New Quantum Algorithm for Principal Component Analysis (2501.07891v1)

Abstract: Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum system using the quantum state itself, QPCA also found potential application in analyzing a large-scale dataset, represented by the so-called covariance matrix. Inspired by recent advancement in quantum algorithms, we give an alternatively new quantum framework for performing principal component analysis. By analyzing the performance in detail, we shall identify the regime in which our proposal performs better than the original QPCA. In addition, we also provide a new approach for preparing the covariance matrix, given classical dataset, on a quantum computer. Thus, our work provides an efficient complementary framework for revealing features of the quantum state, while keeping the philosophy of original QPCA, as the state could play an active role in analyzing itself.