Workflow-Level Scheduling of Hybrid Quantum-Classical Applications on Heterogeneous Resources

Hybrid quantum--classical applications involve coordinated execution of quantum and classical tasks across heterogeneous resources. We model such applications as directed acyclic graphs (DAGs) and formulate workflow scheduling as a mixed-integer linear programming (MILP) problem that captures task dependencies, heterogeneous resource assignment, communication costs, makespan, and tardiness. To account for the the stochastic nature of QPU execution times, we additionally develop a robust counterpart based on budgeted uncertainty. The proposed framework enables workflow-level optimization beyond the performance of individual quantum or classical components. We evaluate the approach using Sample-Based Quantum Diagonalization (SQD) and the Quantum Approximate Optimization Algorithm (QAOA), illustrating how optimized scheduling can improve resource utilization and reduce end-to-end execution time in hybrid quantum--classical environments.