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.

主成分分析 (PCA) 是机器学习算法中广泛使用的工具，但其计算成本可能很高。 2014 年，Lloyd、Mohseni 和 Rebentrost 提出了量子 PCA（qPCA）算法 [ Nat.物理。 10, 631 (2014)]，由于准备多个量子态副本和实现量子相位估计方面的挑战，尚未通过实验证明。在这项研究中，我们提出了一种硬件高效的 qPCA 方法，利用迭代方法有效地重置核磁共振 (NMR) 量子处理器中的相关量子位。此外，我们引入了量子散射电路，可以有效地确定特征值和特征向量（主成分）。作为 PCA 的一个重要应用，我们专注于对 COVID-19 患者的胸部 CT 图像进行分类，并使用在 NMR 系统上实现的 qPCA 电路实现了图像分类的高精度。我们的实验凸显了近期量子设备加速 qPCA 的潜力，为量子机器学习算法的实际应用开辟了新途径。