  Accurate quantum chemistry simulations remain challenging on classical
computers for problems of industrially relevant sizes and there is reason for
hope that quantum computing may help push the boundaries of what is technically
feasible. While variational quantum eigensolver (VQE) algorithms may already
turn noisy intermediate scale quantum (NISQ) devices into useful machines, one
has to make all efforts to use the scarce quantum resources as efficiently as
possible. We combine the so-called seniority-zero, or paired-electron,
approximation of computational quantum chemistry with techniques for simulating
molecular chemistry on gate-based quantum computers and obtain a very resource
efficient quantum simulation algorithm. While some accuracy is lost through the
paired-electron approximation, we show that using the freed-up quantum
resources for increasing the basis set can lead to more accurate results and
reductions in the necessary number of quantum computing runs by several orders
of magnitude, already for a simple system like lithium hydride. We also discuss
an error mitigation scheme based on post-selection which shows an attractive
scaling when the given Hamiltonian format is considered, increasing the
viability of its NISQ implementation.
