The principal possibility of implementation of the simplest logical operations on picosecond timescale has been confirmed by both analytical and numerical modelling of dynamics of superconducting flux qubit in magnetic field. Individual current pulses, propagating through distributed Josephson junctions and transmission lines of rapid single flux quantum logic have been proved to be an instrument for realization of such an operation. Using of flux-qubit interaction affecting the so-called X-components of the «Josephson atom» Hamiltonian has been shown to be the way of realization of the simplest coherent manipulations on «Josephson atom» states. The methods of approximate analytical (by matrix exponent) and exact numerical research of magnetic moment dynamics in two- and threelevel systems have been developed for the cases of both oscillating (  1 ) and unipolar ( 1) magnetic fields. Developed methods have been used for modelling of the «Write» logical operation on: a) Josephson quantum bit by individual unipolar magnetic field pulses on picosecond timescale ( ~ 1 10 ps ), b) atomic system magnetic moment by oscillating magnetic field on picosecond timescale ( ~ 1 10 ps ), c) Josephson quantum bit by oscillating magnetic field on picosecond timescale (  ~ 40 ps ). Mathematical analogy between quantum and classical magnetic moment dynamics in external magnetic field has been demonstrated within a designations under the conditions on duration of magnetic field pulse, which should be long enough for oscillating field (   1 ) and should be short enough for unipolar field (  1 ). Principal impossibility of «Write» logical operation implementation has been demonstrated for intermediate values of  ~ 1.