We consider a unitary transformation which maps any given pure 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 2ⁿ⁺²-4n-4 CNOT gates and 2ⁿ⁺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.
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Möttönen et al. (2005) studied this question.