GQE demo using Pennylane

[JosephRRB]

Before submitting

Please complete the following checklist when submitting a PR:

• [ ] Ensure that your tutorial executes correctly, and conforms to the guidelines specified in the README.

• [ ] Remember to do a grammar check of the content you include.

• [ ] All tutorials conform to PEP8 standards. To auto format files, simply pip install black, and then run black -l 100 path/to/file.py.

When all the above are checked, delete everything above the dashed line and fill in the pull request template.

---

Title: Generative quantum eigensolver demo using Pennylane

Summary: We use Pennylane to generate a static molecular dataset and calculate the corresponding energies to train a small GPT model as described by https://arxiv.org/abs/2401.09253. We show that as training progresses, the GPT model generates operator sequences whose predicted energies more accurately resembles the true energies calculated by Pennylane. In addition, the sampling process is shown to better generate the ground state for better performing models.

• Story ticket: https://app.shortcut.com/xanaduai/story/64095/contribute-gqe-demo-as-a-pennylane-demo

Relevant references:

Possible Drawbacks:

Related GitHub Issues:

---

If you are writing a demonstration, please answer these questions to facilitate the marketing process.

• GOALS — Why are we working on this now?

  Eg. Promote a new PL feature or show a PL implementation of a recent paper.

• AUDIENCE — Who is this for?

  Eg. Chemistry researchers, PL educators, beginners in quantum computing.

• KEYWORDS — What words should be included in the marketing post?

• Which of the following types of documentation is most similar to your file? (more details here)

• [ ] Tutorial
• [ ] Demo
• [ ] How-to