Synthesis of quantum superpositions by quantum computation

The quantum search algorithm can be looked at as a technique for synthesizi ng a particular kind of superposition-one whose amplitude is concentrated i n a single basis state. This basis state is defined by a binary function f( (x) over bar) that is nonzero in this desired basis state and zero everywhe re else. This paper extends the quantum search algorithm to an algorithm th at can create an arbitrarily specified superposition on a space of size N i n O(root N) steps. The superposition is specified by a complex valued funct ion f((x) over bar) that specifies the desired amplitude of the system in b asis state (x) over bar.