Impact of encoder-induced redundancy on spectral bias in training

Investigate how encoder-side redundancy, which scales coefficient variances via path multiplicity in the circuit harmonic analysis, affects spectral bias during training of parametrized quantum circuits.

Background

The analysis links encoder redundancy (multiple paths contributing to the same input frequency) to coefficient variances via C, suggesting a mechanism for spectral bias where low-frequency components may receive larger variance. The open task is to connect this architectural effect to actual training dynamics and spectral bias behavior.

References

Exploring how this affects spectral bias in training is left to future work, however, currently spectral bias analysis in variational quantum circuits can be found in .

— Circuit Harmonic Matrices: A Spectral Framework for Quantum Machine Learning  (2604.04292 - Campbell et al., 5 Apr 2026) in Section 4.3 (Expressivity, redundancy, and architectural coupling)