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Algorithms, Volume 12, Issue 4 (April 2019)
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Cover Story (view full-size image) Quantum annealers such as the D-Wave machines are designed to propose solutions for quadratic [...] Read more. Quantum annealers such as the D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit. While many NP-hard problems can be easily formulated as binary quadratic optimization problems, such formulations almost always contain constraints which are not allowed in a QUBO, whose embeddings as quadratic penalties have drawbacks such as introducing large coefficients and using too many couplers. In this paper, we propose an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type ∑xi=k for binary variables xi. Our approach is scalable to any number of variables and uses a linear number of ancillary variables for a fixed k. View this paper.