  This paper examines QAOA in the context of parity network synthesis. We
propose a pair of algorithms for parity network synthesis and linear circuit
inversion. Together, these algorithms can build the diagonal component of the
QAOA circuit, generally the most expensive in terms of two qubit gates. We
compare the CNOT count of our strategy to off-the-shelf compiler tools for
random, full, and graph-based optimization problems and find that ours
outperforms the alternatives.
