Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914161541251072 |
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| author | Yao, Xiaojun |
| author_facet | Yao, Xiaojun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories Yao, Xiaojun Quantum Physics High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories |
| topic | Quantum Physics High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.13721 |