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arXiv · 2209.02943

Skeleton structure inherent in discrete-time quantum walks

Tomoki Yamagami·Etsuo Segawa·Ken'ichiro Tanaka·Takatomo Mihana·André Röhm·Ryoichi Horisaki·Makoto Naruse
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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 newly found 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.

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Tomoki Yamagami, Etsuo Segawa, Ken'ichiro Tanaka, Takatomo Mihana, André Röhm, Ryoichi Horisaki, Makoto Naruse. 2022-09-07. Skeleton structure inherent in discrete-time quantum walks. https://doi.org/10.1103/physreva.107.012222

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