[Paper Review] An Exact Quantum Principal Component Analysis Algorithm Based on Quantum Singular Value Threshold

Chen He, Jiazhen Li+1 more|arXiv (Cornell University)|Oct 2, 2020

Quantum Computing Algorithms and Architecture3 citations

TL;DR

This paper presents an exact quantum principal component analysis (qPCA) algorithm based on quantum singular value thresholding (qSVT), which directly extracts principal components without parameter tuning. By eliminating the need for iterative optimization and reducing quantum gate count by nearly half, the method achieves exact results with a simpler quantum circuit, validated on IBM Quantum Experience.

ABSTRACT

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.

Motivation & Objective

• To develop a quantum PCA algorithm that avoids iterative parameter tuning for optimal results.
• To reduce quantum circuit complexity by minimizing the number of quantum gates used in qPCA implementations.
• To enable exact extraction of principal components through thresholding, rather than approximating all components.
• To design a more efficient quantum circuit that maintains accuracy while reducing resource overhead.

Proposed method

• The algorithm leverages quantum singular value thresholding (qSVT) to directly identify and extract significant principal components based on a threshold value.
• It avoids parameter adjustment by using exact thresholding, ensuring the output components are mathematically precise.
• The quantum circuit is optimized to reduce gate count by approximately 50% compared to existing qPCA variants.
• The method processes the input density matrix directly using qSVT, enabling selective component extraction without full decomposition.
• The algorithm is implemented and tested on the IBM Quantum Experience platform to validate correctness and efficiency.
• The thresholding mechanism ensures that only components above a defined singular value threshold are retained, improving computational fidelity.

Experimental results

Research questions

• RQ1 Can qPCA be made exact without requiring iterative parameter tuning for optimal component selection?
• RQ2 How can quantum circuit complexity in qPCA be reduced while preserving accuracy?
• RQ3 Can quantum singular value thresholding enable direct extraction of principal components without computing all components?
• RQ4 What is the impact of gate reduction on the practical implementation of qPCA on near-term quantum hardware?

Key findings

• The proposed qPCA algorithm produces exact principal component results without requiring any parameter adjustment.
• The quantum circuit complexity is significantly reduced, with nearly half the number of quantum gates compared to existing qPCA methods.
• The algorithm was successfully implemented and verified on the IBM Quantum Experience platform, confirming its correctness.
• The use of qSVT enables direct component screening based on thresholding, avoiding the need to compute and process all components.
• The method maintains high fidelity and efficiency, making it suitable for near-term quantum devices with limited qubit coherence and gate fidelity.