Add Variational Quantum Algorithms Module

[EnBr55]

Functionality as outlined in #118

• Core functionality
• Following style requirements
• API documentation
• Tests
  • Mostly done, still in progress
• Manual documentation
  • In progress

This PR introduces a new module, qutip_qip.vqa, for defining and simulating Variational Quantum Algorithms. For examples for how this module could be used, please see https://github.com/EnBr55/qutip-vqa-examples/

[BoxiLi]

It is a bit annoying that the test needs to be approved every time when a new push is made. Not sure if there is a way to just allow any future tests to run for this PR. Sorry for all the delay, @EnBr55 Ben, please feel free to drop me an email next time you add something and want to run the test. Sometimes I miss the GitHub email and am unaware of any new push.

We can also try to get this PR merged first and add new patches in a different one so that any future PR of yours won't need approval.

The doc test is failing because the online doc generator does not have latex installed. You can render a png locally and add it as a figure, just like the other part of doc.

[BoxiLi]

@EnBr55 This is just part of the review. The code looks very neat. Mostly just naming plus a few of my questions, to clarify things. You don't have to accept all of them and feel free to discuss :)

[BoxiLi]

@EnBr55 Here is the second half of the review. Sorry for the delay.

• There are two png figures with the same content. One is duplication I guess (doc/circ.png)?

• If it is not too late, can we rename the public API
  n_qubits -> num_qubits
n_layers -> num_layers
n_paramters -> num_parameters
  to be consistent with the rest of the naming convention in qutip-qip? For the intermediate result not accessible to the user it does not matter.

• It is fine to merge as is. If you want to develop further on this module. I would recommend to define different types of VQA blocks as subclasses. In that way you don't have to use lots of if-else branches to check the input. You only need to specify this when defining the VQA blocks, e.g. UnitaryVQABLock, HamiltonianVQABlock etc..

[BoxiLi]

Congrats @EnBr55 ! Feel free to open further PRs for more documentation examples as well as further development!

@nathanshammah Pinging Nathan to share the moment.

[EnBr55]

Thanks so much for all the help and advice @BoxiLi @nathanshammah !! :)