### Abstract

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

Original language | English |
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Pages (from-to) | 13773-13785 |

Number of pages | 13 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 45 |

DOIs | |

Publication status | Published - 9 Nov 2007 |

Externally published | Yes |

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*40*(45), 13773-13785. https://doi.org/10.1088/1751-8113/40/45/016