  The problem of simulating through quantum walks Dirac fermions in arbitrary
curved space-times and coordinates is revisited, taking (1 + 1)D space-times as
an example. A new shift or translation operator on the grid is introduced, to
take into account arbitrary geometries. The new, generalised quantum walks
built with this operator can simulate Dirac fermions in arbitrary curved
space-times and coordinates, and their wave functions have exactly the same
number of components as standard Dirac spinors, and not twice that number, as
previously believed. In particular, in $(1 + 1)$D space-times, only one qubit
is needed at each lattice point, which makes it easier to perform quantum
simulations of the Dirac dynamics on current NISQs quantum devices. Numerical
simulations of the Dirac dynamics in the post Newtonian, so-called
Gravitoelectromagnetism regime are presented as an illustration.
