Problems and Solutions in Quantum Computing and Quantum Information

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.

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Contents:

• Finite-Dimensional Hilbert Spaces:

  • Qubits
  • Kronecker Product and Tensor Product
  • Matrix Properties
  • Density Operators
  • Trace and Partial Trace
  • Boolean Functions and Quantum Gates
  • Unitary Transforms and Quantum Gates
  • Entropy
  • Measurement
  • Entanglement
  • Bell Inequality
  • Teleportation
  • Cloning
  • Quantum Algorithms
  • Quantum Error Correction
  • Quantum Cryptography
  • Quantum Channels

• Infinite-Dimensional Hilbert Spaces:

  • Bose Operators and Number States
  • Coherent States
  • Squeezed States
  • Trace and Partial Trace
  • Entanglement
  • Continuous Variable Teleportation
  • Swapping and Cloning
  • Homodyne Detection
  • Hamilton Operators

• Bibliography

• Index

Readership: Graduates and researchers in theoretical and mathematical physics.
Key Features:

• New material includes quantum channels and quantum gates