Quantum walks simulating non-commutative geometry in the Landau problem

Non-Commutative Geometry (NCG) is considered in the context of a charged particle moving uniform magnetic field. The classical and quantum mechanical treatments are revisited, new marker NCG introduced. This then used to investigate Quantum Walks (QWs). It proven that these walks exhibit at near continuum limit. For purely discrete regime, two illustrative different complexities studied full detail. most complex walk does NCG, but simplest, degenerate one not. Thus, can be simulated by QWs, not only limit also regime.