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This study investigates the makespan minimization problem that arises when compiling a general class of quantum algorithms into near-term quantum hardware. The problem is referred to as quantum circuit compilation problem (QCCP). Two new heuristics are proposed for solving the problem. Firstly, a rollout based sequential decision making approach is investigated. This heuristic decides on which operation to schedule next based on the makespan projection given by a guiding priority rule. Secondly, a stochastic version of rollout heuristic is proposed which iteratively switches between rollout and a simple priority rule to explore the search space. The two proposed heuristics are able to show improvement in makespan across a range of instance sizes and characteristics.