Documentation Improvements

[pmenczel]

1. The explanation of the GRAPE and CRAB methods in the users' guide is very detailed, but the explanation of GOAT is very brief and JOPT is still missing there. Eventually, it might be nice to have explanations for all methods at a similar level of detail.
2. Currently, the search function in https://qutip-qoc.readthedocs.io/en/latest/ seems to be broken.
3. It would be good to have example notebooks and link to them in the documentation and from the github readme page.

(These are issues that I believe could be tackled after the first proper release of qutip-qoc.)

[BoxiLi]

It would be nice to revisit the documentation at some point. The code in the doc seems wrong as the Hamiltonian is defined as

# continuous control
control = [[qt.sigmax(), lambda t, p: p[0] * t + p[1]],
           [qt.sigmay(), lambda t, q: p[0] * t + p[1]]]

H = [drift, control]

without providing a gradient while the GOAD algorithm is used:

  algorithm_kwargs={
    "fid_err_targ": 0.1,
    "alg": "GOAT",
  },

This gives an error on my machine.

[rochisha000]

@BoxiLi @flowerthrower I came across this issue as well. What is the fix for this? I'm trying to learn qutip-qoc

[BoxiLi]

Maybe for now you can check the test code in https://github.com/qutip/qutip-qoc/blob/main/tests/test_fidelity.py.

[flowerthrower]

You can also have a look at the examples in this PR: qutip/qutip-tutorials#104