What is the current state of research about the Hayden-Preskill circuit?

Question

Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a framework to see how the black-hole can thermalize in a $log (entropy)$ time scale. What next?

To start off,

The sort of problem with the Hayden-Preskill circuit is that it works via random unitary transformations on disjoint pairs of qubits and hence doesn't have an Hamiltonian interpretation. I believe one has always believed that matrix models (of matrix size $\sqrt{entropy}$) can saturate this logarithmic thermalization bound via Hamiltonian evolution.

• Has this above belief about the matrix models been proven yet?

• Is there an intuitive explanation as to why a theory with finite dimensional matrices should behave like an infinite dimensional system?

This post imported from StackExchange Physics at 2014-07-13 09:10 (UCT), posted by SE-user user6818