  Of late, we are witnessing spectacular developments in Quantum Information
Processing with the availability of Noisy Intermediate-Scale Quantum devices of
different architectures and various software development kits to work on
quantum algorithms. Different problems, which are hard to solve by classical
computation, but can be sped up (significantly in some cases) are also being
populated. Leveraging these aspects, this paper examines unsupervised graph
clustering by quantum algorithms or, more precisely, quantum-assisted
algorithms. By carefully examining the two cluster Max-Cut problem within the
framework of quantum Ising model, an extension has been worked out for max
3-cut with the identification of an appropriate Hamiltonian. Representative
results, after carrying out extensive numerical evaluations, have been provided
including a suggestion for possible futuristic implementation with qutrit
devices. Further, extrapolation to more than 3 classes, which can be handled by
qudits, of both annealer and gate-circuit varieties, has also been touched upon
with some preliminary observations; quantum-assisted solving of Quadratic
Unconstrained D-ary Optimisation is arrived at within this context. As an
additional novelty, a qudit circuit to solve max-d cut through Quantum
Approximate Optimization algorithm is systematically constructed.
