Figure 11. Comparing SNAQ logical operations to baselines under $(p_\text{g}, p_\text{sh}, p_\text{id}) = (10^{-3}, 10^{-5}, 10^{-4})$ for various $\rho.$ SNAQ’s tCNOT outperforms baseline lattice surgery methods by over 2x even for low $\rho$ and can provide up to 14.6x improvement in the range studied here. Lattice surgery on SNAQ is fast for higher $p_L$ and $\rho$, but becomes less efficient for lower $p_L$ due to the significant increase in required code distance (making each SE round take much longer).