  Quantum state engineering, namely the generation and control of arbitrary
quantum states, is drawing more and more attention due to its wide applications
in quantum information and computation. However, there is no general method in
theory, and the existing schemes also depend heavily on the selected
experimental platform. In this manuscript, we give two schemes for the
engineering task of arbitrary quantum state in $c$-partite $d$-dimensional
system, both of which are based on discrete-time quantum walk with a
$2^c$-dimensional time- and position-dependent coin. The first procedure is a
$d$-step quantum walk where all the $d$ coins are non-identity, while the
second procedure is an $O(d)$-step quantum walk where only $O(\log d)$ coins
are non-identity. A concrete example of preparing generalized Bell states is
given to demonstrate the first scheme we proposed. We also show how these
schemes can be used to reduce the cost of long-distance quantum communication
when the particles involved in the system are far away from each other.
Furthermore, the first scheme can be applied to give an alternative approach to
the quantum state preparation problem which is one of the fundamental tasks of
quantum information processing. We design circuits for quantum state
preparation with the help of our quantum state engineering scheme that match
the best current result in both size and depth of the circuit asymptotically.
