New circuits and an open source decoder for the color code
Craig Gidney, Cody Jones
TL;DR
This work targets the color code decoding bottleneck by introducing two new circuit families—superdense and middle-out—and an open-source Möbius decoder, Chromobius. The authors show that middle-out circuits, despite hook-induced distance loss, enable larger, more compact color-code implementations and yield competitive thresholds, reducing the gap to surface codes at realistic noise levels. Chromobius demonstrates fast decoding (around 3e5 detection events per second) and reveals that decoders can perform better with reduced information, underscoring room for improvement in color-code decoding. Collectively, the contributions provide practical tooling and circuit designs that push color-code performance closer to surface codes while enabling broader exploration of color-code architectures.
Abstract
We present two new color code circuits: one inspired by superdense coding and the other based on a middle-out strategy where the color code state appears halfway between measurements. We also present ``Chromobius'', an open source implementation of the möbius color code decoder. Using Chromobius, we show our new circuits reduce the performance gap between color codes and surface codes. Under uniform depolarizing noise with a noise strength of $0.1\%$, the middle-out color code circuit achieves a teraquop footprint of 1250 qubits (vs 650 for surface codes decoded by correlated matching). Finally, we highlight that Chromobius decodes toric color codes better when given *less* information, suggesting there's substantial room for improvement in color code decoders.