  We consider a unitary transformation which maps any given state of an
$n$-qubit quantum register into another one. This transformation has
applications in the initialization of a quantum computer, and also in some
quantum algorithms. Employing uniformly controlled rotations, we present a
quantum circuit of $2^{n+2}-4n-4$ CNOT gates and $2^{n+2}-5$ one-qubit
elementary rotations that effects the state transformation. The complexity of
the circuit is noticeably lower than the previously published results.
Moreover, we present an analytic expression for the rotation angles needed for
the transformation.
