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As cloud quantum computing gains broader acceptance, a growing quantity of researchers are directing their focus towards this domain. Nevertheless, the rapid surge in demand for cloud-based quantum computing resources has led to a scarcity, which in turn hampers users from achieving optimal satisfaction. Therefore, cloud quantum computing service providers require a unified analysis and scheduling framework for their quantum resources and user jobs to meet the ever-growing usage demands. This paper introduces a new multi-programming scheduling framework for quantum computing in a cloud environment. The framework addresses the issue of limited quantum computing resources in cloud environments and ensures a satisfactory user experience. It introduces three innovative designs: 1) Our framework automatically allocates tasks to different quantum backends while ensuring fairness among users by considering both the cloud-based quantum resources and the user-submitted tasks. 2) Multi-programming mechanism is employed across different quantum backends to enhance the overall throughput of the quantum cloud. In comparison to conventional task schedulers, our proposed framework achieves a throughput improvement of more than two-fold in the quantum cloud. 3) The framework can balance fidelity and user waiting time by adaptively adjusting scheduling parameters.
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