Class of quantum error correcting codes
In quantum error correction, CSS codes, named after their inventors, Robert Calderbank, Peter Shor[1]
and Andrew Steane,[2] are a special type of stabilizer code constructed from classical codes with some special properties. An example of a CSS code is the Steane code.
Construction
Let
and
be two (classical)
,
codes such, that
and
both have minimal distance
, 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
.