Discrete-time quantum walk with feed-forward quantum coin


Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a quantum-mechanical cellular automaton, a discrete-time quantum walk is defined to include various quantum dynamical behavior. Here we generalize a discrete-time quantum walk on a line into the feed-forward quantum coin model, which depends on the coin state of the previous step. We show that our proposed model has an anomalous slow diffusion characterized by the porous-medium equation, while the conventional discrete-time quantum walk model shows ballistic transport.

DOI: 10.1038/srep04427

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@inproceedings{Shikano2014DiscretetimeQW, title={Discrete-time quantum walk with feed-forward quantum coin}, author={Yutaka Shikano and Tatsuaki Wada and Junsei Horikawa}, booktitle={Scientific reports}, year={2014} }