Liu Jie, Wan Lingyun, Li Zhenyu, Yang Jinlong
Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
J Chem Theory Comput. 2020 Nov 10;16(11):6904-6914. doi: 10.1021/acs.jctc.0c00881. Epub 2020 Oct 19.
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE algorithm for simulating periodic systems. However, the numerical study of a one-dimensional (1D) infinite hydrogen chain using existing VQE algorithms shows a remarkable deviation of the ground-state energy with respect to the exact full configuration interaction (FCI) result. Here, we present two schemes to improve the accuracy of quantum simulations for periodic systems. The first one is a modified VQE algorithm, which introduces a unitary transformation of Hartree-Fock orbitals to avoid the complex wave function. The second one is combining VQE with the quantum subspace expansion approach (VQE/QSE). Numerical benchmark calculations demonstrate that both of the two schemes provide an accurate description of the potential energy curve of the 1D hydrogen chain. In addition, excited states computed with the VQE/QSE approach also agree very well with FCI results.
变分量子本征求解器（VQE）是在近期有噪声的中等规模量子设备上模拟分子电子结构性质最具吸引力的量子算法之一。在这项工作中，我们推广了用于模拟周期系统的VQE算法。然而，使用现有VQE算法对一维（1D）无限氢链进行的数值研究表明，基态能量相对于精确的全组态相互作用（FCI）结果存在显著偏差。在此，我们提出两种提高周期系统量子模拟精度的方案。第一种是改进的VQE算法，它引入了哈特里 - 福克轨道的酉变换以避免复杂的波函数。第二种是将VQE与量子子空间展开方法（VQE/QSE）相结合。数值基准计算表明，这两种方案都能准确描述一维氢链的势能曲线。此外，用VQE/QSE方法计算的激发态也与FCI结果非常吻合。
