Giuseppe Di Molfetta, University of Marseille
As we know, spacetime is not flat at the cosmological scale. In order to describe spacetime, in General Relativity theory (GR), we need a continuous and differentiable manifold and a formal way to account for the continuous distortion of the metrics. The main point is that changing coordinate systems should not affect physics laws (General Covariance). However at the Planck length, matter is not continuous and obeys Quantum Theory (QT). Although one century has passed, finding an intrinsically discrete counterpart of GR is still an open question. In fact, discretized GR does not turn out in just a mere finite difference scheme of the old formula. I recently showed that one way to describe a discrete curved spacetime is by using Quantum Walks. From a physical perspective a QW describes situations where a quantum particle is taking steps on a discrete grid conditioned on its internal state (say, spin states). The particle dynamically explores a large Hilbert space associated with the positions of the lattice and allows thus to simulate a wide range of transport phenomena. It is surprising that this unitary and local dynamics, defined on a rigid space-time lattice coincides in the continuous limit with the dynamical behavior of a quantum spinning-particle spreading on a curved spacetime. This could really turn out to be a powerful quantum numerical method to discretize GR.