Restructure of examples and applications

[zohimchandani]

Examples section: aim is to show how to use CUDA-Q syntax.

Applications section: aim to show various useful things you can build with CUDA-Q.

Restructure of both sections, added new ones, deleted repeated ones and condensed ones that could be condensed.

This work is in collaboration with @mawolf2023 who did most of the heavy lifting here.

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[sacpis]

Can we run this notebook and save the output in this file?

[sacpis]

When running vqe_advanced.ipynb, I am getting the following error as I have only 1 GPU on my system as the program is intended to run on nvidia-mqpu (tried target as nvidia as well).

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[20], [line 1](vscode-notebook-cell:?execution_count=20&line=1)
----> [1](vscode-notebook-cell:?execution_count=20&line=1) gradient = batched_gradient_function(kernel, x0, spin_ham, epsilon)
      [3](vscode-notebook-cell:?execution_count=20&line=3) exp_vals = []
      [6](vscode-notebook-cell:?execution_count=20&line=6) def objective_function(parameter_vector: list[float], \
      [7](vscode-notebook-cell:?execution_count=20&line=7)                        gradient=gradient, hamiltonian=spin_ham, kernel=kernel):

Cell In[19], [line 36](vscode-notebook-cell:?execution_count=19&line=36)
     [26](vscode-notebook-cell:?execution_count=19&line=26) g_plus.append(
     [27](vscode-notebook-cell:?execution_count=19&line=27)     cudaq.observe_async(kernel,
     [28](vscode-notebook-cell:?execution_count=19&line=28)                         hamiltonian,
   (...)
     [31](vscode-notebook-cell:?execution_count=19&line=31)                         xplus[i],
     [32](vscode-notebook-cell:?execution_count=19&line=32)                         qpu_id=qpu_counter))
     [33](vscode-notebook-cell:?execution_count=19&line=33) qpu_counter += 1
     [35](vscode-notebook-cell:?execution_count=19&line=35) g_minus.append(
---> [36](vscode-notebook-cell:?execution_count=19&line=36)     cudaq.observe_async(kernel,
     [37](vscode-notebook-cell:?execution_count=19&line=37)                         hamiltonian,
     [38](vscode-notebook-cell:?execution_count=19&line=38)                         qubit_count,
     [39](vscode-notebook-cell:?execution_count=19&line=39)                         electron_count,
     [40](vscode-notebook-cell:?execution_count=19&line=40)                         xminus[i],
     [41](vscode-notebook-cell:?execution_count=19&line=41)                         qpu_id=qpu_counter))
     [42](vscode-notebook-cell:?execution_count=19&line=42) qpu_counter += 1
     [44](vscode-notebook-cell:?execution_count=19&line=44) if qpu_counter % num_qpus == 0:

ValueError: Provided qpu_id is invalid (must be <= to platform.num_qpus()).

@zohimchandani Would you mind running this notebook and saving the output?

[sacpis]

Few changes are needed.

[sacpis]

/ok to test

Command Bot: Processing...

[sacpis]

/ok to test

Command Bot: Processing...

[sacpis]

@efratshabtai Adding Efrat for visibility as the Python examples have been moved.

[sacpis]

/ok to test

Command Bot: Processing...

[sacpis]

/ok to test

Command Bot: Processing...

[sacpis]

@zohimchandani Seems like as we have purged *.py files from examples/python, we will need to update .rst files under docs/sphinx/using/examples/.rst. Would you please update those *.rst files?