Discretizing spacetime is often a natural step towards modelling physical systems. For
quantum systems, if we also demand a strict bound on the speed of information propagation …

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 …

In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that
incorporates a linear quantum walk as a special case. In particular, we rigorously prove that …

We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a
vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set …

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 family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U (N)
gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it …

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 …

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal
quantum computers is a challenging problem. In this paper, a generalization of the …

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a
single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs …

A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum
computer is developed and analyzed. The time evolution is performed by an operator …