Quantum and Classical Algorithms for Bounded Distance Decoding

Richard Allen; Ratip Emin Berker; Sílvia Casacuberta; Michael Gul

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arXiv · 2203.05019

Quantum and Classical Algorithms for Bounded Distance Decoding

Richard Allen·Ratip Emin Berker·Sílvia Casacuberta·Michael Gul

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Abstract

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 $\lambda_1 2^{-\Omega(\sqrt{k \log q})}$-BDD in polynomial time for lattices of periodicity $q$, finite group rank $k$, and shortest lattice vector length $\lambda_1$. 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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BibTeX RIS

Richard Allen, Ratip Emin Berker, Sílvia Casacuberta, Michael Gul. 2022-02-18. Quantum and Classical Algorithms for Bounded Distance Decoding. https://arxiv.org/abs/2203.05019

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