Fig. 2. Entangling gates between ion pairs in the same row or the same column.

a Population for the LR ion pair after an entangling gate. b Parity oscillation for the LR ion pair after an entangling gate. c Theoretical estimation of gate errors for the LR and the UD ion pairs. The laser dephasing, motional dephasing and motional heating effects are modeled by Lindblad operators. The intensity fluctuation is described by a shot-to-shot variation. d Experimentally measured Bell-state fidelity for the LR ion pair vs. the number of entangling gates. The blue and the orange data points represent the population and parity, respectively, while the fidelity is their average as the green dots. By fitting the slope of the fidelity, we extract a gate infidelity of about 1.4(2)%. e Similar plot for the UD ion pair with an extracted gate infidelity of about 1.6(1)%. All the error bars represent one standard deviation.