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A quantum cellular automaton for one-dimensional QED

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Abstract

We propose a discrete spacetime formulation of quantum electrodynamics in one dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance and a maximum speed of information propagation. In this picture, the interacting quantum field theory is defined as a “convergent” sequence of quantum cellular automata, parameterized by the spacetime lattice spacing—encompassing the notions of continuum limit and renormalization, and at the same time providing a quantum simulation algorithm for the dynamics.

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Acknowledgements

CB was supported by the National Research Foundation of Korea (NRF-2018R1D1A1A02048436). PA would like to thank Pablo Arnault, Nathanaël Éon and Giuseppe Di Molfetta for helpful discussions. TCF would like to thank Tony Short and Tobias Osborne for useful discussions.

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Authors and Affiliations

  1. Aix-Marseille Univ, CNRS, LIS and Univ Paris-Saclay, ENS Paris-Saclay, CNRS, INRIA, LSV, Marseille, France

    Pablo Arrighi

  2. Department of Applied Mathematics, Hanyang University (ERICA), 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do, 426-791, Korea

    Cédric Bény

  3. Institut für Theoretische Physik, Leibniz Universität Hannover, Hannover, 30167, Germany

    Terry Farrelly

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  1. Pablo Arrighi
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  2. Cédric Bény
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  3. Terry Farrelly
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Correspondence to Pablo Arrighi.

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Arrighi, P., Bény, C. & Farrelly, T. A quantum cellular automaton for one-dimensional QED. Quantum Inf Process 19, 88 (2020). https://doi.org/10.1007/s11128-019-2555-4

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