Polynomial degree vs. quantum query complexity

Andris Ambainis

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Polynomial degree vs. quantum query complexity

Andris Ambainis

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Abstract

The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function with polynomial degree M and quantum query complexity Ω(M^{1.321...}). This is the first superlinear separation between polynomial degree and quantum query complexity. The lower bound is shown by a new, more general version of quantum adversary method.

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Andris Ambainis. 2004-11-23. Polynomial degree vs. quantum query complexity. https://arxiv.org/abs/quant-ph/0305028

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