  Classical machine learning theory and theory of quantum computations are
among of the most rapidly developing scientific areas in our days. In recent
years, researchers investigated if quantum computing can help to improve
classical machine learning algorithms. The quantum machine learning includes
hybrid methods that involve both classical and quantum algorithms. Quantum
approaches can be used to analyze quantum states instead of classical data. On
other side, quantum algorithms can exponentially improve classical data science
algorithm. Here, we show basic ideas of quantum machine learning. We present
several new methods that combine classical machine learning algorithms and
quantum computing methods. We demonstrate multiclass tree tensor network
algorithm, and its approbation on IBM quantum processor. Also, we introduce
neural networks approach to quantum tomography problem. Our tomography method
allows us to predict quantum state excluding noise influence. Such
classical-quantum approach can be applied in various experiments to reveal
latent dependence between input data and output measurement results.
