Kostyantyn Kechedzhi
Recently, digital quantum processors surpassed classical supercomputers on Random Circuit Sampling (RCS) tasks despite the presence of a finite level of noise. Noise suppresses quantum correlations and therefore may limit the extent of quantum correlation across the system. It is important to identify the boundary between the weak and strong noise regimes where in the former case all of the Hilbert space of the quantum processor may be leveraged and in the latter quantum correlations are limited by noise. In this presentation we demonstrate that a discontinuous phase transition can be identified in the statistics of the noisy random circuit output which separates weak and strong noise regimes. We describe a statistical model in which the phase transition can be identified and described analytically in the thermodynamic limit. We demonstrate the signatures of the transition in numerics and experiments on a digital quantum processor. The phase transition separates the parameter regimes where XEB is a reliable estimator of fidelity and where it is not. The presence of the discontinuous phase transition also allows us to identify bounds on the best performance of the so-called spoofing algorithms which attempt to reproduce samples with XEB equal to that of the noisy quantum processor using only polynomial resources.