Certified Bounds on the Measurement Cost of Molecular Hamiltonians
Abstract
Quantum estimates of molecular energy require repeated state preparation and measurement. We bound the minimum repetition count for given measurements and processing rules from above with a practical schedule and from below with independently verified inequalities. For an H4 chain at H-H distances of 0.90 and 1.80 Åwith 2 per cent uniform noise in the ground state, entangling Clifford measurements, which map Pauli products onto one another, cut leading-order repetitions by at least 65.9 and 61.0 per cent, respectively, relative to any schedule using only single-qubit Pauli measurements and Hamiltonian terms. With 69 unaltered measurement settings, each a basis change followed by qubit readout, processing further observables saves at least 12.04 and 6.70 per cent. For four lanthanide and actinide Hamiltonians with depolarized Hartree-Fock covariances, reducing the sum of absolute Hamiltonian coefficients does not proportionally reduce sampling. The bounds cover linear unbiased estimates from independent batches at small error.
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BibTeX
@misc{zahariev2026certified,
title = {{Certified Bounds on the Measurement Cost of Molecular Hamiltonians}},
author = {Federico Zahariev and Vanda Glezakou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16866},
eprint = {2607.16866},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16866},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Certified Bounds on the Measurement Cost of Molecular Hamiltonians
AU - Federico Zahariev
AU - Vanda Glezakou
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2607.16866
UR - https://arxiv.org/abs/2607.16866
AB - Quantum estimates of molecular energy require repeated state preparation and measurement. We bound the minimum repetition count for given measurements and processing rules from above with a practical schedule and from below with independently verified inequalities. For an H_4 chain at H-H distances of 0.90 and 1.80 Åwith 2 per cent uniform noise in the ground state, entangling Clifford measurements, which map Pauli products onto one another, cut leading-order repetitions by at least 65.9 and 61.0 per cent, respectively, relative to any schedule using only single-qubit Pauli measurements and Hamiltonian terms. With 69 unaltered measurement settings, each a basis change followed by qubit readout, processing further observables saves at least 12.04 and 6.70 per cent. For four lanthanide and actinide Hamiltonians with depolarized Hartree-Fock covariances, reducing the sum of absolute Hamiltonian coefficients does not proportionally reduce sampling. The bounds cover linear unbiased estimates from independent batches at small error.
ER -