Sampling random quantum circuits: a pedestrian's guide

Understand

Recent experiments completed by collaborating research groups from Google, NASA Ames, UC Santa Barbara, and others provided compelling evidence that quantum supremacy has finally been achieved on a superconducting quantum processor.

• The theoretical basis for these experiments depends on sampling the output distributions of random quantum circuits; unfortunately, understanding how this theoretical basis can be used to define quantum supremacy is an extremely difficult task.
• Anyone attempting to understand how this sampling task relates to quantum supremacy must study concepts from random matrix theory, mathematical analysis, quantum chaos, computational complexity, and probability theory.
• Resources connecting these concepts in the context of quantum supremacy are scattered and often difficult to find.