Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The complexity of entanglement is at the root of the onset of quantum chaos, universal distribution of entanglement spectrum statistics, hardness of a disentangling algorithm and of the quantum machine learning of an unknown random circuit, and universal temporal entanglement fluctuations. In this paper, we numerically show how a crossover from a simple pattern of entanglement to a universal, complex pattern can be driven by doping a random Clifford circuit with $T$ gates. This work shows that quantum complexity and complex entanglement stem from the conjunction of entanglement and non-stabilizer resources, also known as magic.

中文翻译：

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随机电路中纠缠复杂度的转变

纠缠是量子力学的定义特征。二分纠缠的特征是冯诺依曼熵。然而，纠缠不仅仅用数字来描述；它的特点还在于其复杂程度。纠缠的复杂性是量子混沌开始的根源，纠缠谱统计的普遍分布，解纠缠算法和未知随机电路的量子机器学习的难度，以及普遍的时间纠缠涨落。在本文中，我们以数字方式展示了如何通过在带有 $T$ 门的随机 Clifford 电路中实现从简单的纠缠模式到通用复杂模式的交叉。这项工作表明，量子复杂性和复杂纠缠源于纠缠和非稳定资源的结合，