  Principal component analysis 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
largest eigenvalues. However, due to the substantial resource requirement, its
experimental implementation remains challenging. Here, we develop a resonant
analysis algorithm with the 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$\times$4 density matrix, with the efficiency of
86.0% and fidelity of 0.90. This work shows the speed-up ability of quantum
algorithm in dimension reduction of data and thus could be used as part of
quantum artificial intelligence algorithms in the future.
