Shallow quantum generative models become strictly more powerful when augmented with classical randomness—a weak resource that enables long-range correlations impossible for unitary-only circuits at fixed depth.
This paper proves that adding shared classical randomness to shallow quantum circuits can generate probability distributions that require much deeper purely quantum circuits to replicate. The authors show this separation is achievable with simple local operations controlled by a single random bit, and demonstrate how measurement-based quantum computation naturally implements this approach.