Random Circuit Sampling Supremacy Conjecture

Determine whether any classical algorithm can efficiently perform random circuit sampling within polynomial time while achieving a small, reasonable error margin, i.e., sample from the output distribution generated by random quantum circuits to within a small error bound using polynomial computational resources.

Background

Random circuit sampling (RCS) is proposed as a leading task for demonstrating quantum advantage, where a quantum processor samples bit strings from the output distribution of randomly chosen quantum circuits. The authors note that the computational complexity of RCS has been investigated theoretically and highlight a central conjecture asserting the classical intractability of achieving efficient sampling within a small error bound.

This conjecture underpins experimental claims of quantum supremacy using superconducting qubit processors (e.g., Sycamore). Resolving the conjecture would clarify the hardness landscape of RCS and strengthen or refute the theoretical foundation of beyond-classical demonstrations in the noisy, intermediate-scale regime.