Efficient Block Encodings for Ensembles of Molecular Hamiltonians
Abstract
Accurately characterizing molecular properties and reactivity often requires electronic-structure calculations across an ensemble of molecular geometries. Quantum algorithms that process such ensembles coherently could address this challenge, but they require Hamiltonian block encoding circuits that combine advanced factorization techniques with sublinear scaling in ensemble size. Here, we introduce SVD-THC, which extends tensor hypercontraction to sets of Hamiltonians defined at different nuclear geometries through a singular value decomposition of the ensemble. We use SVD-THC to construct a single multiplexed block encoding circuit for all geometries in an ensemble. We then evaluate the approach on ensembles generated by varying internal rotational coordinates in 1-bromo-2-chloroethane as well as in glycine and alanine dipeptides, corresponding to established model systems for peptide conformational landscapes, with up to 5,184 geometries. Across several resolutions of the internal-coordinate grids, the Toffoli complexity of the resulting circuits grows only weakly with the number of geometries, changing by at most 12\% over grids that differ in size by up to 576×. In an energy-thresholding circuit, this yields 35--200× fewer Toffoli gates than slicing together single-geometry block encodings. This approach could help make coherent processing of molecular geometry ensembles a useful primitive for fault-tolerant quantum computing.
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BibTeX
@misc{cortes2026efficient,
title = {{Efficient Block Encodings for Ensembles of Molecular Hamiltonians}},
author = {Cristian L. Cortes and Andrew J. Jenkins and William Pol and Dario Rocca and Mark Steudtner and Gian-Luca R. Anselmetti and Matthias Degroote and Nikolaj Moll and Raffaele Santagati and Michael Streif and Markus R. Hermann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25968},
eprint = {2610.25968},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25968},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient Block Encodings for Ensembles of Molecular Hamiltonians
AU - Cristian L. Cortes
AU - Andrew J. Jenkins
AU - William Pol
AU - Dario Rocca
AU - Mark Steudtner
AU - Gian-Luca R. Anselmetti
AU - Matthias Degroote
AU - Nikolaj Moll
AU - Raffaele Santagati
AU - Michael Streif
AU - Markus R. Hermann
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25968
UR - https://arxiv.org/abs/2610.25968
AB - Accurately characterizing molecular properties and reactivity often requires electronic-structure calculations across an ensemble of molecular geometries. Quantum algorithms that process such ensembles coherently could address this challenge, but they require Hamiltonian block encoding circuits that combine advanced factorization techniques with sublinear scaling in ensemble size. Here, we introduce SVD-THC, which extends tensor hypercontraction to sets of Hamiltonians defined at different nuclear geometries through a singular value decomposition of the ensemble. We use SVD-THC to construct a single multiplexed block encoding circuit for all geometries in an ensemble. We then evaluate the approach on ensembles generated by varying internal rotational coordinates in 1-bromo-2-chloroethane as well as in glycine and alanine dipeptides, corresponding to established model systems for peptide conformational landscapes, with up to 5,184 geometries. Across several resolutions of the internal-coordinate grids, the Toffoli complexity of the resulting circuits grows only weakly with the number of geometries, changing by at most 12\% over grids that differ in size by up to 576×. In an energy-thresholding circuit, this yields 35--200× fewer Toffoli gates than slicing together single-geometry block encodings. This approach could help make coherent processing of molecular geometry ensembles a useful primitive for fault-tolerant quantum computing.
ER -