Quantum walks and gravitational waves

A new family of discrete-time quantum walks (DTQWs) propagating on a regular (1+2)D spacetime lattice is introduced. The continuum limit of these DTQWs is shown to coincide with the dynamics of a Dirac fermion coupled to an arbitrary relativistic gravitational field. This family is used to model the influence of arbitrary linear gravitational waves (GWs) on DTQWs. Pure shear GWs are studied in detail. We show that on large spatial scales, the spatial deformation generated by the wave induces a rescaling of the eigen-energies by a certain anisotropic factor which can be computed exactly. The effect of pure shear GWs on fermion interference patterns is also investigated, both on large scales and on scales comparable to the lattice spacing.