Error-corrected function estimation advantage in multiparameter Hamiltonians
Abstract
We establish the ultimate precision limits for estimating a function of multiple Hamiltonian parameters in the presence of Markovian noise. By reducing multiparameter function estimation to an optimization over effective single-parameter embeddings, we derive tight bounds on the quantum Fisher information. We identify a necessary and sufficient functional Hamiltonian-not-in-Lindblad-span condition for Heisenberg-limited scaling in time. When this condition holds, we construct a code that simultaneously removes the noise and nuisance Hamiltonian parameters while preserving the target signal. When it fails, we derive the optimal standard quantum-limit coefficient and show that it is asymptotically attainable using approximate quantum error correction. Finally, we demonstrate that direct function estimation can substantially outperform estimating all parameters individually and subsequently evaluating the function. This advantage can scale with both the evolution time and the number of parameters.
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BibTeX
@misc{abbasgholinejad2026errorcorrected,
title = {{Error-corrected function estimation advantage in multiparameter Hamiltonians}},
author = {Erfan Abbasgholinejad and Lorcán O. Conlon and Sean R. Muleady and Jacob Bringewatt and Ali Fahimniya and Yu-Xin Wang and Alexey V. Gorshkov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16226},
eprint = {2609.16226},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16226},
}
RIS
TY - UNPB
TI - Error-corrected function estimation advantage in multiparameter Hamiltonians
AU - Erfan Abbasgholinejad
AU - Lorcán O. Conlon
AU - Sean R. Muleady
AU - Jacob Bringewatt
AU - Ali Fahimniya
AU - Yu-Xin Wang
AU - Alexey V. Gorshkov
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16226
UR - https://arxiv.org/abs/2609.16226
AB - We establish the ultimate precision limits for estimating a function of multiple Hamiltonian parameters in the presence of Markovian noise. By reducing multiparameter function estimation to an optimization over effective single-parameter embeddings, we derive tight bounds on the quantum Fisher information. We identify a necessary and sufficient functional Hamiltonian-not-in-Lindblad-span condition for Heisenberg-limited scaling in time. When this condition holds, we construct a code that simultaneously removes the noise and nuisance Hamiltonian parameters while preserving the target signal. When it fails, we derive the optimal standard quantum-limit coefficient and show that it is asymptotically attainable using approximate quantum error correction. Finally, we demonstrate that direct function estimation can substantially outperform estimating all parameters individually and subsequently evaluating the function. This advantage can scale with both the evolution time and the number of parameters.
ER -