Quantum Information, 2 Volume Set, 2nd Edition

7 Quantum Error Correction

Markus Grassl

Max‐Planck‐Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany

7.1 Introduction

In the theory of quantum information processing, it is usually assumed that the quantum mechanical system is completely decoupled from its environment. On the other hand, when implementing quantum operations on a real quantum mechanical system, some interaction with the system is needed in order to control the dynamics of the system. Moreover, this control has only finite precision. So it seems to be inevitable that the state of the quantum systems decoherence, and, eventually the behavior of the system, becomes more and more classical. Before Shor's first paper on quantum error correction ...