Abstract
Finally, the sixth and last lesson dealt with error-correcting codes. These codes are a kind of jewel in the crown of quantum algorithms. Without them, the quantum computer would be no more than a theoretical machine with no possibility of practical realization. The formalism of stabilizers, accumulated in previous lessons, finds its full power here. The lesson began with a reminder of how error-correcting codes work in a classical register. We then tackled the quantum case of partial error correction, limiting ourselves to bit-flip error correction. This requires two ancillary qubits and several CNOT gates. The correction signal can be calculated classically outside the quantum processor, which requires a fast feedback loop, or it can be calculated quantumly outside the quantum processor, which requires a fast feedback loop
feedback loop, or it can be calculated quantumly, which requires a Toffoli gate (reversible quantum NAND) and a reset of the two ancillary qubits. Before turning to complete error-correcting codes, we explained the concept of generalized error and why simultaneous error correction along both X and Z is sufficient for complete correction of all possible errors. In the quantum case, errors are much more diverse than in the classical case. So the relaxation phenomenon, which seems relatively elementary, needs the full arsenal of the general correction algorithm to be corrected.
