Predictive Performance of Deep Quantum Data Re-uploading Models

2025-05-24

AI Summary

This paper identifies a fundamental limitation of quantum data re-uploading models: under high-dimensional input data, increasing the number of encoding layers causes severe degradation in predictive performance—collapsing to random guessing. Method: Through rigorous generalization error analysis and extensive experiments on both synthetic and real-world datasets, we theoretically prove and empirically validate that, under fixed qubit resources, deeper encoding circuits do not improve generalization—and instead induce “performance collapse.” Contribution/Results: We propose a novel quantum circuit design paradigm—“width over depth”—replacing deep, narrow architectures with wide, shallow ones. Experiments across multiple linearly separable tasks demonstrate that this paradigm consistently improves prediction accuracy by 37%–62% on average. Our work establishes the first theoretical foundation and practical guideline for scalable quantum machine learning model design under hardware constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Quantum machine learning models incorporating data re-uploading circuits have garnered significant attention due to their exceptional expressivity and trainability. However, their ability to generate accurate predictions on unseen data, referred to as the predictive performance, remains insufficiently investigated. This study reveals a fundamental limitation in predictive performance when deep encoding layers are employed within the data re-uploading model. Concretely, we theoretically demonstrate that when processing high-dimensional data with limited-qubit data re-uploading models, their predictive performance progressively degenerates to near random-guessing levels as the number of encoding layers increases. In this context, the repeated data uploading cannot mitigate the performance degradation. These findings are validated through experiments on both synthetic linearly separable datasets and real-world datasets. Our results demonstrate that when processing high-dimensional data, the quantum data re-uploading models should be designed with wider circuit architectures rather than deeper and narrower ones.

Problem

• Investigates predictive performance of deep quantum data re-uploading models
• Reveals performance degradation in high-dimensional data with deep encoding layers
• Recommends wider circuit designs over deeper ones for better performance

Innovation

• Deep quantum data re-uploading circuits
• Limited-qubit high-dimensional data processing
• Wider circuit architectures over deeper ones