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Abstract: Even as quantum computers continue to increase in number of qubits, high error rates limit the size of quantum circuits that can be executed. This results in low throughput and poor resource utilization on quantum computers. To address this, recent research has focused on extending circuit optimization and compilation techniques to support simultaneous execution of quantum circuits (i.e. quantum parallelism). While much work has been spent developing parallel mapping and gate scheduling techniques, there are few approaches to the problem of parallel job scheduling on quantum computers. There are several constraints that make quantum job scheduling different from classical scheduling. We propose a scheduling algorithm, QGroup, for parallelizing circuits of different lengths and shot counts while mitigating parallel slowdowns due to measurement synchronization. QGroup achieves a better parallelism-runtime tradeoff, with significant speedup and fidelity increase over existing methods. QGroup achieves improvement in both fidelity and runtime for noise-sensitive, diverse workloads.