Quantum alternating operator ansatz for solving the minimum exact cover problem - Wang, Sha-Sha; Liu, Hai-Ling; Song, Yan-Qi; Gao, Fei; Qin, Su-Juan; Wen, Qiao-Yan (Physica A, 2023)
The Quantum Alternating Operator Ansatz (QAOA+) is an extension of the Quantum Approximate Optimization Algorithm (QAOA), where the search space is smaller in solving constrained combinatorial optimization problems. However, QAOA+ requires a trivial feasible solution as the initial state, so it cannot be applied directly for problems that are difficult to find a trivial feasible solution. For simplicity, we call them as Non-Trivial-Feasible-Solution Problems (NTFSP). In this paper, we take the Minimum Exact Cover (MEC) problem as an example, studying how to apply QAOA+ to NTFSP. As we know, Exact Cover (EC) is the feasible space of MEC problem, which has no trivial solutions. To overcome the above problem, the EC problem is divided into two steps to solve. First, disjoint sets are obtained, which is equivalent to solving independent sets. Second, on this basis, the sets covering all elements (i.e., EC) are solved. In other words, we transform MEC into a multi-objective constrained optimization problem, where feasible space consists of independent sets that are easy to find. Finally, we also verify the feasibility of the algorithm from numerical experiments. Furthermore, we compare QAOA+ with QAOA, and the results demonstrated that QAOA+ has a higher probability of finding a solution with the same rounds of both algorithms. Our method provides a feasible way for applying QAOA+ to NTFSP, and is expected to expand its application significantly. •As a feasible space for MEC problem, Exact Cover (EC) has no trivial solutions. We transform MEC into a multi-objective constrained optimization problem, where feasible solutions are independent sets that are easy to find, and solve the problem using QAOA+ for the first time.•We verify the feasibility of the algorithm, and the numerical results show that the solution can be obtained with high probability, even though rounds of the algorithm is low.•To optimize quantum circuit, we remove rotating gates RZ. The results show that p-level optimized circuit only needs p parameters, which can achieve an experimental effect similar to original circuit with 2 p parameters.•We compare QAOA+ with QAOA, and the results demonstrated that QAOA+ has a higher probability of finding a solution with the same rounds of both algorithms.