Block encoding of the 3D heterogeneous Poisson matrix enables quantum linear system algorithms to solve discretized fracture flow problems with runtime O(N^{2/3} polylog N log(1/ε)) and exponential memory savings over classical O(N log N log(1/ε)) methods.
(dind, mhi, mlo) does not satisfy any of the above conditions
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Block encoding the 3D heterogeneous Poisson equation with application to fracture flow
Block encoding of the 3D heterogeneous Poisson matrix enables quantum linear system algorithms to solve discretized fracture flow problems with runtime O(N^{2/3} polylog N log(1/ε)) and exponential memory savings over classical O(N log N log(1/ε)) methods.