发表机构
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin; Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno; INFN, Sezione di Napoli, Gruppo Collegato di Salerno（柏林自由大学达勒姆复杂量子系统中心; 萨莱诺大学工业工程系; 意大利国家核物理研究所那不勒斯分部萨莱诺协作组）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出通用魔法态浓缩协议，以6个输入副本蒸馏1个精确CCZ态，由M³^lin决定最优成功概率，可实现渐近最优蒸馏速率，证明任意未知纯量子比特魔法态可用于通用量子计算。
AI 中文摘要
魔法在量子计算中扮演双重角色：它将稳定器动力学从高效的经典可模拟性提升至通用性，但也对容错性构成核心挑战，因为非稳定器操作更难抵御噪声。魔法态蒸馏可解决该问题；然而，现有协议通常假设输入具有先验结构，例如接近目标态或特定噪声模型。本文提出通用魔法态浓缩：一种固定稳定器协议，可将少量未知纯非稳定器量子比特态转换为精确的目标魔法态。受精确T态浓缩的阻碍启发，本文证明CCZ态表现出根本不同的特性：6个输入副本是蒸馏出1个精确CCZ态的必要且充分条件，最优成功概率由线性三阶稳定器Rényi熵M³^lin决定。此外，本文表明M³^lin决定了最多9个输入副本的任何协议的最优态依赖性，并展示了一个具有更高成功概率的8副本协议。进一步，本文协议的块重复可产生渐近蒸馏速率，其在对数因子内达到最优缩放。作为推论，任何未知纯量子比特魔法态均可通过精确CCZ注入用于通用量子计算。这些结果共同确定稳定器Rényi熵是魔法态蒸馏中的基本操作量。
英文摘要
Magic plays a dual role in quantum computation: it promotes stabilizer dynamics from efficient classical simulability to computational universality, but also challenges fault-tolerant architectures, since non-stabilizer operations are harder to protect against noise. Magic state distillation addresses this issue, yet existing protocols remain largely tailored to specific assumptions about the input or noise model and, more fundamentally, no general information-theoretic theory of optimal magic-state conversion currently exists. Here we develop such a characterization for pure qubit states through universal magic state concentration: a fixed stabilizer protocol that converts a few copies of an unknown pure non-stabilizer qubit state into an exact target magic state. Motivated by the impossibility of exact $T$-state concentration, we build six- and eight-copy protocols producing an exact $\mathrm{CCZ}$ state, with six copies being minimal. Their success probabilities are governed by the linearized order-three stabilizer Rényi entropy $M^{\mathrm{lin}}_3$. We show that this connection is structural: for up to nine input copies, $M^{\mathrm{lin}}_3$ fully determines the success probability of every universal Clifford-invariant stabilizer protocol. Remarkably, this characterization persists asymptotically: our constructions achieve optimal rates among universal single-output protocols and remain optimal up to logarithmic factors among arbitrary stabilizer protocols. As a corollary, we show that any unknown pure non-stabilizer state suffices for universal quantum computation via probabilistic $\mathrm{CCZ}$-state injection. Together, these results identify the stabilizer Rényi entropy as a fundamental operational quantity in magic state distillation.
