Large-scale Quantum Approximate Optimization via Divide-and-Conquer

TL;DR

This paper introduces DC-QAOA, a divide-and-conquer approach that enables large-scale graph MaxCut solutions using small quantum computers, significantly improving approximation ratio and reducing time complexity.

Contribution

The paper proposes a novel divide-and-conquer framework for QAOA, allowing scalable solutions for large graphs on limited quantum hardware.

Findings

Achieves 97.14% approximation ratio, 20.32% higher than classical methods.

Reduces QAOA time complexity from exponential to quadratic.

Outperforms quantum annealing with 15.80% higher expectation value.

Abstract

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.