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arXiv · 1208.1122

Optimal quantum query bounds for almost all Boolean functions

Andris Ambainis·Arturs Backurs·Juris Smotrovs·Ronald de Wolf
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Abstract

We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is essentially optimal for almost all functions. Our proof uses the fact that the acceptance probability of a T-query algorithm can be written as the sum of squares of degree-T polynomials.

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Andris Ambainis, Arturs Backurs, Juris Smotrovs, Ronald de Wolf. 2012-08-06. Optimal quantum query bounds for almost all Boolean functions. https://arxiv.org/abs/1208.1122

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