Problems And Solutions In Quantum Computing And Quantum Information

Description

Review of the 2nd Edition: "This is a nice collection of standard problems and solutions, the latter being formulated on a level as elementary as possible. So it is especially useful for students who want to become acquainted with quantum information and computation. It is also useful for lecturers when they have to prepare exercises." Zentralblatt MATH Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book presents a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. Each chapter gives a comprehensive introduction to the topics. All the important concepts and areas such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, teleportation, Bell states, Bell measurement, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, quantum games, number states and Bose operators, coherent states, squeezed states, Gaussian states, coherent Bell states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton operator are included. A chapter on quantum channels has also been added. Furthermore a chapter on boolean functions and quantum gates with mapping bits to qubits is included. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Each chapter also contains supplementary problems to challenge the reader. Programming problems with Maxima and SymbolicC++ implementations are also provided. Contents Preface Notation I Finite-Dimensional Hilbert Spaces 1 Qubits 1.1 Introduction 1.2 Solved Problems 1.3 Supplementary Problems 2 Kronecker Product and Tensor Product 2.1 Introduction 2.2 Solved Problems 2.3 Supplementary Problems 3 Matrix Properties 3.1 Introduction 3.2 Solved Problems 3.3 Supplementary Problems 4 Density Operators 4.1 Introduction 4.2 Solved Problems 4.3 Supplementary Problems 5 Trace and Partial Trace 5.1 Introduction 5.2 Solved Problems 5.3 Supplementary Problems 6 Boolean Functions and Quantum Gates 6.1 Introduction 6.2 Solved Problems 6.3 Supplementary Problems 7 Unitary Transforms and Quantum Gates 7.1 Introduction 7.2 Solved Problems 7.3 Supplementary Problems 8 Entropy 8.1 Introduction 8.2 Solved Problems 8.3 Supplementary Problems 9 Measurement 9.1 Introduction 9.2 Solved Problems 9.3 Supplementary Problems 10 Entanglement 10.1 Introduction 10.2 Solved Problems 10.3 Supplementary Problems 11 Bell Inequality 11.1 Introduction 11.2 Solved Problems 11.3 Supplementary Problems 12 Teleportation 12.1 Introduction 12.2 Solved Problems 12.3 Supplementary Problems 13 Cloning 13.1 Introduction 13.2 Solved Problems 13.3 Supplementary Problems 14 Quantum Algorithms 14.1 Introduction 14.2 Solved Problems 14.3 Supplementary Problems 15 Quantum Error Correction 15.1 Introduction 15.2 Solved Problems 15.3 Supplementary Problem 16 Quantum Cryptography 16.1 Introduction 16.2 Solved Problems 16.3 Supplementary Problem Chapter 17 Quantum Channels 17.1 Introduction 17.2 Solved Problems 17.3 Supplementary Problems II Infinite-Dimensional Hilbert Spaces 18 Bose Operators and Number States 18.1 Introduction 18.2 Solved Problems 18.3 Supplementary Problems 19 Coherent States 19.1 Introduction 19.2 Solved Problems 19.3 Supplementary Problems 20 Squeezed States 20.1 Introduction 20.2 Solved Problems 20.3 Supplementary Problems 21 Trace and Partial Trace 21.1 Introduction 21.2 Solved Problems 21.3 Supplementary Problems 22 Entanglement 22.1 Introduction 22.2 Solved Problems 22.3 Supplementary Problems 23 Continuous Variable Teleportation 23.1 Introduction 23.2 Solved Problems 23.3 Supplementary Problem 24 Swapping and Cloning 24.1 Introduction 24.2 Solved Problems 24.3 Supplementary Problems 25 Homodyne Detection 25.1 Introduction 25.2 Solved Problems 25.3 Supplementary Problems 26 Hamilton Operators 26.1 Introduction 26.2 Solved Problems 26.3 Supplementary Problems Bibliography Index