Spectral Quantum Memory for Implicit Neural Representations

Implicit neural representations (INRs) model signals as continuous functions from coordinates to values, but their performance depends strongly on how spectral capacity is allocated. Yet most Quantum INR (QINR) architectures treat spectral components as independent outputs of separate quantum blocks. We introduce the Spectral Quantum Memory Model (SQMM), a memory coupled quantum INR in which sequential hybrid data reuploading layers (bands) communicate through a shared coherent quantum memory register. The construction gives a controlled way to share spectral information across quantum modules while preserving the finite Fourier structure of a band. When memory read and write layers are input independent, we prove that the memory state forms an operator valued Fourier series whose support grows by Minkowski summation of local band spectra. Downstream bands then condition their Fourier coefficients on the spectral content stored by earlier bands. This theory motivates a spectral memory alignment loss that encourages memory to encode the spectrum expressed by the deployed prefix of the model. Across audio and image reconstruction benchmarks, SQMM improves over QINR and INR baselines, achieving state of the art results.