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.

翻译：本文在现有文献相同假设条件下，重新审视了用于求解含噪线性问题的量子算法。本研究的发现包括：一方面，将量子傅里叶变换的适用范围扩展至环上容错学习问题，该问题在Grilo等人首次设计出利用量子样本求解含噪线性问题的多项式时间量子算法后一直悬而未决；另一方面，本文亦证明若提供先前研究所用的量子样本，则对于短整数解问题及尺寸约化容错学习问题存在高效的经典算法。