Max-cut Clustering Utilizing Warm-Start QAOA and IBM Runtime

TL;DR

This paper compares warm-start QAOA and standard QAOA for Max-Cut clustering, evaluating their performance and speed using IBM's Qiskit Runtime, and explores a non-convex optimizer for relaxation.

Contribution

It introduces a comparison between warm-start and standard QAOA for clustering, and assesses the impact of IBM's Qiskit Runtime on optimization speed and performance.

Findings

Warm-start QAOA outperforms other algorithms in clustering quality.

Standard QAOA is the fastest optimization method.

Qiskit Runtime provides significant speedups for quantum optimization algorithms.

Abstract

Quantum optimization algorithms can be used to recreate unsupervised learning clustering of data by mapping the problem to a graph optimization problem and finding the minimum energy for a MaxCut problem formulation. This research tests the "Warm Start" variant of Quantum Approximate Optimization Algorithm (QAOA) versus the standard implementation of QAOA for unstructured clustering problems. The performance for IBM's new Qiskit Runtime API for speeding up optimization algorithms is also tested in terms of speed up and relative performance compared to the standard implementation of optimization algorithms. Warm-start QAOA performs better than any other optimization algorithm, though standard QAOA runs the fastest. This research also used a non-convex optimizer to relax the quadratic program for the Warm-start QAOA.