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Preface; Contents; Introduction; 1.1What Is Quantum Computing?; 1.1.1Intuitive Definition of Quantum Computers; 1.1.2History of Quantum Computers; 1.2What Is Quantum Mechanics?; 1.2.1Classical Physics; 1.2.2Quantum Theory; Models of a Computer; 2.1Neumann-Type Computer; 2.1.1ENIAC and EDVAC; 2.1.2Architecture of Neumann-Type Computers; 2.2Turing Machine; 2.2.1Structure of Turing Machine; 2.2.2Formal Definition of Turing Machine; 2.3Boolean Algebra; 2.3.1Axiomatization of Boolean Algebras; 2.3.2Truth-Value Table; 2.3.3Boolean Algebra and Hardware; Quantum Mechanics
3.1Basics of Quantum Mechanics3.1.1History; 3.1.2From Classical Mechanics to Quantum Mechanics; 3.2Wave Mechanics; 3.2.1Wave Function; 3.2.2Schrödinger Equation; 3.3Matrix Mechanics; 3.3.1Linear Algebra; 3.3.2Measurement; 3.3.3Bra-Ket Notation; 3.4Uncertainty Principle; 3.4.1Starting Point; 3.4.2Mathematical Formulation; 3.5Quantum Systems; 3.5.1Postulates of Quantum Systems; 3.5.2Some Foundational Problems; Quantum Computers; 4.1Origins of Quantum Computers; 4.1.1Feynman's Ideas; 4.1.2Simulating Quantum Mechanics; 4.2Quantum Turing Machine; 4.2.1Church-Turing Hypothesis and Beyond
4.2.2Universal Quantum Computer4.2.3Formalization of Quantum Turing Machine; 4.3Qubit; 4.3.1Bit vs. Qubit; 4.3.2Polarization of Photons; 4.4Quantum Gates; 4.4.1Outline of Quantum Gates; 4.4.2Useful Quantum Gates; 4.4.3No-Cloning Theorem; 4.5Shor's Algorithm; 4.5.1RSA Code; 4.5.2Description of Shor's Algorithm; 4.5.3Discrete Fourier Transform and Quantum Algorithm; 4.6Other Quantum Algorithms; 4.6.1Grover's Algorithm; 4.6.2HS Algorithm; 4.6.3Quantum Walks; 4.6.4Adiabatic Quantum Algorithm; Applications of Quantum Computing; 5.1Quantum Codes; 5.1.1Quantum Key Distribution
5.1.2Example of Quantum Code5.2Quantum Communications; 5.2.1Holevo Bound; 5.2.2Quantum Teleportation; 5.3Quantum Programming; 5.3.1QCL; 5.3.2Other Quantum Programming Languages; Future of Quantum Computing; 6.1Implementations of Quantum Computers; 6.1.1NMR Quantum Computer; 6.1.2Trapped Ion Quantum Computer; 6.1.3Other Approaches; 6.1.4DiVincenzo's Five Criteria; 6.2Problems of Quantum Computing; 6.2.1Theoretical Problems; 6.2.2Practical Problems; References; Glossary; Index
3.1Basics of Quantum Mechanics3.1.1History; 3.1.2From Classical Mechanics to Quantum Mechanics; 3.2Wave Mechanics; 3.2.1Wave Function; 3.2.2Schrödinger Equation; 3.3Matrix Mechanics; 3.3.1Linear Algebra; 3.3.2Measurement; 3.3.3Bra-Ket Notation; 3.4Uncertainty Principle; 3.4.1Starting Point; 3.4.2Mathematical Formulation; 3.5Quantum Systems; 3.5.1Postulates of Quantum Systems; 3.5.2Some Foundational Problems; Quantum Computers; 4.1Origins of Quantum Computers; 4.1.1Feynman's Ideas; 4.1.2Simulating Quantum Mechanics; 4.2Quantum Turing Machine; 4.2.1Church-Turing Hypothesis and Beyond
4.2.2Universal Quantum Computer4.2.3Formalization of Quantum Turing Machine; 4.3Qubit; 4.3.1Bit vs. Qubit; 4.3.2Polarization of Photons; 4.4Quantum Gates; 4.4.1Outline of Quantum Gates; 4.4.2Useful Quantum Gates; 4.4.3No-Cloning Theorem; 4.5Shor's Algorithm; 4.5.1RSA Code; 4.5.2Description of Shor's Algorithm; 4.5.3Discrete Fourier Transform and Quantum Algorithm; 4.6Other Quantum Algorithms; 4.6.1Grover's Algorithm; 4.6.2HS Algorithm; 4.6.3Quantum Walks; 4.6.4Adiabatic Quantum Algorithm; Applications of Quantum Computing; 5.1Quantum Codes; 5.1.1Quantum Key Distribution
5.1.2Example of Quantum Code5.2Quantum Communications; 5.2.1Holevo Bound; 5.2.2Quantum Teleportation; 5.3Quantum Programming; 5.3.1QCL; 5.3.2Other Quantum Programming Languages; Future of Quantum Computing; 6.1Implementations of Quantum Computers; 6.1.1NMR Quantum Computer; 6.1.2Trapped Ion Quantum Computer; 6.1.3Other Approaches; 6.1.4DiVincenzo's Five Criteria; 6.2Problems of Quantum Computing; 6.2.1Theoretical Problems; 6.2.2Practical Problems; References; Glossary; Index