Reduced density matrix and cumulant approximations of quantum linear response

TL;DR

This paper explores approximations to quantum linear response calculations using reduced density matrices and cumulants to reduce quantum computational workload, analyzing their effectiveness on various molecular systems.

Contribution

It introduces and evaluates RDM and RDC approximations to quantum LR, providing insights into their accuracy and measurement costs for different molecular models.

Findings

Approximations to 4-body RDMs and RDCs work well at equilibrium geometries.

3-body RDM and RDC approximations severely degrade results.

Approximations fail for strongly correlated systems.

Abstract

Linear response (LR) is an important tool in the computational chemist's toolbox. It is therefore no surprise that the emergence of quantum computers has led to a quantum version, quantum LR (qLR). However, the current quantum era of near-term intermediary scale quantum (NISQ) computers is dominated by noise, short decoherence times, and slow measurement speed. It is therefore of interest to find approximations that greatly reduce the quantum workload while only slightly impacting the quality of a method. In an effort to achieve this, we approximate the naive qLR with singles and doubles (qLRSD) method by either directly approximating the reduced density matrices (RDMs) or indirectly through their respective reduced density cumulants (RDCs). We present an analysis of the measurement costs behind qLR with RDMs, and report qLR results for model Hydrogen ladder systems; for varying active space sizes of OCS, SeH$_2$, and H$_2$S; and for symmetrically stretched H$_2$O and BeH$_2$. Discouragingly, while approximations to the 4-body RDMs and RDCs seem to produce good results for systems at the equilibrium geometry and for some types of core excitations, they both tend to fail when the system exhibits strong correlation. All approximations to the 3-body RDMs and/or RDCs severely affect the results and cannot be applied.