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This research establishes rigorous finite-shot error bounds for virtual distillation and symmetry verification, moving beyond asymptotic approximations to define trustworthy sampling regimes on real quantum hardware. By certifying operating windows that account for estimator instability and resource costs, the study provides a falsifiable framework for selecting optimal mitigation strategies under strict budget constraints. The findings confirm that no single method universally dominates; instead, performance depends heavily on specific noise rates and device overheads like interferometry penalties.
Certified Finite-Shot Operating Windows for Virtual Distillation and Symmetry Verification
arXiv:2606.15464v1 Announce Type: new Abstract: Quantum error mitigation methods are usually compared through their infinite-shot bias, but on real devices the comparison is decided by finite sampling budgets, estimator instabilities, and per-shot resource costs. We develop a finite-shot operating-window theory that makes this comparison certifiable for virtual distillation (VD) and symmetry verification (SV): for each method we derive a mean-squared-error law with explicit, non-asymptotic remainder constants. For VD, the law captures the statistical bias and denominator instability of its quotient estimator, with a concentration certificate locating the sample size beyond which the quotient is trustworthy; for SV, it isolates the bias floor left by undetectable errors and the sampling penalty set by the acceptance probability. A selection trichotomy classifies any two-method comparison into a tie, uniform dominance, or a genuine tradeoff with a certified crossing window, including a self-consistency test that rejects spurious crossings. The theory makes falsifiable predictions -- operating-window locations scaling as $p^{-2}$ or $p^{-1}$ in the noise rate, and the sign pattern of all pairwise comparisons -- which exact white-box experiments confirm with fitted exponent $-1.97$ against the predicted $-2$ and with $300/300$ sign agreement, within a pre-registered analysis whose single failed gate, an over-strict all-instance criterion, is reported and audited in full. Gate-level simulation and archived runs on two IBM backends then test the windows under device conditions: idealized VD windows exist, but realistic interferometry overhead and denominator instability erase them, and calibrated SV is the practical winner in the tested QAOA instances. This absence of a universal winner is not a failure of mitigation; it is the regime structure that certified operating windows predict.
Abstract:Quantum error mitigation methods are usually compared through their infinite-shot bias, but on real devices the comparison is decided by finite sampling budgets, estimator instabilities, and per-shot resource costs. We develop a finite-shot operating-window theory that makes this comparison certifiable for virtual distillation (VD) and symmetry verification (SV): for each method we derive a mean-squared-error law with explicit, non-asymptotic remainder constants. For VD, the law captures the statistical bias and denominator instability of its quotient estimator, with a concentration certificate locating the sample size beyond which the quotient is trustworthy; for SV, it isolates the bias floor left by undetectable errors and the sampling penalty set by the acceptance probability. A selection trichotomy classifies any two-method comparison into a tie, uniform dominance, or a genuine tradeoff with a certified crossing window, including a self-consistency test that rejects spurious crossings. The theory makes falsifiable predictions -- operating-window locations scaling as $p^{-2}$ or $p^{-1}$ in the noise rate, and the sign pattern of all pairwise comparisons -- which exact white-box experiments confirm with fitted exponent $-1.97$ against the predicted $-2$ and with $300/300$ sign agreement, within a pre-registered analysis whose single failed gate, an over-strict all-instance criterion, is reported and audited in full. Gate-level simulation and archived runs on two IBM backends then test the windows under device conditions: idealized VD windows exist, but realistic interferometry overhead and denominator instability erase them, and calibrated SV is the practical winner in the tested QAOA instances. This absence of a universal winner is not a failure of mitigation; it is the regime structure that certified operating windows predict.
55 pages, 8 figures, 6 tables. Code and data: this https URL (archived at doi:https://doi.org/10.5281/zenodo.20670996)
arXiv:2606.15464 [quant-ph]
(or arXiv:2606.15464v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.15464 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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