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3120 results in Quantum Physics, Quantum Information and Quantum Computation

Page 53 of 156

  • 4 - Model Checking Quantum Automata

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 50-86

  • Summary

    Quantum systems are modelled as different mathematical structures, depending on their nature and complexity. This chapter considers one of the simplest (discrete-time) models of quantum systems, namely quantum automata. It introduces a way of describing linear-time (dynamic) properties of quantum systems and presents several algorithms for checking certain linear-time properties of quantum automata, for example, invariants andreachability.

  • 2 - Basics of Model Checking

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 6-30

  • Summary

    Model checking is an algorithmic technique for verification of computing and communication hardware and software. This book extends the technique of model checking for quantum systems. As preliminaries, this chapter introduces basics of model checking for both classical non-probabilistic and probabilistic systems.

  • 5 - Model Checking Quantum Markov Chains

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 87-137

  • Summary

    This chapter develops model-checking techniques for a much larger class of quantum systems modelled as quantum Markov chains or more generally, quantum Markov decision processes. The differences between quantum automata and quantum Markov systems require us to develop algorithms for the latter that are fundamentally different from those for the former.

  • 3 - Basics of Quantum Theory

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 31-49

  • Summary

    This chapter is intended to introduce some basic notions of quantum theory needed in the subsequent chapters for the reader who is not familiar with them. Quantum mechanics is a fundamental physics subject that studies the phenomena at the atomic and subatomic scales. This chapter introduces the required mathematical tools and presents the postulates mainly through their mathematical formalisms. The physics interpretation of these is only very briefly discussed.

  • 6 - Model Checking Super-Operator-Valued Markov Chains

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 138-174

  • Summary

    This chapter is devoted to studying a class of even more complex quantum systems modelled as so-called super-operator-valued Markov chains (SVMCs). This new model is particularly useful in modelling the high-level structure of quantum programs and quantum communication protocols. Several algorithms for checking SVMCs are presented in this chapter.

  • 7 - Conclusions and Prospects

  • Mingsheng Ying, University of Technology, Sydney, Yuan Feng, University of Technology, Sydney
  • Book:
    Model Checking Quantum Systems
    Published online:
    14 January 2021
    Print publication:
    04 February 2021, pp 175-180

  • Summary

    This is the concluding chapter of the book. It briefly discusses several possible directions for the further development, including the problem of state space explosion in model checking quantum systems, possible applications in verification and analysis of quantum circuits, quantum cryptographic protocols, and more generally, quantum programs.

Model Checking Quantum Systems
  • Principles and Algorithms
  • Mingsheng Ying, Yuan Feng
  • Published online:
    14 January 2021
    Print publication:
    04 February 2021
  • Model checking is one of the most successful verification techniques and has been widely adopted in traditional computing and communication hardware and software industries. This book provides the first systematic introduction to model checking techniques applicable to quantum systems, with broad potential applications in the emerging industry of quantum computing and quantum communication as well as quantum physics. Suitable for use as a course textbook and for self-study, graduate and senior undergraduate students will appreciate the step-by-step explanations and the exercises included. Researchers and engineers in the related fields can further develop these techniques in their own work, with the final chapter outlining potential future applications.

Modern Quantum Mechanics
  • 3rd edition
  • J. J. Sakurai, Jim Napolitano
  • Published online:
    10 October 2020
    Print publication:
    17 September 2020
  • Modern Quantum Mechanics is a classic graduate level textbook, covering the main concepts from quantum mechanics in a clear, organized and engaging manner. The original author, J. J. Sakurai, was a renowned particle theorist. This third edition, revised by Jim Napolitano, introduces topics that extend its value into the twenty-first century, such as modern mathematical techniques for advanced quantum mechanical calculations, while at the same time retaining fundamental topics such as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequalities. A solutions manual is available.

Page 53 of 156