A Reproducible Evaluation Protocol for Quantum Non-Linearity in Variational Quantum Models

Variational quantum models are linear maps of the input state: any useful non-linearity must be engineered through the data encoding, entanglement pattern, ancilla tracing, classical readouts, or explicit classical layers. Although many such mechanisms have been proposed, there is no standard protocol that scores them on a common footing. Most published comparisons reduce non-linearity to either the accuracy on a single downstream benchmark or a single abstract expressibility number, and the two are rarely measured under matched training budgets, circuit widths, and noise assumptions. We introduce a reproducible evaluation protocol that decomposes non-linearity quality into four complementary scalar scores covering frequency reach, gradient-variance scaling, trainability efficiency on a chaotic dynamical task, and stability under depolarizing noise. In addition, we define a composite index with published weights, enabling methods to be ranked under a single criterion while preserving full access to the underlying components. We instantiate the protocol with six variational ansatzes spanning the standard taxonomy of quantum non-linearity sources (data reuploading, ancilla tracing, their combination, strongly entangling layers, a quantum convolutional network, and a quantum reservoir), together with a classical multilayer perceptron and a hybrid quantum-classical network as non-quantum reference points. The evaluation surfaces a central mismatch that single-number reporting hides: in our reference run, the composite leader (data reuploading) is near the bottom on held-out Lorenz one-step $R^2$, while the Lorenz leader (ancilla reuploading) is only third on the composite. The main outcome is a practical benchmark that makes these trade-offs visible and testable: with fixed tasks, budgets, and seeds, new methods can be added by registering a circuit builder and rerunning the same protocol, and multi-seed aggregates can be updated without changing metric definitions.