Uniform approximation by (quantum) polynomials
Andrew Drucker, Ronald de Wolf · Quantum Information and Computation · 2011
We show that quantum algorithms can be used to re-prove a classical theorem in approx-imation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version ofWeierstrass's Theorem on uniform approximation of continuous functions by polynomi-als. We provide two proofs, based respectively on quantum counting and on quantumphase estimation.