Adaptive Stabilizer State Fidelity Certification

• URL: http://arxiv.org/abs/2605.29820v1
• Date: Thu, 28 May 2026 12:02:58 GMT
• Title: Adaptive Stabilizer State Fidelity Certification
• Abstract summary: We develop an adaptive extension that reports the full certified fidelity interval.<n>We prove monotonic tightening, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage.
• Score: 3.2669518901121672
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [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 exact endpoint linear programs and chooses a new gauge by a witness elimination policy. We prove monotonic tightening, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage. Finally, we identify structured syndrome distributions for which adaptivity beats this exponential benchmark, and we numerically confirm faster concentration.

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