Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes

Yiming Li, Zimu Li, Zi-Wen Liu · 2026 · arXiv 2026

| 编号 QE165 | 主题 qLDPC 码 | 链接 arXiv:2604.01874 |

摘要

摘要保留原文（英文）

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We exhibit nontrivial transversal logical multi-controlled-$Z$ gates on $[![N,\Theta (N),\tilde{\Theta }(N)]!]$ quantum low-density parity-check (qLDPC) codes with soundness $\tilde{\Theta }(1)$, combining nearly optimal code parameters with fault-tolerant non-Clifford gates on qLDPC and quantum locally testable codes for the first time. Remarkably, our proofs proceed through highly general algebraic arguments. Building on insights from [Li et al.,~arXiv:2603.25831], we develop a general covering space framework for constructing and computing a rich family of cohomological invariant forms on sheaf codes that induce transversal logical multi-controlled-$Z$. To certify their nontriviality, we further demonstrate

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