Algorithm for Gradient Descent Disentangler

[gunheepark0229]

Hi! I was checking the documents for the Gradient Descent Disentangler, and I had some concepts that I cannot understand.
The document says \(dS = {\partial S(Utheta,n)} / {\partial U} \)

R[i] is given by \( {\partial S(Y,n)} / {\partial Y_i}\)

The point I cannot understand is how dS is given by:

Python: Select all

|     .----X--R--Z----.
|     |    |     |    |
|     |    q0    q1   |
|     |               |
|     |    q0*   q1*  |
|     |    |     |    |
|     .----X*-Y--Z*---.

Furthermore, is applying exp(- tdS) a heuristic way to update U?
Usually, some variable w is updated by \({w_{new} = w - \eta dS/dw}\), but in our case, we need to keep U unitary, so we are applying unitary exponentials (if dS is anti-hermitian).
Is it a correct approach?