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A reproducible toolkit for auditing symmetry-organised complexity in equivariant quantum neural network ansatz, reporting sector occupation, cross-sector coherence, sectoral fluctuation, and generator-sum compliance against U(1), SU(2), and permutation symmetry before training.
Compiling equivariant quantum neural networks can break their symmetry at the structural level, with up to 22.5% CZ-count asymmetry between symmetry-related sparse-graph inputs on IBM Heron's Fez. We classify ansätze by where the input enters and fix the affected case via compile-once-and-relabel.