Fig. 7: Population dynamics of basis states under relaxation and dephasing Noise.

The logical basis states are represented by the red lines. a The population of the state \({| 0;0\rangle }_{L}\) decreases due to relaxation, while the populations of the leakage states \(| 10;00\rangle\) (blue dashed) and \(| 00;10\rangle\) (green circle) increase. b The population of the logical state \({| 0;1\rangle }_{L}\) decreases, accompanied by a decay in the leakage state \(| 11;00\rangle\) (blue dashed). c The population of the logical state \({| 1;1\rangle }_{L}\) decreases due to relaxation, whereas the leakage states \(| 02;00\rangle\) (blue dashed) and \(| 00;02\rangle\) (green circle) show negligible decay.