Steanekoodit

Steanekoodit, also known as the Steane code, are a family of quantum error-correcting codes named after Andrew M. Steane, who proposed them in 1996. They are Calderbank-Shor-Steane (CSS) codes constructed from the classical [7,4,3] Hamming code and its dual. The code encodes one logical qubit into seven physical qubits and has a code distance of three, enabling correction of any single-qubit error (bit-flip, phase-flip, or combined).

Construction and operation: The stabilizer group consists of six generators, three X-type and three Z-type, derived from the parity-check matrices of the Hamming code. Logical operators act on the encoded qubit, with transversal implementation of many Clifford gates preserved by the CSS structure.

Significance: The Steane code is a canonical example of a quantum error-correcting code and is widely used in theoretical and experimental studies of fault-tolerant quantum computation. It illustrates how quantum information can be protected against errors without measuring the logical state.

Extensions and related ideas: The code can be concatenated to build larger codes and can serve as the base layer in fault-tolerant schemes. Universal quantum computation with Steane codes requires non-Clifford gates implemented via magic-state distillation or code switching.

See also: Quantum error correction, CSS codes, Steane code, concatenated codes.