Quantum Process Algebra
- 1st Edition - March 6, 2025
- Imprint: Morgan Kaufmann
- Author: Yong Wang
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 7 5 1 3 - 5
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 7 5 1 4 - 2
Quantum Process Algebra introduces readers to the algebraic properties and laws for quantum computing. The book provides readers with all aspects of algebraic theory for quantu… Read more
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Request a sales quoteQuantum Process Algebra introduces readers to the algebraic properties and laws for quantum computing. The book provides readers with all aspects of algebraic theory for quantum computing, including the basis of semantics and axiomatization for quantum computing. With the assumption of a quantum system, readers will learn to solve the modelling of the three main components in a quantum system: unitary operator, quantum measurement, and quantum entanglement, with full support of quantum and classical computing in closed systems. Next, the book establishes the relationship between probabilistic quantum bisimilarity and classical probabilistic bisimilarity, including strong probabilistic bisimilarity and weak probabilistic bisimilarity, which makes an axiomatization of quantum processes possible. With this framework, quantum and classical computing mixed processes are unified with the same structured operational semantics. Finally, the book establishes a series of axiomatizations of quantum process algebras. These process algebras support nearly all main computation properties. Quantum and classical computing in closed quantum systems are unified with the same equational logic and the same structured operational semantics under the framework of ACP-like probabilistic process algebra. This unification means that the mathematics in the book can be used widely for verification of quantum and classical computing mixed systems, for example, most quantum communication protocols. ACP-like axiomatization also inherits the advantages of ACP, for example, and modularity means that it can be extended in an elegant way.
- Provides readers with an introduction to the algebraic properties and laws relevant to quantum computing
- Shows how quantum and classical computing mixed processes are unified with the same structured operational semantics through the framework of quantum process configuration
- Establishes a series of axiomatizations of quantum process algebras
Computer Science researchers, software engineers, programmers, machine learning, AI, and Quantum technology researchers in academia and industry
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- Chapter 1: Introduction
- Chapter 2: Backgrounds
- 2.1. Basic quantum mechanics
- 2.2. Structured operational semantics
- 2.3. Proof techniques
- 2.4. Truly concurrent process algebra – APTC
- 2.4.1. Basic algebra for true concurrency
- 2.4.2. APTC with left parallel composition
- 2.4.3. Recursion
- 2.4.4. Abstraction
- 2.5. Probabilistic truly concurrent process algebra – APPTC
- 2.5.1. Basic algebra for probabilistic true concurrency
- 2.5.2. Algebra for parallelism in probabilistic true concurrency
- 2.5.3. Recursion
- 2.5.4. Abstraction
- 2.6. APTC with guards – APTCG
- 2.6.1. BATC with guards
- 2.6.2. APTC with guards
- 2.6.3. Recursion
- 2.6.4. Abstraction
- 2.7. APPTC with guards – APPTCG
- 2.7.1. BAPTC with guards
- 2.7.2. APPTC with guards
- 2.7.3. Recursion
- 2.7.4. Abstraction
- 2.8. APTC with localities
- 2.8.1. Operational semantics
- 2.8.2. BATC with localities
- 2.8.3. APTC with localities
- 2.8.4. Recursion
- 2.8.5. Abstraction
- 2.9. APPTC with localities
- 2.9.1. Operational semantics
- 2.9.2. BAPTC with localities
- 2.9.3. APPTC with localities
- 2.9.4. Recursion
- 2.9.5. Abstraction
- 2.10. Reversible truly concurrent process algebra – APRTC
- 2.10.1. Basic algebra for reversible true concurrency
- 2.10.2. Algebra for parallelism in reversible true concurrency
- 2.10.3. Recursion
- 2.10.4. Abstraction
- 2.11. Structured operational semantics extended to support quantum processes
- Chapter 3: APTC for open quantum systems
- 3.1. BATC for open quantum systems
- 3.2. APTC for open quantum systems
- 3.3. Recursion
- 3.4. Abstraction
- 3.5. Quantum entanglement
- 3.6. Unification of quantum and classical computing for open quantum systems
- Chapter 4: APPTC for closed quantum systems
- 4.1. BAPTC for closed quantum systems
- 4.2. APPTC for closed quantum systems
- 4.3. Recursion
- 4.4. Abstraction
- 4.5. Quantum measurement
- 4.6. Quantum entanglement
- 4.7. Unification of quantum and classical computing for closed quantum systems
- Chapter 5: APTCG for open quantum systems
- 5.1. BATCG for open quantum systems
- 5.2. APTCG for open quantum systems
- 5.3. Recursion
- 5.4. Abstraction
- 5.5. Quantum entanglement
- 5.6. Unification of quantum and classical computing for open quantum systems
- Chapter 6: APPTCG for closed quantum systems
- 6.1. BAPTCG for closed quantum systems
- 6.2. APPTCG for closed quantum systems
- 6.3. Recursion
- 6.4. Abstraction
- 6.5. Quantum measurement
- 6.6. Quantum entanglement
- 6.7. Unification of quantum and classical computing for closed quantum systems
- Chapter 7: APTC with localities for open quantum systems
- 7.1. BATC with localities for open quantum systems
- 7.2. APTC with localities for open quantum systems
- 7.3. Recursion
- 7.4. Abstraction
- 7.5. Quantum entanglement
- 7.6. Unification of quantum and classical computing for open quantum systems
- Chapter 8: APPTC with localities for closed quantum systems
- 8.1. BAPTC with localities for closed quantum systems
- 8.2. APPTC with localities for closed quantum systems
- 8.3. Recursion
- 8.4. Abstraction
- 8.5. Quantum measurement
- 8.6. Quantum entanglement
- 8.7. Unification of quantum and classical computing for closed quantum systems
- Chapter 9: APRTC for open quantum systems
- 9.1. BARTC for open quantum systems
- 9.2. APRTC for open quantum systems
- 9.3. Recursion
- 9.4. Abstraction
- 9.5. Quantum entanglement
- 9.6. Unification of quantum and classical computing for open quantum systems
- Chapter 10: Algebra for parallelism in reversible probabilistic true concurrency
- 10.1. Basic algebra for reversible probabilistic true concurrency
- 10.1.1. Axiom system of BARPTC
- 10.1.2. Properties of BARPTC
- 10.1.3. Structured operational semantics of BARPTC
- 10.2. Algebra for parallelism in reversible probabilistic true concurrency
- 10.2.1. Axiom system of parallelism
- 10.2.2. Structured operational semantics of parallelism
- 10.2.3. Encapsulation
- 10.3. Recursion
- 10.3.1. Guarded recursive specifications
- 10.3.2. Recursive definition and specification principles
- 10.3.3. Approximation induction principle
- 10.4. Abstraction
- 10.4.1. Guarded linear recursion
- 10.4.2. Algebraic laws for the silent step
- 10.4.3. Abstraction
- Chapter 11: APRPTC for closed quantum systems
- 11.1. BARPTC for closed quantum systems
- 11.2. APRPTC for closed quantum systems
- 11.3. Recursion
- 11.4. Abstraction
- 11.5. Quantum measurement
- 11.6. Quantum entanglement
- 11.7. Unification of quantum and classical computing for closed quantum systems
- Chapter 12: APRTC with guards
- 12.1. Reversible operational semantics
- 12.2. BARTC with guards
- 12.3. APRTC with guards
- 12.4. Recursion
- 12.5. Abstraction
- Chapter 13: APRTCG for open quantum systems
- 13.1. Reversible operational semantics for quantum computing
- 13.2. BARTCG for open quantum systems
- 13.3. APRTCG for open quantum systems
- 13.4. Recursion
- 13.5. Abstraction
- 13.6. Quantum entanglement
- 13.7. Unification of quantum and classical computing for open quantum systems
- Chapter 14: APRPTC with guards
- 14.1. Reversible probabilistic operational semantics
- 14.2. BARPTC with guards
- 14.3. APRPTC with guards
- 14.4. Recursion
- 14.5. Abstraction
- Chapter 15: APRPTCG for closed quantum systems
- 15.1. Reversible probabilistic operational semantics for quantum computing
- 15.2. BARPTC for closed quantum systems
- 15.3. APRPTCG for closed quantum systems
- 15.4. Recursion
- 15.5. Abstraction
- 15.6. Quantum measurement
- 15.7. Quantum entanglement
- 15.8. Unification of quantum and classical computing for closed quantum systems
- Chapter 16: Applications of algebras for open quantum systems
- 16.1. Verification of BB84 protocol
- 16.2. Verification of E91 protocol
- 16.3. Verification of B92 protocol
- 16.4. Verification of DPS protocol
- 16.5. Verification of BBM92 protocol
- 16.6. Verification of SARG04 protocol
- 16.7. Verification of COW protocol
- 16.8. Verification of SSP protocol
- 16.9. Verification of S09 protocol
- 16.10. Verification of KMB09 protocol
- 16.11. Verification of S13 protocol
- Chapter 17: Applications of algebras for close quantum systems
- 17.1. Verification of quantum teleportation protocol
- 17.2. Verification of BB84 protocol
- 17.3. Verification of E91 protocol
- 17.4. Verification of B92 protocol
- 17.5. Verification of DPS protocol
- 17.6. Verification of BBM92 protocol
- 17.7. Verification of SARG04 protocol
- 17.8. Verification of COW protocol
- 17.9. Verification of SSP protocol
- 17.10. Verification of S09 protocol
- 17.11. Verification of KMB09 protocol
- 17.12. Verification of S13 protocol
- References
- Index
- Edition: 1
- Published: March 6, 2025
- No. of pages (Paperback): 424
- No. of pages (eBook): 450
- Imprint: Morgan Kaufmann
- Language: English
- Paperback ISBN: 9780443275135
- eBook ISBN: 9780443275142
YW
Yong Wang
Dr. Yong Wang is an Associate Professor of Computer Science and Technology, Faculty of Information, at Beijing University of Technology. He holds a PhD in Computer Science from Beihang University, China. He has more than 20 years of research and teaching experience in parallel and distributed computing. Dr. Wang’s research interests include Theory of Parallel Computing, including algebraic theory for true concurrency and its extensions and applications, algebraic theory for reversible computing, and quantum process algebra and its application in quantum communication protocol. Dr. Wang’s other research interests include SOA, grid computing, cloud computing, and big data. Dr. Wang has published more than 120 research papers in leading Computer Science journals, including Wiley-Blackwell International Journal of Communication Systems, Springer International Journal of Theoretical Physics, and IEEE Transactions on Network and Service Management.
Affiliations and expertise
Associate Professor of Computer Science and Technology, Faculty of Information, Beijing University of Technology, ChinaRead Quantum Process Algebra on ScienceDirect