Quantum Local Search with the Quantum Alternating Operator Ansatz

TL;DR

This paper introduces a hybrid quantum local search algorithm for solving large constrained combinatorial optimization problems, demonstrating its effectiveness on various graph types with limited qubits.

Contribution

It proposes a novel quantum local search method using the Quantum Alternating Operator Ansatz, capable of handling larger problem instances on near-term quantum devices.

Findings

Successfully solved large problem instances with few qubits

Effective on multiple graph types including 3-regular, Community, and Erdős-Rényi graphs

Demonstrates potential for quantum advantage in combinatorial optimization

Abstract

We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. This hybrid algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We study the performance of this algorithm on 3-regular, Community, and Erd\H{o}s-R\'{e}nyi graphs with up to 100 nodes.