Fig. 4: Logical error rate and decoding frequency on a d × d × Nrounds rotated planar code using Minimum Weight Perfect Matching (MWPM) under circuit-level noise with p = 0.5% (see Methods).
From: Parallel window decoding enables scalable fault tolerant quantum computation
a Logical error rates as a function of the number of rounds of syndrome extraction for different code sizes for both the global offline MWPM (shaded bands), and using the parallel window algorithm (points). The parallel window decoder has no numerically significant drop in logical fidelity compared to the global decoder. Additional data with a different noise rate p and using phenomenological noise is presented in Supplementary Figures 2 and 3. b The decoding frequency (number of rounds decoded per second) as a function of the number of decoding processes for the parallel window algorithm. The decoding frequency increases with the number of processes, achieving approximately linear speed-up with the number of processes for harder decoding scenarios (d ≥ 15). The sub-linearity most noticeable on small decoding problems is due to the parallelization overhead in the software implementation. Error bars represent standard deviation over samples. Where the error bars are not visible, they are smaller than the marker size. Here we plot the decoding frequency rdec, therefore the rate of syndrome processing is rproc = rdec(d2 − 1).
