Geodesic quantum walks

We propose a family of discrete space-time quantum walks capable propagating on any arbitrary triangulations. Moreover, we also extend and generalize the duality principle introduced by Arrighi et al. [Sci. Rep. 9, 10904 (2019)], linking continuous local deformations given triangulation inhomogeneity unitaries that guide walker. proved in formal limit, both space time, this converges to ($1+2$)D massless Dirac equation curved manifolds. believe result has relevance modeling simulating transport structures, such as fullerene molecules or dynamical causal triangulation, addressing fast efficient optimization problems context methods.