Topological Quantum Computation (Cbms Regional Conference Series in Mathematics)

Detailed Summary of the Book

In "Topological Quantum Computation," Zhenghan Wang delves into the theoretical framework where topological phases of matter are used to process and store information robustly. This book offers a comprehensive look at how the principles of topology can enhance quantum computing, providing secure, stable, and fault-tolerant computational processes. Through an in-depth discussion, the author explores fascinating concepts such as anyons, topological states, and the mathematical structures that support these phenomena, instituting the foundation of a new era in information technology.

The book begins with an introduction to the basics of topology and quantum mechanics, setting the stage for more advanced topics. It then progresses into the details of topological quantum field theories and their role in creating stable computational systems. Furthermore, Wang illustrates the utilization of braid groups and modular tensor categories as fundamental mechanisms to create and manipulate quantum information. By the end of the book, readers will have gained insight into the physical and mathematical principles that point toward the feasibility of building a quantum computer based on topologically protected operations.