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

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