Uniform Approximation by (Quantum) Polynomials

Abstract

We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectively on quantum counting and on quantum phase estimation.

9 pages; minor improvements based on journal version; http://www.rintonpress.com/journals/qiconline.html#v11n34