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arXiv · 1603.06442

Discrete time Dirac quantum walk in 3+1 dimensions

Giacomo Mauro D'Ariano·Nicola Mosco·Paolo Perinotti·Alessandro Tosini
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Abstract

In this paper we consider quantum walks whose evolution converges to the Dirac equation one in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two and three space dimensions. The behaviour of particle states, defined as states smoothly peaked in some wave-vector eigenstate of the walk, is described by an approximated dispersive differential equation that for small wave-vectors gives the usual Dirac particle and antiparticle kinematics. The accuracy of the approximation is provided in terms of a lower bound on the fidelity between the exactly evolved state and the approximated one. The jittering of the position operator expectation value for states having both a particle and an antiparticle component is analytically derived and observed in the numerical implementations.

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Giacomo Mauro D'Ariano, Nicola Mosco, Paolo Perinotti, Alessandro Tosini. 2016-03-21. Discrete time Dirac quantum walk in 3+1 dimensions. https://doi.org/10.3390/e18060228

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