论文标题
有限距离解码的量子和经典算法
Quantum and Classical Algorithms for Bounded Distance Decoding
论文作者
论文摘要
在本文中，我们详细概述了有关量子距离解码（BDD）的量子与经典溶解性的最新辩论。具体而言，我们回顾了Eldar和Hallgren [EH22]的工作，[HAL21]演示了求解$λ_12^{ - ω（\ sqrt {k \ log q}} $ - bdd in Potiality $ q $ Q $ Q $ $ k $ k $ k $ k $ k $ k $ k的量子算法$λ_12^{ - ω（\ sqrt {k \ log q}）} $ - bdd。随后，我们证明了[dvw21a]，[dvw21b]的结果，其细节和详细说明要比原始工作更大。也就是说，我们表明存在一种确定性的经典算法，可实现相同的结果。
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.
