Dear Noelia and quantum group,
First, thanks Noelia, this was a tough paper to read and I enjoyed the presentation a lot.
I keep wondering about the assumptions behind the Google result. I would like to share a few questions and possibly interesting papers, in case you would like to look into this paper further.
a) It is not so clear to me that XEB is a good proxy of the fidelity under general error models. If I understand correctly, they tested depolarizing noise. But it is known that XEB is not the fidelity for error channels such as amplitude damping. My impression is that they have a hidden strong assumption about the type of noise that is present on their superconducting chip. (This was also the case in their famous quantum supremacy paper.)
b) Also, maybe I missed this, but I didnt fully understand how robust the phase transition is for large system sizes. I wonder if the results are system size dependent and how much.
I am of the impression there might be open questions in both of these directions (what is a good metric of entanglement here and scaling of the results), and that perhaps one can test their hypothesis for classically simulable circuits on the cluster. I saw a recent flow up where they use the logarithmic entanglement negativity to measure correlations and do classical simulations of stabilizer circuits:
Circuits with a few number of T gates can also approximate arbitrary moments of the Haar measure, additively, as shown here, so perhaps they can be used as a proxy to universal random quantum circuits:
If anyone is interested in this and wants to keep reading let me know. At this point I mostly am trying to understand the result and the implications.
Best,
Juani