Quantum Alternating Operator Ansatz for Solving the Minimum Exact Cover Problem

• URL: http://arxiv.org/abs/2211.15266v1
• Date: Mon, 28 Nov 2022 12:45:52 GMT
• Title: Quantum Alternating Operator Ansatz for Solving the Minimum Exact Cover Problem
• Authors: Sha-Sha Wang, Hai-Ling Liu, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen
• Abstract summary: We adopt quantum alternating operator ansatz (QAOA+) to solve minimum exact cover (MEC) problem. The numerical results show that the solution can be obtained with high probability when level $p$ of the algorithm is low. We also optimize the quantum circuit by removing single-qubit rotating gates $R_Z$.
• Score: 4.697039614904225
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The minimum exact cover (MEC) is a common combinatorial optimization problem, with wide applications in tail-assignment and vehicle routing. In this paper, we adopt quantum alternating operator ansatz (QAOA+) to solve MEC problem. In detail, to obtain a trivial feasible solution, we first transform MEC into a constrained optimization problem with two objective functions. Then, we adopt the linear weighted sum method to solve the above constrained optimization problem and construct the corresponding target Hamiltonian. Finally, to improve the performance of this algorithm, we adopt parameters fixing strategy to simulate, where the experimental instances are 6, 8, and 10 qubits. The numerical results show that the solution can be obtained with high probability when level $p$ of the algorithm is low. Besides, we optimize the quantum circuit by removing single-qubit rotating gates $R_Z$. We found that the number of quantum gates is reduced by $np$ for $p$-level optimized circuit. Furthermore, $p$-level optimized circuit only needs $p$ parameters, which can achieve an experimental effect similar to original circuit with $2p$ parameters.

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