  Variational quantum algorithms have been a promising candidate to utilize
near-term quantum devices to solve real-world problems. The powerfulness of
variational quantum algorithms is ultimately determined by the expressiveness
of the underlying quantum circuit ansatz for a given problem. In this work, we
propose a sequentially generated circuit ansatz, which naturally adapts to 1D,
2D, 3D quantum many-body problems. Specifically, in 1D our ansatz can
efficiently generate any matrix product states with a fixed bond dimension,
while in 2D our ansatz generates the string-bond states. As applications, we
demonstrate that our ansatz can be used to accurately reconstruct unknown pure
and mixed quantum states which can be represented as matrix product states, and
that our ansatz is more efficient compared to several alternatives in finding
the ground states of some prototypical quantum many-body systems as well as
quantum chemistry systems, in terms of the number of quantum gate operations.
