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arXiv · 1503.02868

Quantum Algorithm for Monotonicity Testing on the Hypercube

Aleksandrs Belovs·Eric Blais
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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 $\varepsilon = 1/\sqrt{n}$.

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Aleksandrs Belovs, Eric Blais. 2015-03-10. Quantum Algorithm for Monotonicity Testing on the Hypercube. https://arxiv.org/abs/1503.02868

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