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 …

A particular example is produced to prove that quantum walks can be used to simulate full-
fledged discrete gauge theories. A family of two-dimensional walks is introduced and its …

The aim of this paper is to build quantum circuits that implement discrete-time quantum
walks having an arbitrary position-dependent coin operator. The position of the walker is …

We introduce an analytically treatable discrete time quantum walk in a one-dimensional
lattice which combines non-Markovianity and hyperballistic diffusion associated with a …

We propose a nonlinear quantum walk model inspired in a photonic implementation in
which the polarization state of the light field plays the role of the coin-qubit. In particular, we …

Contrary to the ballistic dynamics of standard quantum walks, the behavior of stochastic
quantum walks is known to be diffusive. Here we study discrete time quantum walks in weak …

We introduce a spacetime discretization of the Dirac equation that has the form of a quantum
automaton and that is invariant upon changing the representation of the Clifford algebra, like …

A quantum computer, ie utilizing the resources of quantum physics, superposition of states
and entanglement, could furnish an exponential gain in computing time. A simulation using …

We analyse a nonlinear QW model which can be experimentally implemented using the
components of the electric field on an optical nonlinear Kerr medium, which translates into a …