Characterizing Scaling Trends of Post-Compilation Circuit Resources for NISQ-era QML Models

Abstract: This work investigates the scaling characteristics of post-compilation circuit resources for Quantum Machine Learning (QML) models on connectivity-constrained NISQ processors. We analyze Quantum Kernel Methods and Quantum Neural Networks across processor topologies (linear, ring, grid, star), focusing on SWAP overhead, circuit depth, and two-qubit gate count. Our findings reveal that entangling strategy significantly impacts resource scaling, with circular and shifted circular alternating strategies showing steepest scaling. Ring topology demonstrates slowest resource scaling for most QML models, while Tree Tensor Networks lose their logarithmic depth advantage after compilation. Through fidelity analysis under realistic noise models, we establish quantitative relationships between hardware improvements and maximum reliable qubit counts, providing crucial insights for hardware-aware QML model design across the full-stack architecture.