All Codes Available in this Benchmark Database
Toric
The famous toric code, the first topological code. Terrible rate, ok-ish distance, awesome locality – a tradeoff that will turn out to be fundamental to codes with only 2D connectivity.
Shor9
One of the earliest proof-of-concept error correcting codes, a concatenation of a 3-bit classical repetition code dedicated to protecting against bit-flips, and a 3-bit repetition code dedicated to protecting against phase-flips.
Gottesman
The [[2ʲ, 2ʲ - j - 2, 3]] family of codes, the quantum equivalent of the Hamming codes, capable of correcting any single-qubit error.
Perfect5
One of the earliest proof-of-concept error correcting codes. The smallest code that can protect against any single-qubit error. Not a CSS code.
Cleve8
The [[8,3,3]] code from Cleve and Gottesman (1997), a convenient pedagogical example when studying how to construct encoding circuits, as it is one of the smallest codes with more than one logical qubit.
Steane7
One of the earliest proof-of-concept error correcting codes.
NithinCode
My friend Nithin made this one. It is here as an example placeholder as we built out the page for this code family.
Surface
An open-boundary version of the famous toric code, the first topological code. Terrible rate, ok-ish distance, awesome locality – a tradeoff that will turn out to be fundamental to codes with only 2D connectivity.