Hardware-efficient quantum principal component analysis for medical image recognition

Principal component analysis (PCA) is a widely used tool in machine learning algorithms, but it can be computationally expensive. In 2014, Lloyd, Mohseni & Rebentrost proposed a quantum PCA (qPCA) algorithm [Nat. Phys. 10, 631 (2014)] that has not yet been experimentally demonstrated due to challenges in preparing multiple quantum state copies and implementing quantum phase estimations. In this study, we presented a hardware-efficient approach for qPCA, utilizing an iterative approach that effectively resets the relevant qubits in a nuclear magnetic resonance (NMR) quantum processor. Additionally, we introduced a quantum scattering circuit that efficiently determines the eigenvalues and eigenvectors (principal components). As an important application of PCA, we focused on classifying thoracic CT images from COVID-19 patients and achieved high accuracy in image classification using the qPCA circuit implemented on the NMR system. Our experiment highlights the potential of near-term quantum devices to accelerate qPCA, opening up new avenues for practical applications of quantum machine learning algorithms.