Quantum Algorithm for Spectral Regression for Regularized Subspace Learning

In this paper, we propose an efficient quantum algorithm for spectral regression which is a dimensionality reduction framework based on the regression and spectral graph analysis. The quantum algorithm involves two core subroutines: the quantum principal eigenvectors analysis and the quantum ridge regression algorithm. The quantum principal eigenvectors analysis can be performed by an efficient sparse Hamiltonian simulation. For the ridge regression, we propose a quantum algorithm that is derived from the quantum singular value decomposition method. Our quantum ridge regression algorithm is more suitable for data matrices that are non-sparse and skewed. Our analysis demonstrates that the quantum subroutines can be implemented with an approximatively polynomial speedup on a quantum computer over their classical counterparts.