Synthesis of quantum superpositions by quantum computation

The quantum search algorithm can be looked at as a technique for synthesizing a particular kind of superposition-one whose amplitude is concentrated in a single basis state. This basis state is defined by a binary function f(&xmacr;) that is nonzero in this desired basis state and zero everywhere else. This paper extends the quantum search algorithm to an algorithm that can create an arbitrarily specified superposition on a space of size N in O(sqrt[N] ) steps. The superposition is specified by a complex valued function f(&xmacr;) that specifies the desired amplitude of the system in basis state &xmacr;.