Quantum alternating operator ansatz for solving the minimum exact cover problem

The Quantum Alternating Operator Ansatz (QAOA+) is an extension of the Approximate Optimization Algorithm (QAOA), where search space smaller in solving constrained combinatorial optimization problems. However, QAOA+ requires a trivial feasible solution as initial state, so it cannot be applied directly for problems that are difficult to find solution. For simplicity, we call them Non-Trivial-Feasible-Solution Problems (NTFSP). In this paper, take Minimum Exact Cover (MEC) problem example, studying how apply NTFSP. As know, (EC) MEC problem, which has no solutions. To overcome above EC divided into two steps solve. First, disjoint sets obtained, equivalent independent sets. Second, on basis, covering all elements (i.e., EC) solved. other words, transform multi-objective consists easy find. Finally, also verify feasibility algorithm from numerical experiments. Furthermore, compare with QAOA, and results demonstrated higher probability finding same rounds both algorithms. Our method provides way applying NTFSP, expected expand its application significantly.