Fault-Tolerant Quantum Computing
Frank Gaitan · 2008
Having surveyed the necessary background in Chapter 1, this chapter begins developing the theory of quantum error correcting codes and fault-tolerant quantum computing. Section 2.1 introduces the dynamical framework of quantum operations. In this approach a quantum computer is treated as an open quantum system and a superoperator describes the effective interaction it has with its environment. The operator-sum representation for a quantum operation is derived, as are some of its essential properties. This section also shows how the noise model introduced in Section 1.4.1 can be represented as a quantum operation, and briefly describes other important noise models. Sec tion 2.2 introduces a number of fundamental notions associated with quantum error correcting codes, and the seven-qubit Calderbank-Shor-Steane code is used in Section 2.3 to show how these notions manifest in a specific quantum error correcting code.