Recent advancements in quantum annealing hardware and numerous studies inthis area suggests that quantum annealers have the potential to be effective insolving unconstrained binary quadratic programming problems. Naturally, one maydesire to expand the application domain of these machines to problems withgeneral discrete variables. In this paper, we explore the possibility ofemploying quantum annealers to solve unconstrained quadratic programmingproblems over a bounded integer domain. We present an approach for encodinginteger variables into binary ones, thereby representing unconstrained integerquadratic programming problems as unconstrained binary quadratic programmingproblems. To respect some of the limitations of the currently developed quantumannealers, 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 thecoefficients of the encoding using the precision of the machine and thecoefficients of the original integer problem. Finally, we experimentally showthat this approach is far more resilient to the noise of the quantum annealerscompared to traditional approaches for the encoding of integers in base two.
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