1. Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China 2. Department of Physics, Hong Kong University of Science and Technology, ClearWaterBay, Kowloon, Hong Kong, China 3. International Quantum Academy, Shenzhen 518055, China 4. Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China 5. Quantum Science Center of Guangdong–HongKong–Macao Greater Bay Area, Shenzhen–HongKong International Science and Technology Park, No. 3 Binlang Road, Futian District, Shenzhen 518045, China
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.
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