
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:
https://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/Ph...
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:
https://urldefense.com/v3/__https://arxiv.org/pdf/2002.09524__;!!D9dNQwwGXtA...
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
El mar, 7 ene 2025 a las 13:57, Daniel Manzano (
Dear all, tomorrow we continue with our Journal Club.
Noelia Sánchez (Fisymat student) will update us about phase transitions in quantum circuits.
Attached is the paper we'll see:
Best,
Dani.
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