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

• URL: http://arxiv.org/abs/2511.13721v1
• Date: Mon, 17 Nov 2025 18:59:59 GMT
• Title: Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• Abstract summary: We construct two quantum error correction codes for pure SU(2) lattice gauge theory.<n>The codes are able to correct single-qubit errors.<n>The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes.
• Score: 1.4213973379473652
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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