Efficient Estimation of Logical Sensitivities Through Fault-Counting
Abstract
Quantum error-correcting circuits are affected by multiple physical noise mechanisms, whose contributions to logical failure must be understood to evaluate code performance and guide improvements in hardware. The individual error budget contributions for an error type i can be characterized by its logical sensitivity νi = (∂ pL)/(∂ pi), which measures the response of the logical error rate pL to each physical noise parameter pi. Normally, νi is measured using linear fits such as finite differences, where pL is measured at two or more values of pi to calculate partial derivatives. In this paper, we develop a differentiable estimator to obtain all components of ∇ppL simultaneously from a single Monte Carlo data set at one noise configuration, using information about the underlying fault configurations. In surface code simulations with circuit-level noise, the estimator agrees with conventional finite differences while requiring one to two orders of magnitude fewer shots to achieve the same variance. We apply this technique to quantify error budgets, resolve sensitivities at the individual qubit level, and infer effective code distance. Finally, we incorporate the sensitivities into Newton root finding to locate and trace threshold contours in multidimensional noise models. These results provide an efficient method for extracting and applying logical sensitivity information from standard quantum error correction simulations.
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BibTeX
@misc{fu2026efficient,
title = {{Efficient Estimation of Logical Sensitivities Through Fault-Counting}},
author = {Winston Fu and J. Wilson Staples and Jeff D. Thompson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10531},
eprint = {2610.10531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10531},
}
RIS
TY - UNPB
TI - Efficient Estimation of Logical Sensitivities Through Fault-Counting
AU - Winston Fu
AU - J. Wilson Staples
AU - Jeff D. Thompson
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10531
UR - https://arxiv.org/abs/2610.10531
AB - Quantum error-correcting circuits are affected by multiple physical noise mechanisms, whose contributions to logical failure must be understood to evaluate code performance and guide improvements in hardware. The individual error budget contributions for an error type i can be characterized by its logical sensitivity ν_i = (∂ p_L)/(∂ p_i), which measures the response of the logical error rate p_L to each physical noise parameter p_i. Normally, ν_i is measured using linear fits such as finite differences, where p_L is measured at two or more values of p_i to calculate partial derivatives. In this paper, we develop a differentiable estimator to obtain all components of ∇_pp_L simultaneously from a single Monte Carlo data set at one noise configuration, using information about the underlying fault configurations. In surface code simulations with circuit-level noise, the estimator agrees with conventional finite differences while requiring one to two orders of magnitude fewer shots to achieve the same variance. We apply this technique to quantify error budgets, resolve sensitivities at the individual qubit level, and infer effective code distance. Finally, we incorporate the sensitivities into Newton root finding to locate and trace threshold contours in multidimensional noise models. These results provide an efficient method for extracting and applying logical sensitivity information from standard quantum error correction simulations.
ER -