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

Haijian Shao, Bowen Yang, Wei Liu, Xing Deng, Yingtao Jiang

TL;DR

Quantum neural networks suffer from over-parameterization and hardware constraints. LiePrune introduces a principled one-shot structured pruning framework that blends a dual Lie-group/Lie-algebra representation with quantum geometric information to identify redundant gates and merge them efficiently. It partitions gates by minimal closed Lie subgroups, uses geometry-informed distances to guide pruning, and provides provable bounds on functional preservation with linear-like complexity, achieving 8–12× compression on classification benchmarks. However, chemistry-focused VQE tasks reveal sensitivity to aggressive pruning, underscoring the need for chemistry-aware regularization or structure-preserving strategies for quantum simulations.

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.

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

TL;DR

Quantum neural networks suffer from over-parameterization and hardware constraints. LiePrune introduces a principled one-shot structured pruning framework that blends a dual Lie-group/Lie-algebra representation with quantum geometric information to identify redundant gates and merge them efficiently. It partitions gates by minimal closed Lie subgroups, uses geometry-informed distances to guide pruning, and provides provable bounds on functional preservation with linear-like complexity, achieving 8–12× compression on classification benchmarks. However, chemistry-focused VQE tasks reveal sensitivity to aggressive pruning, underscoring the need for chemistry-aware regularization or structure-preserving strategies for quantum simulations.

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

Paper Structure

This paper contains 14 sections, 5 theorems, 19 equations, 2 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Lie Group and Quantum Geometric Dual Representation
  4. Lie Group Representation of Unitary Gates
  5. Quantum Geometric Features
  6. Dual-Space Identifier
  7. LiePrune Algorithm
  8. Lie Subgroup Partitioning
  9. Geometry-Accelerated Fubini--Study Distance
  10. Redundancy Graph and One-Shot Pruning
  11. Experiments
  12. Experimental Setup
  13. Main Results
  14. Discussion and Conclusion

Key Result

Theorem 4.1

Let $G$ be the redundancy graph constructed in Algorithm alg:lieprune. Then every edge $(i,j)$ of $G$ connects two gates drawn from the same subgroup $S_k$. Equivalently, candidate redundant pairs considered by LiePrune are restricted to gates inside a common minimal closed Lie subgroup.

Figures (2)

  • Figure 1: LiePrune across datasets. Each group corresponds to one dataset and contains three bars: Original, LiePrune (no FT), and LiePrune (+FT).
  • Figure 2: LiePrune on LiH VQE at $R=1.60$ Å across multiple compression ratios. We report the deviation from the unpruned baseline for direct pruning ($\Delta E_\text{direct}$) and post-finetuning ($\Delta E_\text{ft}$). Mild compression is recoverable, whereas aggressive compression produces multi-Hartree errors that fine-tuning cannot fully mitigate.

Theorems & Definitions (11)

  • Theorem 4.1: Redundancy Pre-Constraint
  • proof
  • Lemma 4.1: Geometry-accelerated approximation
  • proof
  • Definition 4.1: Dataset-level $\varepsilon$-redundancy
  • Theorem 4.2: Redundancy completeness inside subgroups
  • proof
  • Theorem 4.3: Approximate functional preservation after pruning
  • proof
  • Theorem 4.4: Complexity under bounded local degree
  • ...and 1 more