Efficient scheme for initializing a quantum register with an arbitrary superposed state

Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as |i₁i₂⋯iₙ〉 with iⱼ being either 0 or 1, but it is a nontrivial task to construct an arbitrary superposed quantum state. We present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires O(Nn²) standard 1- and 2-bit gate operations, without introducing additional quantum bits. Application of the scheme in some special cases is discussed.