Exponential algorithmic speedup by a quantum walk

Authors: Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, Daniel A. Spielman.

Bibliographic Information: Available at http://arxiv.org/abs/quant-ph/0209131.


We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve thisproblem with high probability in subexponential time.
Daniel A. Spielman
Last modified: Sun Sep 8 13:04:42 EDT 2002