Variational quantum algorithms for dimensionality reduction and classification
Jin‐Min Liang, Shu‐Qian Shen, Ming Li, Lei Li
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 ${2}^{5}\ifmmode\times\else\texttimes\fi{}{2}^{5}$ 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.