The sixth lesson concluded the lecture with a brief overview of error-correcting code methods in quantum information (9th chapter). We began by summarizing the methods of decoherence control based on observation and manipulation of the environment, described in the previous lessons, and concluded that these methods are insufficient to solve the decoherence problem of the quantum computer. None of these methods provides a universal answer to the problem of decoherence: how can a system of qubits be protected from the disruptive effects of an arbitrary environment?
Quantum corrector codes offer a different approach to the problem. Their principle is similar to that of error-correction codes in a conventional computer. A logical qubit is encoded redundantly in several physical qubits. These qubits are mutually intricate (a property of course absent from the classical problem). Any errors are detected by measuring a set of operators on the intricate qubits, and a correction is made to reconstitute the original logical qubit.
Quantum error-correcting codes thus meet, in principle, the operating requirements of a quantum computer. They are applicable to general decoherence processes in arbitrary environments. There is a finite threshold of elementary operation fidelity beyond which errors do not accumulate critically. It was the existence of the "fault-tolerant computation" theorem that triggered active research into quantum computing. However, the critical threshold is very low and poses a considerable challenge to experimenters. It is far from certain that this threshold can be reached with realistic qubits. Coding is also extremely resource-intensive, requiring the ability to control a very large number of qubits. This is still far from being the case, and building a practical quantum computer still poses formidable problems.
