  In quantum computation every unitary operation can be decomposed into quantum
circuits-a series of single-qubit rotations and a single type entangling
two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are
important when judging the complexity of the circuit: the total number of CNOT
gates needed to implement it and the depth of the circuit, measured by the
minimal number of computation steps needed to perform it. Here we give an
explicit and simple quantum circuit scheme for preparation of arbitrary quantum
states, which can directly utilize any decomposition scheme for arbitrary full
quantum gates, thus connecting the two problems. Our circuit reduces the depth
of the best currently known circuit by a factor of 2. It also reduces the total
number of CNOT gates from 2^n to 23/24 2^n in the leading order for even number
of qubits. Specifically, the scheme allows us to decrease the upper bound from
11 CNOT gates to 9 and the depth from 11 to 5 steps for four qubits. Our
results are expected to help in designing and building small-scale quantum
circuits using present technologies.
