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A quantum cellular automaton for one-dimensional QED

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arxiv 1903.07007 v2 pith:WISOPU2Y submitted 2019-03-17 quant-ph cond-mat.othercs.DMhep-latmath-phmath.MP

Pablo Arrighi , Cédric Bény , Terry Farrelly This is my paper · ORCID
classification quant-phcond-mat.othercs.DMhep-latmath-phmath.MP
keywords quantumcellularautomataspacetimealgorithmautomatoncircuitscontinuum
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Causal Decompositions of 1D Quantum Cellular Automata

    quant-ph 2025-06 conditional novelty 8.0 of 10

    For N > 4r, every 1D quantum cellular automaton of causality radius r is exactly a routed unitary circuit of nearest-neighbour interactions, and translation-invariant automata get translation-invariant circuits.

  2. Fermion-doubling problem in Chiral discretizations of Quantum field theory: Definitive proof, Fixing, and Computation of two-point correlation function

    hep-lat 2026-07 conditional novelty 6.0 of 10

    The (1+1)D Dirac quantum cellular automaton has fermion-doubling poles that genuinely contribute to its Green's function; its one-step Green's function has a closed form, and the flavor-staggered fixed model's Green's...

  3. Non-Abelian Gauge-Invariant Cellular Automata

    cs.FL 2019-08 conditional novelty 5.0 of 10

    The authors build a non-abelian gauge-invariant cellular automaton by adding a permutation-valued gauge field to a basic shift rule, then define and characterize equivalence and invariant sets for gauge-invariant CA.

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