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A systematic method to building Dirac quantum walks coupled to electromagnetic fields

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Abstract

A 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.

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Notes

  1. Our third direction across this lattice will still be the same as the x-direction in the square lattice.

  2. This works similarly for b and d.

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Authors and Affiliations

  1. Physics Department, The University of Western Australia, Perth, WA, 6009, Australia

    Gareth Jay & Jingbo Wang

  2. LERMA, CNRS, Observatoire de Paris, Université PSL, Sorbonne Université, 75005, Paris, France

    Fabrice Debbasch

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  1. Gareth Jay
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Jay, G., Debbasch, F. & Wang, J. A systematic method to building Dirac quantum walks coupled to electromagnetic fields. Quantum Inf Process 19, 422 (2020). https://doi.org/10.1007/s11128-020-02933-w

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