双幺正XXZ模型中长程稳定器雷尼熵的精确解
Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
AI总结：
针对量子系统的量子魔法生成问题，本文聚焦双幺正XXZ模型和稳定器雷尼熵（SRE），利用ZX演算及图形规则得到长程SRE的精确解，还通过数值验证低雷尼参数情形并给出其他二分划分结果。
摘要：
量子系统因存在纠缠和非稳定器性（又称量子魔法）而无法被经典高效模拟。本文研究量子线路演化下魔法的生成。为得到精确解，我们聚焦双幺正XXZ模型及一种名为稳定器雷尼熵（SRE）的魔法度量，还关注无法被短深度量子线路消除的长程SRE。我们采用ZX演算表示及图形规则计算所需表达式，在热力学极限下得到短时演化后的SRE精确解，以及特定状态划分下所有时间和雷尼参数的长程SRE精确解；因这些量的数值计算在雷尼参数上呈指数代价，我们对低雷尼参数和可及系统尺寸进行数值验证，并给出其他二分划分下长程SRE的数值结果。
英文摘要：
Quantum systems can not be efficiently simulated classically due to the presence of entanglement and nonstabilizerness, also known as quantum magic. Here we study the generation of magic under evolution by a quantum circuit. To be able to provide exact solutions, we focus on the dual-unitary XXZ model and a measure of magic called stabilizer Rényi entropy (SRE). Moreover, we focus also on long-range SRE, which cannot be removed by short-depth quantum circuits. To obtain exact solutions we use a ZX-calculus representation and graphical rules for the evaluation of the required expressions. We obtain exact results for SRE after short-time evolution in the thermodynamic limit and for long-range SRE for all times and all Rényi parameters for a particular partition of the state. Since the numerical evaluation of these quantities is exponentially costly in the Rényi parameter, we verify this numerically for low Rényi parameters and accessible system sizes and provide numerical results for the long-range SRE in other bipartitions.
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