The birth of topological quantum computation took place when Alexei Kitaev (2003) made the ingenious step of turning a quantum error correcting code into a many-body interacting system. In particular, he defined a Hamiltonian whose eigenstates are also states of a quantum error correcting code. Beyond the inherited error correcting characteristics, topological systems protect the encoded information with the presence of the Hamiltonian that energetically penalises transformations between states. This opens the door for employing a large variety of many-body effects to combat errors.

Storing or manipulating information with a real physical system is naturally subject to errors. To obtain a reliable outcome from a computation we need to be certain that the processed information remains resilient to errors at all times. To overcome errors we need to detect and correct them. The error detection process is based on an active monitoring of the system and the possibility of identifying errors without destroying the encoded information. Error correction employs the error detection outcome and performs the appropriate steps to correct it, thus reconstructing the original information.

Classical error correction uses redundancy to spread information in many copies so that errors can be detected, for example by majority voting, and then corrected. Similarly, quantum error correction aims to detect and correct errors of stored quantum information. Quantum states cannot be cloned (Wootters and Zurek, 1982), so the repetition encoding cannot be employed.