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arXiv · 2607.27051

Quasi-polar Decomposition of Quantum Neural Networks via Adaptive Non-local Observables

Shih-Hao Ho·Yan Li·Huan-Hsin Tseng·Hsin-Yi Lin·Samuel Yen-Chi Chen·Shinjae Yoo
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Abstract

We use Diagonal Adaptive Non-local Observables (DANO) as a canonical decomposition for studying Variational Quantum Circuit model evolution. Separating each learned observable into a diagonal spectrum and a unitary basis gives a quasi-polar description: the spectral weights are viewed as radial coordinates, while the unitary circuit serves as angular coordinates through Lie group identifications. This turns the training process into a trajectory in spectral and Lie-algebra space. Experiments on two classification tasks show that DANO radial spectral expansion correlates with accuracy. DANO angle coordinates reveal a dominant accuracy-correlated component. The framework provides a different perspective to characterize quantum model behavior.

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Shih-Hao Ho, Yan Li, Huan-Hsin Tseng, Hsin-Yi Lin, Samuel Yen-Chi Chen, Shinjae Yoo. 2026-07-29. Quasi-polar Decomposition of Quantum Neural Networks via Adaptive Non-local Observables. https://arxiv.org/abs/2607.27051

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