4 problems

Consider random circuits formed by placing random gates on the edges of a connected interaction graph, and let $n$ denote the number of qudits. A $k$-design is an ensemble reproduc…

The 1D brickwork channel is defined by applying random two-qudit unitaries in alternating layers: $\Phi_{BR1}$ acts on $(1,2),(3,4),\dots$, $\Phi_{BR2}$ acts on $(2,3),(4,5),\dots$…

Let $A_\lambda$ be the operator whose spectral contribution to the purity is given by Eq. (Ifp), and let the kernel contribution arising from the localized left and right generaliz…

Let $\mathcal{A}$ be an architecture over circuits, let $\mathcal{H}_{\mathcal{A}}$ be the distribution over circuits in $\mathcal{A}$ whose local gates are independently drawn fro…