Chapter 13 Correcting quantum channels

About the one big problem that hinders us from physically implementing everything that we’ve learnt so far: decoherence. But also about how we can start to deal with it via some elementary error correction, including the Shor [[9,1,3]] quantum code, which generalises the classical [3,1,3]-code.

As the adage goes, “in theory, theory and practice rarely differ; in practice, they often do”. In theory, we know how to build a quantum computer: we can start with simple quantum logic gates and try to integrate them together into quantum networks. However, if we keep on putting quantum gates together into networks we will quickly run into some serious problems in practice: the more interacting qubits involved, the harder it is to prevent them from getting entangled with the environment. This unwelcome entanglement, also known as decoherence, destroys the interference, and thus the power, of quantum computing. To counteract this problem, we will look at the idea of error correcting codes, which protect our data against unwanted errors, but at the cost of encoding it across more ancillary qubits.