Self-avoiding quantum walk in the subspace and its limit theorems
Takuya Machida, C. M. Chandrashekar, Norio Konno, Thomas Busch · arXiv (Cornell University) · 2013
Completely self-avoiding quantum walks have distinct properties in that they lead to a trivial unidirectional transport of a quantum state. An interesting and non-trivial dynamics of the quantum walk can be constructed by choosing a self-avoiding in the subspace of the complete Hilbert space. Here, we present a comprehensive study of two-dimensional quantum walk which is self-avoiding in coin space and self-avoiding in both, coin and position space, respectively. In particular, we obtain analytical results for the evolution in the form of a limit distribution for both forms of self-avoiding quantum walks.