Stabilizer Code

A stabilizer code on qubits is a quantum error-correcting code that is the common eigenspace of an abelian group contained in the -qubit Pauli group, with . The group is the quantum stabilizer group of the quantum error-correcting code.

If has independent generators, the code encodes logical qubits and has dimension . Error detection and correction can be studied through commutation with the stabilizer generators and the Knill-Laflamme conditions.

Existence bounds for stabilizer codes can be obtained from symplectic self-orthogonal linear codes. Yuan and Zhu (2026) proved a finite-length factor- improvement of a quantum Gilbert-Varshamov bound in a restricted relative-distance range. The classical self-orthogonal dimension is subtracted from the block length to obtain the number of encoded logical systems.