Scrambling in Random Unitary Circuits: Exact Results

Understand

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 R\'enyi-$2$ 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.