We explicitly construct a quantum circuit, which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single-qubit elementary rotations, parametrized by fourteen independent angles. The explicit distribution of these angles is derived, showing that the joint distribution is a product of independent distributions of individual angles apart from four angles.

• Received 24 March 2009

DOI:https://doi.org/10.1103/PhysRevA.80.042309