Efficiently Solving the Max-cut Problem via a Quantum Qubit Rotation Algorithm

Optimizing parameterized quantum circuits promises efficient use of near-term quantum devices to achieve potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter ansatz. We find that in combinatorial optimization problems, since the solutions are described by bit strings, one can trade the expressiveness of the ansatz for high train ability. To be specific, by focusing on the max-cut problem we introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA). The quantum circuits are comprised with single-qubit rotation gates implementing on each qubit. The rotation angles of the gates can be trained free of barren plateaus. It is demonstrated that the approximation ratio of QQRA can be close to 1 for complete graphs. To illustrate the effectiveness of QQRA, we compare it with the well known quantum approximate optimization algorithm and the classical Goemans- Williamson algorithm.