Quantum discrete-time walkers have, since their introduction, demonstrated applications in algorithmic and in modeling and simulating 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 generalized 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.

翻译：自量子离散时间行走者被提出以来，已在算法设计以及多种输运现象的建模与模拟中得到应用。长期以来，它们被视为狄拉克方程在离散时间和离散空间中的类比，并因其内部对称性被用作模拟量子场论的基本工具。本文引入一类新型量子行走，称为扭曲量子行走，其连续极限可导出带有色散项的广义狄拉克算子。此外，能谱中的这一二次项可充当有效质量，从而对著名的费米子倍增问题进行正则化处理。