Fig. 3: Median quality of recovery of one 2-qubit coupling using interpolation methods and those based on numerical derivatives^30,31,32 as a function of the standard deviation of the shot noise.

The initial time for this estimate is 30 ns and here we also generated 1000 instances of the noise with a given standard deviation. The plot shows the median quality of the recovery and the 25 and 75 percentiles. We see that the quality of the recovery for the interpolation decays approximately linearly with the shot noise, before plateauing at shot noise −6. For the numerical derivative, we see two regimes: first a linear decay of the error until a shot of noise of order 10⁻³. After that, the error plateaus and does not improve even with smaller shot noise. This is because for numerical derivative methods, at this point the dominant error source comes from the choice of initial time, whereas for interpolation it is at −6. Importantly, we see that interpolation consistently provides estimates that are no worse than the numerical derivatives method.