Quantum-Assisted Graph Clustering and Quadratic Unconstrained D-ary Optimisation

Abstract

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 simulation studies, 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, has also been touched upon with some preliminary observations; quantum-assisted solving of Quadratic Unconstrained D-ary Optimisation is arrived at within this context. The paper also demonstrates how quantum description/formulation can sometimes lead to a different perspective and way of solving problems by providing the results for subgraph identification in graphs.

Power Network Optimization: A Quantum Approach

“…Recently, quantum computers have been used to model and solve the graph partitioning problem, see e.g., [36], [37], [38], and [39]. In this paper, we shall focus on solving the graph partitioning of a power network with quantum annealing, which uses quantum physics to find low-energy states of a problem and which can be mapped to the optimal or nearoptimal solution of the optimization problem.…”