Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.
Quantum algorithmic measurement
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Strict Hierarchy for Quantum Channel Certification to Unitary
Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.