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| Domain | Problem Statement | JUQ103‑Enabled Solution | |--------|-------------------|--------------------------| | | Compute ground‑state energies of strongly correlated electron systems. | VQE with a custom UCCSD ansatz, distributed over 128 classical nodes; quantum sub‑routines executed on a 27‑qubit superconducting processor. | | Finance | Portfolio optimization under stochastic constraints. | QAOA with adaptive depth; error‑mitigated results feed a Monte‑Carlo simulation pipeline. | | Machine Learning | Train a hybrid quantum‑classical classifier on high‑dimensional image data. | Parameterized quantum circuit as a feature map; gradients computed via JUQ103’s AD engine; classical optimizer (Adam) runs on GPU. | | Logistics | Solve large‑scale vehicle‑routing problems with time windows. | Decompose problem into sub‑problems solved via QAOA; results aggregated using classical linear programming. | | Education | Provide students with a sandbox for experimenting with quantum algorithms. | One‑click Docker image with JUQ103 + simulators; auto‑graded notebooks for assignments. | | VQE with a custom UCCSD ansatz, distributed