CohAlign: Predicting the first-order noise susceptibility of gradients in equivariant quantum neural networks

Quantum neural networks learn by following gradients, and on real hardware those gradients are washed out by noise. Predicting how quickly this happens, before any finite noise experiment or circuit sweep is run, remains an open problem. We present CohAlign, an open source toolkit that computes the first order noise susceptibility of the ensemble second moment of a specified parameter gradient in a charge conserving brickwork quantum neural network. The computation needs only a classical description of the circuit, the noise model, the prepared state, the readout and the initialisation prior. The predicted quantity is distinct from training convergence or final accuracy. The key observation is that only the part of the noise that a measurement can actually see matters. A purposefully constructed control channel makes this clear, damaging the operator carrying a gradient at nearly the maximal rate while the measured gradient remains exactly as predicted and untouched. We validate the predictions against separately evaluated finite difference slopes across the benchmark suite, including a signed coherent case, in exact simulations at eight and ten qubits and on two circuit topologies.