Resonant quantum principal component analysis

Zhaokai Li; Zihua Chai; Yuhang Guo; Wentao Ji; Mengqi Wang; Fazhan Shi; Ya Wang; Seth Lloyd; Jiangfeng Du

doi:10.1126/sciadv.abg2589

Resonant quantum principal component analysis

Sci Adv. 2021 Aug 18;7(34):eabg2589. doi: 10.1126/sciadv.abg2589. Print 2021 Aug.

Authors

Zhaokai Li^{1

2

3

4}, Zihua Chai^{1

2

3}, Yuhang Guo^{1

2

3}, Wentao Ji^{1

2

3}, Mengqi Wang^{1

2

3}, Fazhan Shi^{1

2

3}, Ya Wang^{5

2

3}, Seth Lloyd⁴, Jiangfeng Du^{5

2

3}

Affiliations

¹ Hefei National Laboratory for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China.
² CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China.
³ Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China.
⁴ Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
⁵ Hefei National Laboratory for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China. ywustc@ustc.edu.cn djf@ustc.edu.cn.

Abstract

Principal component analysis (PCA) has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e., the eigenvectors of the density matrix with the largest eigenvalues. However, because of the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with minimal resource for ancillary qubits, in which only one frequency-scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4 × 4 density matrix, with an efficiency of 86.0% and a fidelity of 0.90. This work shows the speedup ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.

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