Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes

@misc{li2026parallelizable,
  title = {{Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes}},
  author = {Yiming Li and Zimu Li and Zhengyi Han and Zi-Wen Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.26691},
  eprint = {2609.26691},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26691},
}

TY  - UNPB
TI  - Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes
AU  - Yiming Li
AU  - Zimu Li
AU  - Zhengyi Han
AU  - Zi-Wen Liu
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.26691
UR  - https://arxiv.org/abs/2609.26691
AB  - We achieve linearly many parallelizable and addressable transversal logical multi-controlled-Z gates with asymptotically optimal parameters simultaneously on good quantum low-density parity check codes and quantum locally testable codes, by applying the gate framework of [arXiv:2604.01874] to good qLTC constructions. To establish the nontriviality of the logical operation, we express the cup product pairing as a coefficient in a product of Moore determinants and prove that this coefficient is nonzero. Moreover, we use the symmetries of the covering spaces to construct large spaces of cocycles. By multiplying the initial cocycles by suitable elements of these spaces, we obtain linearly many independent pairings, each selected by a corresponding cycle constructed using Poincaré duality. This yields linearly many parallelizable and addressable multi-controlled-Z gates and enables asymptotically constant-overhead magic state distillation with good qLDPC codes.
ER  -