AI 中文总结
本文通过实空间重整化群方法计算自旋链中量子态的稳定子Rényi熵，得到低能大距离极限下的闭式表达式，并分析量子魔法在粗粒化及不同参数和量子相中的演化。
AI 中文摘要
稳定子态是一类重要的量子态，可由计算基态通过泡利算符和克利福德门生成。尽管它们可能展现出显著的多体纠缠，但限制在稳定子操作的量子电路可以在经典上高效模拟，因此它们本身无法提供量子计算优势。这种优势需要非稳定子资源，通常称为量子魔法。在本文中，我们通过计算一类自旋哈密顿量中出现的量子态的稳定子Rényi熵来研究其非稳定子性质。利用实空间重整化群技术，我们得到了在低能、大距离极限下有效的闭式表达式。我们分析了量子魔法在粗粒化过程中如何演化，并探讨了其在不同参数区间和量子相中的行为。
英文摘要
Stabilizer states constitute an important class of quantum states that can be generated from computational-basis states using Pauli operators and Clifford gates. Although they may exhibit substantial multipartite entanglement, quantum circuits restricted to stabilizer operations can be efficiently simulated classically and therefore cannot, by themselves, provide a quantum computational advantage. Such an advantage requires non-stabilizer resources, commonly referred to as quantum magic. In this paper, we investigate the non-stabilizerness of quantum states arising in a class of spin Hamiltonians by computing their stabilizer Rényi entropies. Using real-space renormalization-group techniques, we obtain a closed-form expression valid in the low-energy, large-distance regime. We analyze how quantum magic evolves under coarse-graining and explore its behavior across different parameter regimes and quantum phases.
