Solving the MAX-k-CUT problem for hypergraphs with quantum computing
V. S. Yarmus, Kh. P. Gnatenko
Abstract
We investigate the MAX-k-CUT problem on hypergraphs by considering their representation as spin systems with Ising interactions. The corresponding cost Hamiltonian for MAX-k-CUT problem on hypergraphs is reduced to an Ising Hamiltonian with pairwise interactions. This reduction simplifies the solution of the MAX-k-CUT problem using quantum computing. As illustrative examples, a 3-uniform tight-star hypergraph and a sunflower hypergraph are considered. The corresponding Hamiltonians are constructed, and quantum protocols for the MAX-k-CUT problems are presented. The MAX-3-CUT and MAX-4-CUT instances are investigated for these hypergraphs by varying the number of Quantum Approximate Optimization Algorithm (QAOA) layers from (p=2) to (p=15) with quantum computing on IBM's Qiskit AerSimulator.
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