  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. The neural network
incorporates the information from "flag qubits" to avoid reduction in the
effective code distance caused by the circuit. As a test, we apply the neural
network decoder to a density-matrix based simulation of a superconducting
quantum computer, demonstrating that the logical qubit has a longer life-time
than the constituting physical qubits with near-term experimental parameters.
