What is Density Matrix

Quantum chemistry was a compute intensive field from the beginning. It was also an early adopter of parallel computing, and hence, has more than twenty years of experience with parallelism. However, recently parallel computing has seen dramatic changes, such as the rise of multi-core architectures, hybrid computing, and the prospect of exa-scale machines requiring 1 billion concurrent threads. It is doubtful that current approaches can address the challenges ahead. As a result, the field finds itself at a crossroads, facing the challenge to successfully identify the way forward. This chapter tells a story in two parts. First, the achievements to date are considered, offering insights learned so far. Second, we look at paradigms based on directed acyclic graphs (DAG). The computer science community is strongly advocating this paradigm, but the quantum chemistry community has no experience with this approach. Therefore recent developments in that area will be discussed and their suitability for future parallel quantum chemistry computing demands considered.