The Polynomial Method Strikes Back: Tight Quantum Query Bounds via Dual Polynomials

STOC '18: Symposium on Theory of Computing Los Angeles CA USA June, 2018, pp. 297-310, 2018.

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Abstract:

The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. The approximate degree of f is known to be a lower bound on the quantum query complexity of f (Beals et al., FOCS 1998 and J. ACM 2001). We resolve or nearly resolve the approximate degree and quant...More

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