  We investigate the properties of a quantum walk which can simulate the
behavior of a spin $1/2$ particle in a model with an ordinary spatial
dimension, and one extra dimension with warped geometry between two branes.
Such a setup constitutes a $1+1$ dimensional version of the Randall-Sundrum
model, which plays an important role in high energy physics. In the continuum
spacetime limit, the quantum walk reproduces the Dirac equation corresponding
to the model, which allows to anticipate some of the properties that can be
reproduced by the quantum walk. In particular, we observe that the probability
distribution becomes, at large time steps, concentrated near the "low energy"
brane, and can be approximated as the lowest eigenstate of the continuum
Hamiltonian that is compatible with the symmetries of the model. In this way,
we obtain a localization effect whose strength is controlled by a warp
coefficient. In other words, here localization arises from the geometry of the
model, at variance with the usual effect that is originated from random
irregularities, as in Anderson localization. In summary, we establish an
interesting correspondence between a high energy physics model and localization
in quantum walks.
