While the circuit-level results are still at the proof-of-principle stage, we hope performance can be significantly improved in future work. To give you a sense of the difficult, here is the eldritch horror that is the TN which corresponds to d=5 circuit-level noise

As well as improvements in the thresholds, we see significant improvements in the logical error rates for all four setups considered.

Going to 3D TNs allow us to decode 3D codes such as the 3D surface code. It also lets us decode noisy 2D codes, such as the toric code under phenomenological noise, or even full-on circuit-level noise. For all but circuit noise, our decoder gives state-of-the-art thresholds.