Qubo model for the Closest Vector Problem

04/07/2023

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by   Eduardo Canale, et al.

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In this paper we consider the closest vector problem (CVP) for lattices Λ⊆ℤ^n given by a generator matrix A∈ℳ_n× n(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))).