Finite-size boundary of classical hardness for noisy random circuit sampling

For random circuit sampling with $n$ qubits, depth $D$ and per-gate error $\epsilon$, Aharonov et al. (2023) give a classical algorithm polynomial in $n$ at constant $\epsilon$, with cost exponential in $1/\epsilon$. Determine the best classical cost to reach the experimental linear cross-entropy fidelity $F_{\mathrm{XEB}} \sim \exp(-\epsilon n D)$ as a function of $(n, D, \epsilon)$, and locate the easy-hard boundary for parameters of current experiments ($n \sim 70-100$, $\epsilon \sim 10^{-3}$).

Classical algorithms and complexity bounds that place each published experiment on a quantified side of the boundary.