Clifford电路中的单个T门驱动向普适纠缠谱统计的转变
Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
摘要：
Clifford电路不足以用于通用量子计算或使用$t\ge 4$创建$t$ -设计。虽然纠缠熵并不能说明这一不足，但纠缠谱是：对于仅限于Clifford门集的电路，纠缠水平是泊松分布的，而当使用通用门时，纠缠水平遵循Wigner-Dyson统计。在本文中，我们表明，使用有限尺寸标度分析的不同措施的水平间距统计，在热力学极限，插入一个单一的T $(π/8)$门在中间的随机Clifford电路是足以改变纠缠谱从泊松到Wigner-Dyson分布。
英文摘要：
Clifford circuits are insufficient for universal quantum computation or creating $t$-designs with $t\ge 4$. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T $(π/8)$ gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.
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