# Variational Quantum Algorithms for Dimensionality Reduction and Classification

arXiv: https://arxiv.org/abs/1910.12164 · HTML: https://mlsanity.com/paper/1910.12164/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Quantum Distributed Deep Learning Architectures: Models, Discussions, and Applications](https://mlsanity.com/paper/2202.11200/) (2022)
- [Transition Role of Entangled Data in Quantum Machine Learning](https://mlsanity.com/paper/2306.03481/) (2023)
- [Efficient and Accurate Estimation of Lipschitz Constants for Hybrid Quantum-Classical Decision Models](https://mlsanity.com/paper/2503.07992/) (2025)
- [Dimension reduction with structure-aware quantum circuits for hybrid machine learning](https://mlsanity.com/paper/2508.00048/) (2025)

## Abstract (arXiv)

In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their respectively classical counterparts. Along the way, we propose a variational quantum generalized eigenvalue solver that finds the generalized eigenvalues and eigenstates of a matrix pencil (G,S). As a proof-of-principle, we implement our algorithm to solve 25×25 generalized eigenvalue problems. Finally, our results offer two optional outputs with quantum or classical form, which can be directly applied in another quantum or classical machine learning process.