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.
1. Chapter 1: Introduction - p. 1 2. Chapter 2: Backgrounds - p. 3 3. Chapter 3: APTC for open quantum systems - p. 117 4. Chapter 4: APPTC for closed quantum systems - p. 129 5. Chapter 5: APTCG for open quantum systems - p. 143 6. Chapter 6: APPTCG for closed quantum systems - p. 157 7. Chapter 7: APTC with localities for open quantum systems - p. 173 8. Chapter 8: APPTC with localities for closed quantum systems - p. 187 9. Chapter 9: APRTC for open quantum systems - p. 203 10. Chapter 10: Algebra for parallelism in reversible probabilistic true concurrency - p. 221 11. Chapter 11: APRPTC for closed quantum systems - p. 255 12. Chapter 12: APRTC with guards - p. 271 13. Chapter 13: APRTCG for open quantum systems - p. 297 14. Chapter 14: APRPTC with guards - p. 319 15. Chapter 15: APRPTCG for closed quantum systems - p. 347 16. Chapter 16: Applications of algebras for open quantum systems - p. 371 17. Chapter 17: Applications of algebras for close quantum systems - p. 389 18. References - p. 411 19. Index - p. 413
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.
1. Chapter 1: Introduction - p. 1 2. Chapter 2: Backgrounds - p. 3 3. Chapter 3: APTC for open quantum systems - p. 117 4. Chapter 4: APPTC for closed quantum systems - p. 129 5. Chapter 5: APTCG for open quantum systems - p. 143 6. Chapter 6: APPTCG for closed quantum systems - p. 157 7. Chapter 7: APTC with localities for open quantum systems - p. 173 8. Chapter 8: APPTC with localities for closed quantum systems - p. 187 9. Chapter 9: APRTC for open quantum systems - p. 203 10. Chapter 10: Algebra for parallelism in reversible probabilistic true concurrency - p. 221 11. Chapter 11: APRPTC for closed quantum systems - p. 255 12. Chapter 12: APRTC with guards - p. 271 13. Chapter 13: APRTCG for open quantum systems - p. 297 14. Chapter 14: APRPTC with guards - p. 319 15. Chapter 15: APRPTCG for closed quantum systems - p. 347 16. Chapter 16: Applications of algebras for open quantum systems - p. 371 17. Chapter 17: Applications of algebras for close quantum systems - p. 389 18. References - p. 411 19. Index - p. 413
