How Quantum Circuits Actually Learn: A Causal Identification of Genuine Quantum Contributions

Abstract

Attributing performance gains in quantum machine learning to genuine quantum resources rather than to classical architectural scaling remains an open methodological challenge. We address this by introducing a counterfactual causal mediation framework that decomposes inter-architectural performance differences into direct effects, attributable to circuit parameterization and expressivity, and indirect effects mediated by quantum information-theoretic observables: entanglement entropy, purity, linear entropy, and quantum mutual information. Applying this framework to five circuit topologies and three benchmark datasets (across 43 validated configurations) reveals that direct architectural contributions systematically exceed quantum-mediated effects, with a mean ratio of 13.1:1 and a mean indirect contribution of 0.82%. These results suggest that current variational quantum circuits operate substantially below their quantum potential, and that principled resource-aware circuit design represents a tractable path toward measurable quantum-mediated performance gains.