渐近良好的二元三正交码与高层横向门
Asymptotically good binary triorthogonal codes and higher-level transversal gates
- Department of Mathematics Virginia Tech（弗吉尼亚理工大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构造了从第三层起每层Clifford层级中支持对角横向门的渐近良好二元CSS码，首次得到渐近良好的二元三正交码族，并实现恒定开销的T态蒸馏。
AI中文摘要：
对于从第三层开始的Clifford层级中的每一层，我们构造了显式的渐近良好的二元CSS码，这些码支持该层中的对角横向门。我们利用二元扩展域上的代数几何码，并通过字母表缩减将扩展域上的正交条件转化为二元重叠条件来实现这一点。特别地，我们获得了第一个渐近良好的二元三正交码族。我们还给出了一种参数较差的更强构造，该构造无需后续校正。最后，通过调整基于纠错的蒸馏协议，在足够弱的输入噪声和理想的稳定子操作下，我们的二元T门族实现了恒定开销的T态块蒸馏。
英文摘要：
For each level of the Clifford hierarchy from the third level onward, we construct explicit asymptotically good binary CSS codes for which a strongly transversal diagonal rotation, followed by a correction from the preceding level, implements the corresponding logical rotation. We achieve this using algebraic geometry codes over binary extension fields and performing an alphabet reduction that translates orthogonality conditions over the extension field to binary overlap conditions. In particular, we obtain the first asymptotically good family of binary triorthogonal codes. We also give a stronger construction with worse parameters for which the strongly transversal physical rotation implements the desired logical rotation, with no subsequent correction. Finally, adapting an error-correction-based distillation protocol, our binary $T$-gate families yield direct constant-overhead $T$-state block distillation from noisy $T$-state inputs under sufficiently weak input noise and ideal stabilizer operations.
