Foundations of Quantum Programming

 
 
Morgan Kaufmann (Verlag)
  • 1. Auflage
  • |
  • erschienen am 28. März 2016
  • |
  • 372 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-0-12-802546-8 (ISBN)
 

Foundations of Quantum Programming discusses how new programming methodologies and technologies developed for current computers can be extended to exploit the unique power of quantum computers, which promise dramatic advantages in processing speed over currently available computer systems. Governments and industries around the globe are now investing vast amounts of money with the expectation of building practical quantum computers. Drawing upon years of experience and research in quantum computing research and using numerous examples and illustrations, Mingsheng Ying has created a very useful reference on quantum programming languages and important tools and techniques required for quantum programming, making the book a valuable resource for academics, researchers, and developers.


  • Demystifies the theory of quantum programming using a step-by-step approach
  • Covers the interdisciplinary nature of quantum programming by providing examples from many different fields including, engineering, computer science, medicine, and life sciences
  • Includes techniques and tools to solve complex control flow patterns and synchronize computations
  • Presents a coherent and self-contained treatment that will be valuable for academics and industrial researchers and developers


Mingsheng Ying (h-index: 34) is currently a Distinguished Professor at the University of Technology Sydney (UTS) and Research Director of the Center for Quantum Computation and Intelligent Systems, at UTS. He was the Cheung Kong Chair Professor, in the Department of Computer Science and the Scientific Director of the National Key Laboratory of Intelligent Technology and Systems at Tsinghua University. His research interests are quantum computation and quantum information, programming language theory and artificial intelligence. In 2008 he received The National Science and Technology Award for contributions in computer science from China.
He is an Associate Editor of Artificial Intelligence (Elsevier) and he has published more than 100 papers in top international journals and conferences such as ACM Transactions on Programming Languages and Systems, Artificial Intelligence, IEEE Transactions on Information Theory, IEEE Transactions on Software Engineering, Information and Computation, Journal of Computer and System Sciences, Physical Review Letters, POPL, CONCUR, IJCAI. He is also the author of the book Topology in Process Calculus - Approximate Correctness and Infinite Evolution of Concurrent Programs (Springer 2001).
  • Englisch
  • San Francisco
  • |
  • USA
Elsevier Science
  • 14,51 MB
978-0-12-802546-8 (9780128025468)
0128025468 (0128025468)
weitere Ausgaben werden ermittelt
  • Front Cover
  • Foundations of Quantum Programming
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • Part I: Introduction and preliminaries
  • Chapter 1: Introduction
  • 1.1 Brief history of quantum programming research
  • 1.1.1 Design of Quantum Programming Languages
  • 1.1.2 Semantics of Quantum Programming Languages
  • 1.1.3 Verification and Analysis of Quantum Programs
  • 1.2 Approaches to quantum programming
  • 1.2.1 Superposition-of-Data - Quantum Programs with Classical Control
  • 1.2.2 Superposition-of-Programs - Quantum Programs with Quantum Control
  • 1.3 Structure of the Book
  • Chapter 2: Preliminaries
  • 2.1 Quantum mechanics
  • 2.1.1 Hilbert Spaces
  • 2.1.2 Linear Operators
  • 2.1.3 Unitary Transformations
  • 2.1.4 Quantum Measurements
  • 2.1.5 Tensor Products of Hilbert Spaces
  • 2.1.6 Density Operators
  • 2.1.7 Quantum Operations
  • 2.2 Quantum circuits
  • 2.2.1 Basic Definitions
  • 2.2.2 One-Qubit Gates
  • 2.2.3 Controlled Gates
  • 2.2.4 Quantum Multiplexor
  • 2.2.5 Universality of Gates
  • 2.2.6 Measurement in Circuits
  • 2.3 Quantum algorithms
  • 2.3.1 Quantum Parallelism and Interference
  • 2.3.2 Deutsch-Jozsa Algorithm
  • 2.3.3 Grover Search Algorithm
  • 2.3.4 Quantum Walks
  • 2.3.5 Quantum-Walk Search Algorithm
  • 2.3.6 Quantum Fourier Transform
  • 2.3.7 Phase Estimation
  • 2.4 Bibliographic remarks
  • Part II: Quantum programswith classicalcontrol
  • Chapter 3: Syntax and semantics of quantum programs
  • 3.1 Syntax
  • 3.2 Operational semantics
  • 3.3 Denotational semantics
  • 3.3.1 Basic Properties of Semantic Functions
  • 3.3.2 Quantum Domains
  • 3.3.3 Semantic Function of Loop
  • 3.3.4 Change and Access of Quantum Variables
  • 3.3.5 Termination and Divergence Probabilities
  • 3.3.6 Semantic Functions as Quantum Operations
  • 3.4 Classical recursion in quantum programming
  • 3.4.1 Syntax
  • 3.4.2 Operational Semantics
  • 3.4.3 Denotational Semantics
  • 3.4.4 Fixed Point Characterization
  • 3.5 Illustrative example: Grover quantum search
  • 3.6 Proofs of lemmas
  • 3.7 Bibliographic remarks
  • Chapter 4: Logic for quantum programs
  • 4.1 Quantum predicates
  • 4.1.1 Quantum Weakest Preconditions
  • 4.2 Floyd-Hoare logic for quantum programs
  • 4.2.1 Correctness Formulas
  • 4.2.2 Weakest Preconditions of Quantum Programs
  • 4.2.3 Proof System for Partial Correctness
  • 4.2.4 Proof System for Total Correctness
  • 4.2.5 An Illustrative Example: Reasoning aboutthe Grover Algorithm
  • 4.3 Commutativity of quantum weakest preconditions
  • 4.4 Bibliographic remarks
  • Chapter 5: Analysis of quantum programs
  • 5.1 Termination analysis of quantum while-loops
  • 5.1.1 Quantum while-Loops with Unitary Bodies
  • 5.1.2 General Quantum while-Loops
  • 5.1.3 An Example
  • 5.2 Quantum graph theory
  • 5.2.1 Basic Definitions
  • 5.2.2 Bottom Strongly Connected Components
  • 5.2.3 Decomposition of the State Hilbert Space
  • 5.3 Reachability analysis of quantum Markov chains
  • 5.3.1 Reachability Probability
  • 5.3.2 Repeated Reachability Probability
  • 5.3.3 Persistence Probability
  • 5.4 Proofs of technical lemmas
  • 5.5 Bibliographic remarks
  • Part III: Quantumprograms withquantum control
  • Chapter 6: Quantum case statements
  • 6.1 Case Statements: from Classical to Quantum
  • 6.2 QuGCL: A Language with Quantum Case Statement
  • 6.3 Guarded Compositions of Quantum Operations
  • 6.3.1 Guarded Composition of Unitary Operators
  • 6.3.2 Operator-Valued Functions
  • 6.3.3 Guarded Composition of Operator-Valued Functions
  • 6.3.4 Guarded Composition of Quantum Operations
  • 6.4 Semantics of QuGCL Programs
  • 6.4.1 Classical States
  • 6.4.2 Semi-Classical Semantics
  • 6.4.3 Purely Quantum Semantics
  • 6.4.4 Weakest Precondition Semantics
  • 6.4.5 An Example
  • 6.5 Quantum Choice
  • 6.5.1 Choices: from Classical to Quantum via Probabilistic
  • 6.5.2 Quantum Implementation of Probabilistic Choice
  • 6.6 Algebraic Laws
  • 6.7 Illustrative Examples
  • 6.7.1 Quantum Walks
  • 6.7.2 Quantum Phase Estimation
  • 6.8 Discussions
  • 6.8.1 Coefficients in Guarded Compositions of Quantum Operations
  • 6.8.2 Quantum Case Statements Guarded by Subspaces
  • 6.9 Proofs of Lemmas, Propositions and Theorems
  • 6.10 Bibliographic Remarks
  • Chapter 7: Quantum recursion
  • 7.1 Syntax of quantum recursive programs
  • 7.2 Motivating examples: Recursive quantum walks
  • 7.2.1 Specification of Recursive Quantum Walks
  • 7.2.2 How to Solve Recursive Quantum Equations
  • 7.3 Second quantization
  • 7.3.1 Multiple-Particle States
  • 7.3.2 Fock Spaces
  • 7.3.3 Observables in Fock Spaces
  • 7.3.4 Evolution in Fock Spaces
  • 7.3.5 Creation and Annihilation of Particles
  • 7.4 Solving recursive equations in the free fock space
  • 7.4.1 A Domain of Operators in the Free Fock Space
  • 7.4.2 Semantic Functionals of Program Schemes
  • 7.4.3 Fixed Point Semantics
  • 7.4.4 Syntactic Approximation
  • 7.5 Recovering symmetry and antisymmetry
  • 7.5.1 Symmetrization Functional
  • 7.5.2 Symmetrization of the Semantics of Quantum Recursive Programs
  • 7.6 Principal system semantics of quantum recursion
  • 7.7 Illustrative examples: Revisit recursive quantum walks
  • 7.8 Quantum while-loops (with quantum control)
  • 7.9 Bibliographic remarks
  • Part IV: Prospects
  • Chapter 8: Prospects
  • 8.1 Quantum Programs and Quantum Machines
  • 8.2 Implementation of quantum programming languages
  • 8.3 Functional Quantum Programming
  • 8.4 Categorical semantics of quantum programs
  • 8.5 From Concurrent Quantum Programs to Quantum Concurrency
  • 8.6 Entanglement in quantum programming
  • 8.7 Model-Checking Quantum Systems
  • 8.8 Quantum programming applied to physics
  • Bibliography
  • Index
  • Back cover

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