Strongly trapped two-dimensional quantum walks

Abstract

Discrete time quantum walks (DTQWs) are nontrivial generalizations of random walks with a broad scope of applications. In particular, they can be used as computational primitives, and they are suitable tools for simulating other quantum systems. DTQWs usually spread ballistically due to their quantumness. In some cases, however, they can remain localized at their initial state (trapping). The trapping and other fundamental properties of DTQWs are determined by the choice of the coin operator. We introduce and analyze an up to now uncharted type of walks driven by a coin class leading to strong trapping, complementing the known list of walks. This class of walks exhibit a number of exciting properties with the possible applications ranging from light pulse trapping in a medium to topological effects and quantum search.