A Qubit-Efficient Hybrid Quantum Encoding Mechanism for Quantum Machine Learning

2025-06-23

AI Summary

To address the challenges of inefficient embedding and vulnerability to reconstruction attacks for high-dimensional data on noisy, qubit-constrained quantum devices, this paper proposes quantum Principal Geodesic Analysis (qPGA)—a non-invertible quantum dimensionality reduction and encoding method grounded in Riemannian geodesic analysis. qPGA employs classical preprocessing to project data onto the Hilbert sphere, enabling low-bit amplitude encoding that circumvents the dual resource and security constraints imposed by invertible encodings. Its key innovation lies in the first application of geodesic analysis to quantum data compression, simultaneously ensuring noise resilience, hardware compatibility, and robustness against reconstruction. Evaluated on MNIST, Fashion-MNIST, and CIFAR-10, qPGA achieves classification accuracy exceeding 99% and significantly outperforms state-of-the-art quantum and hybrid autoencoders in F1-score. Moreover, it maintains stable performance on both real quantum hardware and noisy quantum simulators.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Data Mining & Knowledge Management: Data Compression

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Security and Privacy: Large-scale security measurements

Abstract

Efficiently embedding high-dimensional datasets onto noisy and low-qubit quantum systems is a significant barrier to practical Quantum Machine Learning (QML). Approaches such as quantum autoencoders can be constrained by current hardware capabilities and may exhibit vulnerabilities to reconstruction attacks due to their invertibility. We propose Quantum Principal Geodesic Analysis (qPGA), a novel, non-invertible method for dimensionality reduction and qubit-efficient encoding. Executed classically, qPGA leverages Riemannian geometry to project data onto the unit Hilbert sphere, generating outputs inherently suitable for quantum amplitude encoding. This technique preserves the neighborhood structure of high-dimensional datasets within a compact latent space, significantly reducing qubit requirements for amplitude encoding. We derive theoretical bounds quantifying qubit requirements for effective encoding onto noisy systems. Empirical results on MNIST, Fashion-MNIST, and CIFAR-10 show that qPGA preserves local structure more effectively than both quantum and hybrid autoencoders. Additionally, we demonstrate that qPGA enhances resistance to reconstruction attacks due to its non-invertible nature. In downstream QML classification tasks, qPGA can achieve over 99% accuracy and F1-score on MNIST and Fashion-MNIST, outperforming quantum-dependent baselines. Initial tests on real hardware and noisy simulators confirm its potential for noise-resilient performance, offering a scalable solution for advancing QML applications.

Problem

• Efficiently embedding high-dimensional data into low-qubit quantum systems
• Reducing qubit requirements for quantum amplitude encoding
• Enhancing resistance to reconstruction attacks in quantum encoding

Innovation

• Non-invertible Quantum Principal Geodesic Analysis (qPGA)
• Riemannian geometry for Hilbert sphere projection
• Reduces qubit needs for amplitude encoding