Geometry Conservation in Variational Quantum Classifiers and Where Neural Collapse Can Appear
Prior work proved that variational quantum classifiers reach Neural Collapse only at the static optimum. I asked whether collapse actually emerges during training, and found that it happens by an exact rotation, not a contraction: training conjugates every state by one global unitary.
The rotation result holds to machine precision (~10⁻¹⁵ relative change) at 4, 6 and 8 qubits, on MNIST and Fashion-MNIST under two encodings, across a second optimizer and ansatz family. It was also verified on two IBM quantum backends. A matched classical MLP does the opposite: within-class scatter grows 27–163×.
The study ran as preregistered science: 52 predictions across 10 stages, every threshold committed before its metric was computed, on a frozen spec with 173+ tests.