Certified Finite-Shot Operating Windows for Virtual Distillation and Symmetry Verification

• URL: http://arxiv.org/abs/2606.15464v1
• Date: Sat, 13 Jun 2026 20:42:40 GMT
• Title: Certified Finite-Shot Operating Windows for Virtual Distillation and Symmetry Verification
• Abstract summary: We develop a finite-shot operating-window theory that makes comparison certifiable for virtual distillation (VD) and symmetry verification (SV)<n>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.<n>For SV, it isolates the bias floor left by undetectable errors and the sampling penalty set by the acceptance probability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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