Quantum Algorithm for the Set Splitting Problem

Abstract

We present a novel use of quantum annealing to solve the Set Splitting Problem using (QUBO) problem formulation. The contribution of the work is in formulating penalty functions that ensure the ground state of the QUBO Hamiltonian corresponds to valid solutions that split the input subsets. This approach scales linearly in terms of the number of logical qubits relative to problem size. Empirical tests of the proposed solution show convergence to globally optimal solutions, with high accuracy rates over repeated trials.