Quantum Computer Science

Book description

In this text we present a technical overview of the emerging field of quantum computation along with new research results by the authors. What distinguishes our presentation from that of others is our focus on the relationship between quantum computation and computer science. Specifically, our emphasis is on the computational model of quantum computingrather than on the engineering issues associated with its physical implementation. We adopt this approach for the same reason that a book on computer programming doesn't cover the theory and physical realization of semiconductors. Another distinguishing feature of this text is our detailed discussion of the circuit complexity of quantum algorithms. To the extent possible we have presented the material in a form that is accessible to the computer scientist, but in many cases we retain the conventional physics notation so that the reader will also be able to consult the relevant quantum computing literature. Although we expect the reader to have a solid understanding of linear algebra, we do not assume a background in physics. This text is based on lectures given as short courses and invited presentations around the world, and it has been used as the primary text for a graduatecourse at George Mason University. In all these cases our challenge has been the same: how to present to a generalaudience a concise introduction to the algorithmic structure and applications of quantum computing on an extremely short period of time. The feedback from these courses and presentations has greatly aided in making our exposition of challenging concepts more accessible to a general audience.

Table of Contents: Introduction / The Algorithmic Structure of Quantum Computing / Advantages and Limitations of Quantum Computing / Amplitude Amplification / Case Study: Computational Geometry / The Quantum Fourier Transform / Case Study: The Hidden Subgroup / Circuit Complexity Analysis of Quantum Algorithms / Conclusions / Bibliography

Table of contents

  1. Contents (1/2)
  2. Contents (2/2)
  3. Preface
  4. Acknowledgements
  5. Introduction
  6. The Algorithmic Structure of Quantum Computing
    1. Understanding Quantum Algorithmics
      1. Quantum Computing Property #1
      2. Quantum Computing Property #2
      3. Quantum Computing Property #3
      4. Quantum Computing Property #4
      5. Quantum Computing Property #5
      6. Quantum Computing Property #6
      7. Quantum Computing Property #7
      8. Quantum Computing Property #8
    2. Summary
  7. Advantages and Limitations of Quantum Computing
    1. Quantum Computability
    2. Classical and Quantum Complexity Classes
    3. Advantages and Disadvantages of the Quantum Computational Model
    4. Hybrid Computing
    5. The QRAM Architecture
      1. Algorithmic Considerations
      2. Quantum Algorithm Design
    6. Quantum Building Blocks
    7. Summary
  8. Amplitude Amplification
    1. Quantum Search
      1. Quantum Oracles
      2. Searching Data in a Quantum Register
      3. Grover's Algorithm (1/2)
      4. Grover's Algorithm (2/2)
      5. Generalized Quantum Search
    2. Grover's Algorithm with Multiple Solutions
    3. Further Applications of Amplitude Amplification
    4. Summary
  9. Case Study: Computational Geometry
    1. General Spatial Search Problems
      1. QMOS for Object-Object Intersection Identification
      2. QMOS for Batch Intersection Identification
    2. Quantum Rendering
      1. Z-Buffering
      2. Ray Tracing
      3. Radiosity
      4. Level of Detail
    3. Summary
  10. The Quantum Fourier Transform
    1. The Classical Fourier Transform
    2. The Quantum Fourier Transform
    3. Matrix Representation
    4. Circuit Representation
    5. Computational Complexity
    6. Algorithmic Restrictions
      1. Normalization
      2. Initialization
      3. Output
    7. Summary
  11. Case Study: The Hidden Subgroup
    1. Phase Estimation
    2. Period Finding
    3. The Hidden Subgroup Problem
    4. Quantum Cryptoanalysis
    5. Summary
  12. Circuit Complexity Analysis of Quantum Algorithms
    1. Quantum Parallelism
    2. Algorithmic Equity Assumptions
    3. Classical and Quantum Circuit Complexity Analysis
    4. Comparing Classical and Quantum Algorithms
    5. Summary
  13. Conclusions
  14. Bibliography
  15. Biographies (1/2)
  16. Biographies (2/2)

Product information

  • Title: Quantum Computer Science
  • Author(s): Marco Lanzagorta, Jeffrey Uhlmann
  • Release date: January 2009
  • Publisher(s): Morgan & Claypool Publishers
  • ISBN: 9781598297331