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.
de Rezende, Aaron Potechin, and Kilian Risse
2 Pith papers cite this work. Polarity classification is still indexing.
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Explicit families of CNF formulas exist such that tree-like semantic Frege refutations with line size s(n) require superpolynomial length for most formulas in the family, for s(n) in a broad range from nearly quadratic to subexponential in n.
citing papers explorer
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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.
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Superpolynomial Length Lower Bounds for Tree-Like Semantic Proof Systems with Bounded Line Size
Explicit families of CNF formulas exist such that tree-like semantic Frege refutations with line size s(n) require superpolynomial length for most formulas in the family, for s(n) in a broad range from nearly quadratic to subexponential in n.