Low-rank decomposition for quantum simulations with complex basis functions

TL;DR

This paper extends low-rank decomposition techniques for Coulomb operators in quantum simulations to complex basis functions using Schur decomposition, broadening applicability in quantum chemistry.

Contribution

It generalizes previous real-valued basis function methods to complex basis functions through Schur decomposition and matrix symmetry analysis.

Findings

Enables low-rank decomposition for complex basis functions

Broadens the applicability of quantum simulation techniques

Provides a mathematical framework for complex basis sets

Abstract

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.