As quantum computing moves from isolated experiments toward integration with large-scale workflows, the integration of quantum devices into HPC systems has gained much interest. Quantum cloud providers expose shared devices through first-come first-serve queues where a circuit that executes in 3 seconds can spend minutes to an entire day waiting. Minimizing this overhead while maintaining execution fidelity is the central challenge of quantum cloud scheduling, and existing approaches treat the two as separate concerns. We present Qurator, an architecture-agnostic quantum-classical task scheduler that jointly optimizes queue time and circuit fidelity across heterogeneous providers. 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, all of which render classical scheduling techniques ineffective. Fidelity is estimated through a unified logarithmic success score that reconciles incompatible calibration data from IBM, IonQ, IQM, Rigetti, AQT, and QuEra 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, Qurator stays within 1% of the highest-fidelity baseline at low load while achieving 30-75% queue time reduction at high load, at a fidelity cost bounded by a user-specified target.

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