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Update README.md
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oscarhiggott committed Oct 25, 2022
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Expand Up @@ -44,14 +44,12 @@ Our new implementation is **over 100x faster** than previous versions of PyMatch
At 0.1% circuit-noise, PyMatching v2.0 can decode a distance 19 surface code in less than 1 microsecond per
measurement round, and the runtime is approximately linear in the size of the graph.

The benchmarks in the two plots below (run on an M1 chip) compare the performance of PyMatching v2.0 with the previous
version (v0.7) as well as with NetworkX for decoding surface code circuits with circuit-level depolarising noise.
The plot below compares the performance of PyMatching v2.0 with the previous
version (v0.7) as well as with NetworkX for decoding surface code circuits with circuit-level depolarising noise (all decoders were run on an M1 processor).
The equations T=N^x in the legends (and plotted as dashed lines) are obtained from a fit to the same dataset for
distance > 10, where N is the number of detectors (nodes) per round, and T is the decoding time per round.

| Decoding time per round for p=0.1% circuit-level noise | Decoding time per round for p=0.5% circuit-level noise |
|:----------------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------------------------------------------------:|
| ![Below threshold](docs/figures/pymatching_v0_7_vs_pymatching_v2_0_vs_networkx_timing_p_0_001_per_round_fix_ylim.png) | ![Near threshold](docs/figures/pymatching_v0_7_vs_pymatching_v2_0_vs_networkx_timing_p_0_005_per_round_fix_ylim.png) |
![PyMatching new vs old vs NetworkX](https://github.com/oscarhiggott/PyMatching/raw/master/docs/figures/pymatching_v0_7_vs_pymatching_v2_0_vs_networkx_timing_p_0_001_per_round.png)


Sparse blossom is conceptually similar to the approach described in [this paper](https://arxiv.org/abs/1307.1740)
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