发表机构
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences; School of Computer Science and Technology, University of Chinese Academy of Sciences; Shandong University; Thrust of Artificial Intelligence, Information Hub, The Hong Kong University of Science and Technology (Guangzhou)（中国科学院计算技术研究所处理器重点实验室; 中国科学院大学计算机科学与技术学院; 山东大学; 香港科技大学（广州）信息枢纽人工智能领域）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对对称投影纯化协议，建立了其非克利福德资源（T门）的近最优上下界，明确了T门数量随副本数的缩放关系，为量子态纯化的资源需求提供了理论依据。
AI 中文摘要
保护量子信息免受噪声影响对可靠量子计算和量子存储器至关重要。量子态纯化通过处理未知量子态的多个噪声副本，生成保真度更高的输出态，以此应对这一挑战。本文针对对称投影纯化协议所需的非克利福德资源，建立了近紧的上界和下界。对于d维系统的n个副本，我们构造了一个Clifford+T电路，以算子范数误差不超过ε的方式块编码对称投影器，使用的T门数量为Õ(n)，其中Õ符号表示忽略n、d和1/ε中的多对数因子。反之，利用稳定子零化度，我们证明，对于误差ε<(1/2)√(1-1/n)的此类块编码的任何Clifford+T实现，即使允许任意正归一化和干净稳定子辅助比特，也至少需要2n-2个T门。综合这些结果，确定了非克利福德成本随副本数量的近最优缩放关系，并揭示了量子态纯化中相干对称投影的基本资源需求。
英文摘要
Protecting quantum information from noise is essential for reliable quantum computation and quantum memories. Quantum state purification addresses this challenge by processing multiple noisy copies of an unknown quantum state to produce an output state of higher fidelity. Here we establish nearly tight upper and lower bounds on the non-Clifford resources required to implement the symmetric-projection purification protocol. For $n$ copies of a $d$-dimensional system, we construct a Clifford+T circuit that block-encodes the symmetric projector with operator-norm error at most $ε$ using $\widetilde{O}(n)$ T gates, where the tilde-$O$ notation suppresses polylogarithmic factors in $n$, $d$, and $1/ε$. Conversely, using stabilizer nullity, we prove that any Clifford+T implementation of such a block encoding with error $ε<\frac{1}{2}\sqrt{1-1/n}$ requires at least $2n-2$ T gates, even allowing arbitrary positive normalization and clean stabilizer ancillas. Taken together, these results establish the nearly optimal scaling of non-Clifford cost with the number of copies and uncover the fundamental resource requirements for coherent symmetry projection in quantum state purification.
