Arithmetic-Aware Quantum Neural Networks Using Fault-Tolerant BCD-Excess-3 Encoding

Abstract Fault-tolerant quantum neural networks (QNNs) require architectures that balance learning capability with stringent non-Clifford resource constraints. This work proposes an arithmetic-aware QNN architecture that integrates a validity-controlled Binary-Coded Decimal (BCD)-to--Excess-3 transformation as a fault-tolerant preprocessing stage prior to variational learning. The arithmetic module is realized entirely within the Clifford+T gate set and incorporates explicit BCD validity detection, enabling conditional arithmetic execution while introducing only four additional T/T^dagger gates beyond the underlying arithmetic core. The proposed architecture is combined with a COBYLA-optimized variational ansatz and compared against a baseline QNN of identical trainable complexity. While both models achieve identical classification accuracy of 100% on the benchmark single-digit task, the arithmetic-aware architecture demonstrates superior robustness under realistic hardware noise, achieving a robustness integral of 0.080 compared to 0.071 for the baseline model. Furthermore, curvature analysis reveals a substantially flatter optimization landscape, reducing the mean curvature from 36.85 to 27.21 and indicating that the arithmetic transformation acts as an effective inductive bias that stabilizes the learning process. To evaluate scalability, an additional four-class multi-digit (00--99) classification experiment was conducted, achieving an overall accuracy of 70%. These results demonstrate that fault-tolerant arithmetic preprocessing can enhance QNN robustness and stability while maintaining bounded non-Clifford overhead, highlighting the potential of arithmetic-aware representations for robust quantum machine learning.