论文标题
在随机统一电路中争夺：确切的结果
Scrambling in Random Unitary Circuits: Exact Results
论文作者
论文摘要
我们通过关注Hosur等人提出的三方信息来研究局部随机统一电路中量子信息的扰动。在两种情况下，我们为平均rényi-$ 2 $三方信息提供了确切的结果：（i）当地大门是随机的，（ii）当地大门是双重的，并且是从单个站点的HAAR不变措施中随机采样的。我们表明，后一种情况定义了一个参数的电路家族，并证明，对于此家族量子信息的“最大混乱”子集比在HAAR随机案例中更快。我们的方法基于标准映射到平均折叠张量网络上，可以通过适当的复发关系研究。通过相同的方法，我们还重新审视了超时订购的相关函数的计算，重新衍生的HAAR随机统一电路的已知公式，并给出了最大混乱的随机双重独立门的确切结果。
We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged Rényi-$2$ tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a "maximally chaotic" subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is based on a standard mapping onto an averaged folded tensor network, that can be studied by means of appropriate recurrence relations. By means of the same method, we also revisit the computation of out-of-time-ordered correlation functions, re-deriving known formulae for Haar-random unitary circuits, and presenting an exact result for maximally chaotic random dual-unitary gates.
