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arXiv · 2511.13721

Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories

Xiaojun Yao
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Abstract

We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss's law at each vertex into a stabilizer while the second only uses half of the vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.

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Xiaojun Yao. 2025-11-17. Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories. https://doi.org/10.1103/5yg7-6mph

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