Quantum simulations and quantum walks

poster: The Dirac equation as a QW

speaker: Marcelo Forets (CAPP - Laboratoire d'Informatique de Grenoble - Universite Joseph Fourier - FRANCE)

abstract: The Dirac equation can be modelled as a quantum walk (QW), with QW being: discrete in time and space; homogeneous, and causal. This QW model was proposed independently by Succi and Benzi, Bialynicki-Birula and Meyer: we rederive it in a simple way in all dimensions and for hyperbolic symmetric systems in general, studying convergence to the exact solution of the Dirac equation. At the practical level, this result is of interest for the quantum simulation of relativistic particles. At the theoretical level, it reinfornces the status of this QW model as a simple, discrete toy model of relativistic particles.

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