Neural network decoder for topological color codes with circuit level noise

Understand

A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information.

• At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment --- without the need for a priori knowledge of the error model.
• Here, we apply this technique to topological color codes.
• We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate $\epsilon_{\rm L}$ of the encoded logical qubit to values much below the error rate $\epsilon_{\rm phys}$ of the physical qubits --- fitting the expected power law scaling $\epsilon_{\rm L} \propto \epsilon_{\rm phys}^{(d+1)/2}$, with $d$ the code distance.