Exact quantum algorithms have advantage for almost all Boolean functions

Andris Ambainis; Jozef Gruska; Shenggen Zheng

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arXiv · 1404.1684

Exact quantum algorithms have advantage for almost all Boolean functions

Andris Ambainis·Jozef Gruska·Shenggen Zheng

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Abstract

It has been proved that almost all $n$-bit Boolean functions have exact classical query complexity $n$. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all $n$-bit Boolean functions can be computed by an exact quantum algorithm with less than $n$ queries. More exactly, we prove that ${AND}_n$ is the only $n$-bit Boolean function, up to isomorphism, that requires $n$ queries.

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Andris Ambainis, Jozef Gruska, Shenggen Zheng. 2014-09-29. Exact quantum algorithms have advantage for almost all Boolean functions. https://arxiv.org/abs/1404.1684

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