Continuous-time quantum walks with defects and disorder

J. A. Izaac, J. B. Wang, Z. J. Li

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


With the advent of physical implementations of quantum walks, a general theoretical and efficient numerical framework is required for the study of their interactions with defects and disorder. In this paper, we derive analytic expressions for the eigenstates of a one-dimensional continuous-time quantum walk interacting with a single defect, before investigating the effects of multiple diagonal defects and disorder, with emphasis on its transmission and reflection properties. Complex resonance behavior is demonstrated, showing alternating bands of zero and perfect transmission for various defect parameters. Furthermore, we provide an efficient numerical method to characterize quantum walks in the presence of diagonal disorder, paving the way for selective control of quantum walks via the optimization of position-dependent defects. The numerical method can be readily extended to higher dimensions and multiple interacting walkers.

Original languageEnglish
Article number042334
Pages (from-to)1-9
Number of pages9
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
Publication statusPublished - 29 Oct 2013
Externally publishedYes


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