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.
Simple quantum error correcting codes
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abstract
Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where C_1 and C_2 are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing C_1 to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error correcting codes for 3, 4 and 5 information qubits with block lengths of 8, 10 and 11 qubits respectively.
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A new Sparse Stabilizer Tensor cost function enables hyper-optimized contraction schedules for Quantum LEGO WEP calculations, delivering orders-of-magnitude improvements over dense tensor baselines for stabilizer codes.
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Gauss law codes and vacuum codes from lattice gauge theories
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.
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Hyper-optimized Quantum Lego Contraction Schedules
A new Sparse Stabilizer Tensor cost function enables hyper-optimized contraction schedules for Quantum LEGO WEP calculations, delivering orders-of-magnitude improvements over dense tensor baselines for stabilizer codes.