  State preparation is a process encoding the classical data into the quantum
systems. Based on quantum phase estimation, we propose the specific quantum
circuits for a deterministic state preparation algorithm and a probabilistic
state preparation algorithm. To discuss the gate complexity in these
algorithms, we decompose the diagonal unitary operators included in the phase
estimation algorithms into the basic gates. Thus, we associate the state
preparation problem with the decomposition problem of the diagonal unitary
operators. We analyse the fidelities in the two algorithms and discuss the
success probability in the probabilistic algorithm. In this case, we explain
that the efficient decomposition of the corresponding diagonal unitary
operators is the sufficient condition for state preparation problems.
