Quantum Mechanics And Quantum Computing Notes Solutions Manual

Quantum Mechanics and Quantum Computing Notes Solutions Manual

Notes in Quantum Mechanics and Quantum Computing Solutions Manual

The goal throughout this book is to present a series of topics in quantum mechanics and quantum computing. Topics include angular momentum, the hydrogen atom, quantum entanglement, Deutsch's algorithm, Grover's algorithm, Shor's algorithm, and quantum teleportation. There are nine chapters. Chapter one is a review of complex numbers, vectors, and matrices. Chapter two is a review of vector rotations and reflections. Chapter three introduces the postulates of quantum mechanics, state vectors, and the density operator. Chapters four and five introduce angular momentum. Chapter six discusses the hydrogen atom. Chapters seven and eight introduce the fundamental unit of quantum information, the qubit, and present a series of quantum computing topics. Chapter nine discusses polarization states and optical elements, including polarizers and beam splitters. Five appendices are provided which include a quick review of Fourier transforms and Boolean algebra. Extensive use is made of examples and diagrams. The answers to all of the end-of-chapter problems are available in the solutions manual.

The goal throughout this book is to present a series of topics in quantum mechanics and quantum computing. Topics include angular momentum, the hydrogen atom, quantum entanglement, Deutsch's algorithm, Grover's algorithm, Shor's algorithm, and quantum teleportation. There are nine chapters. Chapter one is a review of complex numbers, vectors, and matrices. Chapter two is a review of vector rotations and reflections. Chapter three introduces the postulates of quantum mechanics, state vectors and the density operator. Chapters four and five introduce angular momentum. Chapter six discusses the hydrogen atom. Chapters seven and eight introduce the fundamental unit of quantum information, the qubit, and present a series of quantum computing topics. Chapter nine discusses polarization states and optical elements, including polarizers and beam splitters. Five appendices are provided, which include a quick review of Fourier transforms and Boolean algebra. Extensive use is made of examples and diagrams. The answers to all of the end-of-chapter problems are available in the solutions manual.

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.

Quantum mechanics undergraduate courses mostly focus on systems with known analytical solutions; the finite well, simple Harmonic, and spherical potentials. However, most problems in quantum mechanics cannot be solved analytically. This textbook introduces the numerical techniques required to tackle problems in quantum mechanics, providing numerous examples en route. No programming knowledge is required – an introduction to both Fortran and Python is included, with code examples throughout. With a hands-on approach, numerical techniques covered in this book include differentiation and integration, ordinary and differential equations, linear algebra, and the Fourier transform. By completion of this book, the reader will be armed to solve the Schrödinger equation for arbitrarily complex potentials, and for single and multi-electron systems.

Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems. All the important concepts and topics are included, such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gates, von Neumann entropy quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and Kerr-Hamilton operator. The topics range in difficulty from elementary o advanced. Almost all of the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn from this book important principles and strategies required for problem solving. Teachers will find it useful as a supplement, since important concepts and techniques are developed through the problems. It can also be used as a text or a supplement for linear and multilinear algebra or matrix theory.