One-Shot Structured Pruning of Quantum Neural Networks via $q$-Group Engineering and Quantum Geometric Metrics
Haijian Shao, Wei Liu, Xing Deng, Yingtao Jiang
TL;DR
The paper tackles gate-level redundancy in quantum neural networks by introducing q-iPrune, a one-shot structured pruning method grounded in $SU_q(2)$ quantum-group geometry and a task-conditioned $q$-overlap metric. Redundancy is detected within algebraically consistent subgroups using a state-overlap distance $d_q$ over a task ensemble, and gates are pruned only if their replacement by a subgroup representative keeps task observables within a bound, guided by a noise-adaptive parameter $\lambda$ and a calculable $\varepsilon_q$. The authors prove three guarantees—completeness of pruning, bounded functional equivalence on the task ensemble, and polynomial-time feasibility—and validate the approach on toy quantum classification and TFIM VQE benchmarks, showing substantial gate reduction with bounded performance drift. The framework provides a principled bridge between quantum algebraic structure and practical QNN compression, offering a scalable path to deployable QNNs on NISQ devices. Overall, q-iPrune delivers a rigorous, geometry-informed pruning methodology with concrete guarantees and empirical evidence of effectiveness.
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 $λ$ 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.