Quantum Reservoir

Hi,

On your last paper on Quantum Reservoir (ref : arXiv:2407.02553v1)
I had some questions on the local detuning encoding part. My first question is on the Hamiltonian described in the paper, and my second question is ont the encoding parts in the code on the Github code.
These two questions seem to be linked, this is why I put them together on that topic.

Just to notice, I come from the “computing” part and I may have trouble understanding physical details on neutral atoms, hence my following questions.

First question :
In the paper, it is specified that the data features are encoded into the parameters of the following Hamiltonian :

image

I don’t undersant why the Hamiltonian includes a detuning “splited” in two parts (a global detuning followed by a local detuning). Why do not juste include the local detuning part ? Why does the Delta_g detuning means in a physical way ?

Second question :
In the Quantum Reservoir Computing for Time Series Prediction Demo Code, I do not undersant why the features are encoded by this formula:

Δ_max = 6.0
xs = (train_features .- mean(train_features)) * Δ_max;
ys = (test_features .- mean(train_features)) * Δ_max;

Where does exactly this expression come from ?

Thanks a lot for your help and your insights,