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Trapped Ion Quantum Computing Quantum Machine Learning

Variational Quantum Algorithms for Dimensionality Reduction and Classification

arXiv
Authors: Jin-Min Liang, Shu-Qian Shen, Ming Li, Lei Li

Year

2019

Paper ID

15249

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

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 \(mathcal{G},mathcal{S}\). As a proof-of-principle, we implement our algorithm to solve 25times25 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.

Why This Paper Matters

  • This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
  • It adds a 2019 reference point for readers tracking recent quantum research.
  • In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1910.12164 [2] arXiv https://arxiv.org/abs/1910.12164 [3] Publisher https://arxiv.org/abs/1910.12164

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