  Random circuit sampling, the task to sample bit strings from a random unitary
operator, has been performed to demonstrate quantum advantage on the Sycamore
quantum processor with 53 qubits and on the Zuchongzhi quantum processor with
56 and 61 qubits. Recently, it has been claimed that classical computers using
tensor network simulation could catch on current noisy quantum processors for
random circuit sampling. While the linear cross entropy benchmark fidelity is
used to certify all these claims, it may not capture in detail statistical
properties of outputs. Here, we compare the bit strings sampled from classical
computers using tensor network simulation by Pan et al. [Phys. Rev. Lett. 129,
090502 (2022)] and by Kalachev et al. [arXiv:2112.15083 (2021)] and from the
Sycamore and Zuchongzhi quantum processors. It is shown that all Kalachev et
al.'s samples pass the NIST random number tests. The heat maps of bit strings
show that Pan et al.'s and Kalachev et al.'s samples are quite different from
the Sycamore or Zuzhongzhi samples. The analysis with the Marchenko-Pastur
distribution and the Wasssertein distances demonstrates that Kalachev et al.'s
samples are statistically close to the Sycamore samples than Pan et al.'s while
the three datasets have similar values of the linear cross entropy fidelity.
Our finding implies that further study is needed to certify or beat the claims
of quantum advantage for random circuit sampling.
