  Quantum annealing is a heuristic algorithm for solving combinatorial
optimization problems, and D-Wave Systems Inc. has developed hardware for
implementing this algorithm. The current version of the D-Wave quantum annealer
can solve unconstrained binary optimization problems with a limited number of
binary variables, although cost functions of many practical problems are
defined by a large number of integer variables. To solve these problems with
the quantum annealer, the integer variables are generally binarized with
one-hot encoding, and the binarized problem is partitioned into small
subproblems. However, the entire search space of the binarized problem is
considerably extended compared to that of the original integer problem and is
dominated by unfeasible solutions. Therefore, to efficiently solve large
optimization problems with one-hot encoding, partitioning methods that extract
subproblems with as many feasible solutions as possible are required.
