When Does a Quantum Interaction Matter? Observability and Symmetry in Hybrid Learning

A quantum circuit can change its state under an input transformation while a chosen readout remains unchanged. We study this distinction in hybrid quantum neural networks for surrogate AC optimal power flow. For a real two-layer, non-reuploading ansatz with $R_X$ data encoding, we prove that single-qubit $X$ and $Z$ readouts depend only on the coordinate-wise cosines of the encoded angles, whereas $Y$ carries an odd component. We then use the matched readout pair $Z+X$ versus $Z+Y$ to separate parity information from feature-count and encoder effects. With a frozen encoder, $Z+Y$ improves test MAE over $Z+X$ on all three grid systems. With end-to-end training, the advantage is not consistent and depends on the grid and architecture. A target-aware audit further shows that the learned latent geometry changes around sign-mirror neighborhoods, but does not identify a unique optimization mechanism. The results establish a practical attribution protocol: state dependence, observable invariance, and predictive utility must be tested separately. We make no claim of quantum advantage.