Non-Randomness of Google's Quantum Supremacy Benchmark

TL;DR

This paper critically examines Google's quantum supremacy benchmark, revealing non-random patterns and biases in the generated bit-strings, and suggests new analytical tools for quantum computer performance assessment.

Contribution

The study uncovers non-randomness in Google's quantum random-bit sampling and introduces matrix analysis and Wasserstein distance as novel evaluation methods.

Findings

Google's bit-strings show stripe patterns and bias towards 0s.

Google's data fails NIST randomness tests, unlike classical samples.

Matrix-based analyses indicate deviations from ideal randomness.

Abstract

The first achievement of quantum supremacy has been claimed recently by Google for the random quantum circuit benchmark with 53 superconducting qubits. Here, we analyze the randomness of Google's quantum random-bit sampling. The heat maps of Google's random bit-strings show stripe patterns at specific qubits in contrast to the Haar-measure or classical random-bit strings. Google's data contains more bit 0 than bit 1, i.e., about 2.8\% difference, and fail to pass the NIST random number tests, while the Haar-measure or classical random-bit samples pass. Their difference is also illustrated by the Marchenko-Pastur distribution and the Girko circular law of random matrices of random bit-strings. The calculation of the Wasserstein distances shows that Google's random bit-strings are farther away from the Haar-measure random bit-strings than the classical random bit-strings. Our results imply that random matrices and the Wasserstein distance could be new tools for analyzing the performance of quantum computers.