Fig. 4: Quantum computational advantage.
From: Quantum computational advantage with a programmable photonic processor
a, Measured photon statistics of 106 samples of a high-dimensional Gaussian state compared with those generated numerically from different hypotheses. The inset shows the same distribution in a log scale having significant support past 160 photons, up to 219. b, Scatter plot of two-mode cumulants Cij for all the pairs of modes comparing experimentally obtained ones versus the ones predicted by four different hypotheses. A perfect hypothesis fit (shown in plot) would correspond to the experimentally obtained cumulants lying on a straight line at 45° (shown in plot). Note that the ground truth is the only one that explains the cumulants well. Moreover, to make a fair comparison all the hypothesis have exactly the same first-order cumulants (mean photon in each mode). c, Distribution of classical simulation times for each sample from this experiment, shown as Borealis in red and for Jiuzhang 2.0 in blue2. For each sample of both experiments, we calculate the pair (Nc, G) and then construct a frequency histogram populating this two-dimensional space. Note that because the samples from Jiuzhang 2.0 are all threshold samples they have G = 2, whereas samples from Borealis, having collisions and being photon-number resolved, have G ≥ 2. Having plotted the density of samples for each experiment in (Nc, G) space, we indicate with a star the sample with the highest complexity in each experiment. For each experiment, the starred sample is at the very end of the distribution and occurs very rarely; for Jiuzhang 2.0 this falls within the line G = 2. Finally, we overlay lines of equal simulation time as given by equation (4) as a function of Nc and G. To guide the eye we also show boundaries delineating two standard deviations in plotted distributions (dashed lines).
