CSS Code

In quantum error correction, CSS codes, named after their inventors, Robert Calderbank, Peter Shor
and Andrew Steane, 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 $C_1$ and $C_2$ be two (classical) ,k_1/math>, ,k_2/math> codes such, that $C_2 \subset C_1$ and $C_1 , C_2^\perp$ both have minimal distance $\geq 2t+1$, where $C_2^\perp$ is the code dual to $C_2$. Then define $\text(C_1,C_2)$, the CSS code of $C_1$ over $C_2$ as an ,k_1 - k_2, d/math> code, with $d \geq 2t+1$ as follows:

Define for $x \in C_1 : x + C_2 \rangle :=$ $1 / \sqrt$ $\sum_ x + y \rangle$, where $+$ is bitwise addition modulo 2. Then $\text(C_1,C_2)$ is defined as $\$.

References

External links

Linear algebra
Quantum information science

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