  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.
