Fig. 3: SWAP, CS⁻¹ and Toffoli-like gate.

a A resonant SWAP gate is implemented by applying a Tukey-shaped pulse with an oscillation superimposed to the barrier gate between Q2 and Q3. It is tested using the depicted circuit diagram. b To demonstrate the SWAP gate, a Rabi pulse X(θ) is applied to Q3, followed by a SWAP gate between Q2 and Q3. Then, either Q2 is read out using readout system Q1Q2 (red) or Q3 is read out using readout system Q3Q4 (green). c Circuit diagram of the experiment demonstrating the CS⁻¹ gate. d The CS⁻¹ gate is obtained by calibrating the phase difference to be − π/2, for the experiments with (blue) and without (black) an X² gate on the control qubit Q1. e Circuit diagram of the Toffoli-like gate (gray) composed of CS⁻¹ and CZ gates. f Demonstration of the Toffoli-like gate with target qubit Q4 and control qubits Q1 and Q3. An X(θ) pulse is applied to Q1 and the final state of Q4 is measured using readout system Q3Q4. Results of the experiment in e with (pink) and without (black) a preparation pulse X² on ancilla qubit Q3.