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 processingOCoquantum key distribution Quantum gates Simple yet elucidating examples of quantum algorithms Quantum circuits that implement integral transforms Practical quantum algorithms, including GroverOCOs database search algorithm and ShorOCOs 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 computerLiquid state NMR, one of the well-understood physical systemsIonic and atomic qubitsSeveral types of Josephson junction qubitsThe quantum dots realization of qubitsLooking 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.".