Quantum Information Processing

, Volume 11, Issue 5, pp 1015–1106 | Cite as

Quantum walks: a comprehensive review

  • Salvador Elías Venegas-AndracaEmail author


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.


Quantum walks Quantum algorithms Quantum computing Quantum and classical simulation of quantum systems 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Tecnológico de Monterrey Campus Estado de México and TexiaEstado de MéxicoMéxico

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