Variational Quantum Algorithms for Dimensionality Reduction and Classification
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Dimensionality reduction and classification play an absolutely critical role in pattern recognition and machine learning. In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. These two algorithms have an exponential speedup over their respectively classical counterparts. Along the way, we propose a variational quantum generalized eigenvalue solver (VQGE) that finds the generalized eigenvalues and eigenvectors of a matrix pencil (G,S) with coherence time O(1). We successfully conduct numerical experiment solving a problem size of 2^5×2^5. Moreover, 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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