  Surface codes reach high error thresholds when decoded with known algorithms,
but the decoding time will likely exceed the available time budget, especially
for near-term implementations. To decrease the decoding time, we reduce the
decoding problem to a classification problem that a feedforward neural network
can solve. We investigate quantum error correction and fault tolerance at small
code distances using neural network-based decoders, demonstrating that the
neural network can generalize to inputs that were not provided during training
and that they can reach similar or better decoding performance compared to
previous algorithms. We conclude by discussing the time required by a
feedforward neural network decoder in hardware.
