Elements of quantum computation and quantum communication

✍ Scribed by Pathak, Anirban

• Publisher: CRC Press
• Year: 2013
• Tongue: English
• Leaves: 338
• Category: Library

✦ Synopsis

"This book originated from a course on quantum computing designed for an audience of varied experience, backgrounds and qualifications. Not assuming that the readers have advanced knowledge of information theory or quantum mechanics or linear algebra, this introductory text book provides a lucid introduction to the rapidly developing field of quantum computing and quantum communication, rigorously proving all mathematical sentences"-- Read more...

Abstract: "This book originated from a course on quantum computing designed for an audience of varied experience, backgrounds and qualifications. Not assuming that the readers have advanced knowledge of information theory or quantum mechanics or linear algebra, this introductory text book provides a lucid introduction to the rapidly developing field of quantum computing and quantum communication, rigorously proving all mathematical sentences"

✦ Table of Contents

Content: Introduction and Overview What is information? Why do we need to know how to manage information? A brief history of quantum computation and quantum communication Basic Ideas of Classical and Quantum Computational Models and Complexity Classes Elementary idea of complexity of an algorithm Turing machine Circuit model of computation Computational complexity and related issues Mathematical Tools and Simple Quantum Mechanics Required for Quantum Computing A little bit of algebra required for quantum computing A little bit of quantum mechanics A little more of algebra for quantum computing Quantum Gates and Quantum Circuits Single qubit gates Two qubit gates Three qubit gates A little more on quantum gates Quantum circuits Discussion Quantum Algorithms Deutsch's algorithm Deutsch Jozsa (DJ) algorithm Grover's algorithm Simon's algorithm Shor's algorithm Solution of Pell's equation and the principal ideal problem Discussion Quantum Error Correction Quantum error correction Basic idea of an error model A little more on quantum error correction Decoherence and decoherence free subspace DiVincenzo criteria Quantum Teleportation and Superdense Coding Different types of teleportation schemes A simple scheme for perfect teleportation Probabilistic teleportation Controlled teleportation or quantum information splitting Modified teleportation schemes Superdense coding Quantum Cryptography Jargon related to cryptography Some interesting classical ciphers Different aspects of quantum cryptography Let us develop protocols of QKD Protocol 5: B92 protocol GV protocol: QKD with orthogonal states Ping-pong and modified ping-pong protocols DLL and modified DLL protocols DSQC protocol and its modifications Protocols of quantum dialogue Protocol 18: Quantum secret sharing Discussion Solved Examples, Further Readings, and Exercises appear at the end of each chapter.

✦ Subjects

Quantum computers. Quantum communication. Quantum theory -- Mathematics. Quantum theory / Mathematics. MATHEMATICS / General MATHEMATICS / Advanced SCIENCE / Quantum Theory