Add Hamiltonian energy optimization example

[yanziwei]

Summary

• Add an examples README with setup for ionq-core and IONQ_API_KEY
• Add a Hamiltonian Energy quantum-function example that builds typed model payloads, submits with create_job, waits with wait_for_job, and drives a dependency-free coordinate-search optimizer
• Link the examples directory from the top-level README and update the changelog

Fixes #58

Testing

• .venv/bin/ruff check
• .venv/bin/ruff format --check
• .venv/bin/ty check examples/
• .venv/bin/python -m compileall -q examples
• .venv/bin/pytest -q (242 passed, 28 deselected, 100% coverage)

Note: uv is not available in this local shell, so I ran the equivalent commands through the repository virtualenv.

[veena-vee989]

@yanziwei (cc @splch)

Hello - you are currently over the PR limit for unitaryHACK, so your PRs will be disregarded until you align with the rules. Reach out to hack@unitary.foundation to be reinstated. (PR 7 of 7)

[splch]

Thanks. Two blockers: the ansatz must be OpenQASM 3.0 with input float declarations (not an IonQ JSON circuit string), and the energy lives in results.value, not output. Closing in favor of another submission.