Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the execution time of QAOA scales exponentially with the problem size. We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (MaxCut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size NISQ computers. The overall solution is retrieved from the sub-solutions by applying the combination policy of quantum state reconstruction. Multiple partitioning and reconstruction methods are proposed/ compared. DC-QAOA achieves 97.14% approximation ratio (20.32% higher than classical counterpart), and 94.79% expectation value (15.80% higher than quantum annealing). DC-QAOA also reduces the time complexity of conventional QAOA from exponential to quadratic.

中文翻译：

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通过分而治之的大规模量子近似优化

量子近似优化算法（QAOA）是一种有前途的混合量子经典算法，用于解决组合优化问题。但是，它不能克服大规模问题的量子位限制。此外，QAOA的执行时间与问题的大小成指数关系。我们提出了分而治之的QAOA（DC-QAOA），以解决图形最大割（MaxCut）问题的上述挑战。该算法通过将较大的图递归地划分为较小的图来工作，这些较小的图的MaxCut解决方案是使用小型NISQ计算机获得的。通过应用量子态重构的组合策略，可从子解决方案中检索整体解决方案。提出/比较了多种划分和重构方法。DC-QAOA的逼近率达到97.14％（比经典产品高20.32％），预期值为94.79％（比量子退火高15.80％）。DC-QAOA还可以将传统QAOA的时间复杂度从指数级降低到二次级。