In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take these imperfections into account is considered. However, to implement such a procedure one should have a detailed information about the errors. An approach for obtaining the partial information about them is proposed. It is based on the tomography of the ideal identity gate. This gate could be implemented by performing the measurement right after the initial state preparation. By using the result of the identity gate tomography we were able to significantly improve further QPT procedures. The proposed approach has been tested experimentally on the IBM superconducting quantum processor. As a result, we have obtained an increase in fidelity from 89% to 98% for Hadamard transformation and from 77% to 95% for CNOT gate.

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.

The Schmidt decomposition and the correlational analysis based on it make it possible to identify statistical dependences between various subsystems of a single physical system. The systems under consideration can be both quantum states and classical probability distributions. In this study, two different physical systems are considered: quantum Schrödinger cat states and double-slit interference of microparticles. It is shown that the considered systems have a single internal structure and can be described in general terms of interfering alternatives. An effective approach is developed that allows us to calculate optical characteristics of interference such as visibility and coherence. It is shown that the scalar product of the states of the environment of interfering alternatives acts as a natural generalization of the classical complex parameter of the coherence of light oscillations, which determines the visibility of the interference pattern. A simple quantitative relationship is obtained between the visibility of the interference pattern and the Schmidt number, which determines the level of connection between a quantum system and its environment. The developed approaches are generalized to the case of multidimensional Schrödinger cat states.

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