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.
- Pub Date:
- September 2002
- Quantum Physics;
- Computer Science - Computational Complexity
- 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