Many-body plane wave-basis set simulations and their applicability within quantum algorithms for electronic structure

Although atom-centered Gaussian basis sets are used ubiquitously in conventional quantum chemistry codes to solve the electronic Schrodinger Eq., on quantum processors, the favorable-scaling of the quantum version of the fast Fourier transform (FFT) makes orbital representations in terms of underlying plane-wave basis functions a potentially superior option, possibly even for non-periodic systems. Developed in this work are estimates of the number of plane-waves needed in a full (or selective) configuration interaction (CI) calculation to achieve a desired accuracy for various standard isolated atomic and molecular systems. This is achieved by re-expressing the usual 1- and 2-body electronic integrals in terms of orbitals decomposed into Fourier components subjected to a kinetic energy cutoff. It is found that the number of plane-waves required depends heavily on the extent to which the original Gaussian basis-optimized orbitals are localized in real-space and hence, essentially, on the atomic numbers of the constituent atoms. For larger atomic numbers, even if one invokes the frozen-core approximation, it is estimated that many millions of plane-waves are required to adequately represent the most highly-localized molecular orbitals and to calculate CI energies to high accuracy.