Quantum improvement in Spatial Discretization

Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically improves spatial discretization within these constraints. Implemented in the quantum software library Pennylane, our algorithm bridges the gap from theoretical models to tangible quantum circuitry. The approach promises enhanced efficiency in quantum spatial analysis, with simulations and hardware experiments validating its potential.