Make shallow circuit demo Catalyst-Compatible

[tzunghanjuang]

Context: Convert Shallow Circuit Demo into a Catalyst-compatiable one.

Description of the Change: Mainly replace jax.jit with qjit. However, it introduces errors related to functools.partial (#814 and #815). Right now I circumvent the errors by avoiding using functools.partial. Will open the other PRs to fix the issues.

• Since catalyst has trouble parsing State information from optax optimizers, we use pytree to handle such information.
• Also exclude optax from the AutoGraph conversion.

Related GitHub Issues: [sc-65901]

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[paul0403]

Just a note that codecov/project coverage failure usually means (a) the feature branch's new feature is not covered by a new test and/or (b) the feature branch is out of sync with main branch.