Recently, the Institute of Quantum Science and Engineering (referred to as the "Quantum Institute") and the Department of Physics of Southern University of Science and Technology have made important progress in quantum machine learning research.

Assistant researcher Xin Tao of the Institute of Quantum Research, associate researcher Li Jun, associate professor Lu Dawei of the Department of Physics, and collaborator Dong Ying, professor of the Quantum Sensing Research Center of Zhijiang Laboratory, jointly worked on a quantum computing platform based on nuclear magnetic resonance (NMR).

A quantum principal component analysis algorithm based on parameterized quantum circuits was implemented on a four-qubit spin system. The research results were published in the internationally renowned journal Physical Review Letters under the title "Experimental Quantum Principal Component Analysis via Parameterized Quantum Circuits".

Principal component analysis (PCA) is a commonly used and time-consuming unsupervised learning algorithm in machine learning.

This method uses orthogonal transformation to convert the observation data represented by linearly related variables into a few data represented by linearly independent variables. The linearly independent variables are called principal components.

This algorithm is mainly used to discover the basic structure in the data, that is, the relationship between variables in the data.

In 2014, Lloyd, Mohseni and Rebentros proposed the quantum principal component analysis algorithm (qPCA) and published it in the internationally renowned journal Nature Physics. It can exponentially speed up the classic principal component analysis algorithm. However, implementing this algorithm requires a large amount of experimental resources, resulting in

The proposal of quantum principal component analysis still lacks experimental proof.

Figure: Experimental flow chart of face recognition using quantum principal component analysis. Figure: Experimental results of classical-quantum hybrid control method. Figure (a) shows the optimization results of the objective function with the number of iterations. Figure (b) shows the eigenvectors obtained from the experiment and

The theoretical eigenvector similarity continues to increase through iteration. The eigenvalue obtained experimentally in Figure (c) continues to approach the ideal eigenvalue with iteration. The dotted line is the theoretical eigenvalue.

To this end, the research team proposed a quantum principal component algorithm that is very friendly to the current experimental system based on parameterized quantum circuits (PQC), which can diagonalize unknown quantum states to extract their eigenvalues ??and eigenvectors.

PQC usually consists of fixed gates (such as controlled NOT) and adjustable gates (such as qubit rotation).

PQC formalizes the target problem as a parameter optimization problem and uses a hybrid system of quantum and classical hardware to find approximate solutions. It has become a popular tool for currently studying quantum problems.

For example, the variational quantum eigensolver (VQE) has been used to search for the ground state of the molecular Hamiltonian.

The research team further applied the algorithm to the face recognition problem, iteratively optimized PQC through a classical-quantum hybrid control method, and implemented a small-scale quantum version of the face recognition experiment in a nuclear magnetic resonance quantum simulator.

The objective function and gradient are measured on a quantum processor, and the storage and update of parameters and face recognition are implemented on a classical computer.

This innovative achievement experimentally implements the quantum principal component analysis algorithm for the first time through the method of parametric quantum circuits, and finds a new way for the theoretical and experimental application research of quantum principal component analysis.

In this research result, Xin Tao is the first author and corresponding author, Che Liangyu, a doctoral candidate in the Department of Physics, is the first and co-first author, and Li Jun and Lu Dawei are the co-corresponding authors.

Southern University of Science and Technology is the first unit of the paper.

This research has also received strong support from the Ministry of Science and Technology, the National Natural Science Foundation of China, the Guangdong Provincial Department of Science and Technology, the Shenzhen Municipal Science and Technology Innovation Commission, and the Southern University of Science and Technology.