Information scrambling and entanglement in quantum approximate optimization algorithm circuits

Variational quantum algorithms, which consist of optimal parameterized quantum circuits, are promising for demonstrating quantum advantages in the noisy intermediate-scale quantum (NISQ) era. Apart from classical computational resources, different kinds of quantum resources have their contributions in the process of computing, such as information scrambling and entanglement. Characterizing the relation between complexity of specific problems and quantum resources consumed by solving these problems is helpful for us to understand the structure of VQAs in the context of quantum information processing. In this work, we focus on the quantum approximate optimization algorithm (QAOA), which aims to solve combinatorial optimization problems. We study information scrambling and entanglement in QAOA circuits, respectively, and discover that for a harder problem, more quantum resource is required for the QAOA circuit to obtain the solution in most of the cases. We note that in the future, our results can be used to benchmark complexity of quantum many-body problems by information scrambling or entanglement accumulation in the computing process.