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Quantum Computation and Quantum Information

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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.

700 pages, Paperback

First published January 1, 2000

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Michael A. Nielsen

5 books9 followers

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5 stars
265 (56%)
4 stars
131 (28%)
3 stars
53 (11%)
2 stars
15 (3%)
1 star
3 (<1%)
Displaying 1 - 26 of 26 reviews
Profile Image for Michael Nielsen.
Author 6 books946 followers
January 21, 2017
A real thriller, beautifully written, tightly plotted, characters I cared about, couldn't put it down!
Profile Image for Jovany Agathe.
276 reviews
March 19, 2018
Quantum Computation and Quantum Information: 10th Anniversary Edition
This book is definitely THE source to turn to for an understanding of Quantum Computation and Information. One can only read through the first chapter and you are given the key feature of Quantum Computation and Information. The advantage of this approach is that Chapter 1 establishes a Quantum roadmap of what you need to know. You can stop there or you can dive deeper into the technology. Using the remaining chapters as a reference or continuation of course studies.

But, it is the 10th Edition and I would have liked to see some new information associated with current trends in Quantum Computing. For examples:
1) Adiabatic verses Gate Arrays,
2) Quantum instructions examples, whether it is by circuit manipulation or by an Objective function,
3) A review section on quantum Notations (logic, Bra-kets, linear algebra) to help readers get back into it again.

This is THE book for those interested in finding out what is Quantum computers, but go slow with the first chapter and use the internet to clarify topics that are new to you, or to just refresh your memory. If you can skip through Chapter 1, you don't need the book.
Profile Image for Natan.
138 reviews12 followers
March 14, 2008
An excellent course textbook for Quantum Information Theory. I'm currently doing chapter 4. Anyone who wants to compare solutions for exercises is welcome.
Profile Image for Christopher Elliott.
116 reviews7 followers
January 27, 2023
Very accessible even though I can't do the math. This really cements the ideas of the power of the abstract qubit so you don't have to bite off understanding quantum mechanics. I'm amazed that there are actually useful things we could do with qc (it has felt a little like coming to understand how modern computer language constructs are built up from the lambda calculus which at first seems too simple to build anything powerful).
Profile Image for Brian.
33 reviews3 followers
August 13, 2013
Great introduction because it reviews both the basic of quantum and computer science, giving a broad perspective that fills in a lot of gaps left by other texts.
December 20, 2021
La biblia de la computación cuántica.

Muy buen libro. Una exposición clara y muy detallada. Yo al menos no tenía ni idea del tema y después de trabajarlo durante unos meses me siento mucho más cómodo. Tiene un estilo peculiar, un tanto denso, pero en general las explicaciones son muy buenas. (Al menos la parte de compu, para la parte de información usaré otras fuentes)

Igual lo ideal es tener otras fuentes para contrastar ciertas explicaciones, pero en general 100% recomendado.
Profile Image for Zach.
189 reviews
December 15, 2018
I'm sure this is a great graduate book covering and summarizing a lot of ground, but it was far too proof-focused for me. Apparently quantum computing is just matrix multiplication, we haven't gotten further than logic gates, and there's no intuition for what it means. I think I learned more through the Microsoft videos and doing some Quantum katas in Q#.
Profile Image for auden.
6 reviews
November 19, 2017
If you are interested in really learning about quantum computing, this is the book for you. Really well written and describes pretty much every subject you could be interested in (at least as a newbie to the field).
Profile Image for Eddie.
18 reviews
August 28, 2022
i claim that there is not a singular textbook out there that does a better job at what it promises to do, or more, than this one. if you or someone you know are a physics undergrad student, or --- to (literally) borrow a phrase --- a gifted amateur, you HAVE to get a copy of this masterpiece.
Profile Image for Michelangelo Rubino.
47 reviews2 followers
October 18, 2022
I honestly have read only the first of the three parts of the book. Starting from the second part, the maths is beyond my knowledge even if I own an MSc, too much. However, the first part was very interesting. This can be considered the bible of the quantum computing
Profile Image for Giorgos Vachtanidis.
22 reviews31 followers
November 12, 2020
The best book for someone who wants to enter the wonderful field of Quantum Information and Quantum Computing!
Profile Image for Erickson.
270 reviews104 followers
June 26, 2021
*Second reading*: Finished Chapter 8,9,11,12 and also Chapter 2 for my comprehensive exams. I still hold onto my earlier view that this book is really a reference text rather than learning stuff from the very basic, although it is also true that I think that there is unlikely any textbook that can go simpler than this one (though they can be less comprehensive but spend more effort on something else). One way to tell whether a book is reference text or not is to see if a beginner finds the book size overwhelming.

For the most part, what I have found very useful for studying with this book is to complement it with other books or lecture notes. The reason is very simple: quantum information is actually very close to pure mathematics in their arguments, although mostly linear algebra. Linear algebra is easy to grasp but hard to master. For this reason, even some proofs in the book can appear very demanding and unnecessarily complicated without the right tools. Two examples I like the most
to illustrate this is (1) the proof of strong subadditivity theorem, and (2) the proof that any CPTP map has the operator sum representation. For (1), the issue is that if Nielsen/Chuang introduced monotonicity of relative entropy first, then the proof comes very quickly, but they decided to do it the opposite. For (2), if you learn from other books/lecture notes about "Choi representation" and vectorization map, then the proof is actually very natural: you are trying to "invert" Choi matrix of a quantum channel by constructing relevant states to take partial trace. But that's simply inverse-vectorizing the eigenvectors of the Choi matrix. Hence the proof looked opaque for beginners (like me).

There is also the proof about fidelity as maximization over all purification; the proof used two purifications that are not at all obvious unless you know the answer already; in costrast, if you look at Wilde's lecture notes/book, he simply used "canonical" purification that anyone can write down for any density matrix in five seconds (this is also done in Watrous' textbook, using vectorization language). The proofs are all equivalent in essence, but the presentation is more confusing and unnecessarily general.

Overall, a nice book to keep and refer to, but you are better off having something else with you while keeping this one in your bookshelves. I recommend keeping this together with Mark Wilde's and John Watrous' textbooks; you will probably need not to get any other texts beyond these.


Stopped at the place where I used for my QI course. This book is more like a reference text which you should keep with you at all times for referring to details or refresher, so it is somewhat unsuitable to read cover-to-cover unless you are very free.
Profile Image for Erfan Abedi.
65 reviews8 followers
November 14, 2020
I think the books sometimes strays far away from the novel ideas and methods that make Quantum Computation useful and gets too caught up into mathematical formulas, which, in my opinion, isn't the best way to teach this subject. Anyway, I read the first 2 out of its 3 sections and I'm going to study Quantum Information in depth by reading Watrous' book, as I'm hoping his book is as good or even better than his lecture notes.
Profile Image for Ian Durham.
259 reviews5 followers
August 3, 2011
Still relevant after a decade in print, it's a must-have reference and a reasonably good teaching tool. My only beef is the complete lack of even a handful of worked examples. There seems to be a trend in that direction with some authors and I think they are missing out on an excellent pedagogical tool. I agree there shouldn't be many, but there should be *some.*
Profile Image for Piotr.
22 reviews
April 13, 2012
One of the best book in the field. Of course is not perfect, becuase not all aspects of the field have been covered nicely and some chapters required ad initio quite deep knowledge of QIT and quantum mechanics but still, for me, together with the book by Mermin is the necessary position as well for rookies and experienced scientists.
24 reviews
Currently reading
April 25, 2011
Much better than any other quantum text, I've ever read.
Profile Image for Divyanshu Jha.
7 reviews150 followers
July 25, 2012
4 stars for what I could understand. The rest must have been 5 stars or more
Profile Image for Alex Bush.
2 reviews
January 16, 2015
Great introduction into the concepts of Quantum Computing. A strong background in linear algebra is necessary to fully follow the material.
Displaying 1 - 26 of 26 reviews

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