Abstract
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate long-time integration. These hardware bottlenecks confine quantum PDE solvers to low-fidelity regimes despite their theoretical potential for computational speedup. We introduce a multifidelity learning framework that corrects coarse quantum solutions to high-fidelity accuracy using sparse classical training data, facilitating the path toward practical quantum utility for scientific computing. The approach trains a low-fidelity surrogate on abundant quantum solver outputs, then learns correction mappings through a multifidelity neural architecture that balances linear and nonlinear transformations. Demonstrated on benchmark nonlinear PDEs including viscous Burgers equation and incompressible Navier-Stokes flows via quantum lattice Boltzmann methods, the fra