Trainability-Aware Quantum Gate Pruning for Variational Quantum Circuits Using Saliency and Quantum Fisher Information

Abstract

Variational quantum circuits (VQCs) suffer from barren plateaus, where gradients vanish exponentially with system size, limiting effective optimization. While prior mitigation strategies focus on circuit design and initialization, the effect of circuit compression – specifically, which gates are removed – on trainability remains comparatively unexplored. In this work we study quantum gate pruning from a trainability perspective in a controlled, noiseless 6-qubit simulation testbed, and report numerical evidence that gate-selection criterion plays a substantial role in preserving the optimization landscape of compressed circuits. We propose Q-AGASP, a saliency-based pruning framework that ranks parameterized quantum gates using a combination of gradient-weight sensitivity and quantum activation, and introduce a Quantum Fisher Information (QFI)-motivated saliency variant that targets parameters associated with low gradient variance. Both approaches are applied through an iterative pruning schedule with frozen weights. Experiments on a hybrid quantum-classical model (6-qubit, 144-parameter VQC) show that saliency-guided pruning improves the gradient variance of the surviving parameters relative to uninformed methods – by 6–9 $\times $ at 90% gate sparsity in our tested regime – while random or magnitude-based pruning can produce near-zero gradient variance in some seeds. We further find that post-fine-tuning accuracy converges across methods under our 15-epoch fine-tuning budget, which suggests that accuracy and pre-fine-tuning gradient variance are complementary rather than interchangeable diagnostics, with accuracy becoming less discriminative precisely when the fine-tuning budget is generous relative to circuit size. To analyze how gate rankings evolve during compression we introduce saliency drift, a Spearman-rank-correlation-based metric, and derive a distribution-free bound relating the observed correlation to the magnitude of ranking reshuffles; drift increases with sparsity in our experiments, consistent with iterative recomputation capturing structural changes not visible to one-shot pruning. We are explicit that these findings are numerical observations from a single ansatz, qubit count, and dataset rather than architecture-independent theorems, and we discuss how ansatz topology, entanglement structure, and circuit depth would be expected to modulate them, together with the changes needed to extend the framework to noisy hardware and to chemistry-motivated ansätze.