Provide workaround for TwoQubitWeylDecomposition error for large circuits (backport #100)

[mergify]

Hi!

When using the generate_ansatz_from_circuit function with a large circuit, I've encountered an error with Qiskit's TwoQubitWeylDecomposition. See the below error message.

qiskit.exceptions.QiskitError: 'TwoQubitWeylDecomposition: failed to diagonalize M2. Please report this at https://github.com/Qiskit/qiskit-terra/issues/4159. 

This originates from the lines:

mat = Operator(couple_qc).data
d = TwoQubitWeylDecomposition(mat)

in from_connectivity.py (304-305). You can recreate the error using:

from qiskit import QuantumCircuit
from qiskit_addon_aqc_tensor import generate_ansatz_from_circuit

N = 50
qc = QuantumCircuit(N)

for _ in range(10):
    for i in range(0, N, 2):
        qc.cx(i, i + 1)
    for i in range(1, N - 1, 2):
        qc.cx(i, i + 1)


_, _ = generate_ansatz_from_circuit(qc, qubits_initially_zero=True)

Many of the calls to TwoQubitWeylDecomposition occur without error, but for large circuits, there comes a point where one of the matrices fails to diagonalise. Interestingly, this is reproducible behaviour, and always occurs at the same point for a given circuit.

This error has been mentioned in quite a few issues on GitHub/StackExchange (Qiskit/qiskit#4159, Qiskit/qiskit#14233, Qiskit/qiskit#7120, https://quantumcomputing.stackexchange.com/questions/41866/twoqubitweyldecomposition-failed-to-diagonalize-m2). I believe it usually arises when the matrix being decomposed is not unitary, however in all the cases I tested, the matrix was unitary to numerical precision (and returned Operator(couple_qc).is_unitary() = True. It seems others have had this issue as well.

I found a work-around by transpiling couple_qc before passing it to TwoQubitWeylDecomposition. From playing around, it looks like the matrices produced by Operator(couple_qc).data are identical to numerical precision before and after this transpilation, however one causes an error, and the other doesn't. I'm not sure exactly why this is the case, or if it works all the time, but it seems to work for the cases I looked into.

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This is an automatic backport of pull request #100 done by Mergify.

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Pull Request Test Coverage Report for Build 18148242511

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• 13 of 13 (100.0%) changed or added relevant lines in 1 file are covered.
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