#
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.

## Abstract

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