Expressibility of the alternating layered ansatz for quantum computation

The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz often used, thanks its implementability and expressibility; however, has critical issue in trainability sense that it generically suffers from so-called gradient vanishing problem. This can be resolved by limiting circuit class of shallow alternating layered ansatz. However, though high proved, still unclear whether rich expressibility state generation. In paper, with proper definition found literature, we show almost same level Hence coexist, giving new designing method for circuits computing era.