Double bracket iterations

[Edoardo-Pedicillo]

This PR implements a DoubleBracket class and solves #1034.

TODO

• Implement features 2 and 3 of Marek's issue
• Add examples with plotting functions under examples @MatteoRobbiati
• Compute energy @Edoardo-Pedicillo
• Compute energy fluctuations @Edoardo-Pedicillo
• Find minimization flow step (gradient descent) @MatteoRobbiati
• GPU acceleration @andrea-pasquale

Checklist:

• Reviewers confirm new code works as expected.
• Tests are passing.
• Coverage does not decrease.
• Documentation is updated.

[Edoardo-Pedicillo]

A small working example is provided in the documentation, now the algorithm does not converge because the step is not optimized.

@scarrazza now the DoubleBracket class is in qibo/hamiltonians folder, let me know if I should move it in qibo/models

@andrea-pasquale @MatteoRobbiati feel free to open PRs on top of this branch to contribute :)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (7f9f663) 100.00% compared to head (5046e3b) 100.00%.
Report is 29 commits behind head on master.

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  Files           63        64    +1     
  Lines         8865      8936   +71     
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+ Hits          8865      8936   +71     

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[MatteoRobbiati]

Thanks a lot @Edoardo-Pedicillo for this.

@scarrazza now the DoubleBracket class is in qibo/hamiltonians folder, let me know if I should move it in qibo/models

I think it should be better to have it as a model in Qibo.

[scarrazza]

Thanks @Edoardo-Pedicillo, I agree with @MatteoRobbiati , better to move in models. Could you please proceed and include some basic tests?

[andrea-pasquale]

I've moved the class to models and I've also added a few minimal tests.
I've tested the implementation on all CPU backends and it seems to be working, I need to check if on GPU everything is working correctly.
Feel free to review/add suggestions :)
Here is a quick example:

from qibo.models.double_bracket import DoubleBracketFlow, DoubleBracketFlowMode
from qibo import set_backend
import numpy as np
from qibo.hamiltonians.hamiltonians import Hamiltonian
from qibo.quantum_info import random_hermitian
import matplotlib.pyplot as plt

set_backend("numpy")

NSTEPS=100
nqubits = 4
h0 = random_hermitian(2**nqubits)

# define DBF
dbf = DoubleBracketFlow(Hamiltonian(nqubits=nqubits, matrix=h0))
for i in range(NSTEPS):
    # evolution under canonical commutator
    dbf(0.01, DoubleBracketFlowMode.canonical)

# plot matrix
plt.imshow(np.absolute(dbf.h.matrix), cmap='hot', interpolation='nearest')

I will proceed with the TODOs.

[andrea-pasquale]

@Edoardo-Pedicillo @andrea-pasquale
I commented a review of the DBI conventions change by @MatteoRobbiati and suggested that the enum generator type will better be called DoubleBracketGeneratorType and not IterationGeneratorType which makes sense in the DBI context but will surely confuse somebody working elsewhere in QIBO if it shows up as an available class

Thanks @marekgluza for the feedback.
I just changed IterationGeneratorType to DoubleBracketGeneratorType as you suggested.

[MatteoRobbiati]

@Edoardo-Pedicillo @andrea-pasquale I commented a review of the DBI conventions change by @MatteoRobbiati and suggested that the enum generator type will better be called DoubleBracketGeneratorType and not IterationGeneratorType which makes sense in the DBI context but will surely confuse somebody working elsewhere in QIBO if it shows up as an available class

Thanks @marekgluza for the feedback, it is a good idea. And thanks @andrea-pasquale for the fast fix.

[Edoardo-Pedicillo]

@Sam-XiaoyueLi could you move your commit in a new branch and open a PR pointing to dbf branch ?
Look here
https://stackoverflow.com/questions/1628563/move-the-most-recent-commits-to-a-new-branch-with-git#:~:text=Moving%20to%20a,branch%2C%20e.g%3A (instead of master you have to use dbf).

I suggest installing pre-commit https://pre-commit.com/#:~:text=eslint%20without%20root.-,Installation,-%C2%B6

[marekgluza]

For currently the first checkbox the point number 3 which is Hamiltonian simulation from primitive gates in #1034 can now be linked with #1138 for a more detailed discussion. @Edoardo-Pedicillo, can you split the box first checkbox and for the 3rd point link the issue #1138 and tag @shangtai?

I will write a more detailed description of point number 2 in #1034 which is about transpiling DBIs. This will be in two stages DBI - > Hamiltonian simulation and Hamiltonian simulation -> primitive gates