  In previous work, it was shown that non-trivial gapped states can be
generated from a product state using a sequential quantum circuit. Explicit
circuit constructions were given for a variety of gapped states at exactly
solvable fixed points. In this paper, we show that a similar generation
procedure can be established for chiral topological states as well, despite the
fact that they lack an exactly solvable form. Instead of sequentially applying
local unitary gates, we sequentially evolve the Hamiltonian by changing local
terms in one subregion and then the next. The Hamiltonian remains gapped
throughout the process, giving rise to an adiabatic evolution mapping the
ground state from a product state to a chiral topological state. We demonstrate
such a sequential adiabatic generation process for free fermion chiral states
like the Chern Insulator and the $p+ip$ superconductor. Moreover, we show that
coupling a quantum state to a discrete gauge group can be achieved through a
sequential quantum circuit, thereby generating interacting chiral topological
states from the free fermion ones.
