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arXiv:1810.10710 · Quantum Information Processing

Quantum data compression by principal component analysis

Chao‐Hua Yu, Fei Gao, Song Lin, Jingbo B. Wang

Published Jul 1, 2019• 86 citations
arXivHTMLPDF
DOI
10.1007/s11128-019-2364-9

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The rapid growth of Internet of Things (IoT) devices necessitates efficient data compression techniques to manage the vast amounts of data they generate. Chemiresistive sensor arrays (CSAs), a simple yet essential component in IoT systems, produce large datasets due to their simultaneous multi-sensor operations. Classical principal component analysis (cPCA), a widely used solution for dimensionality reduction, often struggles to preserve critical information in complex datasets. In this study, the self-adaptive quantum kernel (SAQK) PCA is introduced as a complementary approach to enhance information retention. The results show that SAQK PCA outperforms cPCA in various back end machine-learning tasks, particularly in low-dimensional scenarios where quantum bit resources are constrained. Although the overall improvement is modest in some cases, SAQK PCA proves especially effective in preserving group structures within low-dimensional data. These findings underscore the potential of noisy intermediate-scale quantum (NISQ) computers to transform data processing in real-world IoT applications by improving the efficiency and reliability of CSA data compression and readout, despite current qubit limitations.
Abstract Theoretical approaches to quantum many-body physics require developing compact representations of the complexity of generic quantum states. This paper explores an interpretable data-driven approach utilizing principal component analysis (PCA) and autoencoder neural networks to compress the two-particle vertex, a key element in Feynman diagram approaches. We show that the linear PCA offers more physical insight and better out-of-distribution generalization than the nominally more expressive autoencoders. Even with ∼10–20 principal components, we find excellent reconstruction across the phase diagram suggesting the existence of heretofore unrealized structures in the diagrammatic theory. We show that the principal components needed to describe the ferromagnetic state are not contained in the low rank description of the Fermi liquid (FL) state, unlike those for antiferromagnetic and superconducting states, suggesting that the latter two states emerge from pre-existing fluctuations in the FL while ferromagnetism is driven by a different process.
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.