LiePrune: Lie Group and Quantum Geometric Dual Representation for One-Shot Structured Pruning of Quantum Neural Networks

TL;DR

LiePrune introduces a mathematically grounded one-shot structured pruning method for quantum neural networks, leveraging Lie group and quantum geometric structures to achieve significant compression with minimal performance loss.

Contribution

It is the first pruning framework for QNNs that uses Lie group and quantum geometry for principled redundancy detection and aggressive compression.

Findings

Achieves over 10x compression on various quantum tasks.

Maintains or improves task performance after pruning.

Provides provable guarantees on redundancy detection and complexity.

Abstract

Quantum neural networks (QNNs) and parameterized quantum circuits (PQCs) are key building blocks for near-term quantum machine learning. However, their scalability is constrained by excessive parameters, barren plateaus, and hardware limitations. We propose LiePrune, the first mathematically grounded one-shot structured pruning framework for QNNs that leverages Lie group structure and quantum geometric information. Each gate is jointly represented in a Lie group--Lie algebra dual space and a quantum geometric feature space, enabling principled redundancy detection and aggressive compression. Experiments on quantum classification (MNIST, FashionMNIST), quantum generative modeling (Bars-and-Stripes), and quantum chemistry (LiH VQE) show that LiePrune achieves over $10\times$ compression with negligible or even improved task performance, while providing provable guarantees on redundancy detection, functional approximation, and computational complexity.