Speakers
Description
Data-reuploading quantum neural networks provide a useful setting for examining how variational quantum circuits represent structured classical functions. This talk studies modular addition as a finite-group learning problem in which generalisation requires recovery of a cyclic rule, rather than interpolation from local numerical regularities. We consider simulated seven-qubit, four-layer data-reuploading circuits trained on sparse subsets of operand pairs over prime moduli, and introduce layerwise Fourier-Dirac supervision as both a training intervention and diagnostic tool. The method attaches finite-modular Fourier readouts to intermediate reuploading layers, so that each layer can be evaluated for residue-aligned evidence before the final circuit state.
We compare auxiliary layerwise supervision, learned residual aggregation, and fixed uniform averaging of layerwise logits. Across the robust p = 97 and p = 127 regimes, fixed averaging gives the strongest held-out exact accuracies among the QNN variants, while the p = 31 setting reveals sensitivity to training coverage and feature basis. Ablations further indicate that intermediate Fourier coefficients are useful as supervised readout signals, but not necessarily as feedback into later circuit rotations. The findings support the use of modular arithmetic as a controlled probe for representation formation, generalisation failure, and layerwise interpretability in variational quantum machine learning.
| Topic | Quantum variational circuits and their applications |
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| Additional Topic | Encoding and processing of data in quantum systems |