Abstract
The Quantum Max-d-Cut (d-QMC) problem is a special instance of a 2-local Hamiltonian problem, representing the quantum analog of the classical Max-d-Cut problem. The d-QMC problem seeks the largest eigenvalue of a Hamiltonian defined on a graph with n vertices, where edges correspond to swap operators acting on (C^d)^⊗ n. In recent years, progress has been made by investigating the algebraic structure of the d-QMC Hamiltonian. Building on this approach, this article solves the d-QMC problem for complete tripartite graphs for small local dimensions, d ≤ 3.