  Discrete-time Quantum Walks (QWs) are transportation models of single quantum
particles over a lattice. Their evolution is driven through causal and local
unitary operators. QWs are a powerful tool for quantum simulation of
fundamental physics as some of them have a continuum limit converging to
well-known physics partial differential equations, such as the Dirac or the
Schr\"odinger equation. In this work, we show how to recover the Dirac equation
in (3+1)-dimensions with a QW evolving in a tetrahedral space. This paves the
way to simulate the Dirac equation on a curved spacetime. This also suggests an
ordered scheme for propagating matter over a spin network, of interest in Loop
Quantum Gravity where matter propagation has remained an open problem.
