Quantum Computing

With derivations, exercises, and solutions, this book examines the theoretical aspects of quantum computing and focuses on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria. It covers theoretical tools, such as vectors, matrices, quantum gates, and integral and Fourier transforms.
Covering both theory and progressive experiments, Quantum Computing: From Linear Algebra to Physical Realizations explains how and why superposition and entanglement provide the enormous computational power in quantum computing. This self-contained, classroom-tested book is divided into two sections, with the first devoted to the theoretical aspects of quantum computing and the second focused on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria.
Topics in Part I

Linear algebra
Principles of quantum mechanics
Qubit and the first application of quantum information processing-quantum key distribution
Quantum gates
Simple yet elucidating examples of quantum algorithms
Quantum circuits that implement integral transforms
Practical quantum algorithms, including Grover's database search algorithm and Shor's factorization algorithm
The disturbing issue of decoherence
Important examples of quantum error-correcting codes (QECC)

Topics in Part II

DiVincenzo criteria, which are the standards a physical system must satisfy to be a candidate as a working quantum computer
Liquid state NMR, one of the well-understood physical systems
Ionic and atomic qubits
Several types of Josephson junction qubits
The quantum dots realization of qubits

Looking at the ways in which quantum computing can become reality, this book delves into enough theoretical background and experimental research to support a thorough understanding of this promising field.