Tutorial for the ODE QNN Regressor

[RobertoFlorez]

Hi!

In this PR, I made a tutorial for the QNN ODE solver.

The logistic differential equation, a special case of the Bernoulli Differential Equation, is solved and compared to its analytical solution.

If this example is too trivial, I can search for another one.

To include the tutorial, I also:
- Created docs/examples/example_quantum_bayesian_optimization.nblink (which I think it was necessary but I am not sure)
- Included --ignore=examples/tutorials/qnn_ode_solver.ipynb, in pyproject.toml so that it is not checked by pychecks (as the solution takes a long time)

Furthermore:
- I fixed one small typo in examples/tutorials/quantum_bayesian_optimization.ipynb, "structre->structure"
- I fixed a small bug in the KyriienkoEncodingCircuit for the chebyshev_product

Feel free to let me know what should I improve or change. Thankss!

Roberto

[David-Kreplin]

After our conversiation, here the are todos summerized:

• setting x0
• check eq 6
• check reference of eq 6 (wrongly ref as eq.1)
• use Differential Equations instead of DE
• remove \bm
• fix documentation test

[RobertoFlorez]

Hi!

I implemented all the suggested changes:

• setting x0
• check eq 6
• check reference of eq 6 (wrongly ref as eq.1)
• use Differential Equations instead of DE
• remove \bm
• fix documentation test

Thus, I believe is ready to be checked again @David-Kreplin.

Thank you very much !

Any other feedback, I am happy to help :)

[David-Kreplin]

There are a few rendering errors left:

• For the logistic differential equation, we take $ Q(x) = P(x) = -6 $ and $ n = 2$ in the Eq.
• This is, $:nbsphinx-math:mathcal{L}{:nbsphinx-math:theta} = :nbsphinx-math:mathcal{L}{\theta}(dy/dx, y, x) + \eta :nbsphinx-math:left(y(x_0) - u_0 \right)^2 $, where

The problem is that you probably have no possibility to look at the final rendered HTML file; the notebook looks fine, on the other hand.

[David-Kreplin]

Loos great now, thank you!