AI 中文总结
该研究提出稳定器统计力学框架，通过构建稳定器配分函数与稳定器功，实现魔术态的有效量化分类，可应用于低秩稳定器模拟等场景，为量子系统魔术性质研究提供新途径。
AI 中文摘要
配分函数是统计力学对指数级大谱的解决方案，将其提炼为单个解析对象，其温度依赖性可解析基础系综的完整结构。我们证明，将通用量子计算与经典可模拟稳定器动力学区分开的资源——魔术，恰好可采用此类描述。将量子态的泡利谱映射到虚构多体系统（泡利气体）的能级上，我们构建其正则配分函数（稳定器配分函数），并从其相关自由能中得到一种我们称为稳定器功的魔术单调量。这两个对象均为类逆温度参数的解析函数，可通过贝尔采样有效估计，且该框架具有解析可处理性。我们推导了哈尔随机态、ν-可压缩态和伪魔术态的精确系综平均配分函数，以及集中度保证。我们证明，对于参数的每个值，稳定器功都是忠实的次可加魔术单调量，同时在量子硬件上仍可有效获取，并具有操作解释。与探测泡利分布单个矩的度量不同，稳定器功本质上是矩生成型的。当温度从高到低调谐时，它在稳定器2-雷尼熵和稳定器零性之间连续插值，揭示了两个先前不相关的单调量作为单个对象的极限情况。我们在低秩稳定器模拟、资源互转换、分子基态和量子多体系统上演示了该框架。因此，魔术的热力学不仅是类比，更是实用工具，为量子系统的魔术性质开辟了统计力学途径，这是任何单一度量都无法获取的。
英文摘要
The partition function is statistical mechanics' answer to an exponentially large spectrum, distilling it into a single analytic object whose temperature dependence resolves the full structure of the underlying ensemble. We show that magic, the resource separating universal quantum computation from classically simulable stabilizer dynamics, admits precisely such a description. Mapping the Pauli spectrum of a quantum state onto the energy levels of a fictitious many-body system, the Pauli gas, we construct its canonical partition function, the stabilizer partition function, and from its associated free energy a magic monotone that we call the stabilizer work. Both these objects are analytic functions of an inverse-temperature-like parameter and are efficiently estimable via Bell sampling. The framework is analytically tractable. We derive exact ensemble-averaged partition functions for Haar-random, $ν$-compressible, and pseudomagic states, together with concentration guarantees. We show that for every value of its parameter, the stabilizer work is a faithful, Subadditive magic monotone, while remaining efficiently accessible on quantum hardware and admitting an operational interpretation. Unlike measures that probe a single moment of the Pauli distribution, the stabilizer work is intrinsically moment-generating. As the temperature is tuned from high to low, it interpolates continuously between the stabilizer 2-Rényi entropy and the stabilizer nullity, revealing two previously disconnected monotones as limiting cases of a single object. We demonstrate the framework on low-rank stabilizer simulation, resource interconversion, molecular ground states, and quantum many-body systems. A thermodynamics of magic is therefore not merely an analogy but a working toolkit, opening a statistical-mechanical route to magic properties of quantum systems that no single measure can access.
Comments42 pages, 11 figures. Comments are welcome. William E. Salazar and Gaurav Saxena contributed equally to this work
