发表机构
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对容错量子编译中合成任意n量子比特幺正矩阵的T门计数优化问题，提出基于块编码、块扁平化与量子奇异值变换的新方法，将T门计数的指数缩放从2^(4n/3)改进为2^(5n/4)。
AI 中文摘要
利用尽可能少的非克利福德门合成任意n量子比特幺正矩阵，是容错量子编译的核心问题。本文提出一种克利福德+T量子电路构造，可近似实现任意经典指定的幺正矩阵，误差不超过ε，且当log(1/ε)=poly(n)时，最坏情况下的T门计数具有2^(5n/4)的领先指数缩放，优于此前最佳的2^(4n/3)缩放。关键创新在于将目标幺正矩阵视为单个块编码对象，而非多个简单操作的长乘积。块扁平化技术在保持块编码高效实现的同时控制归一化；随后量子奇异值变换将其公共奇异值映射为1，从而恢复目标幺正矩阵。
英文摘要
Synthesizing arbitrary $n$-qubit unitaries using as few non-Clifford gates as possible is a central problem in fault-tolerant quantum compilation. We present a Clifford+$T$ quantum circuit construction that approximately implements any classically specified unitary to within error $ε$ and achieves a worst-case $T$-count with leading exponential scaling of $2^{5n/4}$ whenever $\log(1/ε)=\operatorname{poly}(n)$. This improves upon the best previous $2^{4n/3}$ scaling. The key innovation lies in treating the target unitary as a single block-encoded object rather than a long product of simpler operations. A technique of block flattening controls the normalization while preserving an efficient implementation of the block encoding; subsequently, quantum singular value transformation maps its common singular value to one, thereby recovering the target unitary.
Comments13 pages
