Efficient construction of three- and four-qubit quantum gates by global entangling gates

Understand

We present improved circuits for the control-control-phase (Toffoli) gate and the control-swap (Fredkin) gate using three and four global two-qubit gates, respectively.

• This is a nearly double speed-up compared to the conventional circuits, which require five (for Toffoli) and seven (for Fredkin) conditional two-qubit gates.
• We apply the same approach to construct the conditional four-qubit phase gate by seven global two-qubit gates.
• We also present construction of the Toffoli and the Fredkin gates with five nearest-neighbour interactions.