有限距离译码的量子和经典算法
Quantum and Classical Algorithms for Bounded Distance Decoding
摘要：
在本文中，我们提供了一个全面的概述最近的争论量子与经典的有界距离解码（BDD）的可解性。具体来说，我们回顾了Eldar和Hallgren [EH 22]，[Hal 21]的工作，证明了一个量子算法在多项式时间内求解周期性$q$，有限群秩$k$和最短格向量长度$λ_1$的格的$λ_1 2^{-Ω(\sqrt{k \log q})}$ -BDD。随后，我们证明了[DvW 21 a]，[DvW 21 b]的结果，比原来的工作更详细和详细。也就是说，我们表明，存在一个确定性的，经典的算法实现相同的结果。
英文摘要：
In this paper, we provide a comprehensive overview of a recent debate over the quantum versus classical solvability of bounded distance decoding (BDD). Specifically, we review the work of Eldar and Hallgren [EH22], [Hal21] demonstrating a quantum algorithm solving $λ_1 2^{-Ω(\sqrt{k \log q})}$-BDD in polynomial time for lattices of periodicity $q$, finite group rank $k$, and shortest lattice vector length $λ_1$. Subsequently, we prove the results of [DvW21a], [DvW21b] with far greater detail and elaboration than in the original work. Namely, we show that there exists a deterministic, classical algorithm achieving the same result.
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