Fig. 5: Empirical error distribution.
From: Practical Hamiltonian learning with unitary dynamics and Gibbs states
On the left, we show the maximum absolute error across all 159 coefficients of the 80-qubit TFIM model, plotted against the total number of samples used by the learning protocol, and on the right, we show the quotient of the theoretical error upper bound and the empirical errors from numerical simulations (note the log-log scale for both plots). The violin plots show the distribution of maximum absolute errors from 100 random initializations of the TFIM (with coefficients sampled uniformly between −1 and 1). The distributions show the [1%, 99%] interval in a narrow line, a [16%, 84%] interval in a wider line, and the median marked in white. The violin plots are offset by a small amount for visualization purposes, but each cluster of four violin plots used the same number of queries marked by the dotted gray lines. We set the failure probability to δ = 15%.
