✨ 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.
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• 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.

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[codecov]

Codecov Report

❌ Patch coverage is 97.80220% with 10 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/bench/JSON.cpp	88.2%	8 Missing ⚠️
...bench/programs/ControlledMultiplicationModuloN.cpp	98.1%	2 Missing ⚠️

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