  A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion
propagation in $2$D curved space-time is revisited. Usual continuous covariant
derivatives and spin-connections are generalized into discrete covariant
derivatives along the lattice coordinates and discrete connections. The
concepts of metrics and $2$-beins are also extended to the discrete realm. Two
slightly different Riemann curvatures are then defined on the space-time
lattice as the curvatures of the discrete spin connection. These two curvatures
are closely related and one of them tends at the continuous limit towards the
usual, continuous Riemann curvature. A simple example is also worked out in
full.
