Problems with analog error correction in Quantum Computing
Anwar Y. Shiekh · arXiv (Cornell University) · 2006
While the task of digital error correction seems resolved in the context of quantum computing, that of analog error correction does not seem so clear. 1 Error correction In classical digital computing a discrete set of states is employed, normally just 0 and 1, and as a result the system is implicitly error correcting, for if we were to detect a signal that is close to that representing say 1, we would not only recognize the error, but also be in a position to correct it exactly. Such is not the case with analog computing, where all signal strengths are valid and so any corrections cannot be exact. Such computers soon get swamped by their own errors, and as a result digital computing now totally dominates. This discussion is relevant to quantum computing, for both digital and analog aspects are present due to the very nature of quantum theory. 1.1 Problems with Quantum analog error correction Quantum error correction is made somewhat more subtle by the fact that one needs to locate and correct errors without making a measurement on the sate; but this is not quite so limiting as might at first seem the case. The following encoder followed by a decoder/corrector circuit [1] protects the state |ψ 〉 = a |0 〉 + b |1〉