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Physical Review Letters

Experimental Quantum Principal Component Analysis via Parametrized Quantum Circuits

Tao Xin, Liangyu Che, Xi Cheng, Amandeep Singh, Xinfang Nie, Jun Li, Ying Dong, Dawei Lu

Published Mar 18, 2021• 60 citations
Publisher

Abstract

Principal component analysis (PCA) is a widely applied but rather time-consuming tool in machine learning techniques. In 2014, Lloyd, Mohseni, and Rebentrost proposed a quantum PCA (qPCA) algorithm [Lloyd, Mohseni, and Rebentrost, Nat. Phys. 10, 631 (2014)NPAHAX1745-247310.1038/nphys3029] that still lacks experimental demonstration due to the experimental challenges in preparing multiple quantum state copies and implementing quantum phase estimations. Here, we propose a new qPCA algorithm using the hybrid classical-quantum control, where parameterized quantum circuits are optimized with simple measurement observables, which significantly reduces the experimental complexity. As one important PCA application, we implement a human face recognition process using the images from the Yale Face Dataset. By training our quantum processor, the eigenface information in the training dataset is encoded into the parameterized quantum circuit, and the quantum processor learns to recognize new face images from the test dataset with high fidelities. Our work paves a new avenue toward the study of qPCA applications in theory and experiment.

DOI
10.1103/physrevlett.126.110502

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•Oct 2, 2020•2 citations
Principal component analysis (PCA) is a widely applied but rather time-consuming tool in machine learning techniques. In 2014, Lloyd, Mohseni, and Rebentrost proposed a quantum PCA (qPCA) algorithm [Lloyd, Mohseni, and Rebentrost, Nat. Phys. 10, 631 (2014)NPAHAX1745-247310.1038/nphys3029] that still lacks experimental demonstration due to the experimental challenges in preparing multiple quantum state copies and implementing quantum phase estimations. Here, we propose a new qPCA algorithm using the hybrid classical-quantum control, where parameterized quantum circuits are optimized with simple measurement observables, which significantly reduces the experimental complexity. As one important PCA application, we implement a human face recognition process using the images from the Yale Face Dataset. By training our quantum processor, the eigenface information in the training dataset is encoded into the parameterized quantum circuit, and the quantum processor learns to recognize new face images from the test dataset with high fidelities. Our work paves a new avenue toward the study of qPCA applications in theory and experiment.
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.
Quantum Principal Component Analysis (QPCA) offers a theoretical exponential speedup over classical PCA, but its practical performance under realistic conditions remains underexplored. This work-in-progress research investigates QPCA's viability by implementing a Quantum Phase Estimation (QPE)based QPCA circuit using Qiskit and benchmarking it on ten well known classical datasets in the IBM Quantum simulator environment. We evaluated both the fidelity of eigenvalue and eigenvector reconstruction as well as the downstream impact of QPCA versus classical PCA on regression and classification tasks. Our results confirm that QPCA can reproduce classical eigenvalues with high precision (error<10−4<10^{-4}<10−4), but its eigenvector fidelity degrades in cases of near-degenerate spectra. We further observe that PCA benefits classification more consistently than regression, regardless of the implementation method. These findings establish a preliminary empirical foundation for understanding QPCA's strengths and limitations and serve as a baseline for future work incorporating hardware noise, scalable circuit design, and hybrid approaches.
This paper presents a hybrid classical-quantum algorithm for face biometric verification that enhances the traditional eigenface method using Quantum Principal Component Analysis (QPCA). Classical preprocessing is used for image normalization and mean subtraction, while QPCA performs efficient eigen decomposition of facial data. Quantum projection and similarity measurement are implemented using SWAP test circuits, enabling exponential speedup in highdimensional operations. The proposed system significantly reduces computational complexity, particularly in eigenvalue decomposition, without compromising recognition accuracy. Our implementation demonstrates measurably improved verification performance compared to classical methods, while substantially reducing processing time. Simulation results on reduced-size facial datasets validate the feasibility and computational advantages of our approach. Comparative analysis demonstrates scalability advantages for high-resolution images and large datasets. This work lays a foundation for efficient and secure biometric authentication systems by utilizing the quantum computing advancements.
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis on quantum computer was obtained by computing the Hamiltonian simulation of unknown density operators. The complexity is O((log⁡d)t2/ε)O((\log d)t^2/ε)O((logd)t2/ε), where ddd is the dimension, ttt is the evolution time and εεε is the precision. We improve this result into O((log⁡d)t1+1k/ε1k)O((\log d)t^{1+\frac{1}{k}}/ε^{\frac{1}{k}})O((logd)t1+k1​/εk1​) for arbitrary constant integer k≥1k\geq 1k≥1. As a result, we show that the Hamiltonian simulation of low-rank dense Hermitian matrices can be implemented in the same time.
Facial biometrics play a crucial role in identity verification, yet classical approaches face challenges related to computational complexity and security vulnerabilities. This paper explores the integration of quantum computing with eigenface-based face verification to enhance efficiency and security. By utilizing the advantages of Quantum Principal Component Analysis (QPCA), we achieve exponential speedups in eigenvalue decomposition, significantly reducing the computational burden of high-dimensional facial data processing. Our hybrid classical-quantum approach optimizes quantum state encoding and similarity measurement via the Swap Test techniques. Experimental results demonstrate improved verification accuracy and scalability compared to classical eigenfaces, particularly for large databases. Despite current hardware constraints, our findings establish a foundational framework for quantum-enhanced biometric systems. This work highlights the potential of quantum computing in facial recognition, and prepares the way for more efficient, secure, and scalable biometric authentication systems.
Quantum principal component analysis (qPCA) is the quantum version of principal component analysis (PCA). In this paper, based on the quantum singular value threshold (qSVT), we propose an exact quantum principal component analysis algorithm, which screens the data components through the threshold, rather than output all components of data. Compared with other improved qPCA algorithms, our proposed algorithm does not require to adjust the parameters to obtain estimated results. Instead, it yields exact results directly, and the quantum circuit designed is simpler because almost half of the quantum gates are reduced. We implemented our qPCA algorithm on the IBM quantum computing platform: IBM Quantum Experience, and the experimental results verified correctness of our algorithm.