  Most quantum compiler transformations and qubit allocation techniques to date
are either peep-hole focused or rely on sliding windows that depend on a number
of external parameters. Thus, global optimization criteria are still lacking.
In this paper we explore the synergies and impact of affine loop
transformations in the context of qubit allocation and mapping. With this goal
in mind, we have implemented a domain specific language and source-to-source
compiler for quantum circuits that can be directly described with affine
relations. We conduct an extensive evaluation spanning 8 quantum circuits taken
from the literature, 3 distinct coupling graphs, 4 affine transformations
(including the Pluto dependence distance minimization and Feautrier's minimum
latency algorithms), and 4 qubit allocators. Our results demonstrate that
affine transformations using global optimization criteria can cooperate
effectively in several scenarios with quantum qubit mapping algorithms to
reduce the circuit depth, size and allocation time.
