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. 2017 Sep 12;7:11276. doi: 10.1038/s41598-017-11732-w

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) The truth table and the physical connection governing the interactions between spin units. Here x _v,j acts as the input to x _u,i and they lie either on the same row or same column. The MTJ in each device has been replaced by a variable resistance R _MTJ. (b) Top panel: the variation of V _OUT with x _v,j, obtained from a behavioral model (V _OUT = A tanh (Bx _u,i)). Bottom panel: the switching probability of x _u,i vs applied voltage, V _IN (stochastic LLG simulation). The polarity of this voltage tends to switch x _u,i from ‘1’ to ‘0’. (c) Top panel: a sample simulation of x _u,i for two cases: x _v,j = ‘0’ and ‘1’. Bottom panel: A plot of the Hamiltonian cycle, H _A with time. H _A is concentrated around 0, since the interactions are designed to make each product term x _v,j x _u,i = 0.