论文标题
QAOA QAOA：在小量子机上解决大规模的最大问题
QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines
论文作者
论文摘要
合并优化的快速算法的设计极大地有助于众多的物流，金融和化学。量子近似优化算法（QAOAS）利用量子机的力量并继承绝热的进化精神，是解决与潜在运行时加速的组合问题的新方法。但是，由于如今的量子资源有限，Qaoas无法操纵大规模问题。为了解决这个问题，在这里，我们通过分裂和争议的启发式来重新审视最大问题：在并行寻求子图的解决方案，然后合并这些解决方案以获取全球解决方案。由于Maxcut中的$ \ Mathbb {Z} _2 $对称性，我们证明可以将合并过程进一步施放到新的Maxcut问题中，因此可以通过Qaoas或其他MaxCut求解器来解决。在这方面，我们建议使用小量子机求解qaoa-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-in-caoa（qaoa}^2 $）。我们还证明，$ \ text {qaoa}^2 $的近似值较低。实验结果表明，在不同的图形设置下，$ \ text {qaoa}^2 $在节点计数大约在2000年左右时，比最知名的经典算法具有竞争性甚至更好的性能。我们的方法可以将我们的方法无缝地嵌入其他高级策略中，以增强大型组合优化问题中QAOA的能力。
The design of fast algorithms for combinatorial optimization greatly contributes to a plethora of domains such as logistics, finance, and chemistry. Quantum approximate optimization algorithms (QAOAs), which utilize the power of quantum machines and inherit the spirit of adiabatic evolution, are novel approaches to tackle combinatorial problems with potential runtime speedups. However, hurdled by the limited quantum resources nowadays, QAOAs are infeasible to manipulate large-scale problems. To address this issue, here we revisit the MaxCut problem via the divide-and-conquer heuristic: seek the solutions of subgraphs in parallel and then merge these solutions to obtain the global solution. Due to the $\mathbb{Z}_2$ symmetry in MaxCut, we prove that the merging process can be further cast into a new MaxCut problem and thus be addressed by QAOAs or other MaxCut solvers. With this regard, we propose QAOA-in-QAOA ($\text{QAOA}^2$) to solve arbitrary large-scale MaxCut problems using small quantum machines. We also prove that the approximation ratio of $\text{QAOA}^2$ is lower bounded by 1/2. Experiment results illustrate that under different graph settings, $\text{QAOA}^2$ attains a competitive or even better performance over the best known classical algorithms when the node count is around 2000. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale combinatorial optimization problems.
