Fix and speed-up DBI tests

[andrea-pasquale]

Now DBI tests are much faster and the implementation is GPU compatible.

Checklist:

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

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.95%. Comparing base (62c4dfd) to head (054e045).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1245   +/-   ##
=======================================
  Coverage   99.95%   99.95%           
=======================================
  Files          72       72           
  Lines       10452    10454    +2     
=======================================
+ Hits        10447    10449    +2     
  Misses          5        5           

Flag	Coverage Δ
unittests	99.95% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[renatomello]

Maybe this is out of the scope of this PR, but the generate_Z_operators and str_to_symbolic in qibo.models.dbi.utils can be replaced by this faster implementation below:

from functools import reduce
from itertools import product

import numpy as np

from qibo import matrices
from qibo.models.dbi.utils import generate_Z_operators

def generate_Z_operators_new(nqubits):
    combination_strings = list(product(["I", "Z"], repeat=nqubits))[1:]

    dictionary = {}
    dictionary["I"*nqubits] = np.eye(2**nqubits, dtype=complex)
    for string in combination_strings:
        matrix = [getattr(matrices, s) for s in string]
        matrix = reduce(np.kron, matrix)
        dictionary["".join(string)] = matrix
        del matrix  # maybe this is needed to control memory usage for nqubits >= 7-ish

    return dictionary

nqubits = 2
%timeit generate_Z_operators(nqubits)
%timeit generate_Z_operators_new(nqubits)

nqubits = 5
%timeit generate_Z_operators(nqubits)
%timeit generate_Z_operators_new(nqubits)

This is in line of how qibo.quantum_info.basis.pauli_basis is implemented, and it might even be added to it using the pauli_order argument.
However, even though this is faster than the current implementation in dbi, it is still inefficient overall for a number of qubits greater than 7-ish. I had a conversation with @BrunoLiegiBastonLiegi about rewriting the pauli_basis function in a way that returns a generator instead of all these big matrices, so this might be even one more reason to do it.

[marekgluza]

Maybe this is out of the scope of this PR, but the generate_Z_operators and str_to_symbolic in qibo.models.dbi.utils can be replaced by this faster implementation below:

from functools import reduce
from itertools import product

import numpy as np

from qibo import matrices
from qibo.models.dbi.utils import generate_Z_operators

def generate_Z_operators_new(nqubits):
    combination_strings = list(product(["I", "Z"], repeat=nqubits))[1:]

    dictionary = {}
    dictionary["I"*nqubits] = np.eye(2**nqubits, dtype=complex)
    for string in combination_strings:
        matrix = [getattr(matrices, s) for s in string]
        matrix = reduce(np.kron, matrix)
        dictionary["".join(string)] = matrix
        del matrix  # maybe this is needed to control memory usage for nqubits >= 7-ish

    return dictionary

nqubits = 2
%timeit generate_Z_operators(nqubits)
%timeit generate_Z_operators_new(nqubits)

nqubits = 5
%timeit generate_Z_operators(nqubits)
%timeit generate_Z_operators_new(nqubits)

This is in line of how qibo.quantum_info.basis.pauli_basis is implemented, and it might even be added to it using the pauli_order argument. However, even though this is faster than the current implementation in dbi, it is still inefficient overall for a number of qubits greater than 7-ish. I had a conversation with @BrunoLiegiBastonLiegi about rewriting the pauli_basis function in a way that returns a generator instead of all these big matrices, so this might be even one more reason to do it.

@Sam-XiaoyueLi please have a look

Thank you @renatomello for the useful suggestion!

[renatomello]

@MatteoRobbiati may I ask you to review this soon because #1202 depends on it? Thanks.

[MatteoRobbiati]

Thanks @andrea-pasquale for the fix and @renatomello for the reminder.
There is one test failing in test_quantum_info_metrics.py with the tensorflow backend, but I guess we can face it elsewhere.