- Peter Shor's 9-qubit-code, a.k.a. the Shor code, encodes 1 logical qubit in 9 physical qubits and can correct for arbitrary errors in a single qubit.
- Andrew Steane found a code that does the same with 7 instead of 9 qubits, see Steane code.
- Raymond Laflamme and collaborators found a class of 5-qubit codes that do the same, which also have the property of being fault-tolerant. A 5-qubit code is the smallest possible code that protects a single logical qubit against single-qubit errors.
Emphasis mine. The Raymond Laflamme code is highlighted as being fault tolerant. What does fault tolerant mean? I thought all error correction schemes were meant to make a quantum computer fault tolerant. But the grammar in this sentence makes it sound like "fault tolerant" is being used in some technical way to apply to error correcting codes. If so, what is the definition of a fault tolerant quantum error correction code? And what are examples of non-fault-tolerant and fault-tolerant error correction codes?