Predictive Assessment of Qiskit Transpilation Costs Using Layer II Structural Diagnostics on IBM Heavy-Hex Architectures

This technical note investigates whether Layer II structural diagnostics can predict transpilation costs in IBM Heavy-Hex quantum architectures before compilation is performed. The study evaluates Heavy-Hex coupling maps generated through Qiskit for distances d = 3, 5, 7, and 9. Structural observables are computed directly from the architecture graph and compared against normalized transpilation metrics obtained from Quantum Fourier Transform (QFT), GHZ-state preparation, and Hardware-Efficient Ansatz (HEA) circuits. A leave-one-out validation procedure is used to assess predictive capability on unseen architecture instances. Results indicate that mediation, normalized structural cost, and feasibility observables contain measurable predictive information regarding transpilation overhead. The strongest performance is observed for HEA and GHZ workloads, where several prediction targets achieve low error levels. The benchmark provides preliminary evidence that circuit-independent structural observables may support predictive assessment of compilation costs during early-stage quantum architecture evaluation.