Hierarchical Fourier Approximation for Variational Quantum Distribution Learning
We study variational quantum distribution learning through a hierarchy of Walsh--Fourier approximations on the Boolean cube. At each level, a selected set of target Fourier coefficients defines a spectral truncation, which is projected onto the probability simplex and used as the target of a quantum circuit Born machine. Parameters learned at one level initialize the next through a warm-start map. We prove an end-to-end expected learning guarantee where the approximation term is determined by the omitted Fourier mass, while a normalized unbiased estimator yields an explicit statistical bound for empirical truncations. We then instantiate the abstract discrepancy conditions for total varia...
| Authors | Taha Hoseinpour Asli, Sajjad Hashemian, Ebrahim Ardeshir-Larijani |
|---|---|
| Primary category | quant-ph |
| Published | 5 September 2026 |
| Last updated at source | 5 September 2026 |
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