Add a how-to for catalyst-compiling "Symmetry-invariant quantum machine learning force fields"

[paul0403]

The how-to contains the full code listing, and some primitive tutorial words.

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Title: How to Quantum Just-In-Time Compile "Symmetry-invariant quantum machine learning force fields" with Catalyst

Summary: As part of Catalyst's work on identifying 10 demos to compile with catalyst, we convert "Symmetry-invariant quantum machine learning force fields", a machine learning workflow that calls a training step function repeatedly and thus can have significant performance boosts with catalyst compilation.

Note: the original demo is from an external user, so we should NOT merge this until we have reached out to them. Update: we have obtained their permission.

Relevant references:

Possible Drawbacks: Because lightning does not support differentiation through QubitUnitary, we have to resort to finite difference method for gradients, which brings a big performance degradation.

Related GitHub Issues: [sc-72938]

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

• GOALS — Why are we working on this now?

  Promote Catalyst by demonstrating the performance improvements it offers by QJIT compiling a relatively complex end-to-end quantum workflow.

• AUDIENCE — Who is this for?

  Chemistry and quantum machine learning researchers.

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

  • Quantum machine learning
  • Catalyst
  • QJIT

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• [ ] Demo
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