The present study is devoted to development of a technique for numerical simulation of the wave function dynamics the single Josephson qubits and arrays of noninteracting qubits controlled by ultra-short pulses. We wish to demonstrate the feasibility of a new principle of basic logical operations on the picosecond timescale. The influence of the unipolar pulse ("fluxon") form on the evolution of the state during the execution of the quantum onequbit operations - "NOT", "READ" and "{formula}"-is investigated in the presence of decoherence. In the array of non interacting qubits, the question of the influence of the spread of their energy parameters (tunnel constants) is studied. It is shown that a single unipolar pulse can control a huge array of artificial atoms with 10% spread of geometric parameters in the array.
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