We present Qurator, a quantum-classical task scheduler that jointly optimizes queue time and circuit fidelity across heterogeneous architectures. Qurator models hybrid workloads as dynamic DAGs with explicit quantum semantics, including entanglement dependencies, synchronization barriers, no-cloning constraints, and circuit cutting and merging decisions. Fidelity is estimated through a unified logarithmic success score that reconciles incompatible calibration data from IBM, IonQ, IQM, Rigetti, AQT, Pasqal and other providers into a canonical set of gate error, readout fidelity, and decoherence terms. We evaluate Qurator on a simulator driven by four months of real queue data using circuits from the Munich Quantum Toolkit benchmark suite. Across load conditions from 5 to 35,000 quantum tasks with up to 120,000 classical tasks, Qurator stays within 1% of the highest-fidelity baseline at low load, achieves 30-75% queue time reduction at high load, all at a fidelity cost bounded by a user-specified target while improving on list and fair schedulers as well as state of the art schedulers on both metrics.

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