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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables
Can a quantum PDE algorithm avoid the polynomial cost of resolving a fine spatial mesh? For standard fixed-order discretizations, direct classical methods require work polynomial in $h^{-1}$, or equivalently in the number of spatial degrees of freedom $N_h=Θ(h^{-d})$. Direct quantum implementations
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