Automatic decomposition of quantum circuits onto small quantum machines

In the last few years, there has been a great deal of progress in making real world quantum computers, but the number of physical qubits is remains too small to run larger problem sizes on these computers. The consequence is that the few practical uses of these computers have been problems that only require small amount of working memory to solve. The question we wish to explore relates to how to run algorithms which have larger memory requirements. In particular, there are some theoretical results that promise that if there is low global connectivity between that memory, the circuit can be decomposed into smaller, more densely connected problems that can be run with a smaller numbers of physical qubits. We wish to explore the more applied side of this area by looking at algorithms and trying to exploit features which allow lower qubit requirements.