The goal of this work is to find ways of enhancing the speed of computer memory cells by using structures that employ operating principles other than those of traditional semiconductors’ schemes. One of the applications of the unique properties of Josephson structures is their usage in novel superfast computer memory cells. Thanks to their high working characteristic frequencies close to 1 THz, the Josephson structures are most promising candidates to be used in petaflop computers. Moreover, both Josephson cryotrons and Josephson SQUIDs can be used in qubits, which are basic units in quantum computers, and also for describing a macroscopic quantum behavior, for example, during read-out processes in quantum computations. In the present work, we have created a mathematical model of transition processes in Josephson cryotrons during direct, “1” → ”0”, as well as inverse, “0” → “1”, logical transitions. We have considered controlling the logical state of Josephson memory cells based on Josephson tunneling junctions of the S-I-S type via external current pulses. By means of mathematical modelling, we have studied transition processes in cryotrons during the change of their logical state
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