Realization of the Quantum Toffoli Gate with Trapped Ions

Gates acting on more than two qubits are appealing as they can substitute complex sequences of two-qubit gates, thus promising faster execution and higher fidelity. One important multiqubit operation is the quantum Toffoli gate that performs a controlled NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer, achieving a mean gate fidelity of 71(3)%. Our implementation is particularly efficient as the relevant logic information is directly encoded in the motion of the ion string.

Figure 1

Experimentally obtained truth table of the Toffoli gate: After preparing the three ions in one of the eight basis input states $|SSS⟩$ to $|DDD⟩$ (right axis) the probabilities of all basis output states (left axis) are measured 100 times. On average the correct output state is reached with a probability of $81(\pm 5)\%$. The stated error in the measurements is mainly caused by quantum projection noise.

Figure 2

Comparison between (a) ideal and (b) experimental process $\chi$-matrices of the Toffoli gate. The absolute values of the elements are shown in the operator basis ${\sigma }_{c1}\otimes {\sigma }_{c2}\otimes {\sigma }_t\in \{I\otimes I\otimes I,I\otimes I\otimes X,\dots ,Z\otimes Z\otimes Z\}$. Ideal and experimental process matrix show a chi overlap $\mathrm{Tr}({\chi }_{\mathrm{ideal}}{\chi }_{\exp })=66.6(4)\%$.