title: Discrete-time quantum walk with feed-forward quantum coin.
abstract: 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.
authors.affiliation: 1] Research Center of Integrative Molecular Systems (CIMoS), Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan [2] Institute for Quantum Studies, Chapman University, Orange, California 92866, USA.
authors.forename: Yutaka
authors.initials: Y
authors.lastname: Shikano
authors.affiliation: Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511, Japan.
authors.forename: Tatsuaki
authors.initials: T
authors.lastname: Wada
authors.affiliation: Major in Materials Science, Graduate School of Science and Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511, Japan.
authors.forename: Junsei
authors.initials: J
authors.lastname: Horikawa