Figure 1
From: Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
Numerical error threshold estimates for the sweep decoder applied to the toric code on the rhombic dodecahedral lattice. In (a), we plot the error threshold \(p_{\mathrm{th}}(N)\) as function of the number of error-correction cycles N, for an error model with equal phase-flip (p) and measurement error (q) probabilities (\(\alpha =q/p=1\)). The inset shows the data for \(N=2^{10}\), where we use \(10^4\) Monte Carlo samples for each point. Using the ansatz in Eq. (10), we estimate the sustainable threshold to be \(p_{\mathrm{sus}}\approx 2.1\%\). In (b), we plot \(p_{\mathrm{sus}}\) for error models with different values of \(\alpha\), where we approximate \(p_{\mathrm{sus}}\approx p_{\mathrm{th}}(2^{10})\).
