A scalable quantum-enhanced greedy algorithm for maximum independent set problems

TL;DR

This paper presents a hybrid quantum-classical greedy algorithm for the Maximum Independent Set problem that leverages shallow quantum circuits and pre-computed parameters, demonstrating significant performance improvements over classical methods on both hardware and simulations.

Contribution

It introduces a scalable, hardware-friendly hybrid quantum-classical algorithm that combines QAOA with greedy heuristics, avoiding complex training and enabling implementation on current quantum devices.

Findings

Outperforms classical greedy algorithms at low quantum circuit depth

Successfully implemented on a 20-qubit superconducting device

Shows significant improvements in solution quality in simulations

Abstract

We investigate a hybrid quantum-classical algorithm for solving the Maximum Independent Set (MIS) problem on regular graphs, combining the Quantum Approximate Optimization Algorithm (QAOA) with a minimal degree classical greedy algorithm. The method leverages pre-computed QAOA angles, derived from depth-$p$ QAOA circuits on regular trees, to compute local expectation values and inform sequential greedy decisions that progressively build an independent set. This hybrid approach maintains shallow quantum circuit and avoids instance-specific parameter training, making it well-suited for implementation on current quantum hardware: we have implemented the algorithm on a 20 qubit IQM superconducting device to find independent sets in graphs with thousands of nodes. We perform tensor network simulations to evaluate the performance of the algorithm beyond the reach of current quantum hardware and compare to established classical heuristics. Our results show that even at low depth ($p=4$), the quantum-enhanced greedy method significantly outperforms purely classical greedy baselines as well as more sophisticated approximation algorithms. The modular structure of the algorithm and relatively low quantum resource requirements make it a compelling candidate for scalable, hybrid optimization in the NISQ era and beyond.