论文标题
共形场理论是神奇的
Conformal field theories are magical
论文作者
论文摘要
“魔术”是克利福德·盖茨（Clifford Gates）无法近似国家的程度。我们在$ \ Mathbb Z_3 $ Potts模型的基础状态下研究法力，这是一种魔术的度量，并认为这是多体物理学的广泛有用的诊断。特别是，我们发现$ q = 3 $基础状态在模型的临界点上具有巨大的法术力，并且该法力位于系统的相关性中。我们通过基于状态的MERA表示，通过简单的张量计算来解释法力的形式。由于法力在所有长度尺度上都存在，因此我们得出结论，描述三态POTTS模型临界点的保形场理论是神奇的。这些结果控制了在错误校正的量子计算机上准备POTTS基态的难度，并限制了ADS-CFT的张量网络模型。
"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the $\mathbb Z_3$ Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the $q = 3$ ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.
