We propose replacing the HF wave function with a spin- and spatial-symmetry broken wave function, enhancing convergence by adding a spin operator, $S^2$ as a penalty term to the original molecular Hamiltonian. We verify that this approach provides good convergence behavior towards the lowest energy eigenstate using direct matrix exponentiation for Imaginary Time Evolution (ITE). Numerical simulations were performed on the hydrogen molecule and a square tetrahydrogen cluster using measurement-assisted unitary approximation in QITE. QITE demonstrates faster convergence to the ground state with broken symmetry (BS) compared to HF, particularly after the molecule exhibits a diradical character of 0.56 for hydrogen. Prior to this point, HF remains more effective, suggesting a transition threshold of diradical character for wave function selection. Additionally, the overlap analysis with Complete Active Space Configuration Interaction (CAS-CI) wave function shows that BS has a larger initial overlap than HF in higher-spin, multi-configurational systems like triple bond dissociation in nitrogen molecule. This method provides a pathway for improved energy simulations in open shell systems, where wave function accuracy significantly impacts downstream quantum algorithms and practical applications in quantum chemistry.