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Quantum Algorithm for Monotonicity Testing on the Hypercube (1503.02868v1)
Published 10 Mar 2015 in quant-ph and cs.DS
Abstract: In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n{1/4}\varepsilon{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being monotone. This gives a super-quadratic improvement compared to the best known randomized algorithm for all $\varepsilon = o(1)$. The improvement is cubic when $\varepsilon = 1/\sqrt{n}$.