In quantum error correction

Quantum error correction

Quantum error correction is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum...

, CSS codes, named after their inventors, A. R. Calderbank, Peter Shor

Peter Shor

Peter Williston Shor is an American professor of applied mathematics at MIT, most famous for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical...

 and Andrew Steane

Andrew Steane

Andrew Martin Steane is Professor of physics at the University of Oxford. He is also a fellow of Exeter College, Oxford.He was a student at St Edmund Hall, Oxford where he obtained his MA and DPhil....

, are a special type of Stabilizer code

Stabilizer code

The theory of quantum error correction plays a prominent role in the practical realization and engineering ofquantum computing and quantum communication devices. The first quantumerror-correcting codes are strikingly similar to classical block codes in their...

s constructed from classical codes with some special properties.

Construction

Let and be two (classical) , codes such, that and both have minimal distance

Minimum distance

The term minimum distance is used in several ways:* In geometry, the minimum distance of a collection of points P in a space is the smallest distance between any two points of the space....

  , where is the code dual to . Then define , the CSS code of over as an code, with as follows:

Define for , where is bitwise addition modulo 2. Then is defined as .