Exponential algorithmic speedup by quantum walk
Quantum Physics
2007-05-23 v2
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 this problem with high probability in subexponential time.
Cite
@article{arxiv.quant-ph/0209131,
title = {Exponential algorithmic speedup by quantum walk},
author = {Andrew M. Childs and Richard Cleve and Enrico Deotto and Edward Farhi and Sam Gutmann and Daniel A. Spielman},
journal= {arXiv preprint arXiv:quant-ph/0209131},
year = {2007}
}
Comments
24 pages, 7 figures; minor corrections and clarifications