分析量子机器学习中对称性对模型性能的影响，提供可量化的选择依据。
Twirlator: A Pipeline for Analyzing Subgroup Symmetry Effects in Quantum Machine Learning Ansatzes
- 通过子群大小控制对称性程度，自动构建并评估量子线路
- 对称性越大，电路开销越高，表达能力越弱，但纠缠能力常增强
- 适用于需要权衡硬件成本与模型性能的量子算法设计者
对称性是几何深度学习及其量子对应物中的强归纳偏置，近年来被广泛关注以提升量子机器学习（QML）模型的可训练性。然而，在量子机器学习（QML）变分电路中引入对称性并非无代价：对称化通常增加门数并限制电路结构。为理解这些影响，我们提出Twirlator，一个自动化管道，可对参数化QML变分电路进行对称化，并量化对称性水平增加时的权衡。Twirlator通过子群大小建模部分对称性，实现从“无对称性”到“全对称性”的连续分析。在19种常见变分电路模式上，系统对任意$S_n$的子群进行对称化，测量生成器漂移、电路开销（深度和规模）以及表达能力和纠缠能力。实验聚焦于$S_4$和$S_5$的子群。结果表明，更大的子群通常导致更高的电路开销、更低的表达能力，但往往提升纠缠能力。该管道与结果为选择兼顾硬件成本与模型性能的对称性感知QML变分电路提供了实用指导。
原文摘要 · Abstract (English)
Symmetry is a strong inductive bias in geometric deep learning and its quantum counterpart, and has attracted increasing attention for improving the trainability of QML models. Yet incorporating symmetries into quantum machine learning (QML) ansatzes is not free: symmetrization often adds gates and constrains the circuits. To understand these effects, we present Twirlator, which is an automated pipeline that symmetrizes parameterized QML ansatzes and quantifies the trade-offs as the amount of symmetry increases. Twirlator models partial symmetries by the size of a subgroup of the symmetric group, enabling analysis between the ``no symmetry'' and ``full symmetry'' extremes. Across 19 common ansatz patterns, Twirlator symmetrizes circuits with respect to any subgroup of $S_n$ and measures (1) generator drift, (2) circuit overhead (depth and size), and (3) expressibility and entangling capability. The experimental evaluation focuses on subgroups of $S_4$ and $S_5$. Twirlator reveals that larger subgroups typically increase circuit overhead, reduce expressibility, and often increase entangling capability. The pipeline and results provide practical guidance for selecting ansatz patterns and symmetry levels that balance hardware cost and model performance in symmetry-aware QML applications.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。