Regular Article – Quantum Information
Twisted quantum walks, generalised Dirac equation and Fermion doubling
Ecole Normale Supérieure de Lyon, Lyon, France
2 MINES Paris, Université PSL, Paris, France
3 CNRS, LIS, Aix-Marseille Université, Université de Toulon, Marseille, France
Accepted: 24 April 2023
Published online: 24 May 2023
Quantum discrete-time walkers have since their introduction demonstrated applications in algorithmics and to model and simulate a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalised Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well-known Fermion doubling problem.
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