We show that with the assistance of a third level of qubits an $n$-qubit phase gate can be constructed from $2n-4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike previous schemes, our scheme uses the auxiliary level to “expose” some state to the qutrit-qubit controlled phase gate, instead of using it to “hide” states from the conditional dynamics. Neither the number of the additional levels nor that of single-qutrit operations needs to increase with $n$. We propose a physical implementation of the required elementary gates in cavity QED and show that the total gate time may be greatly reduced compared with that required in previous methods.

• Received 7 February 2012

DOI:https://doi.org/10.1103/PhysRevA.86.012326