Non-unitary matrix ValueError

[soyjdezcurra]

Steps to reproduce the problem

Input non-unitary matrix. I used the following matrix and vector:
matrix = [[ 48, 19, 6, 3],
[ 35, 5, 1, 0],
[ 57, 36, 18, 7],
[105, 95, 85, 75]]
b = [56.98, 31.83, 12.89, 7.46]

What is the current behavior?

Raises ValueError and doesn't run.

What is the expected behavior?

Solver should work with a non-unitary matrix (decompose into linear combination of unitaries).

[NicoRenaud]

Thanks @soyjdezcurra, for vqls to work the A matrix has to be symmetric (and hermitian if complex). Otherwise the pauli decomposition won't work. There was a test to check if the input matrix is symmetric or not, but it apparently got removed since the error you mentioned was a non-unitary one.

Can you try with a symmetric matrix and let me know if that works for you ?

Thanks

[soyjdezcurra]

It does work with a symmetric matrix. Is there no way for vqls to work with a non-symmetric matrix?

Thanks for your time.

[NicoRenaud]

Hi and sorry for the late reply. You can have a non symmetric matrix but you then need to use a Pauli Decomposition to decompose it over unitaries. That may results in a large number of unitaries depending on your input matrix.

You can use:

vqls = VLQS(estimator, ansatz, optimizer, ..., options={'matrix_decomposition':'pauli'})
vqls.solve(A,b)