High-rate CSS codes compile nonlocal Clifford and non-Clifford logical circuits into onsite phases and classical permutations, so MPS bond dimension stays fixed by the encoder while logical entanglement, magic, and non-Gaussianity grow.
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SCALA is a signaling cellular automaton with local attraction that achieves ~7.5% threshold and p_L proportional to p^{d/4} scaling for toric codes while keeping computation strictly local and robust to measurement and decoder noise.
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
citing papers explorer
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Efficiently simulable quantum circuits with large entanglement, magic, and non-Gaussianity via code-compiled tensor networks
High-rate CSS codes compile nonlocal Clifford and non-Clifford logical circuits into onsite phases and classical permutations, so MPS bond dimension stays fixed by the encoder while logical entanglement, magic, and non-Gaussianity grow.
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High-performance cellular automaton decoders for quantum repetition and toric code
SCALA is a signaling cellular automaton with local attraction that achieves ~7.5% threshold and p_L proportional to p^{d/4} scaling for toric codes while keeping computation strictly local and robust to measurement and decoder noise.
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Homological origin of transversal implementability of logical diagonal gates in quantum CSS codes
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.