  We present QFAST, a quantum synthesis tool designed to produce short circuits
and to scale well in practice. Our contributions are: 1) a novel representation
of circuits able to encode placement and topology; 2) a hierarchical approach
with an iterative refinement formulation that combines "coarse-grained" fast
optimization during circuit structure search with a good, but slower,
optimization stage only in the final circuit instantiation stage. When compared
against state-of-the-art techniques, although not optimal, QFAST can generate
much shorter circuits for "time dependent evolution" algorithms used by domain
scientists. We also show the composability and tunability of our formulation in
terms of circuit depth and running time. For example, we show how to generate
shorter circuits by plugging in the best available third party synthesis
algorithm at a given hierarchy level. Composability enables portability across
chip architectures, which is missing from the available approaches.
