Quantum walks, the quantum mechanical counterpart of classical random walks, is an
advanced tool for building quantum algorithms that has been recently shown to constitute a …

We present a quantum cellular automaton model in one space-dimension which has the
Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a …

Constructing a discrete model like a cellular automaton is a powerful method for
understanding various dynamical systems. However, the relationship between the discrete …

That quantum correlations can be generated over time between the spin and the position of
a quantum walker is indisputable. The creation of bipartite entanglement has also been …

The preparation of initial superposition states of discrete-time quantum walks (DTQWs) is
necessary for the study and applications of DTQWs. Based on an encoding method, here …

A thermodynamic theory is developed to describe the behavior of the entanglement between
the coin and position degrees of freedom of the quantum walk on the line. It is shown that, in …

We present two long-time limit theorems of a 3-state quantum walk on the line when the
walker starts from the origin. One is a limit measure which is obtained from the probability …

We study the dynamical behavior of a quantum cellular automaton which reproduces the
Dirac dynamics in the limit of small wave vectors and masses. We present analytical …

We introduce the concept of a driven quantum walk. This work is motivated by recent
theoretical and experimental progress that combines quantum walks and parametric down …

In this paper, we present a detailed study on discrete-time Dirac quantum walks (DQWs) on
triangular and honeycomb lattices. At the continuous limit, these DQWs coincide with the …