One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics

TL;DR

This paper introduces q-iPrune, a novel one-shot structured pruning method for quantum neural networks that leverages algebraic group structures and quantum geometry to reduce gates while preserving task performance.

Contribution

The work presents a theoretically grounded pruning framework for QNNs based on $q$-group algebra and quantum geometry, with formal guarantees on redundancy removal and circuit fidelity.

Findings

Achieves significant gate reduction in QNNs.

Maintains bounded task performance degradation.

Provides polynomial-time pruning algorithm with theoretical guarantees.

Abstract

Quantum neural networks (QNNs) suffer from severe gate-level redundancy, which hinders their deployment on noisy intermediate-scale quantum (NISQ) devices. In this work, we propose q-iPrune, a one-shot structured pruning framework grounded in the algebraic structure of $q$-deformed groups and task-conditioned quantum geometry. Unlike prior heuristic or gradient-based pruning methods, q-iPrune formulates redundancy directly at the gate level. Each gate is compared within an algebraically consistent subgroup using a task-conditioned $q$-overlap distance, which measures functional similarity through state overlaps on a task-relevant ensemble. A gate is removed only when its replacement by a subgroup representative provably induces a bounded deviation on all task observables. We establish three rigorous theoretical guarantees. First, we prove completeness of redundancy pruning: no gate that violates the prescribed similarity threshold is removed. Second, we show that the pruned circuit is functionally equivalent up to an explicit, task-conditioned error bound, with a closed-form dependence on the redundancy tolerance and the number of replaced gates. Third, we prove that the pruning procedure is computationally feasible, requiring only polynomial-time comparisons and avoiding exponential enumeration over the Hilbert space. To adapt pruning decisions to hardware imperfections, we introduce a noise-calibrated deformation parameter $\lambda$ that modulates the $q$-geometry and redundancy tolerance. Experiments on standard quantum machine learning benchmarks demonstrate that q-iPrune achieves substantial gate reduction while maintaining bounded task performance degradation, consistent with our theoretical guarantees.