Accuracy, Decision Risk, and Sampling Cost in Quantum Error Mitigation
Abstract
Quantum error mitigation estimates expectation values that are often used to select or rank candidates. We study how estimation accuracy, decision risk and sampling cost are related in these tasks. The joint law of residual differences determines the risk of a shift-invariant decision; in Gaussian regimes, effective margins and their covariance provide a computable representation. This connects mitigation maps, shared measurement records and shot allocation, and yields an extrapolation design criterion under certified margins. Finite-shot QAOA-MaxCut controls illustrate two forms of this relationship: a positive affine CDR correction reduces mean-squared error while preserving rankings, whereas signed PEC sampling reduces mean-squared error and increases selection failures at equal evaluation cost. A retrospective, oracle-assisted study of 48 landscapes compares Gaussian-risk and MSE-based method selection using separate fitting, selection and evaluation samples. At the primary total shot budget, with learning amortized over 20 decisions per landscape, failure rates are $0.3083$ for Gaussian-risk selection, $0.4719$ for MSE selection and $0.2333$ for unmitigated estimation. These comparisons describe how uncertainty in candidate differences and the allocation of measurements between learning and evaluation jointly enter the assessment of mitigation.
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BibTeX
@misc{alfaro2026accuracy,
title = {{Accuracy, Decision Risk, and Sampling Cost in Quantum Error Mitigation}},
author = {Vicenzo Scavino Alfaro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.02888},
eprint = {2607.02888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.02888},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accuracy, Decision Risk, and Sampling Cost in Quantum Error Mitigation
AU - Vicenzo Scavino Alfaro
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2607.02888
UR - https://arxiv.org/abs/2607.02888
AB - Quantum error mitigation estimates expectation values that are often used to select or rank candidates. We study how estimation accuracy, decision risk and sampling cost are related in these tasks. The joint law of residual differences determines the risk of a shift-invariant decision; in Gaussian regimes, effective margins and their covariance provide a computable representation. This connects mitigation maps, shared measurement records and shot allocation, and yields an extrapolation design criterion under certified margins. Finite-shot QAOA-MaxCut controls illustrate two forms of this relationship: a positive affine CDR correction reduces mean-squared error while preserving rankings, whereas signed PEC sampling reduces mean-squared error and increases selection failures at equal evaluation cost. A retrospective, oracle-assisted study of 48 landscapes compares Gaussian-risk and MSE-based method selection using separate fitting, selection and evaluation samples. At the primary total shot budget, with learning amortized over 20 decisions per landscape, failure rates are $0.3083$ for Gaussian-risk selection, $0.4719$ for MSE selection and $0.2333$ for unmitigated estimation. These comparisons describe how uncertainty in candidate differences and the allocation of measurements between learning and evaluation jointly enter the assessment of mitigation.
ER -