✨ Add controlled multiplication modulo N benchmark

[denialhaag]

Description

🤖 AI text below 🤖

Add a controlled multiplication modulo N benchmark based on Figures 5 and 6 of Beauregard's circuit for Shor's algorithm: https://arxiv.org/abs/quant-ph/0205095

Each instance prepares the control and multiplicand registers in a uniform superposition, then conditionally writes multiplier * multiplicand mod modulus to an n + 1-qubit accumulator. The logical result preserves the control, multiplicand, and accumulator so the analytic reference checks their full correlation.

Expose the benchmark through validated C++ and Python APIs, strict instance specifications and manifests, command-line discovery, and structured MLIR generation. The generator retains the modular Fourier-adder schedule, including its multi-controlled phase operations and work-qubit cleanup.

This PR is stacked on #2408.

AI notice

This PR and its contents were created with the assistance of GPT-5.6 Sol via Codex.

Checklist

• The pull request only contains commits that are focused and relevant to this change.
• I have added appropriate tests that cover the new/changed functionality.
• I have updated the documentation to reflect these changes.
• I have added entries to the changelog for any noteworthy additions, changes, fixes, or removals.
• I have added migration instructions to the upgrade guide (if needed).
• The changes follow the project's style guidelines and introduce no new warnings.
• The changes are fully tested and pass the CI checks.
• I have reviewed my own code changes.

If PR contains AI-assisted content:

• Any agent that created, edited, or submitted GitHub content was explicitly authorized for that scope, as required by our AI Usage Guidelines.
• Every agent-authored or agent-edited public text body begins with the visible disclosure 🤖 *AI text below* 🤖 (titles are exempt).
• I have disclosed AI assistance in the PR description.
• I confirm that I have personally reviewed and understood all AI-generated content, and accept full responsibility for it.

[codecov]

Codecov Report

❌ Patch coverage is 97.59615% with 5 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/bench/JSON.cpp	86.3%	3 Missing ⚠️
...bench/programs/ControlledMultiplicationModuloN.cpp	98.1%	2 Missing ⚠️

📢 Thoughts on this report? Let us know!