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

• URL: http://arxiv.org/abs/2607.27051v1
• Date: Wed, 29 Jul 2026 15:42:14 GMT
• Title: Quasi-polar Decomposition of Quantum Neural Networks via Adaptive Non-local Observables
• Abstract summary: We use Diagonal Adaptive Non-local Observables (DANO) as a canonical decomposition for studying Variational Quantum Circuit model evolution.<n> Separating each learned observable into a diagonal spectrum and a unitary basis gives a quasi-polar description.<n>Experiments on two classification tasks show that DANO radial spectral expansion correlates with accuracy.
• Score: 32.2292784850797
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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