发表机构
Beijing Institute of Technology（北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过移除Clifford惰性背景，将量子码的非稳定化资源计算简化为有限经典计数，并给出Dicke态公式、三次相位码界及最大magic码识别。
AI 中文摘要
非稳定化资源（magic）是量子资源，与稳定化操作相结合，使得通用量子计算成为可能。它出现在容错码和拓扑序中。然而，量化非稳定化资源是困难的。标准度量需要对指数多个泡利算符求和，并且对于量子码，此前没有可用的定量理论。我们通过一个结构性观察解决了这一问题：Clifford扇区不携带magic，可以通过Clifford变换移除，留下一个三阶对象，其magic是一个可精确计算的四阶矩。移除这一惰性背景为几个码族提供了闭式表达式：一个适用于所有Dicke态的公式，将100量子比特的情形从$4^{100}$项缩减为短二项式求和；一个针对三次相位码（扭曲量子双重和非阿贝尔拓扑序）的界，仅由$D_4$码饱和；以及一个针对群乘法态的循环/零判据。这些结果共同将广泛一类码的非稳定化资源计算简化为有限经典计数问题，并识别出其中magic最大的码。
英文摘要
Nonstabilizerness (magic) is the quantum resource that, together with stabilizer operations, makes universal quantum computation possible. However, quantifying nonstabilizerness is difficult. The standard measure sums over exponentially many Pauli operators, and for quantum codes no quantitative theory has been available. A structural observation removes this obstacle: the Clifford sector carries no magic and can be removed by a Clifford transformation, leaving an order-three object whose magic is an exactly evaluable fourth moment. Removing this inert background yields closed forms for several code families: a formula for all Dicke states, reducing a 100-qubit case from $4^{100}$ terms to a short binomial sum; a bound for cubic-phase codes (twisted quantum doubles and non-Abelian topological order), saturated only by the $D_4$ code; and a cyclic/zero criterion for group multiplication states. For codeword-stabilized (CWS) codes, the companion paper \cite{Liu26arXiv} carries this reduction to its conclusion: the most magical codes are exactly the Sidon sets, and the nonstabilizerness bounds the code's transversal non-Clifford power. Together these results reduce the computation of nonstabilizerness for a broad class of codes to finite classical counting problems, and identify the maximally magical codes among them.
