The number of two-qubit gates required to deterministically transform a three-qubit pure quantum state into another is discussed. We show that any state can be prepared from a product state using at most three CNOT gates and that starting from the Greenberger-Horne-Zeilinger state, only two suffice. As a consequence, any three-qubit state can be transformed into any other using at most four CNOT gates. Generalizations to other two-qubit gates are also discussed.

• Received 26 November 2007

DOI:https://doi.org/10.1103/PhysRevA.77.032320