Yoshida Yuichiro, Takemori Nayuta, Mizukami Wataru
Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan.
J Chem Phys. 2024 Aug 28;161(8). doi: 10.1063/5.0213525.
We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.
我们建议引入一种通过从头算降维方法推导的扩展哈伯德哈密顿量，该方法最初是为周期性材料制定的，用于分子电子结构计算的高效量子计算。通过使用这种方法，化学系统的第一性原理哈密顿量可以通过消除高能空间中的电子自由度并将电子排斥积分的项数从O(N4)减少到O(N2)来进行粗粒化。我们的方法在乙烯、丁二烯和己三烯的垂直激发能和激发特性上进行了数值验证。在量子计算之前，动态电子关联被纳入约束随机相位近似的框架内，构建的模型捕捉了实验和高水平量子化学计算结果的趋势。正如预期的那样，费米子到量子比特映射模型哈密顿量的L1范数明显低于传统的从头算哈密顿量，这表明量子计算的可扩展性得到了改善。这些数值结果和激发态采样的模拟结果表明，从头算扩展哈伯德哈密顿量在使用量子计算机进行量子化学计算方面可能具有巨大潜力。
