Uniform Approximation by (Quantum) Polynomials
Quantum Physics
2011-03-15 v3
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.
Keywords
Cite
@article{arxiv.1008.1599,
title = {Uniform Approximation by (Quantum) Polynomials},
author = {Andrew Drucker and Ronald de Wolf},
journal= {arXiv preprint arXiv:1008.1599},
year = {2011}
}
Comments
9 pages; minor improvements based on journal version; http://www.rintonpress.com/journals/qiconline.html#v11n34