Quantum Subspace Expansion for Molecular Excited States: Representability, Stability, and Practical Considerations
- 1Institute of Advanced Intelligence and Computing (IAIC, Agency for Science, Technology and Research (A*STAR, 1 Fusionopolis Way, Connexis, Republic of Singapore, 138632
Abstract
Accurate treatment of excited states remains challenging for classical electronic-structure methods, motivating quantum algorithms that may provide more favorable resource scaling. We systematically assess the practical performance of Quantum Subspace Expansion (QSE) for low-lying electronic states across 28 organic molecules from the Thiel benchmark set. Statevector simulations reveal that QSE representability depends strongly on the target state, active space, and molecular electronic structure, with multiconfigurational character emerging as an important factor. In several cases, the one-body QSE subspace cannot adequately represent the target states, while explicit double-excitation operators improve representability at the cost of a larger operator space. Analysis of the QSE overlap matrix shows that although eigenmodes with small eigenvalues drive numerical instability, they cannot be discarded indiscriminately without compromising spectral accuracy. Under finite-shot sampling, energy errors exhibit an empirical scaling of approximately n2 orb/ √ Nshots, which, combined with the growth in measurement groups, yields a total measurement cost of approximately O(n11 orb) for constant accuracy under our direct-estimation protocol. These results expose a central tension between representability, numerical stability, and measurement cost. Encouragingly, we find that the projected matrices exhibit recurring structural patterns, while the finite-shot perturbations in the Hamiltonian and overlap matrices show nontrivial covariance, suggesting opportunities for more efficient structure-aware measurement and reconstruction strategies. Overall, our results provide an assessment of QSE across chemically-relevant organic molecules, identifying present limitations while highlighting potential routes toward more practical future implementations.
Related
- First-principles and cluster expansion investigation of Ti-V-Mn AB₂ alloys: stability, electronic structure, and mechanical properties.
- A constructive solution to the n-representability problem
- V-Representability Beyond Singular Times in Time-Dependent Density Functional Theory: The Hubbard Dimer Case
- Dynamic Evolution and Stability of Ketenes in MAPO-18 (M = Si or Mg): Molecular Insights into the Reaction Mechanism for CO2-to-Hydrocarbons
- Benchmarking a fast energy model for predicting the stability of solvated surface sites for organic molecular crystals: The paracetamol–water interface
BibTeX
@misc{yeo2026quantum,
title = {{Quantum Subspace Expansion for Molecular Excited States: Representability, Stability, and Practical Considerations}},
author = {Naythan Z. X. Yeo and Shi Jun Ang},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009412/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009412/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Quantum Subspace Expansion for Molecular Excited States: Representability, Stability, and Practical Considerations
AU - Naythan Z. X. Yeo
AU - Shi Jun Ang
PY - 2026
DA - 2026/09/24
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009412/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009412/v1
AB - Accurate treatment of excited states remains challenging for classical electronic-structure methods, motivating quantum algorithms that may provide more favorable resource scaling. We systematically assess the practical performance of Quantum Subspace Expansion (QSE) for low-lying electronic states across 28 organic molecules from the Thiel benchmark set. Statevector simulations reveal that QSE representability depends strongly on the target state, active space, and molecular electronic structure, with multiconfigurational character emerging as an important factor. In several cases, the one-body QSE subspace cannot adequately represent the target states, while explicit double-excitation operators improve representability at the cost of a larger operator space. Analysis of the QSE overlap matrix shows that although eigenmodes with small eigenvalues drive numerical instability, they cannot be discarded indiscriminately without compromising spectral accuracy. Under finite-shot sampling, energy errors exhibit an empirical scaling of approximately n2 orb/ √ Nshots, which, combined with the growth in measurement groups, yields a total measurement cost of approximately O(n11 orb) for constant accuracy under our direct-estimation protocol. These results expose a central tension between representability, numerical stability, and measurement cost. Encouragingly, we find that the projected matrices exhibit recurring structural patterns, while the finite-shot perturbations in the Hamiltonian and overlap matrices show nontrivial covariance, suggesting opportunities for more efficient structure-aware measurement and reconstruction strategies. Overall, our results provide an assessment of QSE across chemically-relevant organic molecules, identifying present limitations while highlighting potential routes toward more practical future implementations.
ER -