Quantum walks as massless Dirac Fermions in curved Space-Time
Résumé
A particular family of time- and space-dependent discrete-time quantum walks is considered in one dimensional physical space. The continuous limit of these walks is de?ned through a new procedure and computed in full detail. In this limit, the walks coincide with the propagation of a massless Dirac fermion in an arbitrary gravitational ?eld. Finally, the limiting procedure and the main result itself are carefully discussed.