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PreprintCC BY 4.0arXiv

Non-abelian quantum cellular automata: 1+1-dimensional SU(2) Yang--Mills with fermions

  • Dogukan Bakircioglu
  • Pablo Arrighi
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Abstract

This work provides a digital quantum simulation scheme for 1+1-dimensional SU(2) Yang--Mills theory with Dirac fermions. It takes the form of a quantum circuit, infinitely repeating across space and time with Δt=Δx=ε, whose wires follow lightlike propagation. The construction mirrors the logic of the standard quantum field theory approach, transposed to the discrete setting. Namely, we start from the Dirac quantum walk, restore SU(2) gauge symmetry by introducing the gauge field, lift the walk to a multi-particle QCA while preserving fermionic anticommutation, and equip the gauge field with its own dynamics. Rather than relying on Clebsch--Gordan decompositions, we use the pointwise-product structure of gauge-link updates, which yields self-contained proofs of unitarity and gauge covariance in quantum-computing notation. The construction provides an explicit algorithmic formulation of the theory, whose continuum limit we discuss.

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Cite

BibTeXRIS
BibTeX
@misc{bakircioglu2026nonabelian,
  title = {{Non-abelian quantum cellular automata: $1+1$-dimensional $SU(2)$ Yang--Mills with fermions}},
  author = {Dogukan Bakircioglu and Pablo Arrighi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30285},
  eprint = {2609.30285},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30285},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-abelian quantum cellular automata: 1+1-dimensional SU(2) Yang--Mills with fermions
AU  - Dogukan Bakircioglu
AU  - Pablo Arrighi
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.30285
UR  - https://arxiv.org/abs/2609.30285
AB  - This work provides a digital quantum simulation scheme for 1+1-dimensional SU(2) Yang--Mills theory with Dirac fermions. It takes the form of a quantum circuit, infinitely repeating across space and time with Δ_t=Δ_x=ε, whose wires follow lightlike propagation. The construction mirrors the logic of the standard quantum field theory approach, transposed to the discrete setting. Namely, we start from the Dirac quantum walk, restore SU(2) gauge symmetry by introducing the gauge field, lift the walk to a multi-particle QCA while preserving fermionic anticommutation, and equip the gauge field with its own dynamics. Rather than relying on Clebsch--Gordan decompositions, we use the pointwise-product structure of gauge-link updates, which yields self-contained proofs of unitarity and gauge covariance in quantum-computing notation. The construction provides an explicit algorithmic formulation of the theory, whose continuum limit we discuss.
ER  -