Discontinuous Galerkin method with Voronoi partitioning for Quantum Simulation of Chemistry

Molecular orbitals are arguably the most employed discretization in quantum chemistry simulations, both on quantum and classical devices. To circumvent a potentially dense electron repulsion integral tensor (ERI) and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) procedure with rectangular partitioning for quasi 1D-systems was recently piloted [1]. The DG approach interpolates in a controllable way between a compact description of the ERI through molecular orbitals and a diagonal characterization through primitive basis sets. Moreover, it gives rise to a block-diagonal representation of the ERI with a reduced number of nonzero terms, which reduces the cost of quantum simulations.
We extend this approach to be applicable to molecular and crystalline systems of arbitrary geometry [2], using the flexibility of the planewave dual basis set and combining the DG procedure with a general partitioning strategy based on the Voronoi decomposition.

[1] New J. Phys. 22, 093015, 2020
[2] arXiv:2011.00367