Foundations of Quantum Programming, 2nd Edition

✍ Scribed by Mingsheng Ying

• Publisher: Elsevier Inc.
• Year: 2024
• Tongue: English
• Leaves: 400
• Edition: 2
• Category: Library

✦ Synopsis

Quantum computers promise dramatic advantages in processing speed over currently available computer systems. Quantum computing offers great promise in a wide variety of computing and scientific research, including Quantum cryptography, machine learning, computational biology, renewable energy, computer-aided drug design, generative chemistry, and any scientific or enterprise application that requires computation speed or reach beyond the limits of current conventional computer systems.

Foundations of Quantum Programming, Second Edition discusses how programming methodologies and technologies developed for current computers can be extended for quantum computers, along with new programming methodologies and technologies that can effectively exploit the unique power of quantum computing. The Second Edition includes two new chapters describing programming models and methodologies for parallel and distributed quantum computers. The author has also included two new chapters to introduce Quantum Machine Learning and its programming models – parameterized and differential quantum programming. In addition, the First Edition's preliminaries chapter has been split into three chapters, with two sections for quantum Turing machines and random access stored program machines added to give the reader a more complete picture of quantum computational models. Finally, several other new techniques are introduced in the Second Edition, including invariants of quantum programs and their generation algorithms, and abstract interpretation of quantum programs.

Demystifies the theory of quantum programming using a step-by-step approach
Includes methodolog
ies, techniques, and tools for the development, analysis, and verification of quantum programs and quantum cryptographic protocols
Covers the interdisciplinary nature of quantum programming by providing preliminaries from quantum mechanics, mathematics, and computer science, and pointing out its potential applications to quantum engineering and physics
Presents a coherent and self-contained treatment that will be valuable for academic and industrial researchers and developers
Adds new developments such as parallel and distributed quantum programming; and introduces several new program analysis techniques such as invariants generation and abstract interpretation

✦ Table of Contents

Cover image
Title page
Table of Contents
Copyright
Biography
Prof. Mingsheng Ying (1964–)
Preface to the second edition
Preface to the first edition
Acknowledgements
Chapter 1: Introduction
Abstract
1.1. From classical programming to quantum programming – “Everything old is new again!”
1.2. Approaches to quantum programming
1.3. Structure of the book
References
Part I: Preliminaries
Introduction
References
Chapter 2: Quantum mechanics
Abstract
2.1. Hilbert spaces
2.2. Linear operators
2.3. Quantum measurements
2.4. Tensor products of Hilbert spaces
2.5. Density operators
2.6. Quantum operations
2.7. Bibliographic remarks and further readings
References
Chapter 3: Models of quantum computation
Abstract
3.1. Quantum circuits
3.2. Quantum Turing machines
3.3. Quantum random access stored-program machines
3.4. Bibliographic remarks and further readings
References
Chapter 4: Quantum algorithms and communication protocols
Abstract
4.1. Quantum parallelism and interference
4.2. Quantum algorithms based on Hadamard transforms
4.3. Quantum Fourier transform
4.4. Grover search algorithm
4.5. Quantum walks
4.6. Basic quantum communication protocols
4.7. Bibliographic remarks and further readings
References
Part II: Sequential quantum programs
Introduction
Chapter 5: Quantum while-programs
Abstract
5.1. Syntax
5.2. Operational semantics
5.3. Denotational semantics
5.4. Illustrative example: Grover search
5.5. Classical recursion in quantum programming
5.6. Adding classical variables
5.7. Bibliographic remarks and further readings
References
Chapter 6: Quantum Hoare logic
Abstract
6.1. Quantum predicates
6.2. Correctness formulas of quantum programs
6.3. Weakest preconditions of quantum programs
6.4. Proof system for partial correctness
6.5. Proof system for total correctness
6.6. An illustrative example: verification of Grover search
6.7. Auxiliary inference rules
6.8. Bibliographic remarks and further readings
References
Part III: Verification and analysis
Introduction
Chapter 7: Verification of quantum programs
Abstract
7.1. Architecture of a quantum program verifier
7.2. Localisation of correctness reasoning
7.3. Birkhoff–von Neumann quantum logic
7.4. Quantum logic with quantum variables
7.5. Quantum logic as an assertion logic
7.6. An effect calculus as assertion logic
7.7. Discussion
7.8. Bibliographic remarks and further readings
References
Chapter 8: Analysis of quantum programs
Abstract
8.1. Control flows of quantum programs
8.2. Invariants and their generation
8.3. Termination analysis – ranking functions
8.4. Termination analysis – reachability
8.5. Quantum abstract interpretation
8.6. Bibliographic remarks and further readings
References
Part IV: Parallel and distributed quantum programs
Introduction
References
Chapter 9: Parallel quantum programs
Abstract
9.1. Syntax of disjoint parallel quantum programs
9.2. Semantics of disjoint parallel quantum programs
9.3. Proof system for disjoint parallel quantum programs
9.4. Syntax of parallel quantum programs with shared variables
9.5. Semantics of parallel quantum programs with shared variables
9.6. Reasoning about parallel quantum programs with shared variables
9.7. Discussions
9.8. Bibliographic remarks and further readings
References
Chapter 10: Distributed quantum programs
Abstract
10.1. Quantum process algebra qCCS
10.2. Bisimulations between quantum processes
10.3. Approximate bisimulations between quantum processes
10.4. Adding classical variables
10.5. Bibliographic remarks and further readings
References
Part V: Quantum control flows
Introduction
Chapter 11: Quantum case statements
Abstract
11.1. Case statements: from classical to quantum
11.2. QuGCL: a language with quantum case statements
11.3. Guarded compositions of quantum operations
11.4. Semantics of QuGCL programs
11.5. Quantum choice
11.6. Algebraic laws
11.7. A new paradigm of quantum programming – superposition-of-programs
11.8. Illustrative examples
11.9. Discussions
11.10. Bibliographic remarks and further readings
References
Chapter 12: Quantum recursion
Abstract
12.1. Syntax of quantum recursive programs
12.2. Motivating examples: recursive quantum walks
12.3. Second quantisation
12.4. Solving recursive equations in the free Fock space
12.5. Recovering symmetry and antisymmetry
12.6. Principal system semantics of quantum recursion
12.7. Illustrative examples: revisit recursive quantum walks
12.8. Quantum while-loops (with quantum control)
12.9. Bibliographic remarks and further readings
References
Part VI: Prospects
Chapter 13: Prospects
Abstract
13.1. Quantum machines and quantum programs
13.2. Implementation of quantum programming languages
13.3. Functional quantum programming
13.4. Categorical semantics of quantum programs
13.5. From concurrent quantum programs to quantum concurrency
13.6. Entanglement in quantum programming
13.7. Model-checking quantum systems
13.8. Programming techniques for quantum machine learning
13.9. Quantum programming applied to physics
References
Appendix A: Omitted proofs in the main text
A.1. Omitted proofs in Chapter 5
A.2. Omitted proofs in Chapter 6
A.3. Omitted proofs in Chapter 7
A.4. Omitted proofs in Chapter 8
A.5. Omitted proofs in Chapter 9
A.6. Omitted proofs in Chapter 10
A.7. Omitted proofs in Chapter 11
References
References
References
Index