Quantum Error Correction

Abstract

Active error correction is necessary to counter the effect of noise. Classical error correction is generally used to protect transmission and storage of data, because in these conditions noise has had a chance to accumulate over space or time. Otherwise, there is no active error correction in computation because the signal levels are extremely high compared to the noise. Amplification cannot be used to achieve stable qubits because it cannot be done on quantum information without destroying it, since classical amplification hides an implicit measurement. This leaves error correction as the only protection of quantum information against noise and the high noise levels in quantum systems make error correction necessary at all times, including during any processing. In this chapter, we cover the most basic tools for the construction of quantum error correction codes and the basic principles of error corrected quantum computation.