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 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2002
- DOI:
- 10.48550/arXiv.quant-ph/0209060
- arXiv:
- arXiv:quant-ph/0209060
- Bibcode:
- 2002quant.ph..9060A
- Keywords:
-
- Quantum Physics;
- Computer Science - Computational Complexity
- E-Print:
- 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