Quantum Spectral Models: New Data Encoding for Matrix Inputs
A new paper on arXiv introduces Quantum Spectral Models (QSMs), a quantum machine learning framework that constructs data-encoding unitaries directly from input matrices. Unlike standard coordinate-wise rotation-gate encodings, QSMs build the generator of the unitary from each matrix, enabling explicit matrix-level representation. Three variants are studied: symmetric, global block, and non-overlapping patch-local block Hamiltonians. The outputs yield truncated Fourier representations where input-dependent spectral gaps determine phase carriers and spectral subspaces influence coefficients. The work aims to align quantum models' inductive bias with matrix-structured data. The preprint is available under arXiv ID 2607.22516.
Key facts
- Paper introduces Quantum Spectral Models (QSMs) for quantum machine learning.
- QSMs construct the generator of the data-encoding unitary directly from each input matrix.
- Three QSM variants: symmetric, global block, and non-overlapping patch-local block Hamiltonians.
- Outputs admit truncated Fourier representations with input-dependent spectral gaps.
- Spectral subspaces help determine Fourier coefficients.
- Standard quantum ML models use coordinate-wise rotation-gate encodings that lack explicit matrix-level representation.
- Aims to align inductive bias with matrix-valued input data.
- Preprint available on arXiv with ID 2607.22516.
Entities
Institutions
- arXiv