Generation of random unitary matrix does not draw matrices from Haar measure

[pgawron]

https://github.com/QISKit/qiskit-sdk-py/blob/5c1c68a5aa3dcccdf5c10f9eb307383ebb40826b/qiskit/tools/qi/qi.py#L346

The method of generation random unitary matrices is faulty. It will not generate random matrices drawn from the Haar measure.

Please refer to "How to generate random matrices from the classical compact groups", Francesco Mezzadri, arXiv:math-ph/0609050 p.11.

[nonhermitian]

I would not say it is faulty. It just doesn't draw from the Haar measure.

…

On Tue, May 29, 2018 at 10:53 AM Piotr Gawron ***@***.***> wrote: https://github.com/QISKit/qiskit-sdk-py/blob/5c1c68a5aa3dcccdf5c10f9eb307383ebb40826b/qiskit/tools/qi/qi.py#L346 The method of generation random unitary matrices is faulty. It will not generate random matrices drawn from the Haar measure. Please refer to "How to generate random matrices from the classical compact groups", Francesco Mezzadri, arXiv:math-ph/0609050 p.11. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#519>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ABMPqXuOYjjJWcOUXwfsonp2rfbyxT_wks5t3WD5gaJpZM4URpzj> .

[jaygambetta]

I agree with @pgawron we should update this to be from the Haar measure. After we do this i agree @nonhermitian we should also make the documentation clear and say a random martix from the Haar measure.

[delapuente]

If this is addressable by improving the documentation, let's do it as soon as possible. Is this the case?

[jaygambetta]

No it needs to write a new algorithm. Its simple but I need to find some time

[ikkoham]

How about using scipy.stats.unitary_group?

https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.unitary_group.html

[jaygambetta]

@ikkoham i agree. Can you just submit a Pr and then we can close this issue. I would put a test with it as well.

[ikkoham]

Thanks. OK, I will submit a PR.