More DBI features

[MatteoRobbiati]

I open this issue in order to keep track of the following @marekgluza comment (we are going to merge #1047 soon).

@Sam-XiaoyueLi we will discuss on Monday that we will be adding the routines as suggested in the issue by @shangtai into a secondary file additional_double_bracket_functions.py next to double_ bracket.py as in 2075cad

Sam, I'll ask you to migrate from the old repo the

• regular 'flow' using the canonical bracket and let's call it GWWDoubleBracketIteration or canonicalDoubleBracketIteration, you choose unless somebody voices some preference. GWW flow is historicall based on the paper by Głazek and Wilson, and independently the paper by Wegner. Canonical is based on the book by Kehrein who calls that bracket canonical, this makes sense for us because of the double-bracket rotation formula $$||\sigma(e^{sW} H e^{- s W} )||- ||\sigma (H )||= s \langle W,M\rangle+O(s^2)$$ so the canonical bracket $M = [\Delta(H),\sigma(H)]= [H,\sigma(H)]= [\Delta(H),H]$ appears on its own.
• the multi qubit Pauli Z generator with $Z(\mu) = (Z_1)^{\mu_1}\ldots (Z_L)^{\mu_L}$ where we optimize over all binary strings $\mu\in {0,1}^L$
• the magnetic field $D = \sum_i B_i Z_i$
• the two qubit Ising model $D = \sum_i B_i Zi + \sum{i,j} J_{i,j} Z_i Z_j$, please follow the tutorial by Matteo and use the QIBO ising model for that with $h=0$

After the meeting on Tuesday, we will discuss with Matteo how to do the gradients similarly to @wrightjandrew

Originally posted by @marekgluza in https://github.com/qiboteam/qibo/issues/1047#issuecomment-1825378975

[marekgluza]

Following the video call discussion:

Currently @Sam-XiaoyueLi is adding strategies into the double_bracket.py class https://github.com/qiboteam/qibo/blob/dbi_Z_search/src/qibo/models/dbi/double_bracket.py

We initially thought there might be a file with additional functions https://github.com/qiboteam/qibo/blob/dbf_migrate/src/qibo/models/dbi/additional_double_bracket_functions.py Sam, can you comment what kind of things would make sense to be added into that file? (The idea was to keep double_bracket.py as basic as possible)

The reason is that doing the Z_search was difficult in the previous workflow without doing it more low level. Sam maybe you can prepare some overview for the reason for the PR?

For me that's fine (and if it's faster to do it that way I'd advocate to accept the PR and maybe make a low-priority feature request for later to restucture it) but @MatteoRobbiati and @andrea-pasquale, Sam will ask you for review whether you agree that this aligns with the qibo-style

Thanks Sam! :+1: :)