Variational Quantum Algorithms for Dimensionality Reduction and Classification
This work addresses computational bottlenecks in machine learning for researchers in quantum computing, though it is incremental as it builds on existing quantum methods.
The authors tackled the problem of dimensionality reduction and classification by developing quantum algorithms that achieve exponential speedup over classical counterparts, demonstrated on 32x32 generalized eigenvalue problems.
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 $2^5\times2^5$ 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.