Realizing Unstructured PDE Forecasting on Superconducting Quantum Processors

arXiv:2611.10351v1 Announce Type: new Abstract: Simulating high dimensional unstructured Partial Differential Equations (PDEs) with quantum processors is a major challenge with significant potential benefit. Existing methods have been demonstrated at small qubit counts, on simplifications of realistic problems. We implement a quantum reservoir network (QRN) for forecasting high-dimensional unstructured PDEs using up to 52 qubits on IBM superconducting hardware. Our method is gradient-free and does not suffer from the challenges of variational quantum algorithms. Instead, the QRN provides a large kernel space, up to 2^52 dimensions and beyond the reach of exact classical simulation, that remains useful under current hardware noise levels.