Classical sampling of random circuits with non-unital noise
In plain words
Noise that scrambles qubits toward randomness makes deep quantum circuits easy to imitate classically. Noise that pushes qubits toward a fixed state, as energy loss does, behaves differently, and whether such noisy circuits can be imitated is open.
Precise statement
For random geometrically local circuits on $n$ qubits (Haar two-qubit gates, brickwork, depth $D$) with single-qubit amplitude damping of strength $\gamma > 0$ after each gate and no mid-circuit measurement, is there a $\operatorname{poly}(n, 1/\delta)$ classical algorithm that samples the output to total-variation error $\delta$ for all $D \ge D_0(\gamma)$, with $D_0$ independent of $n$? Local expectation values are classically computable because this noise limits the effective depth to $O(\log n)$ (Mele et al. 2024), but outputs do not anticoncentrate (Fefferman et al. 2024), so existing sampling arguments fail; for unital depolarizing noise of strength $p$, a 2026 preprint proves efficient sampling for $D \ge \Omega(p^{-1} \log p^{-1})$ in any geometrically local circuit (arXiv:2610.00548).
What would settle it
An efficient sampling algorithm with proof for the non-unital model above a noise-set depth, or a hardness argument for some depth regime growing with n.