Problem
Research questions and friction points this paper is trying to address.
asymptotically good
binary CSS codes
transversal gates
triorthogonal codes
Clifford hierarchy
Asymptotically good binary triorthogonal codes and higher-level transversal gates
🤖 AI Summary
该研究通过使用代数几何码和字母表缩减方法，构建了渐近良好的二进制CSS码，支持不同层级的对角线遍历门，解决了高级别遍历门的支持问题。
📝 Abstract
For each level of the Clifford hierarchy from the third level onward, we construct explicit asymptotically good binary CSS codes supporting diagonal transversal gates in that level. 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 no subsequent correction is required. Finally, adapting an error-correction-based distillation protocol, our binary $T$-gate families yield constant-overhead $T$-state block distillation under sufficiently weak input noise and ideal stabilizer operations.
Innovation
Methods, ideas, or system contributions that make the work stand out.
asymptotically good binary CSS codes
triorthogonal codes
transversal gates
algebraic geometry codes
alphabet reduction
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