Quantum Codes for Topological Quantum Computation
暫譯: 拓撲量子計算的量子碼
Albuquerque, Clarice Dias de, Silva, Eduardo Brandani Da, Soares Jr, Waldir Silva
- 出版商: Springer
- 出版日期: 2022-08-05
- 售價: $2,390
- 貴賓價: 9.5 折 $2,271
- 語言: 英文
- 頁數: 116
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031068327
- ISBN-13: 9783031068324
-
相關分類:
量子 Quantum、量子計算
海外代購書籍(需單獨結帳)
相關主題
商品描述
This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum computation. It combines key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, and classical and quantum coding theory to help readers understand and develop quantum codes for topological quantum computation.
One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes.
The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.
One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes.
The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.
商品描述(中文翻譯)
本書提供了一種結構化的代數和幾何方法，用於分類和構建拓撲量子計算的量子碼。它結合了線性代數、代數拓撲、雙曲幾何、群論、量子力學以及經典和量子編碼理論中的關鍵概念，幫助讀者理解和開發用於拓撲量子計算的量子碼。
構建量子計算機的一種可能方法是基於表面碼，作為穩定器碼運作。表面碼源自Kitaev的環面碼，作為通過在環面表面上分佈的量子位（qubits）來發展拓撲序的模型。表面碼的一個顯著優勢是對局部錯誤的相對容忍度。第二種方法是基於顏色碼，這是一種在幾何局部穩定器生成器的鑲嵌上定義的拓撲穩定器碼。本書提供了基本的幾何概念，如表面幾何、雙曲幾何和鑲嵌，以及基本的代數概念，如穩定器形式，這些都是構建最有前景的量子錯誤更正碼類別（如表面碼和顏色碼）所需的。
本書適合具有線性代數和量子力學基本概念理解的電機工程和數學的高年級本科生及研究生。
作者簡介
Clarice Dias de Albuquerque is an adjoint professor at the Federal University of Cariri, Brazil. She holds Bachelor's and Master's degrees from the Federal University of Ceará, Brazil, and a PhD in Electrical Engineering from the State University of Campinas, Brazil. Eduardo Brandani da Silva is an Associate Professor at the State University of Maringá, Brazil. He holds Bachelor's (1988) and Master's degrees (1992) in Mathematics from the State University of Campinas, Brazil, and a PhD in Electrical Engineering (2000) from the same university.
Waldir Silva Soares Júnior is a Professor at the Federal Technological University of Paraná, Brazil. He holds Bachelor's (2004) and Master's degrees (2008) in Mathematics from the State University of Maringá, and a PhD in Mathematics (2017) from the same university.
Waldir Silva Soares Júnior is a Professor at the Federal Technological University of Paraná, Brazil. He holds Bachelor's (2004) and Master's degrees (2008) in Mathematics from the State University of Maringá, and a PhD in Mathematics (2017) from the same university.
作者簡介(中文翻譯)
Clarice Dias de Albuquerque 是巴西卡里里聯邦大學的副教授。她擁有巴西塞阿拉聯邦大學的學士和碩士學位，以及巴西坎皮納斯州立大學的電機工程博士學位。
Eduardo Brandani da Silva 是巴西馬林加州立大學的副教授。他擁有巴西坎皮納斯州立大學的數學學士（1988年）和碩士（1992年）學位，以及同一所大學的電機工程博士學位（2000年）。Waldir Silva Soares Júnior 是巴西巴拉那聯邦科技大學的教授。他擁有馬林加州立大學的數學學士（2004年）和碩士（2008年）學位，以及同一所大學的數學博士學位（2017年）。
