The standard quantum approximate optimization algorithm (QAOA) has a limited expressive power in shallow circuits, whereas naively increasing the number of layers leads to greater quantum circuit depth and higher noise sensitivity. To address this trade-off, based on the ideas of the multi-angle quantum approximate optimization algorithm (MA-QAOA) and the RY-layer-assisted quantum approximate optimization algorithm (RY-QAOA), this paper proposes an improved algorithm, i.e., MA-RY-QAOA, which integrates parameter multangularization and RY-assisted architecture. In MA-RY-QAOA, the problem block incorporates edge parameter multangularization together with RY extension, while the mixer block implements qubit parameter multangularization. For layer number p=1 and node size n=4~12 , we conduct 50 simulation trials on maximum cut problem respectively for random graph with edge probability of 0.8, complete graph, 2-regular graph and 4-regular graph, by using the average approximation ratio as the evaluation metric. The simulation trial results show that, across these four class graphs, the average approximation ratio of MA-RY-QAOA and MA-QAOA significantly outperforms standard QAOA, RY-QAOA, and QAOA+ for overwhelming majority of node sizes; with respect to complete graph, the average approximation ratio of MA-QAOA outperforms that of MA-RY-QAOA for all node sizes; with regard to 2-regular graph, the average approximation ratio of MA-RY-QAOA exceeds that of MA-QAOA for all node sizes; with regard to 4-regular graph, the average approximation ratio of MA-RY-QAOA takes advantage over that of MA-QAOA for overwhelming majority of node sizes; concerning random graph, the average approximation ratio of MA-RY-QAOA is superior to that of MA-QAOA for both small node sizes and large node sizes, but is inferior to that of MA-QAOA for medium node sizes. Therefore, MA-RY-QAOA provides a useful reference for the structure design of shallow-layer QAOA on noisy intermediate-scale quantum (NISQ) devices.
To address the limited expressive capability of the standard quantum approximate optimization algorithm (QAOA) in shallow circuits and the increased noise sensitivity caused by deeper quantum circuits, an improved QAOA, termed MA-RY-QAOA, was proposed by integrating parameter multi-angleization and an RY-assisted structure. In the proposed algorithm, edge-parameter multi-angleization and RY expansion were incorporated into the problem layer, while qubit-parameter multi-angleization was introduced into the mixing layer. Simulation experiments were conducted on the Max-cut problem of random graphs, complete graphs, 2-regular graphs, and 4-regular graphs with circuit depth ( p=1 <?fx-imagestate width="7.45066643" height="2.87866688"?> <?fx-imagestate width="7.45066643" height="2.87866688"?> ) and node sizes ranging from 4 to 12. The average approximation ratio was adopted as the evaluation metric. The results showed that the average approximation ratios achieved by MA-RY-QAOA and MA-QAOA were generally superior to those obtained by the standard QAOA, RY-QAOA, and QAOA+ algorithms. In particular, MA-RY-QAOA exhibited better performance on 2-regular and 4-regular graphs and achieved higher approximation ratios for certain scales of random graphs. These findings indicate that MA-RY-QAOA improves optimization performance while maintaining a shallow circuit structure and provides a useful reference for the design of QAOA variants on noisy intermediate-scale quantum (NISQ) devices.
The max-cut problem (MCP) is a classic problem in the field of combinatorial optimization and has important applications in various fields, including statistical physics and image processing. However, except for some special cases, the MCP still encounters a non-deterministic polynomial complete problem (an NP-complete problem), and there is currently no known efficient classical algorithm that can solve it in polynomial time. The quantum approximate optimization algorithm (QAOA), as a pivotal algorithm in the noisy intermediate-scale quantum (NISQ) computing era, has shown significant potential for solving the MCP. However, due to the lack of quantum error correction, the reliability of computations in NISQ systems sharply declines as the circuit depth of the algorithm increases. Therefore, designing an efficient, shallow-depth, and low-complexity QAOA for the MCP is a critical challenge in demonstrating the advantages of quantum computing in the NISQ era.In this paper, according to the standard QAOA algorithm, we introduce Pauli Y rotation gates into the target Hamiltonian circuit for the MCP. By enhancing the flexibility of quantum trial functions and improving the efficiency of Hilbert space exploration within a single iteration, we significantly improve the performance of QAOA on the MCP.We conduct extensive numerical simulations using the MindSpore quantum platform, and compare the proposed RY-layer-assisted QAOA with standard QAOA and its existing variants, including MA-QAOA and QAOA+. The experiments are performed on various graph types, including complete graphs, 3-regular graphs, 4-regular graphs, and random graphs with edge probabilities between 0.3 and 0.5. Our results show that the RY-layer-assisted QAOA achieves higher approximation ratios in all graph types, particularly in regular and random graphs, where traditional QAOA variants are difficult to implement. Moreover, the proposed method exhibits strong robustness as the graph size increases, and can maintain high performance even for larger graphs. Importantly, the RY-layer-assisted QAOA requires fewer CNOT gates and has a lower circuit depth than the standard QAOA and its variants, making it more suitable for NISQ devices with limited coherence times and high error rates.In conclusion, the RY-layer-assisted QAOA provides a promising approach for solving MCP in the NISQ era. By improving the approximation ratio while reducing circuit complexity, this method demonstrates significant potential for practical quantum computing applications, thus paving the way for developing more efficient and reliable quantum optimization algorithms.