A Coherence Law for Trainability in Noisy Equivariant Quantum Neural Networks
Symmetry provides a quantum neural network structure, but on its own it does not keep the network trainable once noise is present. We ask which physical quantity decides whether the gradients of an equivariant circuit survive decoherence, and we answer with a compact training law. Working with U(1)-equivariant brickwork circuits that conserve a charge, we find that two distinct effects govern a trainable gradient. Causality fixes where the gradient can live, confining it to the backward light cone of the readout inside the active charge sector. Coherence then determines how fast it decays through the contraction of the off-diagonal sector modes that the projected readout can actually obse...
| Authors | Hassan Ugail, Newton Howard |
|---|---|
| Primary category | quant-ph |
| Published | 28 June 2026 |
| Last updated at source | 28 June 2026 |
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