How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?

Andris Ambainis; Ronald de Wolf

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arXiv · 1206.0717

How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?

Andris Ambainis·Ronald de Wolf

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Abstract

It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.

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Andris Ambainis, Ronald de Wolf. 2013-03-25. How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?. https://arxiv.org/abs/1206.0717

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