All Codes Available in this Benchmark Database
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.
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.
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.
Steane7
One of the earliest proof-of-concept error correcting codes.
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.
Gottesman
The [[2ʲ, 2ʲ - j - 2, 3]] family of codes, the quantum equivalent of the Hamming codes, capable of correcting any single-qubit error.
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.