Can shallow quantum circuits scramble local noise into global white noise?

Understand

Shallow quantum circuits are believed to be the most promising candidates for achieving early practical quantum advantage - this has motivated the development of a broad range of error mitigation techniques whose performance generally improves when the quantum state is well approximated by a global depolarising (white) noise model.

• While it has been crucial for demonstrating quantum supremacy that random circuits scramble local noise into global white noise - a property that has been proved rigorously - we investigate to what degree practical shallow quantum circuits scramble local noise into global white noise.
• We define two key metrics as (a) density matrix eigenvalue uniformity and (b) commutator norm.
• While the former determines the distance from white noise, the latter determines the performance of purification based error mitigation.