Quantum Computation and Logic
How Quantum Computers Have Inspired Logical Investigations
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Beschreibung
This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.
This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.
Presents new approach to quantum logic inspired by quantum computation Offers a logical discussion of the question “can quantum computers be modelled by classical Turing machines?” Shows how the logics suggested by quantum computation can be naturally applied to the semantics of natural and artistic languages Illustrates problems in intuitive and formally rigorous language
Autor*in
Maria Luisa Dalla Chiara
Themen in »Quantum Computation and Logic«
Quantum Logics Non-Classical Logics Quantum Computation Quantum Gates Quantum Teleportation Quantum Computer Entanglement Epistemic Operators Quantum Information and Quantum Logical Gates Mathematical Environment of Quantum Information Quantum Entanglement Quantum Logical Circuits to Quantum Computational Logics Individuals, Quantifiers and Epistemic Operators Classical and Quantum Turing Machines Ambiguity in Natural and Artistic Languages
Stimmen zu »Quantum Computation and Logic«
“A very useful appendix is provided for the reader in order to clearly the notation and make the book easy reader and self-contained. I found the reading of this book extremely pleasant and insightful. … the volume “Quantum Computation and Logic” represents a very deep approach for logical-foundational aspects of quantum computation and it is strongly promising for the next research.” (H. Freytes, Studia Logica, Vol. 107, 2019)
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