Information scrambling and entanglement in quantum approximate optimization algorithm circuits

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