### Algorithm for Gradient Descent Disentangler

Posted:

**22 May 2020, 12:45**Hi! I was checking the documents for the Gradient Descent Disentangler, and I had some concepts that I cannot understand.

The document says \(dS = {\partial S(Utheta,n)} / {\partial U} \)

The point I cannot understand is how dS is given by:
Furthermore, is applying

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?

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:

Code: Select all

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

`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?