Elements of Quantum Computation and Quantum Communication
CRC Press – 2013 – 340 pages
CRC Press – 2013 – 340 pages
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.
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
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
Deutsch Jozsa (DJ) algorithm
Solution of Pell's equation and the principal ideal problem
Quantum Error Correction
Quantum error correction
Basic idea of an error model
A little more on quantum error correction
Decoherence and decoherence free subspace
Quantum Teleportation and Superdense Coding
Different types of teleportation schemes
A simple scheme for perfect teleportation
Controlled teleportation or quantum information splitting
Modified teleportation schemes
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
Solved Examples, Further Readings, and Exercises appear at the end of each chapter.