A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits

Kevissen Sellapillay (1) , Pablo Arrighi (2, 3) , Di Molfetta Giuseppe (4)

1 AMU - Aix Marseille Université
2 QuaCS - Quantum Computation Structures
3 LMF - Laboratoire Méthodes Formelles
4 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)

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.

Mots clés: Physics; Quantum physics; Quantum simulation; Qubits

Domaines: Physique Quantique [quant-ph]

Kevissen Sellapillay, Pablo Arrighi, Di Molfetta Giuseppe. A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits. Scientific Reports, 2022, 12 (1), pp.2198. ⟨10.1038/s41598-022-06241-4⟩. ⟨hal-03594721⟩