Parallel BFS Implementing Optimized Decomposition of Space and kMC simulations for Diffusion of Vacancies for Quantum Storage

We present a novel breadth-first search (BFS) algorithm based on the notion of temporal evolvability that is adaptable to various multicore architectures for simulating diffusion of vacancies in hexagonal silicon carbide (4H-SiC) for information storage. The algorithm is formulated in the semi-ring algebraic framework of BFS and incorporates a real-space grid decomposition to optimize the number of nodes that are evaluated in each frontier of the evolution. Scaling characteristics are first evaluated from performance runs for two formulations: (i) recursive depth-first search (DFS) and (ii) semi-ring implementations of BFS. The results for a real-space grid implementation of BFS are then presented. We demonstrate that each new iteration reduces the communication overhead, enhancing performance. A comparison of the real-space grid based BFS with a kinetic Monte Carlo (kMC) algorithm is also presented for the case of diffusion without the influence of the Coulomb interaction. The efficient parallel implementations of this latter approach enables simulations of larger systems than those studied before.