Qiskit wrapper

[gcattan]

Issue:
pyRiemann/pyRiemann#141

Blocker:
#1

This PR is a "fresh one" but a similar PR with commit history was raised in #3

[qbarthelemy]

Once again, it should be at least nfilter=2, otherwise covariance matrices are reduced to scalars.

[gcattan]

In the case of Xdawn, n_channels = nfilter x nclasses if I do not mistake.

Please, see my previous comment below:
#2 (comment)

[qbarthelemy]

Yes, I think you are right: output matrices are 2x2. However, it remains a rough dimension reduction.

[gcattan]

Yes, there is this limitation on the feature dimension (24 when running on the local simulator).
I will try to do something similar to my last answer in the previous comment for nfilter = 2 and 3.

[gcattan]

Here is the result of nfilter=2, with NaiveDimRed vs PCA (top = classical, bottom = quantum).

The balanced accuracy is very low in quantum as compared to nfilter=1. This is likely due to the fact that the feature dimension increases (from 10 to 18) but the number of measurements stays the same (1024).
But just to give an order, the example displayed in the above figure took 1 day and half to run on my local machine. It would be necessary to use a remote backend to achieve higher computation, but I do not see how we can integrate this in a github action.

That said, the question remains interesting, maybe it would be relevant to add an example of optimization with GridSearchCV on a fewer number of data?

[qbarthelemy]

What are the hyper-parameters of QSVM? Is it a linear or a RBF QSVM?

[gcattan]

There are two cases.

• When quantum=False, it uses SVC with RBF kernel.
• When quantum=True, it uses a QuantumKernel, which is parameterized using a feature map (which entangles the data into a quantum state).

[qbarthelemy]

Ok, but what are the hyper-parameters for QuanticSVM(quantum=False)?
You should use the same as SVC.

And when quantum is True, what are the hyper-parameters of the QuantumKernel?

[gcattan]

For both there is something like this:

• transform the labels 0/1 into -1/1
• get the kernel matrix:
  • for quantum=False, that is call sklearn.rbf_kernel with gamma = None (hence default is 1/nb_features)
  • for quantum=True, that is call QSVM.get_kernel_matrix with feature_map=ZZFeatureMap and enforce_spd=True (set negative eigen values to zero if kernel matrix is not positive semi-definite) as parameters
• optimize the kernel matrix, with similar parameters:
  • number of iteration=500
  • normalization of the output = L2 Norm of y
  • L2 norm regularization factor = 0.001 (C?)

I changed gamma = auto (i.e 1/n_feature according to the doc), and C = 0.001. The figure below show how QuanticSVM(quantum=False) compares to SVC(gamma='auto', C = 0.001):

[qbarthelemy]

Ok. Like SVC, QuanticSVM should allow to set SVM hyper-parameters in its init.

[gcattan]

Yes, you are right. Do you want me also to take this work in a follow-up issue?

[qbarthelemy]

Is it a huge modification of code?

[gcattan]

At first sight, I would say that gamma (for quantum=False), feature_map and L2 regularization (for quantum=True) are easy to access. Same thing for the number of shots, the optimizer and the variational form (for VQC) which might be relevant to expose.
Other parameters: enforce_spd, number of iteration, output normalization and L2 regularisaiton (for quantum=False) might be harder to access.

[qbarthelemy]

Ok for me, because code has been deeply refactored.
The review of this PR has been very time-consuming for me: in the future, I am not sure to have enough time to continue to review such PRs.

@sylvchev , I let you review, approve and squash+merge.
And can you deploy the documentation on RTD?

[gcattan]

@qbarthelemy
Thank you for your hard work on this PR. Your feedback was very valuable and I am happy we achieved this work together.
Let me ensure you that next PRs will be much much smaller with limited scopes and functionalities.

[sylvchev]

Thanks @gcattan, we could merge this PR. Thanks a lot @qbarthelemy for your careful reading!
I'll take care of putting the docs on RTD.