I have promised to you some negative (and positive) comments on Nielsen and Chuang book on quantum computation. Rereading it in that state of mind, I realize I could make a comment at each line, and I despair a little bit because it witnesses the gap between "philosophers" "logicians" and "physicists" ("i" am a mathematician, although I never asked for: I have studied math because I suspected that Godel's theorem and Church thesis bring light to the mechanist approach of the mind-body problem which is the problem I am really working in). First of all let me insist that Nielsen and Chuang book is one of the better book for introducing quantum computation and quantum information. It is also a beautiful book, and a solid one!
Below is a sentence, taken from the introduction, which illustrates my perplexity (page 4) (emphasis by the authors):
"This assertion, known as the *Church-Turing thesis* in honor of Turing and another pioneer of Computer Science, Alonzo Church, asserts the equivalence between the physical concept of what class of algorithms can be performed on *some physical devices* with the rigorous mathematical concept of a Universal Turing Machine. The broad acceptance of this thesis laid the foundation for the development of a rich theory of computer science." (Nielsen & Chuang page 4)
I challenge anyone to find the word "physical" or any allusion to physics in the whole work of Church, or even in the whole logical work of Church, Kleene, Turing, Post, Godel, etc. (See the book edited by Martin Davis "The undecidable" which contains the original papers. Church proposed to identify the set of intuitive or effective computable functions with the mathematical set of functions definissable in his "Lambda formal system". The intuitive idea of effective computability is the idea of computing by finite means whatever big the resource needed in the process are once they are finite but unbounded. Although Church never mentioned the notion of "physical" I do appreciate the idea that going from "physical' to mathematics is interpreted as an increase in rigor. I know David should not appreciate this, because David has proposed a physical version of Church Thesis as a more modern version of it, and of course this is the point where I disagree in FOR. Deutsch thesis is very interesting by itself, and it is better not to confuse it with the proposal of Church. Note that the first who proposes "Church Thesis" is Emil POST, who proposes it as a law of mind, and gives from it the first simple and direct proof of the incompleteness theorem. Post seems to have anticipated the whole story from Godel to the immaterial monism of my thesis! (Well, actually in a footnote added later Post said that after discussing with Turing he came back to dualism, but he did anticipate the form of immaterialism monism which I show inherent to the comp hypothesis.
Another example: more funny and more typical (in the spirit of Copenhagen):
"Furthermore, measurement changes the state of a qubit, collapsing it from from its superposition of I0> and I1> to the specific state consistent with the measurement result. [...] Why does this type of collapse occur? Nobody knows. As discussed in chapter 2, this behavior is simply one of the fundamental postulates of quantum mechanics." (N & C page 15)
I guess Nielsen and Chuang are just stating the quintessence of the don't ask feature of Copenhagen philosophy. But why does people add a "fundamental postulate" nobody knows, and actually nobody can understand especially putted in that way? Here I would have appreciate a footnote telling that some people does not believe that such a collapse ever occur, and pointing to some literature (Everett, Deutsch, etc.) which gives some explanation why the memory of such collapse can be explained in strict respect of quantum linearity. I believe in the long term the collapse gives a wrong idea of what entanglement could possibly be in term of quantum information (as I found apparent in the work of Cerf and Adami).
A last example is the box 8.4 on Schroedinger's cat, it gives the wrong idea that information on a cat which is in a superposition state (alive + dead), by leaking into the external world will transform that superposition state into a ensemble of cat being either alive or dead. I really does not understand what they mean. Such explanation is meaningfull in a MW, or in a non-collapse QM. The box gives the wrong feeling that a real collapse can be explained in QM, ...
OK. It is an excellent book for learning QC and QI, but read a book like "the conceptual foundation of QM" by Bernard d'Espagnat, along with FOR book to prevent some implicit Copenhagen "philosophical" prejudices. Quantum computation is born through very fundamental question asked by Einstein (notably) and dismissed by Bohr. Through the work of Bell, Feynman and Deutsch, those Einsteinian realist questions have been shown testable (Bell ) and even exploitable (Deutsch, Shor, etc.). It is a pity that, when interesting fundamental questions leads to applications, people feel to be allowed to dismiss the original questions. It is on the contrary a sign that the questions were meaningful, and, even if only for possible new future application (!) worth to be taken seriously, and investigate closely.
For quantum computation, you can also read the very excellent book by Gruska. This one is rigorous at all level, i.e. in the math, in the physics, and in the philosophy (that's very rare!). But nothing being perfect, the Gruska book is not so pedagogical, so, read perhaps the book by Nielsen and Chuang, and consult Gruska.
At 09:48 06/05/03 +0200, Bruno Marchal wrote:
At 13:12 05/05/03 +0200, ISING (Barberis) Nicole <[EMAIL PROTECTED]> wrote:
>Is anyone on this list working their way through "Quantum Computation and >Quantum Information", >by Michael A. Nielsen and Isaac L. Chuang? Any comments? Do you know of >any good student links regarding this book?
My opinion is that Nielsen and Chuang 's book is one of the best textbook on Q Comp and Q Information. A good introduction to the Quantum which can serve as a bridge (from elementary math to Nielsen and Chuang) is the book by David Albert (Quantum Mechanic and experience, Harvard University Press 1992). Having said this I should add that Nielsen and Chuang are clearly not interested in foundational matters and there is a definitive lack of rigor in philosophy. I will give some example once I have the book under the hand. (Remind me if I forget)
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