Comparison of Random Circuit Sampling on Quantum and Classical Processors

Random circuit sampling, a task to sample bit-strings from a random unitary operator, has been performed on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits to demonstrate quantum advantage. In parallel, classical computers using tensor networks [Pan et al., Phys. Rev. Lett. 129, 090502 (2022) and Kalachev et al. arXiv:2112.15083 (2021)] could catch up with current quantum processors for random circuit sampling. While the linear cross entropy benchmark fidelity has been used to certify these advantage claims, it may not capture the statistical properties of output bit-strings. Here, we compare the samples generated by the Sycamore and Zuchongzhi quantum processors, and classical computers using tensor networks We found that the heat maps of all samples show stripe patterns. Some Zuchongzhi samples and Kalachev et al.'s samples pass the NIST random number tests. Using the Marchenko-Pastur distribution or the Wasserstein distance, we showed that the distances of the Sycamore samples from classical uniform bit-strings, measured as a function of the number of qubits or the number of cycles are different from those of the Zuchongzhi samples while the linear cross entropy fidelity for both samples decrease exponentially [1,2]. Also, it is shown that Kalachev et al.'s samples are statistically closer to the Sycamore samples than Pan et al.'s samples. Our results imply that various tools are needed to verify quantum advantage.