Variational Quantum Algorithms for Dimensionality Reduction and Classification

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 $2^5\times 2^5$ 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.

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Cited by in corpus (13)

• Abrupt Transitions in Variational Quantum Circuit Training
• A brief introduction to quantum algorithms
• Quantum algorithm for Neighborhood Preserving Embedding
• Quantum algorithms for the generalized eigenvalue problem
• Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems
• Experimental implementation of quantum algorithm for association rules mining
• Variational quantum algorithm for generalized eigenvalue problems and its application to the finite element method
• Improved iterative quantum algorithm for ground-state preparation
• Quantum Information Masking in Non-Hermitian Systems and Robustness
• Photonic variational quantum eigensolver using entanglement measurements
• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
• Revealing hidden standard tripartite nonlocality by local filtering
• Riemannian-geometric generalizations of quantum fidelities and Bures-Wasserstein distance