Variational Quantum Regression using the Parameter Shift Rule

[MatteoRobbiati]

In this example a Variational Quantum Circuit based on the re-uploading strategy is used to tackle a simple 1-dimensional regression problem: (to fit $y= \sin 2x$ ).

This context is exploited for introducing the Parameter Shift Rule, which is useful for evaluating the gradients of a circuit in a quantum-hardware compatible way.

A demo markdown is included.

[codecov]

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[scarrazza]

@MatteoRobbiati thank you very much for this contribution. It is in a really good shape.

I am just wondering if we should place the VQRegressor in a QML / variational module for Qibo and provide the optimizer as a standalone optimizer. @stavros11 what is your opinion about that?

[scarrazza]

@MatteoRobbiati could you please complete this PR by:

• adding this example to the sphinx page: https://github.com/qiboteam/qibo/blob/master/doc/source/code-examples/applications.rst
• including the link to the code: https://github.com/qiboteam/qibo/tree/master/doc/source/code-examples/tutorials

[MatteoRobbiati]

@scarrazza Modifications done, thank you for the comment.

[scarrazza]

This file has a typo.

[scarrazza]

Thank you, but please test sphinx manually every time you perform a change, otherwise you don't really now if things are working well. In fact, at the current state, the tutorial is not appearing in the website due to the typo.

[MatteoRobbiati]

@scarrazza thanks for the advice. I've fixed it and modified the README so that the formulas can be read in documentation.