Cost-Function Locality and Trainability Diagnostics for Quantum Neural Networks: An Empirical and Artifact-Level Study of Layerwise and Local-Cost Training
Fahad Abdullah, Asma Zubair, Farhan Riaz
We report an empirical study of how quantum neural networks (QNNs) train under global and local costfunctions, with layerwise training included as a third point of comparison. The main experiment is a set of 180 training runson binary MNIST (digits 3 and 6), using an 8-qubit hardware-efficient ansatz written in TensorFlow Quantum. A second,separate study measures gradient landscapes at a fixed input across 48 circuit configurations with 4 to 10 qubits. Wecompare three procedures: end-to-end training with a global product-Z readout (the baseline), a layerwise curriculum thatreuses trained parameters between stages, and training on a local averaged-Z cost. Test accuracy barely moves betweenmethods. The global baseline still reaches 87.2% at 8 layers, so we see no accuracy collapse in this regime, andmatched-seed tests at 8 layers find no significant difference (Friedman p = 0.654; every pairwise paired test isnon-significant, as are the tests at 4 and 6 layers). Gradient statistics tell the methods apart much more clearly. At depths 4,6 and 8, the local cost ends training with 1.5 to 2.4 times lower gradient variance than the global baseline (paired p <= 9.4x 10⁻³ after Holm correction; Cohen's d_z up to 2.3). It also costs far more to simulate at depth: 6.57 h per run at 8 layers,against 1.66 h for the baseline. In the landscape study, the local observable's gradient variance is 1.4 to 10 times lower thanthe global observable's over the whole configuration grid, and 4 to 10 times lower at depth 8. Layerwise training follows adifferent path, with gradient variance falling during optimization, yet it gives no
•Oct 19, 2026•0 citations