Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables
The paper addresses how quantum algorithms can estimate observables for parabolic partial differential equations (PDEs) without suffering from high computational costs related to a fine spatial mesh. It introduces a multilevel quantum algorithm that uses coherent encoding of fine-to-coarse cancellations to achieve an exponential reduction in mesh dependence, leading to an overall complexity of Oe(1 + (Tϵ)−1).