Modeling of Assignment Problem in Quantum Approximate Optimization Algorithm

An assignment problem is a mapping between the tasks and agents aiming for the optimal cost. In graph theory, it is represented by a bipartite graph of tasks and agents connected optimally through edges. It is a combinatorial optimization, a type of NP category that makes it hard to solve in a limited time for large inputs. Quantum approximate optimization algorithm (QAOA), a hybrid-quantum optimization, is a possible way to solve such combinatorial problems in quantum computing. Quantum computation exploits the theory of quantum physics for accelerated computation. In this study, the assignment problem is framed to quadratic unconstrained binary optimization and the Ising model for the execution in QAOA. The details of classical to quantum conversion, modeling, circuit implementation, and various analyses are explained with an example.