Abstract

A mathematical model and a computational method for extracting the inductances and spatial distributions of supercurrents in an adiabatic artificial neuron are proposed. This neuron is a multilayer structure containing Josephson junctions. The computational method is based on the simultaneous solution of the London equations for the currents in the superconductor layers and Maxwell’s equations, which determine the spatial distribution of the magnetic field, and on a model of the current sheet, which accounts for the finite depth of conducting layers and current contacts. This approach effectively takes into account interlayer contacts and Josephson junctions in the form of distributed current sources. The resulting equations are solved using the finite element method with large dense matrices. Computational results for the model of neuron with a sigmoid transfer function are presented. To optimize the device design, both the operating (planned in the first phase of the design) and parasitic inductances and the distribution of currents are calculated. The proposed methodology and software can be used for simulating a wide range of superconductor devices based on superconducting quantum interference devices.

中文翻译：

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超导神经元模型中电感和电流空间分布的提取

摘要

提出了一种用于提取绝热人工神经元中超电流的电感和空间分布的数学模型和计算方法。这个神经元是一个包含约瑟夫森连接的多层结构。计算方法基于超导体层中电流的伦敦方程和麦克斯韦方程的联立解，确定磁场的空间分布，并基于电流片的模型，该模型解释了超导体层中的有限深度导电层和电流触点。这种方法有效地考虑了分布式电流源形式的层间接触和约瑟夫森结。所得到的方程使用有限元方法在大的密集矩阵中求解。给出了具有 sigmoid 传递函数的神经元模型的计算结果。为了优化器件设计，计算工作（在设计的第一阶段计划）和寄生电感以及电流分布。所提出的方法和软件可用于模拟各种基于超导量子干涉装置的超导装置。