- Series: Cambridge Series on Information and the Natural Sciences
- Paperback: 675 pages
- Publisher: Cambridge University Press; 1 edition (2000)
- Language: English
- ISBN-10: 0521635039
- ISBN-13: 978-0521635035
- Product Dimensions: 6.8 x 1.6 x 9.7 inches
- Shipping Weight: 3 pounds
- Average Customer Review: 27 customer reviews
- Amazon Best Sellers Rank: #455,286 in Books (See Top 100 in Books)
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Quantum Computation and Quantum Information (Cambridge Series on Information and the Natural Sciences) 1st Edition
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"Quantum Computation and Quantum Information is a challenging text that offers a thorough discussion of the relevant physics and a reference book that guides readers to the original literature...Perhaps the best way to use the book, though, is to ask questions and then search within it for answers. Such a self-guided tour can keep one from getting lost in details and can provide a rewarding journey...Nielsen and Chuang have set a high standard." Science
"Michael Nielsen and Issac L. "Ike" Chuang have produced a highly readable, thorough, and timely survey of the field of theoretical quantum information science. [It] is probably destined to become a standard text for reseachers in this still emerging, rapidly developing field.... [It] is very well written and a pleasure to read." /s Physics Today
"highly readable, thorough, and timely survey of the feild of theorectical quantum information science...probably destained to become a standard text for researchers...The authors rightly choose to examine key issues in depth rather than attempt a mile-wide, inch-deep, catholic approach...is very well written and a pleasure to read." Physics Today Nov 2001
This text is the first comprehensive introduction to an exciting new cross-disciplinary field which utilizes the strange effects of quantum mechanics to enable information processing and computing feats that would be impossible on traditional 'classical' computers. The authors describe what a quantum computer is, how it can be used to solve problems faster than familiar 'classical' computers, and the real-world implementation of quantum computers. This book will provide an in-depth knowledge of the subject to readers without any background in the field.
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with each passing month. It is written at a graduate level, such that
you really need to have had a college-level quantum mechanics course,
or equivalent. Most of the book uses bracket notation.
The theory behind quantum computing is outlined in some detail in the book, but the experimental situation is not, and this is disappointing since it is the laboratory realization of quantum computing that is most interesting. Most implementations of quantum computing theoretically are dependent on the notion of entanglement of states, and in my opinion there is no convincing experimental evidence of entanglement. Theoretical constructions that employ entanglement have grown considerably in recent years, but the experimental situation is far behind these developments. This book unfortunately does not look critically at the experimental justification for entanglement, but uses concepts of entanglement throughout to lay the groundwork for a theory of quantum computation. Indeed one could say that the entire book rests on the notion of entangled states and being able to manipulate these states via various transformations, called 'entanglement transformations' by the authors.
The authors do however devote an entire chapter to the physical realization of quantum computers , although again no real experimental data is given. The role of the decoherence time is emphasized in the discussion, and a chart is given listing rough estimates for decoherence times for various candidate realizations of quantum computers. Several different scenarios for quantum computers are outlined in the chapter, and the discussion gives some credence to the view that the theory of quantum computation has some physical meaning to it, rather than just a theory of computation based on the properties and geometry of Hilbert space. Indeed, one could easily take this later viewpoint, as it is one thing to call a mathematical construction 'quantum' and another to really find a physical (quantum) system that actually behaves in a manner compatible with these constructions. If one is to speak of 'quantum' computation and not just 'Hilbert space' computation, one must show beyond doubt that the system executing the computation is indeed a physical and quantum one. A mere statement that 'physics is computation' is not enough. Indeed, there are a few examples of using Hilbert space properties to enhance the performance of various algorithms. For example, one can speed up the training portion in neural networks by complexifying the weights. In addition, one can employ a tunneling scheme to alleviate the problems of local minima in these networks, and in gradient algorithms in general. These approaches all take advantage of Hilbert space geometry and the ability to do superposition of states, but none of them correspond at all to physical systems, let alone quantum ones. They are merely mathematical tools used to speed up (dramatically in some cases) a particular algorithm.
There has also been a great deal of very exciting research in the employment of the 'quantum' point of view in pure mathematics. New methodologies have been developed for handling difficult mathematical results using such a viewpoint and these have resulted in brilliant developments, especially in differential topology and algebraic geometry. The chapter on distance measures for quantum information in this book could be viewed as part of these developments and strategies. The definition of the fidelity between two quantum states is purely a mathematical convenience that is used (albeit productively) to derive quantities that behave as one would want them to (viewing from a classical standpoint). No physical relevance is given for this metric in the chapter, although it is interesting from a mathematical standpoint. The authors are honest to admit this though, for they state that notions of quantum information are in a state of infancy and no solid (physical) definitions have been given as of yet.
If more time were spent on the analysis of the raw experimental data behind the efforts to build quantum computers, and less on purely theoretical considerations, this book would have been a lot more helpful. The literature is bursting with papers on entanglement and its relation to quantum computing and quantum information, but unfortunately, not enough critical analysis of the experimental situation. This book is no different in this regard, but the authors are still enthusiastic about the prospects for quantum computing, difficult as they are. One can only hope that their efforts are successful, that such machines will be built soon, as the consequences are awesome.