An Adaptive Mixer Allocation Algorithm for the Quantum Alternating Operator Ansatz

Abstract: Recently, Hadfield et al. proposed the quantum alternating operator ansatz algorithm (QAOA+), an extension of the quantum approximate optimization algorithm (QAOA), to solve constrained combinatorial optimization problems (CCOPs). Compared with QAOA, QAOA+ enables the search for optimal solutions within a feasible solution space by encoding problem constraints into the mixer Hamiltonian, thus reducing the search space and eliminating the possibility of yielding infeasible solutions. However, QAOA+ may require substantial gates and circuit depth when the mixer is applied to all qubits in each layer, and the implementation cost of the mixer is high. To address these challenges, we propose the adaptive mixer allocation (AMA) algorithm. AMA constructs a feasible space by selectively applying the mixer to partial qubits in each layer based on the evolution of the optimization process. The performance of AMA in solving the maximum independent set (MIS) problem is investigated. Numerical simulation results demonstrate that, under the same number of optimization runs, AMA achieves a higher optimal approximation ratio--$1.82\%$ ($3.02\%$) higher than QAOA+ on ER (3-regular) graphs. Additionally, AMA significantly reduces the resource consumption, achieving only $34.08\%$ ($29.77\%$) of QAOA+ circuit depth and $15.05\%$ ($18.72\%$) of the number of CNOT gates, respectively, on ER (3-regular) graphs. These results highlight the ability of AMA to enhance computational efficiency and solution quality, making it particularly valuable for resource-constrained quantum devices.