Exponential algorithmic speedup by quantum walk
Authors:
- Andrew M. ChildsACAndrew M. Childs
- Richard CleveRCRichard Cleve
- Enrico DeottoEDEnrico Deotto
- Edward FarhiEFEdward Farhi
- Sam GutmannSGSam Gutmann
- Daniel A. SpielmanDSDaniel A. Spielman
Preprint
Abstract
We construct an oracular 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.Keywords
All Related Versions
- Version 1, 2002-09-24, ArXiv
- Version 2, 2002-10-25, ArXiv
- Published version: , 59.