An introduction to quantum error correction

Communication at high speeds, long distances, and in unknown environments often requires combatting noise that may affect or destroy data before it has reached its intended destination. When designing robust, practical communication systems, it is important to take such effects into account and engineer a system to be as immune to noise as possible. Classical communications often relies upon various error detection and correction schemes, from the simple parity check to a variety of more sophisticated correction algorithms, designed to ensure nearly error-free transmission of data. Classical error-correction systems often employ redundancy and checksums to accomplish error correction; however, error correction in quantum communication channels is complicated by the fact that a qubit’s state is affected by measurement. Furthermore, one may only have a single copy of each qubit to work with in quantum algorithms: in quantum cryptography algorithms such as BB84, for instance, it does not make sense to re-transmit qubits prior to establishing a key. In this paper, we explore the problem of quantum error correction and present some of the simple algorithms that have been proposed to correct errors of various types in a channel of qubits.