docs(notebooks): add QNN tutorial

[MeltemTolunay]

Summary

QNN training tutorial with QCNN ansatz

Details and comments

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Details

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Covered Lines:	290
Relevant Lines:	290

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💛 - Coveralls

[miamico]

Very quick comment, let's move the notebook to the docs/notebooks folder

[miamico]

Other comments to address to make this in shape for a PR:

• Try adding SPSA instead of COBYLA. The vanilla implementation is quite contained so it could be included in the notebook
• Recast the notebook into the Qiskit Patterns framework (1. specify the classical problem and the quantum way to solve it, 2. optimize it for the hardware 3. execute, 4.post-process)
• Add more details explaining what is happening in each cell, right now the explanations are very bare-bone

[MeltemTolunay]

I now added a gradient function with parameter shift rule, qiskit patterns formalism, code to run on hardware and more text explaining the code.

[MeltemTolunay]

New changes include:

• ParameterVectorElements are ordered alphabetically. FeatureMap parameters now have a new parameter_prefix='a' to ensure that input and weight parameters are assigned in correct order.
• Parameter shift rule for computing the gradients are verified.
• Added a new function to compute the gradient of the MSE loss with respect to weight parameters.
• Added new optimizer options. We can now select from a collection of gradient-free optimizers, gradient-based optimizers and SPSA.

In addition, Mirko's previous comments regarding SPSA, Qiskit Patterns framework, and cell explanations are fully addressed.

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❌ Meltem Tolunay
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