Quantum codes for topological quantum computation / / Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares Jr

• Autore: Dias de Albuquerque Clarice
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (123 pages) : illustrations
• Disciplina: 006.3843
• Soggetto topico: Quantum computing; Teoria quàntica; Ordinadors quàntics
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): Brandani da SilvaEduardo; SoaresWaldir Silva Jr.
• Nota di contenuto: Intro -- Contents -- 1 Introduction -- 1.1 Historical Summary -- 1.2 The Quantum Properties -- 1.2.1 Superposition of States -- 1.2.2 Entanglement -- 1.3 Principle of Quantum Error Correction -- 1.3.1 Stabilizer Codes -- 1.4 Quantum Bounds -- 1.5 Codifying with Topology -- 2 Review of Mathematical Concepts -- 2.1 Classical Error-Correcting Codes -- 2.1.1 Basic Definitions -- 2.2 Block Codes -- 2.2.1 Linear Codes -- Examples -- 2.3 Linear Algebra -- 2.3.1 Quantum Bit -- 2.3.2 Matrices and Operators -- 2.4 Quantum Information and Quantum Computation -- 2.5 A Glimpse of Quantum Mechanics -- 2.5.1 Postulates -- 2.5.2 Quantum Gates -- 2.6 Introduction to Quantum Error-Correcting Codes -- 2.6.1 The 3-Qubit Quantum Code -- 2.6.2 Shor Code -- 2.7 Quantum Error-Correction Criterion -- 2.8 CSS Codes -- 2.9 Stabilizer Quantum Codes -- 2.9.1 Anti-commutation -- 2.9.2 Stabilizer Group -- 2.9.3 Stabilizer Code and Examples -- 2.10 Hyperbolic Geometry -- 2.10.1 Isometries of the Hyperbolic Plane -- 2.10.2 Regular Tessellations -- 3 Topological Quantum Codes -- 3.1 Toric Codes -- 3.1.1 Toric Codes from the Homology Point of View -- 3.1.2 Correction at the Physical Level -- 3.2 Projective Plane and Quantum Codes -- 3.3 Other Toric Codes -- 3.3.1 Polyomino Quantum Codes -- 3.4 Hyperbolic Topological Quantum Codes -- 3.4.1 Generation of a Surface from a Polygon P -- Classification of Surfaces -- Planar Model of a Surface -- Tessellations -- 3.4.2 Constructions of Hyperbolic Topological Quantum Codes -- Classes of Hyperbolic Topological Quantum Codes -- 4 Color Codes -- 4.1 Quantum Color Codes -- 4.2 Color Codes on Compact Surfaces -- 4.3 Color Codes on Surfaces with Boundary -- 5 The Interplay Between Color Codes and Toric Codes -- 5.1 Introduction -- 5.2 Quantum Double Models -- 5.2.1 Toric Code -- 5.2.2 Color Codes. ; 5.3 Color Code Equivalence to Two Copies of Toric Codes -- Bibliography.
• Titolo autorizzato: Quantum codes for topological quantum computation
• ISBN: 3-031-06833-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996485662603316
• Lo trovi qui: Univ. di Salerno
• Serie: SpringerBriefs in mathematics.