Add support for trainable quantum kernels to Pegasos Quantum Support Vector Classifier

[puyamirkarimi]

What should we add?

The current version of the Pegasos Quantum Support Vector Classifier does not natively support the training of the parameters in the quantum kernel.
https://qiskit-community.github.io/qiskit-machine-learning/tutorials/07_pegasos_qsvc.html

Since the theoretical benefits of Pegasos relate to its ability to train the kernel efficiently, supporting trainable quantum kernels would be useful.

The publicly accessible code for the following paper implements a version of Pegasos that is able to train parameterised quantum kernels, but it is implemented in Qiskit version 0.42.1.
https://ieeexplore.ieee.org/document/10313634

[edoaltamura]

Thanks for pointing this out. @oscar-wallis and @OkuyanBoga I think we discussed this paper at some point. Did you also try the code? https://zenodo.org/records/7804477

[puyamirkarimi]

Hi, is this feature likely to be added soon or is it not that high on the list of priorities?