Quantum Lower Bound for Recursive Fourier Sampling

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. Like a classical algorithm, a quantum algorithm can solve problems recursively by calling itself as a subroutine. When this is done, though, the algorithm typically needs to call itself twice for each subproblem to be solved. The second call's purpose is to uncompute `garbage' left over by the first call, and thereby enable interference between different branches of the computation. Of course, a factor of 2 increase in running time hardly seems like a big deal, when set against the speedups promised by qu...

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Scott Aaronson
• Keywords: Algorithm, CORR 2002, Education, Quantum, Recursive Fourier Sampling