论文标题
不连续的Galerkin方法和Voronoi分区，用于化学量子模拟
Discontinuous Galerkin method with Voronoi partitioning for Quantum Simulation of Chemistry
论文作者
论文摘要
基于高斯型轨道的线性组合的分子轨道可以说是在量子化学模拟中，无论是在量子和经典设备上使用的量子轨道。为了避免潜在的致密两体相互作用张量并获得化学量子模拟的降低渐近成本，最近采用了矩形分配策略的不连续的Galerkin（DG）程序[McClean等人，New J. Phys。 22，093015，2020]。 DG方法在通过分子轨道对两体相互作用张量的紧凑描述与通过原始基集（例如PlaneWave双基组集）的对角线表征进行可控的方式。 DG程序引起了两体相互作用的块对基形式，并减少了两电子排斥积分的数量，从而降低了量子模拟的成本。在目前的工作中，我们扩展了这种方法，以适用于任意几何形状的分子和结晶系统。我们利用PlaneWave双基集的灵活性，并将不连续的Galerkin程序与基于Voronoi分解的一般分区策略相结合。我们在平均场和相关水平上进行数值研究，使用氢链，h $ _4 $，ch $ _4 $作为示例，使用准1D，2D和3D分区。我们还将方法应用于石墨烯，作为晶体系统的典型示例。
Molecular orbitals based on the linear combination of Gaussian type orbitals are arguably the most employed discretization in quantum chemistry simulations, both on quantum and classical devices. To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) procedure using a rectangular partitioning strategy was recently piloted [McClean et al, New J. Phys. 22, 093015, 2020]. The DG approach interpolates in a controllable way between a compact description of the two-body interaction tensor through molecular orbitals and a diagonal characterization through primitive basis sets, such as a planewave dual basis set. The DG procedure gives rise to a block-diagonal representation of the two-body interaction with reduced number of two-electron repulsion integrals, which in turn reduces the cost of quantum simulations. In the present work we extend this approach to be applicable to molecular and crystalline systems of arbitrary geometry. We take advantage of the flexibility of the planewave dual basis set, and combine the discontinuous Galerkin procedure with a general partitioning strategy based on the Voronoi decomposition. We numerically investigate the performance, at the mean-field and correlated levels, with quasi-1D, 2D and 3D partitions using hydrogen chains, H$_4$, CH$_4$ as examples, respectively. We also apply the method to graphene as a prototypical example of crystalline systems.
