Qubo model for the Closest Vector Problem. (arXiv:2304.03616v1 [cs.CR])

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 $O(n(\log(n)+\log(b)))$.

absolute binary generator lambda length log matrix optimization problem prove