Quantum Lower Bound for Recursive Fourier Sampling
Quantum Physics
2007-05-23 v2 Computational Complexity
Abstract
One of the earliest quantum algorithms was discovered by Bernstein and Vazirani, for a problem called Recursive Fourier Sampling. This paper shows that the Bernstein-Vazirani algorithm is not far from optimal. The moral is that the need to "uncompute" garbage can impose a fundamental limit on efficient quantum computation. The proof introduces a new parameter of Boolean functions called the "nonparity coefficient," which might be of independent interest.
Cite
@article{arxiv.quant-ph/0209060,
title = {Quantum Lower Bound for Recursive Fourier Sampling},
author = {Scott Aaronson},
journal= {arXiv preprint arXiv:quant-ph/0209060},
year = {2007}
}
Comments
8 pages. Revised since appearing in QIC, both to correct an error in the definition of the nonparity coefficient and to emphasize the need to uncompute