Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
Yao, (2025), arXiv:2511.13721 [quant-ph]
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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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A minimal implementation of SU(N) pure Yang-Mills theory on digital quantum computers is presented with simplified Hamiltonians, improved infinite-mass convergence, and SU(2) embedding into R^4, benchmarked by Monte Carlo simulations.
Lattice QED is established as a quantum error-correcting code beyond stabilizers, with explicit recovery operations constructed via quantum reference frames for gauge and fermionic sectors.
Error-mitigated IBM quantum hardware reproduces extrapolated classical simulations of entanglement growth and local thermalization for a truncated SU(2) gauge theory on chains up to 101 plaquettes.
A multi-part truncation for lattice QCD with fermions enables explicit Hamiltonians in 1+1D and 2+1D and string-breaking simulations by capping basis states, electric energy, fermions per site, and using large-Nc matrix element scaling.
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