Sugisaki Kenji, Kato Takumi, Minato Yuichiro, Okuwaki Koji, Mochizuki Yuji
Department of Chemistry, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.
Phys Chem Chem Phys. 2022 Apr 6;24(14):8439-8452. doi: 10.1039/d1cp04318h.
Variational quantum eigensolver (VQE)-based quantum chemical calculations have been extensively studied as a computational model using noisy intermediate-scale quantum devices. The VQE uses a parametrized quantum circuit defined through an "ansatz" to generate approximated wave functions, and the appropriate choice of an ansatz is the most important step. Because most chemistry problems focus on the energy difference between two electronic states or structures, calculating the total energies in different molecular structures with the same accuracy is essential to correctly understand chemistry and chemical processes. In this context, the development of ansatzes that are capable of describing electronic structures of strongly correlated systems accurately is an important task. Here we applied a conventional unitary coupled cluster (UCC) and a newly developed multireference unitary coupled cluster with partially generalized singles and doubles (MR-UCCpGSD) ansatzes to the quasi-reaction pathway of Be insertion into H, LiH molecule under covalent bond dissociation, and a rectangular tetra-hydrogen cluster known as a P4 cluster; these are representative systems in which the static electron correlation effect is prominent. Our numerical simulations revealed that the UCCSD ansatz exhibits extremely slow convergence behaviour around the point where an avoided crossing occurs in the Be + H → BeH reaction pathway, resulting in a large discrepancy of the simulated VQE energy from the full-configuration interaction (full-CI) value. By contrast, the MR-UCCpGSD ansatz can give more reliable results with respect to total energy and the overlap with the full-CI solution, insisting the importance of multiconfigurational treatments in the calculations of strongly correlated systems. The MR-UCCpGSD ansatz allows us to compute the energy with the same accuracy regardless of the strength of multiconfigurational character, which is an essential property to discuss energy differences of various molecular systems.
基于变分量子本征求解器（VQE）的量子化学计算作为一种使用有噪声的中尺度量子器件的计算模型，已得到广泛研究。VQE使用通过“近似波函数”定义的参数化量子电路来生成近似波函数，而近似波函数的恰当选择是最重要的步骤。由于大多数化学问题关注的是两个电子态或结构之间的能量差，以相同精度计算不同分子结构中的总能量对于正确理解化学和化学过程至关重要。在此背景下，开发能够准确描述强关联系统电子结构的近似波函数是一项重要任务。在这里，我们将传统的幺正耦合簇（UCC）和新开发的具有部分广义单双激发的多参考幺正耦合簇（MR-UCCpGSD）近似波函数应用于共价键解离下铍插入氢、氢化锂分子的准反应路径，以及被称为P4簇的矩形四氢簇；这些是静态电子关联效应显著的代表性系统。我们的数值模拟表明，在Be + H → BeH反应路径中出现避免交叉的点附近，UCCSD近似波函数表现出极其缓慢的收敛行为，导致模拟的VQE能量与全组态相互作用（全CI）值存在很大差异。相比之下，MR-UCCpGSD近似波函数在总能量和与全CI解的重叠方面能够给出更可靠的结果，这强调了多组态处理在强关联系统计算中的重要性。MR-UCCpGSD近似波函数使我们能够以相同精度计算能量，而与多组态特征的强度无关，这是讨论各种分子系统能量差的一个基本属性。
