  Recent advancements in quantum annealing hardware and numerous studies in
this area suggests that quantum annealers have the potential to be effective in
solving unconstrained binary quadratic programming problems. Naturally, one may
desire to expand the application domain of these machines to problems with
general discrete variables. In this paper, we explore the possibility of
employing quantum annealers to solve unconstrained quadratic programming
problems over a bounded integer domain. We present an approach for encoding
integer variables into binary ones, thereby representing unconstrained integer
quadratic programming problems as unconstrained binary quadratic programming
problems. To respect some of the limitations of the currently developed quantum
annealers, we propose an integer encoding, named bounded- coefficient encoding,
in which we limit the size of the coefficients that appear in the encoding.
Furthermore, we propose an algorithm for finding the upper bound on the
coefficients of the encoding using the precision of the machine and the
coefficients of the original integer problem. Finally, we experimentally show
that this approach is far more resilient to the noise of the quantum annealers
compared to traditional approaches for the encoding of integers in base two.
