  Current quantum computers can only solve optimization problems of a very
limited size. For larger problems, decomposition methods are required in which
the original problem is broken down into several smaller sub-problems. These
are then solved on the quantum computer and their solutions are merged into a
final solution for the original problem. Often, these decomposition methods do
not take the specific problem structure into account. In this paper, we present
a tailored method using a divide-and-conquer strategy to solve the number
partitioning problem (NPP) with a large number of variables. The idea is to
perform a specialized decomposition into smaller NPPs, which can be solved on a
quantum computer, and then recombine the results into another small auxiliary
NPP. Solving this auxiliary problem yields an approximate solution of the
original larger problem. We experimentally verify that our method allows to
solve NPPs with over a thousand variables using a D-Wave quantum annealer.
