[cl91]

> Toy model of AdS wormhole

It's even less than that. The duality between SYK_4 (SYK with four-fermion interactions) and AdS_2 (2D AdS spacetime) is only (conjectured to be) true at infinite N (where N is the number of fermions) and at the conformal limit (ie. the limit where temperature goes to zero). What they did is a N=7 simulation of a (sparse SYK) Hamiltonian "learned" (a much better word would have been "fitted") from a N=10 dense SYK at various (finite) temperatures. Neither 7 nor 10 is large enough to test this limit.

Now the actual quantum simulation they performed is that they constructed a thermal field double (and this allows them to make the connection with a "wormhole" because the two side of the TFD are basically the left and right quadrant of the Penrose diagram) and evolved it with the "learned" sparse SYK plus some shockwave operator $e^{i\mu V}$. The actual construction of the quantum gates is due to that Jafferis-Gao wormhole teleportaion paper. The supplementary material has some useful information (I find the actual Nature paper to be quite thin on technical details). It is indeed an interesting quantum simulation, in the sense that it demonstrated that the Google quantum computer behaves the way one expects a QC to behave.

Now does this experiment actually tell us anything about quantum gravity? No, and in this sense it is a publicity stunt. My reading of the Nature paper is that the actual paper is about 20% science (mostly due to Google's hardware) and about 80% salesmanship, which is really what you need in order to survive in academia.

> our dS space

To clarify this, our universe is asymptotically a dS spacetime in the distant future where matter and radiation density become zero and the universe becomes dominated by vacuum energy (and this is necessarily a conjecture based on current theory and cosmological observations, because nobody can live this long to see that day). It's not literally a dS spacetime right now.