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Continuous-time quantum walks on the symmetric group

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Abstract

In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that for several natural choices for generating sets, these quantum walks do not have uniform limiting distributions, and are effectively blind to large areas of the graphs due to destructive interference. © Springer-Verlag Berlin Heidelberg 2003.

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Gerhardt, H., & Watrous, J. (2003). Continuous-time quantum walks on the symmetric group. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2764, 290–301. https://doi.org/10.1007/978-3-540-45198-3_25

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