Large-Scale CL-QUBO Compiled Scaling and Backend Eligibility for Fault Tree Circuits Across IBM Proxy Backends

This paper evaluates the compiled scaling behavior and multi-backend eligibility of constraint-level quadratic unconstrained binary optimization (CL-QUBO) fault tree circuits at target sizes from 25 to 100 basic events across three IBM proxy backends (FakeFez, FakeMarrakesh, and FakeTorino). The study extends the feasibility roadmap established through n = 20 basic events in prior work by generating, classifying, selecting, and compiling 94 fault tree instances across nine target sizes. Each compile row represents one (instance, backend, transpiler seed, QAOA depth) tuple that completed transpilation without error. The initial 270-instance generated pool produced only Class A (56) and Class D (214) topology instances, with Class B and Class C entirely absent and Class A missing at n = 75. A four-stage topology recovery program generated 2,124 additional instances through progressively targeted search strategies: balanced widening (v1, 288 instances), expanded parameter ranges (v2, 378 instances), OR-heavy restructuring (v3, 810 instances), and a final AND-heavy Class B closure sweep (v4, 648 instances). The OR-heavy v3 sweep recovered the first Class C instances (4) and several boundary Other cases (3), while the AND-heavy v4 sweep still produced only Class A (77) and Class D (571) with zero Class B. The merged selected cohort of 94 instances yielded 2,454 successful compile rows across the three backends. FakeFez and FakeMarrakesh each supported successful compilation for 70 of 94 selected instances, while FakeTorino supported 66 of 94. The compiled frontier exhibited a clean size-dependent pattern: full selected-instance success from n = 25 through n = 45, backend-specific failures emerging at n = 50 and n = 60, and complete compilation failure for all 23 selected instances at n = 75 and n = 100, where the CL-QUBO circuit qubit requirements exceeded the coupling map capacity of all three backends (133 qubits for FakeTorino, 156 for FakeFez and FakeMarrakesh). This paper does not claim quantum advantage.