# Continuous time limit of the DTQW in 2D+1 and plasticity

Abstract : Abstract We build a quantum cellular automaton (QCA) which coincides with $1+1$ 1 + 1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U (1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut–Susskind staggered version of $1+1$ 1 + 1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation—a strong indication that the model remains accurate in the relativistic regime.
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Journal articles
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https://hal-amu.archives-ouvertes.fr/hal-03594720
Contributor : Giuseppe Di Molfetta Connect in order to contact the contributor
Submitted on : Wednesday, March 2, 2022 - 7:21:16 PM
Last modification on : Friday, April 1, 2022 - 3:54:01 AM

### Citation

Di Molfetta Giuseppe, Kevissen Sellapillay, Pablo Arrighi, Giuseppe Di Molfetta, Nathanaël Eon, et al.. Continuous time limit of the DTQW in 2D+1 and plasticity. Quantum Information Processing, Springer Verlag, 2021, 20 (2), pp.76. ⟨10.1007/s11128-021-03011-5⟩. ⟨hal-03594720⟩

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