Quantum Computing
Published on 16. April 1999
Book
Paperback/Softback
300 pages
978-0-07-709503-1 (ISBN)
Description
In quantum computing, we witness an exciting and very promising merge of two of the deepest and most successful scientific and technological developments of this century: quantum physics and computer science. In spite of the fact that its experimental developments are in their infancy, there has already been a variety of concepts, models, methods and results obtained at the theoretical level that clearly have lasting value.These concepts, methods and results are the main subject of the book. Knowledge from two areas is of importance for understanding the basic developments in quantum computing: namely, quantum physics and theoretical computer science. The book provides elements of both, and concentrates on the presentation of concepts, models, methods and results mainly from a computing point of view. No previous knowledge of quantum mechanics is required. Supporting material for the book can be found on the Authors Web Site, http://www.fi.muni.cz/usr/gruska/foundations.html.
More details
Language
English
Place of publication
New York
United States
Publishing group
McGraw-Hill Education - Europe
Target group
College/higher education
Professional and scholarly
Illustrations
bibliography
ISBN-13
978-0-07-709503-1 (9780077095031)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Content
FUNDAMENTALS Prehistory of quantum computing; From randomized to quantum computing; Probabilistic Turing machines; Quantum Turing machines; Hilbert space basics; Basic concepts; Orthogonality, bases and subspaces; Evolution; Mixed states and density matrices; Tensor products; Experiments; Classical experiments; Quantum experiment; Quantum principles; Amplitudes and states; Measurement ; a projection approach; Evolution of quantum systems; Quantum measurements -interpretations; Classical reversible gates and computing; Reversible gates; Reversible Turing machines; Billiard ball model. ALGORITHMS; Quantum bits and registers; Qubits; Quantum registers; Quantum entanglement; Communication speed-up through entanglement; Quantum networks; Quantum gates; Measurement gates; Universality of quantum gates; Networks for arithmetical operations; Quantum parallelism and simple algorithms; Deutsch'||'''s XOR problem; Deutsch-Jozsa'||'''s problem; Simon'||'''s XOR problem; Fast quantum algorithms; Number theory basics; Quantum Fourier transform; Shor'||'''s factorization algorithm; Shor'||'''s discrete logarithm algorithm ; Grover'||'''s search algorithm; Limitations of quantum algorithms. AUTOMATA; Quantum finite automata; One-way quantum automata; Two-way quantum automata; Quantum Turing machines; Basic concepts; Mutual simulation of QTM; Quantum cellular automata; Basic concepts; Partitioned quantum cellular automata; Universality in quantum cellular automata; Quantum cellular automata versus quantum Turing machines. COMPLEXITY; Quantum computational complexity; Quantum communication complexity. COMMUNICATIONS; Quantum information theory; Classical information theory; Quantum information theory; Quantum data compression; Shannon'||'''s noiseless coding theorem; Schumacher'||'''s noiseless coding theorem; Communication through noisy quantum channel ; Quantum cryptography; Key distribution in classical cryptography ; Quantum key distribution (QKD) protocols; Unconditional security of QKD; Other quantum cryptographic systems; Quantum cryptographic protocols; Classical cryptographic protocols; Quantum coin tossing, bit commitment and oblivious transfer; Quantum teleportation. PROCESSORS; Quantum decoherence ; Quantum error correcting codes; Simulation of quantum algorithms; Experimental quantum processors; A quantum computer. EXERCISES. Historical and bibliographical references. Appendix; Quantum theory; Prehistory of quantum theory; Quantum theory and physical reality ; Quantum measurements; Quantum paradoxes; Interpretations of quantum theory; Hilbert space framework for quantum computing; Hilbert spaces ; Linear operators; Pure and mixed states; Observables and probabilities; Spectral measures in finite dimensional Hilbert spaces; Spectral measures in infinite dimensional Hilbert spaces ; Evolution in quantum systems; Compound systems; Unitary matrices; Complexity theory; Computational models and resources ; Complexity classes; Computational theses. Bibliography