Simple modeling of stochastic classical nano-bit data corruption: Probability distribution consideration

Motivated by a real-world application of quantum-dot cellular automata (QCA) and with the help of Monte-Carlo simulations and analytic continuum theory, we have studied the corruption or error process of a binary nano-bit model resulting from an interaction with stochastically independent Brownian agents (BAs). Besides, the more specific link to a real-world application, in this work, we have extended the scope of the study and have used the new technique to reproduce results from previous works by Newman and Triampo [Phys. Bev. E 59, 5172 (1999) and Phys. Rev. E 60, 1450 (1999)]. The new findings include 1) the effect of a "patch" or "cluster" of bits on the simulation results, 2) the log-normal vs. normal distribution of the local bit density, and 3) new results for local bit corruption in two dimensions. The theory is compared with the results of simulations, and good agreement is found. The connection of this binary nano-bit model with the real world is discussed, especially in the context of molecular electronics and the quantum-dot cellular automata paradigm. With model extension such as taking into account a more realistic correlation between bits, our hope is that this work may contribute to an understanding of the soft error or the corruption of data stored in nano-scale devices.