  Quantum annealing is a heuristic algorithm that solves combinatorial
optimization problems, and D-Wave Systems Inc. has developed hardware
implementation of this algorithm. However, in general, we cannot embed all the
logical variables of a large-scale problem, since the number of available
qubits is limited. In order to handle a large problem, qbsolv has been proposed
as a method for partitioning the original large problem into subproblems that
are embeddable in the D-Wave quantum annealer, and it then iteratively
optimizes the subproblems using the quantum annealer. Multiple logical
variables in the subproblem are simultaneously updated in this iterative
solver, and using this approach we expect to obtain better solutions than can
be obtained by conventional local search algorithms. Although embedding of
large subproblems is essential for improving the accuracy of solutions in this
scheme, the size of the subproblems are small in qbsolv since the subproblems
are basically embedded by using an embedding of a complete graph even for
sparse problem graphs. This means that the resource of the D-Wave quantum
annealer is not exploited efficiently. In this paper, we propose a fast
algorithm for embedding larger subproblems, and we show that better solutions
are obtained efficiently by embedding larger subproblems.
