The Quantum Query Complexity of Ac

Abstract

We show that any quantum algorithm deciding whether an input function f from [n] to [n] is 2-to-1 or almost 2-to-1 requires Θ(n) queries to f . The same lower bound holds for determining whether or not a function f from [2n − 2] to [n] is surjective. These results yield a nearly linear Ω(n/ logn) lower bound on the quantum query complexity of AC0. The best… (More)

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