Resonant quantum principal component analysis

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