Quantum algorithms for solving noisy linear problems are reexamined, under the same assumptions taken from the existing literature. The findings of this work include on the one hand extended applicability of the quantum Fourier transform to the ring learning with errors problem which has been left open by Grilo et al., who first devised a polynomial-time quantum algorithm for solving noisy linear problems with quantum samples. On the other hand, this paper also shows there exist efficient classical algorithms for short integer solution and size-reduced learning with errors problems if the quantum samples used by the previous studies are given.

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