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Journal Articles Quantum Information Processing Year : 2021

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

Kevissen Sellapillay
  • Function : Author
Pablo Arrighi
  • Function : Author
Giuseppe Di Molfetta
  • Function : Author
Nathanaël Eon
  • Function : Author
O. Duranthon
  • Function : Author
Michael Manighalam
  • Function : Author


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.

Dates and versions

hal-03594720 , version 1 (02-03-2022)



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, 2021, 20 (2), pp.76. ⟨10.1007/s11128-021-03011-5⟩. ⟨hal-03594720⟩
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