Learning What to Encode: Representation Selection for Competitive Quantum Tabular Classification

Establishing the predictive competitiveness of quantum machine learning against strong classical baselines remains a central challenge in tabular classification. We propose learned representation selection (LRS), a hybrid quantum–classical classifier that learns a discrete representation choice for each encoding slot under a fixed quantum input budget. Instead of prescribing a representation mixture, LRS assigns each slot a feature from complementary representations, allowing the encoded input to adapt to the prediction task. A select–freeze–refit procedure separates learning these assignments from training the final predictor: the selection stage learns slot-wise choices, the freeze stage fixes the resulting discrete configuration, and the refit stage trains the predictor with that configuration held constant. The selected features are angle-encoded into a variational quantum circuit, whose expectation values are combined with a classical feature branch. Across twenty tabular datasets, LRS achieves accuracy and macro-F1 comparable to tuned random forests, XGBoost, and LightGBM, with advantages on several datasets. These results support slot-wise discrete representation selection as a practical approach to competitive hybrid quantum classification under a constrained encoding budget.