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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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 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
1 Introduction
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
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
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
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
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
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
8 APPTC with Localities for Closed Quantum Systems
8.1 BAPTC with Localities for Closed Quantum Systems
8.2 APPTC with Localites 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
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
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
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
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
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
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
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
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
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
17.10Verification of S09 Protocol
17.11Verification of KMB09 Protocol
17.12Verification of S13 Protocol
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
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
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
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
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
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
8 APPTC with Localities for Closed Quantum Systems
8.1 BAPTC with Localities for Closed Quantum Systems
8.2 APPTC with Localites 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
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
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
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
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
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
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
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
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
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
17.10Verification of S09 Protocol
17.11Verification of KMB09 Protocol
17.12Verification of S13 Protocol
- Edition: 1
- Published: March 6, 2025
- Imprint: Morgan Kaufmann
- Language: English
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