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In this note, we develop a bounded-error quantum algorithm that makes $\tildeO(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts amonotone function, and rejects a function that is $\varepsilon$-far from beingmonotone. This gives a super-quadratic improvement compared to the best knownrandomized algorithm for all $\varepsilon = o(1)$. The improvement is cubicwhen $\varepsilon = 1/\sqrt{n}$.

Quantum Algorithm for Monotonicity Testing on the Hypercube