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 …

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting
quantum spin models. Effective spins are represented by appropriate internal energy levels …

Quantum cellular automata are arrays of identical finite-dimensional quantum systems,
evolving in discrete-time steps by iterating a unitary operator G. Moreover the global …

The quantum walk formalism is a widely used and highly successful framework for modeling
quantum systems, such as simulations of the Dirac equation, different dynamics in both the …

A particular family of time-and space-dependent discrete-time quantum walks (QWs) is
considered in one-dimensional physical space. The continuous limit of these walks is …

The continuous limit of quantum walks (QWs) on the line is revisited through a new, recently
developed method. In all cases but one, the limit coincides with the dynamics of a Dirac …

Quantum non-Markovianity of a quantum noisy channel is typically identified with
information backflow or, more generally, with departure of the intermediate map from …

The Dirac equation can be modelled as a quantum walk (QW), whose main features are
being: discrete in time and space (ie a unitary evolution of the wave-function of a particle on …

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 …

The classical random walk formalism plays an important role in a wide range of applications.
Its quantum counterpart, the quantum walk, is proposed as an important theoretical model …