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

arXiv: https://arxiv.org/abs/2512.09469 · HTML: https://mlsanity.com/paper/2512.09469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 1 of 1)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)

## Abstract (arXiv)

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× compression with negligible or even improved task performance, while providing provable guarantees on redundancy detection, functional approximation, and computational complexity.