ABSTRACT
QUANTUM PHYSICS AND INFORMATION SCIENCE HAVEdeveloped a fruitful relationship over the past few decades. On the one hand, there is the excitement factor: our increasing ability to control the quantum states of individual microsystems bears the promise of new technologies, such as computers that can handle classically intractable problems or cryptographic protocols that are perfectly safe. On the other hand, this relationship has shed new light on fundamental physics problems, including a reconsideration of the foundations of quantum mechanics from an information theoretical perspective. The study of topological quantum phases is another area that has already benefited from this relationship and, most likely, will continue to profit from it. It is this thought that motivates us to provide a very brief introduction to basic concepts in quantum information (Chapter 10) and quantum computation (Chapter 11), with a focus on topological quan-
tum computation (Chapter 12). The goal of this chapter is to familiarize the reader with fundamental concepts and basic problems in quantum information theory. The subsequent two chapters deal with general aspects pertaining to quantum computation and with specific features associated with computation using topological quantum states. The quantum mechanical formalism that is relevant for this discussion is summarized in Chapter 1, in particular Section 1.2, which presents the operational formulation of quantum mechanics — the “natural” language of quantum information theory. The classical analogs of some of the concepts and ideas summarized here are introduced in Chapter 3 (Section 3.2). For a thorough treatment of concepts, problems, and techniques in quantum information theory the reader is referred to the books by Nielsen and Chuang [329] and Wilde [464]. An undergraduate level introduction to this subject can be found, for example, in Schumacher and Westmoreland [394]. Some of the philosophical implications of the relationship between quantum mechanics and information theory are discussed in Timpson [425].
