An algorithm for estimating the amplitude of the output signal passing through an inductively coupled qubit-resonator system is proposed. In the study of the qubit parameters, multiple experimentally obtained results are averaged. A method for calculating the most accurate value of the amplitude of the output signal using complete sufficient statistics, verified using simulation, has been developed. One of the practical applications of this algorithm is to determine the loss of the relaxation energy of a qubit when its state changes when interacting with pulsed signals.

The effective estimations of the linear approximated volt-ampere curve parameters have been developed using the maximum-likelihood method for the case of random measuring signal nature. Numerical modeling has been provided to prove the efficiency of the obtained estimations and the expediency to be applied in the laboratory experiments.

Statistical algorithms for measurement data processing were developed to perform automation of superconducting quantum bits experimental investigations. The first algorithm is aimed to detect the q-bit quantum state changes. The second one is aimed to obtain the efficient resonance frequency estimation for the resonator coupled to a q-bit. All the results were obtained using the statistical approach that employs random nature of measurement data to obtain the optimal estimation rules and statistical hypotheses testing. The numerical modeling was carried out. The results of numerical modeling confirmed the efficiency and expediency of the algorithms obtained.

Statistical model of measuring signals in systems of time domain reflectometry was proposed. On the basis of this reflectometry the estimates of reflected signal parameters were obtained by means of complete sufficient statistics. Simulation modeling, which confirmed the consistency and efficiency of the estimates, was conducted. Based on the principle of unbiasedness the synthesis of uniformly most powerful unbiased detection algorithm of change in slope parameter of linearly-varying measuring signal was carried out. Simulation modeling has indicated the efficiency of the algorithm and expediency of its application to detect small changes in the measuring signal parameters of time domain reflectometry systems.