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- Datasource
- Association for Computing Machinery
- Copyright
- Copyright © 2007 by ACM Inc.
- ISBN
- 978-1-59593-631-8
- doi
- 10.1145/1250790.1250874
- Publisher site
- See Article on Publisher Site
Abstract
Search via Quantum Walk LRI, Univ. Paris-Sud, CNRS F-91405 Orsay, France Fr d ric Magniez e e magniez@lri.fr Ashwin Nayak C&O and IQC, U. Waterloo and Perimeter Institute 200 University Ave. W. Waterloo, Ontario N2L 3G1, Canada Computer Science Division U.C. Berkeley Berkeley, CA 94720, USA J r mie Roland ee jroland@berkeley.edu anayak@uwaterloo.ca Miklos Santha santha@lri.fr LRI, Univ. Paris-Sud, CNRS F-91405 Orsay, France ABSTRACT We propose a new method for designing quantum search algorithms for nding a œmarked element in the state space of a classical Markov chain. The algorithm is based on a quantum walk ` la Szegedy [25] that is de ned in terms of a the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate re ‚ection operator. This operator is then used in an amplitude ampli cation scheme. As a result we considerably expand the scope of the previous approaches of Ambainis [6] and Szegedy [25]. Our algorithm combines the bene ts of these approaches in terms of being able to nd marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov