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Elements of Quantum Computation and Quantum Communication

By Anirban Pathak

CRC Press – 2013 – 340 pages

Purchasing Options:

  • Add to CartHardback: $79.95
    978-1-46-651791-2
    June 19th 2013

Description

While there are many available textbooks on quantum information theory, most are either too technical for beginners or not complete enough. Filling this gap, Elements of Quantum Computation and Quantum Communication gives a clear, self-contained introduction to quantum computation and communication. Written primarily for undergraduate students in physics, mathematics, computer science, and related disciplines, this introductory text is also suitable for researchers interested in quantum computation and communication.

Developed from the author’s lecture notes, the text begins with developing a perception of classical and quantum information and chronicling the history of quantum computation and communication. It then covers classical and quantum Turing machines, error correction, the quantum circuit model of computation, and complexity classes relevant to quantum computing and cryptography. After presenting mathematical techniques frequently used in quantum information theory and some basic ideas from quantum mechanics, the author describes quantum gates, circuits, algorithms, and error-correcting codes. He also explores the significance and applications of two unique quantum communication schemes: quantum teleportation and superdense coding. The book concludes with various aspects of quantum cryptography.

Exploring recent developments and open questions in the field, this text prepares readers for further study and helps them understand more advanced texts and journal papers. Along with thought-provoking cartoons and brief biographies of key players in the field, each chapter includes examples, references, exercises, and problems with detailed solutions.

Contents

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.

Name: Elements of Quantum Computation and Quantum Communication (Hardback)CRC Press 
Description: By Anirban Pathak. While there are many available textbooks on quantum information theory, most are either too technical for beginners or not complete enough. Filling this gap, Elements of Quantum Computation and Quantum Communication gives a clear, self-contained...
Categories: Computation, Quantum Mechanics, Mathematical Physics