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

• URL: http://arxiv.org/abs/2102.13288v1
• Date: Fri, 26 Feb 2021 03:10:30 GMT
• Title: Large-scale Quantum Approximate Optimization via Divide-and-Conquer
• Authors: Junde Li, Mahabubul Alam, Swaroop Ghosh
• Abstract summary: We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the challenges for graph maximum cut (MaxCut) problem. DC-QAOA achieves 97.14% approximation ratio (20.32% higher than classical counterpart) It also reduces the time complexity of conventional QAOA from exponential to quadratic.
• Score: 8.733794945008562
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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