  Low-rank decompositions to reduce the Coulomb operator to a pairwise form
suitable for its quantum simulation are well-known in quantum chemistry, where
the underlying basis functions are real-valued. We generalize the result of
Motta \textit{et al.} [arXiv:1808.02625] to \textit{complex} basis functions
$\psi_p(\mathbf r)\in\mathds C$ by means of the Schur decomposition and
decomposing matrices into their symmetric and anti-symmetric components. This
allows the application of low-rank decomposition strategies to general basis
sets.
