Quantum algorithm for weakly correlated molecular electronic ground states with sub-quintic scaling in the system size
Abstract
Weakly correlated electronic structures are predominant among molecules, and are routinely solved with heuristic classical methods such as the ``gold standard'' CCSD(T) coupled cluster model, incurring a formal time complexity O(n7) in the number of molecular orbitals and with no guarantee of energy error ε at or below chemical accuracy. In this work, a quantum algorithm is presented for ground state energy estimation of weakly correlated molecules using Trotterized time evolution, with an end-to-end quantum operations cost that scales as Õ(n4.8/ε2) in the limit of high-order product formulae when run as a low-depth, shot-noise limited algorithm, or Õ(n4.8 + n3.8/ε) when scaling the simulation time T∝ 1/ε. The algorithm combines adiabatic state preparation using a smoothed Gevrey schedule with eigenstate filtering via quantum prolate diagonalization (QPD). Both steps of the algorithm rely on a size-independent spectral gap assumption, which is validated by numerical studies on alanine chains with up to 64 monomers. We benchmark the performance of our eigenstate filtering algorithm on a set of 28 molecules to compare our approach against prior phase estimation algorithms, finding that QPD achieves state-of-the-art cost tradeoffs for ε-accurate results. Physical quantum resource estimates are obtained for running Trotter step circuits with up to 40 spin-orbitals, providing a clear path for scaling up quantum simulation of chemistry on early fault-tolerant hardware.
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BibTeX
@misc{leimkuhler2026quantum,
title = {{Quantum algorithm for weakly correlated molecular electronic ground states with sub-quintic scaling in the system size}},
author = {Oskar Leimkuhler and Marvin Kronenberger and Davide Castaldo and Timothy Stroschein and Srushti Patil and Rebecca Tomann and Arta Safari and Marek Miller and Gemma C. Solomon and Matthias Christandl and Markus Reiher},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00751},
eprint = {2611.00751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00751},
}
RIS
TY - UNPB
TI - Quantum algorithm for weakly correlated molecular electronic ground states with sub-quintic scaling in the system size
AU - Oskar Leimkuhler
AU - Marvin Kronenberger
AU - Davide Castaldo
AU - Timothy Stroschein
AU - Srushti Patil
AU - Rebecca Tomann
AU - Arta Safari
AU - Marek Miller
AU - Gemma C. Solomon
AU - Matthias Christandl
AU - Markus Reiher
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00751
UR - https://arxiv.org/abs/2611.00751
AB - Weakly correlated electronic structures are predominant among molecules, and are routinely solved with heuristic classical methods such as the ``gold standard'' CCSD(T) coupled cluster model, incurring a formal time complexity O(n^7) in the number of molecular orbitals and with no guarantee of energy error ε at or below chemical accuracy. In this work, a quantum algorithm is presented for ground state energy estimation of weakly correlated molecules using Trotterized time evolution, with an end-to-end quantum operations cost that scales as Õ(n^4.8/ε^2) in the limit of high-order product formulae when run as a low-depth, shot-noise limited algorithm, or Õ(n^4.8 + n^3.8/ε) when scaling the simulation time T∝ 1/ε. The algorithm combines adiabatic state preparation using a smoothed Gevrey schedule with eigenstate filtering via quantum prolate diagonalization (QPD). Both steps of the algorithm rely on a size-independent spectral gap assumption, which is validated by numerical studies on alanine chains with up to 64 monomers. We benchmark the performance of our eigenstate filtering algorithm on a set of 28 molecules to compare our approach against prior phase estimation algorithms, finding that QPD achieves state-of-the-art cost tradeoffs for ε-accurate results. Physical quantum resource estimates are obtained for running Trotter step circuits with up to 40 spin-orbitals, providing a clear path for scaling up quantum simulation of chemistry on early fault-tolerant hardware.
ER -