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. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly resolve the approximate degree and quantum query complexities of the following basic functions:<\/p>\n
Our upper bound for Surjectivity introduces new techniques for approximating Boolean functions by low-degree polynomials. Our lower bounds are proved by significantly refining techniques recently introduced by Bun and Thaler (FOCS 2017).<\/p>\n","protected":false},"excerpt":{"rendered":"
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. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly resolve the approximate degree and quantum query complexities of the following basic functions: 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