Reduced Density Matrix and Cumulant Approximations of Quantum Linear Response

Linear response (LR) is an important tool in the computational chemist's toolbox. It is therefore unsurprising that the emergence of quantum computers has led to a quantum counterpart known as quantum LR (qLR). However, the current quantum era of near-term intermediate-scale quantum (NISQ) computers is dominated by noise, short decoherence times, and slow measurement speeds. It is therefore of interest to find approximations that can 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 the 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 associated with qLR using RDMs and report qLR results for model hydrogen ladder systems; for varying active space sizes in OCS, SeH₂, and H₂S; and for symmetrically stretched H₂O and BeH₂. 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.