Extended Data Fig. 5: Finite sampling analysis for Fc.
From: Preparing random states and benchmarking with many-body quantum chaos
a, Statistical fluctuations of the fidelity estimator, Fc, at N = 13 (dark purple) and N = 22 (light purple), computed both using our ab initio error model (solid lines) and experiment (markers) evaluated with a finite number of M bitstring samples. Data are consistent with a \(1/\sqrt{M}\) scaling, shown here as a guide to the eye (grey dashed line) b, Sample complexity of the fidelity estimator, evaluated at the N-dependent entanglement saturation time for the error model (blue crosses), and for the experimental data in Fig. 4d (red circles). A fit to the experimental data (dashed line) with functional form \(\sigma ({F}_{c})\sqrt{M}={a}^{N}\) yields an estimate of a = 1.037(2) (a similar fit to the error model yields an estimate of a = 1.039(2)).
