Andrew Steane's 1996 code uses a classical Hamming code from 1950 twice, once for bit flips and once for phase flips, so seven physical qubits protect one logical qubit. Its cheap gates alone cannot compute anything a classical machine cannot, and the T gate that fills the gap comes from magic state distillation, the largest cost in any fault-tolerant design.
The Steane Code Explained
Andrew Steane's 1996 code uses a classical Hamming code from 1950 twice, once for bit flips and once for phase flips, so seven physical qubits protect one logical qubit. Its cheap gates alone cannot compute anything a classical machine cannot, and the T gate that fills the gap comes from magic state distillation, the largest cost in any fault-tolerant design.