Statistical Properties of Bit Strings Sampled from Sycamore Random Quantum Circuits.

Quantum supremacy has been recently reported for random circuit sampling on the Sycamore processor with 53 qubits. Here, we analyze the statistical properties of bit strings sampled from random quantum circuits. In contrast to classical random bit strings, bit strings sampled from Sycamore random circuits give rise to heat maps with stripe patterns at specific qubits, have more bit 1 than 0, and do not pass the NIST random number tests. The difference between the Sycamore bit strings and classical random bit strings is also demonstrated by the Marchenko-Pastur distribution and the Girko circular law of random matrices. The calculation of Wasserstein distances shows that the Sycamore bit strings are farther from bit strings sampled from Haar-measure random quantum circuits than classical random bit strings. Our results show that random matrices and Wasserstein distances could be used to analyze the performance of quantum computers.