Task 03: exploit exact product-state contraction (4.44x)

[QingyunQian]

Take-home insight

The circuit never needs a general many-body contraction: preserving its exact product-state structure reduces the computation to vectorized local conditional maps.

Measured result

Comparison	Runtime	Speedup
Public expert	4.101350 s	1.000x
Optimized	0.924608 s	4.435277x

The README keeps the compact factor attribution table and a single result figure.

Reviewer-facing files

• optimized_solutions/challenge-03/README.md
• optimized_solutions/challenge-03/solution_3_product_contraction.py
• optimized_solutions/challenge-03/factor-ablation.svg

Full profiles and research chronology remain in hmyuuu/OrbitBreakersExpertBenchmarks.

[refraction-ray]

This means the problem is also not good enpigh that can be exploit for cheap workaround?

[QingyunQian]

Yes, after checking the exact circuit, the original schedule does admit a structural cheap reduction.

Because every even qubit was projected to |0> after each brickwork layer, every gate touched at most one surviving odd qubit before projection. The nominal 12 qubit selected branch therefore remained exactly six independent one qubit trajectories. This is a workload design degeneracy(milder than Task 07).

I updated this PR with both a compact report and a design fix. Post selection now happens only after each complete even+odd brickwork block (30 events instead of 60), so the odd survivor light cones overlap before projection. A deterministic witness gives two nonzero Schmidt coefficients, 0.999136 and 0.041559 (purity 0.996552), so the old product state induction is no longer valid. The regenerated expert completes all 300 updates and passes every functional criterion; the unchanged cheap-reduction implementation fails the patched evaluator.

Details and the factor table&figure are in optimized_solutions/challenge-03/README.md.

[QingyunQian]

This means the problem is also not good enpigh that can be exploit for cheap workaround?

can be used as a loophole test，who can capture the flag？dont fix it