The distance is the minimum weight of a Pauli operator that preserves the code space but acts nontrivially on its logical information.
An error syndrome records which stabilizer generators commute or anticommute with an error.
The Steane code is a seven-qubit CSS stabilizer code encoding one logical qubit with distance three.
A color code places qubits on a three-colorable lattice and assigns X-type and Z-type stabilizers to each colored plaquette.
A string operator creates excitations at its endpoints. Multiplying by a successive segment moves an endpoint because the shared intermediate excitation is toggled twice.
The surface code is a topological stabilizer code whose electric and magnetic excitations are bosons with mutual-semion braiding.
The toric code has commuting star and plaquette stabilizers. Its electric and magnetic excitations are bosons with mutual-semion statistics, and their fusion is a fermion.
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Stabilizer codes are a class of quantum error-correcting codes that are used to protect quantum information from errors due to decoherence and other quantum noise. They are particularly important in quantum computing and quantum information theory because they provide a way to encode quantum bits (qubits) into larger systems in a way that allows for the detection and correction of errors.