Introduction to Topological Quantum Matter & Quantum Computation

What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts.

Tudor D. Stanescu

Preliminaries: From Quantum Mechanics to Quantum Computation Quatum Theory: Some Fundamentals The Geometric Phase Quantum Mechanics and Information Science Section II: Topological Phases of Matter Symmetry and Topology in Condensed Matter Physics Topological Insulators and Superconductors Interacting Topological Phases Section III: Topological Quantum States: Design and Engineering Theories of Topological Quantum Matter Majorana Zero Modes in Solid State Heterostructures Topological Phases in Cold Atom Systems Section IV: Topological Quantum Computation Elements of Quantum Information Theory Introduction to Quantum Computation Anyons and Topological Quantum Computation