Introduction to Topological Quantum Matter & Quantum Computation

Stanescu, Tudor D.

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商品描述

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. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems.

 

 

 

 

Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.

 

 

商品描述(中文翻譯)

「拓撲」量子狀態中的「拓撲」指的是什麼?有多少種類的拓撲量子相存在?零能量瑪約拉納模式是什麼,如何在固態系統中實現,並如何用作拓撲量子計算的平台?量子計算是什麼,與傳統計算有何不同?

《拓撲量子物質與量子計算入門》回答了這些問題及其他相關問題,提供了一個關於這個迅速發展的研究領域的綜合介紹,該領域交叉於凝態物理、數學和計算機科學。本書提供了整體的觀點,非常適合進入這個領域的研究生和研究人員,因為它可以在不同領域之間進行範式和思想的有益轉移,並包含許多具體的例子來幫助讀者理解抽象且有時具有挑戰性的概念。本書探索了超越眾所周知的拓撲絕緣體和超導體的拓撲量子世界,並強調與量子計算的深刻聯繫。它介紹了拓撲量子相分類背後的關鍵原則和相關的數學概念,並討論了相互作用和非相互作用拓撲系統的模型,如托里克碼和p波超導體。本書還涵蓋了任意子的基本性質,以及關於在固態結構和冷原子系統中實現拓撲狀態的方面。

本書還以廣泛的視角介紹了量子計算,包括量子力學的基本概念,如貝爾定理,計算理論的基本概念,如計算模型和計算複雜性,量子算法的例子,以及經典和量子信息理論的要素。