Add Hamiltonian energy optimization example

[CrewRiz]

Summary

• Add an examples/ directory with a Hamiltonian-energy Quantum Function optimization script.
• Build the workload using typed ionq_core.models, submit with create_job.sync, and poll with wait_for_job.
• Document setup/run steps in examples/README.md and link it from the top-level README.

Closes #58.

Verification

• uv run pytest tests/test_examples.py --no-cov
• uv run pytest
• uv run ruff check
• uv run ruff format --check
• uv run ty check examples/
• uv run ty check ionq_core/ examples/
• uv run python examples/hamiltonian_energy_optimization.py --help

All commands pass locally; pytest reports 100% coverage.

Notes

The example uses a dependency-free coordinate search optimizer to avoid adding runtime dependencies to ionq-core.

Disclosure

Implemented with assistance from OpenAI Codex at my direction.

[splch]

Thanks - the best engineering of the field. But the energy lives in results.value, not output (empty on the live API), and the unit test mocks that wrong shape. Closing in favor of another submission.