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

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.