[qcs] frustration-free: sim-to-real quantum gate calibration

[jiangweiqi001]

Summary

• implement a differentiable open-loop quantum-control model, Hessian/HVP landscape extraction, and query-only CMA-ES closed-loop calibration
• add fair full/model-Hessian/random/oracle comparisons with strict query and shot accounting, restartable atomic artifacts, paired statistical analysis, and publication-figure tooling
• document the verified 9,500-trial production run, reproducible LASG02 Apptainer workflow, scientific interpretation, and prompt history in Chinese

Results

• recover effective Hessian ranks 3 and 15 for one- and two-qubit gates, consistent with the expected d²−1 curved subspace
• complete all 180 Slurm array tasks and strictly validate 9,500/9,500 production trials with no missing or invalid artifacts
• retain the complete production snapshot for restartable bootstrap aggregation and final figure generation

Test plan

• Existing module-level and integration verification completed during development
• Representative 881-query pilot passed strict artifact validation
• Production snapshot: completed=9500, expected=9500, pending=0, errors=[], valid=true
• Report passes git diff --check

Scope

This is an independent Challenge 113 submission branch based directly on main; it does not modify or merge into PR #152.

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