Description

examples/qpe_stretched_n2.ipynb calls the deprecated qdk_mp2_natural_orbitals orbital localizer. QDK/Chemistry 2.0.0 directs new workflows to use qdk_natural_orbitals with a wavefunction that already contains the active-space 1-RDM. This requires a workflow migration rather than a mechanical factory-name replacement.

The notebook is a user-facing end-to-end example, so it should not teach an API that emits a deprecation warning.

Occurrence audit

• examples/qpe_stretched_n2.ipynb invokes the deprecated factory and should be migrated.
• docs/source/_static/examples/python/localizer.py displays the deprecated factory in the generated availability list; review whether the example should identify deprecated implementations explicitly.
• docs/source/user/comprehensive/algorithms/localizer.rst documents the deprecated implementation and replacement guidance; this compatibility documentation should remain while the implementation is supported.
• Implementation, binding, and test references are expected compatibility coverage and should not be removed as part of the example migration.

Acceptance criteria

• Replace the deprecated call in examples/qpe_stretched_n2.ipynb with a supported workflow that preserves the scientific intent of the example.
• Ensure the wavefunction passed to qdk_natural_orbitals contains the required active-space 1-RDM.
• Execute the migrated notebook and review or update numerical results and explanatory text affected by the workflow change.
• Audit other user-facing examples for deprecated MP2 natural-orbital usage or unqualified display references.
• Retain compatibility implementation, deprecation documentation, bindings, and tests while the deprecated API remains supported.