Graphical probabilistic inference for ground state and near-ground state computing in QCA circuits

We propose a graphical probabilistic Bayesian Network based modeling and inference scheme for Clocked Quantum-dot Cellar Automata (QCA) based circuit design that not only specify just the binary discrete states (0 or 1) of the individual cells, but also the probabilities of observing these states for Ground (Most Likely) state computing. The nodes of the Bayesian Network (BN) are the random variables, representing individual cells, and the links between them capture the dependencies among them. The modeling exploits the spatially local nature of the dependencies and the induced causality from the wave propagation and clocking schemes to arrive at a minimal, factored, representation of the overall joint probability of the cell states in terms of local conditional probabilities. This BN model allows us (1) to estimate the most likely (or ground) state configuration and the next lowest-energy configuration that results in output errors and (2) to show how weak spots in clocked QCA circuit designs can be found using these BN models by comparing the (most likely) ground state configuration with the next most likely energy state configuration that results in output error.