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Preprint Sep 2026

Non-Abelian sheaf quantum LDPC codes: good and magical

Non-Abelian quantum codes connect quantum error correction, phases of matter, and computational resources. In this work, we develop a general framework for constructing non-Abelian quantum low-density parity-check (qLDPC) codes by gauging sheaf codes via cup products and use it to obtain families with constant encoding...

Zi-Mu Li, Fu-Chuan Wei, Zhen Han et al. · 1 citation · ⚡1
Preprint Sep 2026

Transversal non-Clifford gates on good quantum locally testable codes

We achieve nontrivial transversal logical multi-controlled-$Z$ gates with asymptotically optimal parameters simultaneously on quantum low-density parity check codes and quantum locally testable codes, by applying the gate framework of [arXiv:2604.01874] to the recent good qLTC construction of [arXiv:2609.20780]. To thi...

Yi-Ming Li, Zi-Mu Li, Zi-Wen Liu · 5 citations

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