Discrete-time quantum walks on full binary trees

Abstract

Discrete-time quantum walks on rooted tree graphs are not straightforward to model since the graph's directionality suggests a non-unitary evolution, and the graph's non-regularity hinders a conventional coin state. We present a discrete-time quantum walk on a one-dimensional lattice that simulates a discrete-time quantum walk on full binary trees. We discuss the evolution of this model and elaborate on two effects on the coin/qubit. Firstly, the chirality of a full binary tree correlates with the probability of flipping the qubit state. Secondly, the model can partition the Bloch sphere of the initial qubit states into a region with a higher probability of remaining in the initial qubit state, and another region with a higher probability of bit flipping. We relate these effects to noise modeling and quantum information processing.