Adaptive stabilizer-state-fidelity certification
Phys. Rev. A 114, 042456 – Published 26 October, 2026
DOI: https://doi.org/10.1103/trg6-b2t9
Abstract
Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. The reference [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer generator gauge, but gauge dependence can leave a large fidelity ambiguity. We develop an adaptive extension that reports the full certified fidelity interval. First, for a single gauge, we derive the complementary optimal worst-case upper bound. We then formulate gauge selection as an adaptive design problem in which each round solves endpoint linear programs and chooses a new gauge by a witness elimination policy. We prove monotonic tightening, simultaneous finite-shot coverage with an explicit uncertainty floor, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage. Finally, we identify affine-subspace-supported syndrome distributions for which adaptivity can beat this exponential benchmark, and we numerically confirm faster concentration.
