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.
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ACKNOWLEDGMENTS
We are grateful to V. Bol’ginov for fruitful discussions of possible implementations of models of artificial neurons.
Funding
This work was supported by the Russian Science Foundation, project no. 20-12-00130 (the development of numerical algorithms for extracting self- and mutual inductances for superconducting circuits), by the Russian Foundation for Basic Research, project no. 19-02-00981 (the development of a model of superconducting neuron), and by grant MD-186.2020.8 of the President of the Russian Federation.
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Translated by A. Klimontovich
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Bakurskiy, S.V., Klenov, N.V., Kupriyanov, M.Y. et al. Extraction of Inductances and Spatial Distributions of Currents in a Model of Superconducting Neuron. Comput. Math. and Math. Phys. 61, 854–863 (2021). https://doi.org/10.1134/S096554252105002X
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DOI: https://doi.org/10.1134/S096554252105002X