  Recently, the makespan-minimization problem of compiling a general class of
quantum algorithms into near-term quantum processors has been introduced to the
AI community. The research demonstrated that temporal planning is a strong
approach for a class of quantum circuit compilation (QCC) problems. In this
paper, we explore the use of constraint programming (CP) as an alternative and
complementary approach to temporal planning. We extend previous work by
introducing two new problem variations that incorporate important
characteristics identified by the quantum computing community. We apply
temporal planning and CP to the baseline and extended QCC problems as both
stand-alone and hybrid approaches. Our hybrid methods use solutions found by
temporal planning to warm start CP, leveraging the ability of the former to
find satisficing solutions to problems with a high degree of task optionality,
an area that CP typically struggles with. The CP model, benefiting from
inferred bounds on planning horizon length and task counts provided by the warm
start, is then used to find higher quality solutions. Our empirical evaluation
indicates that while stand-alone CP is only competitive for the smallest
problems, CP in our hybridization with temporal planning out-performs
stand-alone temporal planning in the majority of problem classes.
