A Short Introduction to Quantum Information and Quantum Computation 量子信息与量子计算导论

2006-6  

Cambridge Univ Pr  

Le Bellac, Michel  

167  

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Quantum information and computation is a rapidly expanding and cross-disciplinary subject. This book gives a self-contained introduction to the field for physicists, mathematicians and computer scientists who want to know more about this exciting subject. After a step-by-step introduction to the quantum bit (qubit) and its main properties, the author presents the necessary background in quantum mechanics. The core of the subject, quantum computation, is illustrated by a detailed treatment of three quantum algorithms: Deutsch, Grover and Shor. The final chapters are devoted to the physical implementation of quantum computers, including the most recent aspects, such as superconducting qubits and quantum dots, and to a short account of quantum information. Written at a level suitable for undergraduates in physical sciences, no previous knowledge of quantum mechanics is assumed, and only elementary notions of physics are required. The book includes many short exercises, with solutions available to instructors through solutions@cambridge.org.

ForewordPreface1 Introduction2 What is a qubit? 2.1 The polarization of light 2.2 Photon polarization 2.3 Mathematical formulation: the qubit 2.4 Principles of quantum mechanics 2.5 Quantum cryptography 2.6 Exercises 2.7 Further reading3 Manipulating qubits 3.1 The Bloch sphere, spin 1/2 3.2 Dynamical evolution 3.3 Manipulating qubits: Rabi oscillations 3.4 Principles of NMR and MRI 3.5 Exercises 3.6 Further reading4 Quantum correlations 4.1 Two-qubit states 4.2 The state operator (or density operator) 4.3 The quantum no-cloning theorem 4.4 Decoherence 4.5 The Bell inequalities 4.6 Exercises 4.7 Further reading5 Introduction to quantum computing 5.1 General remarks 5.2 Reversible calculation 5.3 Quantum logic gates 5.4 The Deutsch algorithm 5.5 Generalization to n ~ m qubits 5.6 The Grover search algorithm 5.7 The quantum Fourier transform 5.8 The period of a function 5.9 Classical algorithms and quantum algorithms 5.10 Exercises 5.11 Further reading6 Physical realizations 6.1 NMR as a quantum computer 6.2 Trapped ions 6.3 Superconducting qubits 6.4 Quantum dots 6.5 Exercises 6.6 Further reading7 Quantum information 7.1 Teleportation 7.2 Shannon entropy 7.3 yon Neumann entropy 7.4 Quantum error correction 7.5 Exercises 7.6 Further readingReferenceslndex

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