Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates, it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open.
In the presented work, we initiate the study of these questions and show how techniques from quantum computation and communication can be combined to arrive at a communication analog of the famous threshold theorem. The threshold theorem says that one can compute (and now also communicate), when the noise per gate is below a certain threshold.
We expect our results to be relevant for satellite communication as well as the execution of quantum software on distributed quantum processor cores.