A Low Complexity Quantum Principal Component Analysis Algorithm

In this paper, we propose a low complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal components of the data matrix, rather than all components of the data matrix, to quantum registers, so that samples of measurement required can be reduced considerably. However, the major advantage of our qPCA over the state-of-the-art qPCA is that it requires much less quantum gates. In addition, it is more accurate due to the simplification of the quantum circuit. We implement the proposed qPCA on the IBM quantum computing platform, and the experimental results are consistent with our expectations.