Discrete Feynman propagator for the Weyl quantum walk in 2 + 1 dimensions
1 QUIT Group, Dipartimento di Fisica - via Bassi 6, 27100 Pavia, Italy
2 INFN Sezione di Pavia - via Bassi, 6, 27100 Pavia, Italy
Received: 3 November 2014
Accepted: 10 February 2015
Recently quantum walks have been considered as a possible fundamental description of the dynamics of relativistic quantum fields. Within this scenario we derive the analytical solution of the Weyl walk in dimensions. We present a discrete path-integral formulation of the Feynman propagator based on the binary encoding of paths on the lattice. The derivation exploits a special feature of the Weyl walk, that occurs also in other dimensions, that is closure under multiplication of the set of the walk transition matrices. This result opens the perspective of a similar solution in the case.
PACS: 03.67.Ac – Quantum algorithms, protocols, and simulations / 03.67.-a – Quantum information
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