Quantum Lower Bound for Recursive Fourier Sampling
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 BernsteinVazirani 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2002
 arXiv:
 arXiv:quantph/0209060
 Bibcode:
 2002quant.ph..9060A
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity
 EPrint:
 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