  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.
