https://hal-insu.archives-ouvertes.fr/insu-03718016Jay, GarethGarethJayDebbasch, FabriceFabriceDebbaschLERMA - Laboratoire d'Etude du Rayonnement et de la Matière en Astrophysique - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - Observatoire de Paris - PSL - Université Paris sciences et lettres - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche ScientifiqueWang, JingboJingboWangA systematic method to building Dirac quantum walks coupled to electromagnetic fieldsHAL CCSD2020Quantum walkDirac equationLattices[SDU] Sciences of the Universe [physics]POTHIER, Nathalie2022-07-08 14:36:292023-03-24 14:53:272022-07-08 14:36:29enJournal articles10.1007/s11128-020-02933-w1A quantum walk whose continuous limit coincides with Dirac equation is usually called a Dirac quantum walk (DQW). A new systematic method to build DQWs coupled to electromagnetic (EM) fields is introduced and put to test on several examples of increasing difficulty. It is first used to derive the EM coupling of a 3D walk on the cubic lattice. Recently introduced DQWs on the triangular lattice are then re-derived, showing for the first time that these are the only DQWs that can be defined with spinors living on the vertices of these lattices. As a third example of the method's effectiveness, a new 3D walk on a parallelepiped lattice is derived. As a fourth, negative example, it is shown that certain lattices like the rhombohedral lattice cannot be used to build DQWs. The effect of changing representation in the Dirac equation is also discussed. Furthermore, we show the simulation of the established DQWs can be efficiently implemented on a quantum computer.