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