In error correction the idea is to protect against noise by encoding information in a way that is resistant to noise, usually by adding some redundancy to the message. We need to be able to protect against any decoherence that occurs when a quantum computer interacts with the environment, and we need to be able to protect against the accumulation of small gate errors since quantum gates need to be unitary operators. Theoretical work on quantum algorithms has shown that quantum computers have the potential to offer speedups for a variety of problems, but in practice we’d also like to be able to eventually build and operate real quantum computers. We are interested in quantum error correction, ultimately, because any real-world computing device needs to be able to tolerate noise. Note that we do assume a very basic familiarity with quantum mechanics, such as that which might be found here or here. We will start by reviewing an example from classical error correction to motivate the similarities and differences when compared against the quantum case, before moving into quantum error correction and quantum channels.
In this blog post, I (Annie Wei) will present a summary of this guest lecture, which builds up quantum error correcting codes starting from classical coding theory. On October 19, we were lucky enough to have Professor Peter Shor give a guest lecture about quantum error correcting codes.
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