Effect of Imperfections on the Cross Entropy Benchmark Fidelity of Random Circuit Sampling

Random circuit sampling (RCS) is a computationally intractable task for exact classical simulations, and thus proposed as a way to demonstrate quantum supremacy. The fidelity of RCS from a realistic quantum device with respect to its ideal case can be quantified by so-called (linear) cross entropy benchmark, which is inevitably reduced by the presence of various imperfections. Here, we present an efficient method to evaluate the amount of average fidelity reduction originating from various kinds of imperfections without any simplifying assumptions. More specifically, we develop an exact relation between the linear cross entropy averaged over random circuit realizations and the partition function of a classical spin model, which allows efficient classical simulations. Using Monte-Carlo algorithms, we quantitatively analyze the average cross entropy in the presence of imperfections for both 1D and 2D systems with various layouts of circuits for reasonably large system sizes.