Quantum computation with topological codes : from qubit to topological fault-tolerance
著者
書誌事項
Quantum computation with topological codes : from qubit to topological fault-tolerance
(Springer briefs in mathematical physics, v. 8)
Springer, c2015
- : pbk
- タイトル別名
-
Quantum computation with topological codes
大学図書館所蔵 全8件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 131-136) and index
内容説明・目次
内容説明
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
目次
1 Introduction to quantum computation 1.1 Quantum bit and elementary operations 1.2 The Solovay-Kitaev algorithm 1.3 Multi-qubit gates 1.4 Universal quantum computation 1.5 Quantum algorithms 1.5.1 Indirect measurement and the Hadamard test 1.5.2 Phase estimation, quantum Fourier transformation, and factorization 1.5.3 A quantum algorithm to approximate Jones polynomial 1.6 Quantum noise
2 Stabilizer formalism and its applications 2.1 Stabilizer formalism 2.2 Clifford operations 2.3 Pauli basis measurements 2.4 Gottesman-Knill theorem 2.5 Graph states 2.6 Measurement-based quantum computation 2.7 Quantum error correction codes 2.8 Magic state distillation 2.8.1 Knill-Laflamme-Zurek protocol 2.8.2 Bravyi-Kitaev protocol
3 Topological stabilizer codes 3.1 Z2 chain complex 3.2 A bit-flip code: exercise 3.3 Definition of surface codes 3.3.1 Surface code on a torus: toric code 3.3.2 Planar surface code 3.4 Topological quantum error correction 3.5 Error correction and spin glass model 3.6 Other topological codes 3.7 Connection to topological order in condensed matter physics
4 Topological quantum computation 4.1 Defect pair qubits 4.2 Defect creation, annihilation, and movement4.3 Logical CNOT gate by braiding 4.4 Magic state injections and distillation 4.5 Topological calculus 4.6 Faulty syndrome measurements and noise thresholds 4.7 Experimental progress
5 Topologically protected MBQC 5.1 Topological cluster state in 3D5.2 Vacuum, defect, and singular qubit regions5.3 Elementary operations in topological MBQC 5.4 Topological quantum error correction in 3D 5.5 Applications for MBQC on thermal states
A Fault-tolerant quantum computation A.1 Fault-tolerant syndrome measurements A.2 Fault-tolerant gate operations A.3 Concatenated quantum computation
B Decoding stabilizer codes
Index
References
「Nielsen BookData」 より