Abstract
The sixth and final lesson was devoted first to the discussion of error correction for the preservation of quantum information. Initially, the notion of quantum error correction seemed paradoxical, since in order to correct an error, one must first have discovered it. However, in quantum mechanics, measuring a system generally leads to the destruction of the information it contains, if the axis along which the measurement is made does not coincide with the axis originally used to encode the information. Such a phenomenon does not exist for a classical system, whose state can in principle be measured without ever disturbing it, even if we ignore the coding process used to retrieve the information associated with this state. However, it is possible to correct the errors affecting a quantum superposition of states if several quantum bits are available : five is the minimum number, but a larger number is often required to simplify the system architecture handling quantum computing. By encoding the desired logical quantum bit from two correctly chosen, interleaved states of the physical quantum bits, it is possible to know that an error has disturbed one of the physical quantum bits without destroying the state superposition of the logical bit. The quantum error-correcting code is designed in such a way that the error translates the logical bit en bloc into the vast space of entangled states of the physical bits. Which of these block translations has taken place is itself a measurable variable, and it can be shown that this measurement does not affect the logic bit, unlike direct measurement of the latter. Once the type of error is known, it's easy to carry out the correction operation by performing a series of logic gates on the physical bits.
