The Hopf binary-tree ansatz provides universal state preparation plus an explicit inverse map, diagonal metric, and exact tangent-state gradients, organizing gradient access into O(log N) circuit families.
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A Compass on the Quantum State Sphere: The Hopf Ansatz for Arbitrary Pure-State Optimization
The Hopf binary-tree ansatz provides universal state preparation plus an explicit inverse map, diagonal metric, and exact tangent-state gradients, organizing gradient access into O(log N) circuit families.