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

Area of Science:

• Quantum Computing
• Statistical Analysis

Background:

• Quantum supremacy was recently demonstrated using random circuit sampling on a 53-qubit Sycamore processor.
• Analyzing the statistical properties of sampled bit strings is crucial for verifying quantum computer performance.

Purpose of the Study:

• To statistically analyze bit strings generated by the Sycamore quantum processor.
• To compare these bit strings against classical random bit strings and ideal quantum random strings.

Main Methods:

• Statistical analysis of bit string properties, including heat map patterns and bit distribution.
• Application of random matrix theory (Marchenko-Pastur distribution, Girko circular law).
• Calculation of Wasserstein distances to quantify differences between distributions.

Main Results:

• Sycamore-sampled bit strings exhibit distinct stripe patterns and a bias towards '1's.
• These strings fail standard NIST random number tests.
• Sycamore bit strings are statistically farther from ideal quantum random strings than classical random strings, as shown by random matrix theory and Wasserstein distances.

Conclusions:

• The statistical properties of Sycamore bit strings differ significantly from both classical random strings and ideal quantum random strings.
• Random matrix theory and Wasserstein distances are effective tools for assessing quantum computer performance.
• These methods can help distinguish true quantum randomness from pseudorandomness.