Divergences in classical and quantum linear response and equation of motion formulations

TL;DR

This paper examines divergences in quantum linear response and equation of motion methods for molecular properties, highlighting how parameter choices and noise influence excitation energy calculations.

Contribution

It identifies how different parameterizations affect divergences and variance in quantum response calculations, emphasizing the impact of redundant orbital rotations.

Findings

Naive and projected parameterizations depend on redundant orbital rotations.

Divergences can occur in excitation energies due to parameter choices.

Statistical noise from quantum sampling increases calculation variance.

Abstract

Calculating molecular properties using quantum devices can be done through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naive, projected, self-consistent, and state-transfer. In the naive and projected parameterizations, the metric is not the identity, and we show that it depends on the redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noise-less setting. Further, this leads to significant variance when calculations include statistical noise from finite quantum sampling.