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- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Springer Science+Business Media, LLC
- Subject
- Physics; Data Structures, Cryptology and Information Theory; Quantum Physics; Quantum Information Technology, Spintronics; Mathematical Physics; Quantum Computing
- ISSN
- 1570-0755
- eISSN
- 1573-1332
- DOI
- 10.1007/s11128-012-0432-5
- Publisher site
- See Article on Publisher Site
Abstract
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks.
Journal
Quantum Information Processing – Springer Journals
Published: Jul 8, 2012