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Reduced Density Matrix and Cumulant Approximations of Quantum Linear Response
Theo Juncker von Buchwald1, Erik Rosendahl Kjellgren2, Jacob Kongsted2
1Department of Chemistry, Technical University of Denmark, Kemitorvet Building 207, Kongens Lyngby DK-2800, Denmark.
Journal of Chemical Theory and Computation
|February 5, 2026
Summary
Approximating quantum linear response (qLR) with singles and doubles (qLRSD) shows promise for reducing quantum workload. However, approximations to 3-body reduced density matrices (RDMs) fail, and 4-body approximations struggle with strong correlation.
Area of Science:
- Quantum computing
- Computational chemistry
- Theoretical chemistry
Background:
- Linear response (LR) is a vital computational chemistry tool.
- Quantum computing offers a quantum counterpart, quantum LR (qLR).
- Near-term intermediate-scale quantum (NISQ) devices face noise and decoherence challenges.
Purpose of the Study:
- To develop approximations for qLR to reduce quantum computational cost.
- To investigate the impact of approximating reduced density matrices (RDMs) and reduced density cumulants (RDCs) on qLR accuracy.
- To analyze the measurement costs associated with qLR.
Main Methods:
- Approximation of naive qLR to qLR with singles and doubles (qLRSD).
- Direct approximation of RDMs or indirect approximation via RDCs.
- Analysis of measurement costs for qLR using RDMs.
- Application of qLRSD to various chemical systems, including hydrogen ladders, OCS, SeH2, H2S, H2O, and BeH2.
Main Results:
- Approximations to 4-body RDMs and RDCs yield good results for equilibrium geometries and some core excitations.
- 4-body approximations fail for systems with strong correlation.
- All approximations involving 3-body RDMs and/or RDCs significantly degrade results and are not viable.
Conclusions:
- qLRSD approximations show potential for reducing quantum workload but require careful consideration of correlation effects.
- Approximations to 3-body RDMs/RDCs are unsuitable for qLR.
- Further research is needed to develop robust qLR approximations for strongly correlated systems.
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