An Adaptive Mixer Allocation Strategy 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, thereby reducing the search space and eliminating the possibility of yielding infeasible solutions. However, QAOA+ may incur high overall gate costs when the mixer is applied to all qubits in each layer, and each mixer is costly to implement. To address this challenge, an adaptive mixer allocation strategy is tailored for QAOA+. The resulting algorithm, which integrates this strategy into the original QAOA+ framework, is referred to as AMA‐QAOA+. Unlike QAOA+, AMA‐QAOA+ adaptively applies the mixer to a subset of qubits in each layer of the mixer unitary operator based on an evaluation function. The performance of AMA‐QAOA+ is evaluated on the maximum independent set problem. Numerical simulation results show that, under the same number of optimization runs, AMA‐QAOA+ achieves better solution quality than QAOA+, with the optimal approximation ratio improved by on Erdős–Rényi random graphs and on 3‐regular graphs. Moreover, AMA‐QAOA+ significantly reduces the CNOT gate consumption, requiring only and of the CNOT gates used by QAOA+ on Erdős–Rényi and 3‐regular random graphs, respectively. These results demonstrate that AMA‐QAOA+ enhances solution quality and computational efficiency, enabling the design of more compact and resource‐efficient quantum circuits.