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Recently, the makespan-minimization problem of compiling a general class ofquantum algorithms into near-term quantum processors has been introduced to theAI community. The research demonstrated that temporal planning is a strongapproach for a class of quantum circuit compilation (QCC) problems. In thispaper, we explore the use of constraint programming (CP) as an alternative andcomplementary approach to temporal planning. We extend previous work byintroducing two new problem variations that incorporate importantcharacteristics identified by the quantum computing community. We applytemporal planning and CP to the baseline and extended QCC problems as bothstand-alone and hybrid approaches. Our hybrid methods use solutions found bytemporal planning to warm start CP, leveraging the ability of the former tofind satisficing solutions to problems with a high degree of task optionality,an area that CP typically struggles with. The CP model, benefiting frominferred bounds on planning horizon length and task counts provided by the warmstart, is then used to find higher quality solutions. Our empirical evaluationindicates that while stand-alone CP is only competitive for the smallestproblems, CP in our hybridization with temporal planning out-performsstand-alone temporal planning in the majority of problem classes.

Comparing and Integrating Constraint Programming and Temporal Planning for Quantum Circuit Compilation