Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth

A single shared random bit lets shallow channel models produce correlations that matching shallow unitary models cannot.

The paper proves a scalable representational separation for bounded-connectivity quantum generative circuits at fixed shallow depth. Its construction adds spatially separated local Pauli operations controlled by one classically sampled bit, creating long-range correlations in the output distribution. In one-dimensional nearest-neighbour settings, a purely unitary model may need depth $\Omega(N)$ to reproduce the same distributions. The authors also describe an MBQC implementation and report numerical experiments consistent with the analysis. ArXiv · AI/CL/LG's note