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

arXiv: https://arxiv.org/abs/2506.19275 · HTML: https://mlsanity.com/paper/2506.19275/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 9 of 9)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Updates-Leak: Data Set Inference and Reconstruction Attacks in Online Learning](https://mlsanity.com/paper/1904.01067/) (2019)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [On compression rate of quantum autoencoders: Control design, numerical and experimental realization](https://mlsanity.com/paper/2005.11149/) (2020)
- [A preprocessing perspective for quantum machine learning classification advantage using NISQ algorithms](https://mlsanity.com/paper/2208.13251/) (2022)
- [A Hybrid Quantum Neural Network for Split Learning](https://mlsanity.com/paper/2409.16593/) (2024)
- [Hybrid Quantum-Classical Autoencoders for End-to-End Radio Communication](https://mlsanity.com/paper/2301.02609/) (2023)

## Abstract (arXiv)

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.