A mixed-integer program for circuit execution time minimization with precedence constraints

We present a mixed-integer programming (MIP) model for scheduling quantum circuits to minimize execution time. Our approach maximizes parallelism by allowing non-overlapping gates (those acting on distinct qubits) to execute simultaneously. Our methods apply to general circuits with precedence constraints. First, we derive closed-formulas for the execution time of circuits generated by ma-QAOA on star graphs for a layered, greedy, and MIP schedules. We then compare the MIP schedule against layered and greedy scheduling approaches on the circuits generated by ma-QAOA for solving the MaxCut problem on all non-isomorphic connected graphs with 3-7 vertices. These experiments demonstrate that the MIP scheduler consistently results in shorter circuit execution times than greedy and layered approaches, with up to 24\% savings.