Quantum Computation and Quantum Information | Michael A. Nielsen, Isaac L. Chuang

Quantum Computation and Quantum Information | Michael A. Nielsen, Isaac L. Chuang | Still the Best Overview on Quantum Computing

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Quantum Computatio...

	Quantum Computation and Quantum Information Michael A. Nielsen, Isaac L. Chuang Cambridge University Press, 2000 - 675 pages average customer review:based on 28 reviews view larger image
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highly recommended

In this first comprehensive introduction to the main ideas and techniques of quantum computation and information, Michael Nielsen and Isaac Chuang ask the question: What are the ultimate physical limits to computation and communication? They detail such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error correction. A wealth of accompanying figures and exercises illustrate and develop the material in more depth. They 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. Their book concludes with an explanation of how quantum states can be used to perform remarkable feats of communication, and of how it is possible to protect quantum states against the effects of noise.

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A book that repays study

My first acquaintance with this book came from a copy which I ordered through interlibrary loan after seeing favorable comments on the internet. The loan period was only two weeks, so I wasn't able to study this 600-page book in detail. But I learned quite a bit just by skimming it. After I saw that it was a book that would repay study, I purchased it.

The first chapter of 58 pages nicely introduces many of the important ideas, leaving the more difficult details to later chapters. For example, I learned about quantum teleportation, which I had never understood from popular accounts.

I read it from cover to cover and was able to follow almost all of it in detail. Since I read it as someone learning this material for the first time, I'll review it from a student's perspective. A much longer review discussing technical issues is available on my web site.

Chapter 2 gives a nice summary of basic quantum mechanics. It includes an introduction to necessary concepts from abstract linear algebra, including important specific applications (e.g., the Schmidt decomposition) which are not likely to be covered even in advanced linear algebra courses.

The third chapter gives an introduction to computer science concepts.
This gives a conceptual framework within which to present the ideas of quantum computation. More material is included here than is necessary to understand the rest of the book. Readers may find it efficient to skim this chapter initially and return for more detail when necessary.

The next three chapters present the essentials of quantum circuits, the quantum Fourier transform, and quantum search algorithms. Here there is perhaps room for a little improvement. I thought that important details were sometimes omitted from the exposition, and I occasionally had to go to the original literature to understand the ideas.

Also, there is a bad misuse of the "Big-O" notation throughout these
chapters, startling in a book so generally carefully written. Sophisticated readers will take this in stride, but it might demoralize beginners. For details, see the longer review on my web site.

The mathematics of quantum computation is easy compared to the problems of physically realizing it. Chapter 7 gives an extensive discussion of these problems and various proposals for overcoming them. This concludes the "quantum computation" section of the book, which is a little more than half of the 600-odd pages.

The rest deals with quantum information theory. This is presented in less detail than the quantum computation chapters, and demands more from the reader. A summary of classical information theory is included, with sketches of proofs of important results. I found this very helpful in refreshing my memory of Khinchin's book on information theory, which I read decades ago.

Some of the more complicated proofs are only sketched. I didn't get as much from the quantum information section of the book as from the quantum computation section. I think it gives a useful overview of the field, but if I wanted to learn quantum information in detail, I would look for a book dedicated to this topic, perhaps reading Nielsen/Chuang first as an introduction.

The book concludes with a 12-page introduction to quantum cryptography.
I couldn't follow this section in detail. Perhaps it could be followed with enough work, but I wasn't motivated. I imagine that a proper treatment of cryptography would require many more than 12 pages. Again, if I wanted to learn this material, I would seek an expository text dedicated to it.

In summary, this is an exceptionally fine text which can be read on many levels. The 58-page overview of quantum computation should be comprehensible to anyone familiar with the basic ideas of quantum mechanics. The rest of the book may possibly be readable with great effort by well-prepared undergraduates, but I think a graduate-level
background in quantum mechanics and linear algebra would be more realistic prerequisites, and also more efficient. These prerequites will have to be mastered anyway for anyone who wants to work in a field dependent on quantum theory. Those who lack the prerequisites may still be able to get a feel for the problems of quantum computation and information from the book, even if the details seem too difficult.

Although this is a serious book suitable for obtaining a professional knowledge of its subjects, it is unusually carefully written in an expository style. There are many exercises interspersed with the exposition, but no solutions are provided. Most of them should be solvable on sight by anyone following the presentation, so they provide
a useful check on one's understanding of the material. (I am a professional mathematician; students may find the exercises less easy.)

Each chapter ends with "History and further reading'' sections, often extensive. I found these very helpful.

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Still the Best Overview on Quantum Computing

This is an excellent book about a topic which becomes more important
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.

A great comprehensive study of the field

As a grad. student in the field, I would recommend this book to every new beginning student. It helped me understand the basics if quantum information, particularly physical notions that I had previously wondered about.

Read a bit - and seems great

I've recently purchased this book, and have only read the first 50 or so pages. However, it is clear thus far that the authors have invested alot of time in making such a complex topic as clear as possible, with simple examples to express fundamental concepts. I'm looking forward to reading the rest.

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Complete, but sloppy

This is absolutely the standard introductory text to quantum information and quantum computation. Nielsen and Chuang certainly covered all the basis, and tried to give a self contained book including many reviews of related topics in the appendices. The main complain about the book is that some times it is sloppy, making hard to grasp the concepts. In some parts of the book there are even grammatical errors. My advice, get it, read it, but be very careful.

reviews: page 1, 2, 3, 4, 5, 6

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