This work contributes a generalized model for quantum computation
called NChooseK. NChooseK is based on a single parametrized primitive
suitable to express a variety of problems that cannot be
solved efficiently using classical computers but may admit an
efficient quantum solution. We implement a code generator
that, given arbitrary parameters for N and K, generates code suitable
for execution on IBM Q quantum hardware. We assess the performance
of the code generator, limitations in the size of circuit depth and
number of gates, and propose optimizations. We identify future work to improve
efficiency and applicability of the NChooseK model.