Fig. 4

Error fluctuations across the measurements. Here we visualize the statistical fluctuations in the measurement outcomes over the course of the transmon qubit experiment. a For the experiment with Δt = 300 ns, we split up the N=1.04 × 10⁶ sequential measurement outcomes into equally large and chronologically ordered segments and calculate the error rates e _x and e _z on each segment. For a meaningful and comparable quantity for comparison, we calculate the asymptotic bound \(q - h\left( {{e_x}} \right) - h\left( {{e_z}} \right)\) for each of segment with q = 0.9, that is, the bound on the capacity rate that would be obtained if infinitely many measurements with the error rates as on the respective segments would be measured. As expected, the fluctuations decrease with the number of segments, or in other words, the larger the segments, the smaller the differences between them. Note that in contrast to all other plots, this is a linear plot. b For a glimpse on the cumulative effect of the fluctuations, we set 1000 logarithmically distributed “break points” and calculate the bound as if the experiment ended at each of those points where q = 0.9, ε = 10⁻⁶, and we pick p = 1/2. The resulting plot is to be compared with the plots in Fig. 5. The fluctuations that make the curve deviate from a smooth curve come from the fact that the measured error rates are not constant throughout the experiment, indicating that the noise affecting the transmon qubit is indeed unlikely to correspond to an i.i.d. process