More ansatzes and example scripts

[chmwzc]

Summary

This pull request aims to (eventually) implement two additional VQE circuit ansatzes for chemistry using Qibo.
In addition, sample scripts examining the use of the Parameter Shift Rule implemented in Qibo for chemistry applications with these ansatzes (Currently in: psr_*.py) will be added to the /examples folder.

Reference papers:

1. paper2.py: https://doi.org/10.1038/s41534-019-0240-1
2. paper3-*.py: https://doi.org/10.22331/q-2022-06-20-742

Task List:

• Circuit ansatzes:
  • Finish and check the code for the circuit ansatzes
  • Migrate finished code to /ansatz
  • Documentation
  • Tests
• PSR example:
  • Cleanup scripts after first part done
  • Add examples to documentation

Acknowledgements

The original drafts of these scripts, in the form of Jupyter notebooks, was prepared by Caleb Seow and Sng Yi Xin from Eunoia Junior College, and Conan Tan from National Junior College.
The students were attached to IHPC in December 2023 under the A*STAR Research Attachment Programme for Junior College students.

No paper1.py?

For the interested, there were supposed to be three ansatzes; one for each student.
The code for the last circuit ansatz, by Yordanov et al. (link here) wasn't finished within their attachment period, which is why there's no paper1.py here.

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (7d34af4) to head (c4ef7d3).
Report is 37 commits behind head on main.

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[yjmaxpayne]

Hi Zicheng, please remember to incorporate the acknowledgement in the future sphinx Doc as well. Thanks.

[damarkian]

I was wondering if the students have their own GitHub accounts? If so, it would be nice to have them do a commit of some form here, and have ownership in the qibochem zenodo.

[chmwzc]

I don't think they can commit directly into this repository - they need to be added to the qiboteam team right?
Alternatively, I think I'll add on or edit a page in the documentation for this, seems like a simpler solution?