Skeleton structure inherent in discrete-time quantum walks
Phys. Rev. A 107, 012222 – Published 31 January, 2023
DOI: https://doi.org/10.1103/PhysRevA.107.012222
Abstract
In this paper we claim that a common underlying structure—a skeleton structure—is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the initial state, and partially, even of the coin matrix. This structure is best interpreted in the context of quantum-walk-replicating random walks (QWRWs), i.e., random walks that replicate the probability distribution of quantum walks, where this structure acts as a simplified formula for the transition probability. Additionally, we construct a random walk whose transition probabilities are defined by the skeleton structure and demonstrate that the resultant properties of the walkers are similar to both the original QWs and QWRWs.
