Manipulations with qubit states by short control pulses: the interpolation method for evolution operator and fidelity

In this article the dynamics of the qubits states based on solution of the time-dependent Schrödinger equation is investigated. Using the Magnus method we obtain an explicit interpolation representation for the propagator, which allows to find wave function at an arbitrary time. To illustrate the effectiveness of the approach, the population of the levels a single and two coupled qubits have been calculated by applying the Magnus propagator and the result have been compared with the numerical solution of the Schrödinger equation. As a measure of the approximation of the wave function, we calculate fidelity, which indicates proximity when the exact and approximate evolution operator acts on the initial state. We discuss the possibility of extending the developed methods to multi-qubits system, when high-speed calculation methods of the operators of evolution is particularly relevant. (paper)