In this paper we consider the closest vector problem (CVP) for lattices $\Lambda \subseteq \mathbb{Z}^n$ given by a generator matrix $A\in \mathcal{M}_{n\times n}(\mathbb{Z})$. Let $b>0$ be the maximum of the absolute values of the entries of the matrix $A$. We prove that the CVP can be reduced in polynomial time to a quadratic unconstrained binary optimization (QUBO) problem in $O(n^2(\log(n)+\log(b)))$ binary variables, where the length of the coefficients in the corresponding quadratic form is $O(n(\log(n)+\log(b)))$.

翻译：本文研究由生成矩阵$A\in \mathcal{M}_{n\times n}(\mathbb{Z})$给出的格$\Lambda \subseteq \mathbb{Z}^n$上的最近向量问题(CVP)。设$b>0$为矩阵$A$元素绝对值的最大值。我们证明，CVP可以在多项式时间内归约为一个具有$O(n^2(\log(n)+\log(b)))$个二元变量的二次无约束二元优化(QUBO)问题，其中相应二次型系数的长度为$O(n(\log(n)+\log(b)))$。