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.

翻译：当前量子计算机仅能求解规模极其有限的优化问题。对于更大规模的问题，需要采用分解方法将原始问题拆解为若干较小的子问题，这些子问题在量子计算机上求解后，再将其解合并为原始问题的最终解。然而，现有分解方法通常未考虑特定问题的结构特征。本文提出一种基于分治策略的定制化方法，用于求解包含大量变量的数分割问题（NPP）。其核心思想是通过专门化分解生成更小规模的NPP子问题，这些子问题可在量子计算机上求解，随后将子问题的结果重组成一个辅助性小规模NPP。通过求解该辅助问题，即可获得原始大规模问题的近似解。实验验证表明，该方法借助D-Wave量子退火器可求解包含超过一千个变量的NPP问题。