New Quantum Algorithm for Principal Component Analysis

TL;DR

This paper introduces a new quantum algorithm framework for principal component analysis that improves performance over existing methods and offers a novel way to prepare covariance matrices from classical data on quantum computers.

Contribution

It presents an alternative quantum PCA framework and a new method for preparing covariance matrices from classical datasets, enhancing quantum machine learning capabilities.

Findings

The new framework outperforms original QPCA in certain regimes.

A novel covariance matrix preparation method from classical data.

Provides an efficient way to analyze quantum states using PCA.

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.