A key challenge in practical quantum machine learning (QML), particularly for discriminative tasks such as classification, is the limited capacity of near-term quantum devices to encode high-dimensional classical data into small quantum registers. In
A key challenge in practical quantum machine learning (QML), particularly for discriminative tasks such as classification, is the limited capacity of near-term quantum devices to encode high-dimensional classical data into small quantum registers. In optimized basis-encoded (bit-bit) settings, this constraint leads to cross-class collisions, where samples with different labels are mapped to the same discrete bit-string and thus become indistinguishable to any downstream model. In this work, we investigate how data representation affects QML performance under such severe information bottlenecks. We introduce discretization-aware fine-tuning (DAFT), a method that adapts a pre-trained chemical foundation model to produce representations that remain informative after quantization. DAFT reduces collision probability through a differentiable soft collision loss. We evaluate both quantum and classical models under a controlled setting in which they receive identical discretized bit-string inputs, isolating the effect of representation from model architecture. On the blood-brain barrier penetration (BBBP) molecular property prediction benchmark using ChemBERTa-77M, DAFT reduces collision counts by several orders of magnitude and improves quantum classification accuracy by more than 12 percentage points compared to a frozen backbone. Importantly, without DAFT, classical models outperform QML under the same input constraints. With DAFT, however, this comparison reverses at higher qubit counts. At 10 qubits, the quantum model surpasses a matched classical baseline trained on identical bit-strings (0.883 vs. 0.855, p = 0.026). These results show that, in information-constrained regimes, achieving a quantum advantage critically depends on aligning continuous representations with discrete quantum encodings.