Impact of Single Rotations and Entanglement Topologies in Quantum Neural Networks

2025-09-19

AI Summary

Designing expressive and generalizable variational quantum circuits (VQCs) for quantum neural networks (QNNs) remains challenging due to the interplay between entanglement topology and parameterized gate placement. Method: We systematically evaluate four entanglement topologies—linear, ring, pairwise, and fully connected—in combination with single- and double-rotation layer configurations across three canonical quantum machine learning tasks: probability distribution modeling, image generation, and classification. Contribution/Results: (1) Adding a final rotation layer significantly enhances model expressivity and generalization; (2) circuit performance strongly correlates with both entangling capability and theoretical expressibility; (3) the alternating VQC architecture augmented with a terminal rotation layer consistently achieves superior performance across all tasks. This work provides empirical evidence and structural design principles for interpretable, task-adapted QNNs, bridging theoretical expressibility analysis with practical quantum architecture optimization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In this work, an analysis of the performance of different Variational Quantum Circuits is presented, investigating how it changes with respect to entanglement topology, adopted gates, and Quantum Machine Learning tasks to be performed. The objective of the analysis is to identify the optimal way to construct circuits for Quantum Neural Networks. In the presented experiments, two types of circuits are used: one with alternating layers of rotations and entanglement, and the other, similar to the first one, but with an additional final layer of rotations. As rotation layers, all combinations of one and two rotation sequences are considered. Four different entanglement topologies are compared: linear, circular, pairwise, and full. Different tasks are considered, namely the generation of probability distributions and images, and image classification. Achieved results are correlated with the expressibility and entanglement capability of the different circuits to understand how these features affect performance.

Problem

• Investigating quantum circuit performance with entanglement topologies
• Analyzing rotation layer impact on Quantum Neural Networks
• Optimizing circuit construction for quantum machine learning tasks

Innovation

• Variational Quantum Circuits with entanglement topologies
• Alternating rotation and entanglement layers design
• Comparing expressibility and entanglement capability impacts