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 …

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 …

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 …

We propose a discrete spacetime formulation of quantum electrodynamics in one dimension
(aka the Schwinger model) in terms of quantum cellular automata, ie translationally invariant …

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 …

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

We provide first evidence that under certain conditions, 1/2-spin fermions may naturally
behave like a Grover search, looking for topological defects in a material. The theoretical …

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 …

A discrete-time quantum walk (QW) is essentially an operator driving the evolution of a
single particle on the lattice, through local unitaries. Some QWs admit a continuum limit …