Solving the Kemeny ranking aggregation problem with quantum optimization algorithms

The aim of a ranking aggregation problem is to combine several rankings into single one that best represents them. A common method for solving this due Kemeny and selects as the aggregated minimizes sum Kendall distances be aggregated. Unfortunately, identification said ranking—called ranking—is known computationally expensive task. In paper, we study different ways computing with quantum optimization algorithms, in particular, provide some alternative formulations search an problem. To our knowledge, first time addressed techniques. We propose four formulating problem, novel work. Two algorithms—Quantum Approximate Optimization Algorithm Quantum Adiabatic Computing—are used evaluate each formulations. experimental results show choice formulation plays big role on performance algorithms.