|
|
|
|
|
Comments and Corrections (Version 1.1)
|
Error p104 (Simon Johnson) - Thursday, January 10, 2008
Page 104: More simple -> simpler and 'used to dedice to theory' -> 'used to
deduce the theory'
|
Error p129(Simon Johnson) - Thursday, January 10, 2008
Page 129, example box, fourth equation: In the case where the first qubit is
| 0 >, the second qubits are the wrong way round.
|
Error (Simon Johnson) - Thursday, January 10, 2008
"The uncertainty is due to the uncontrollable effect on the particle of any
attempt to observe it". According to most texts that I have read (including
Whitacker's *Einstein, Bohr and the Quantum Dilemma*) this is not the
correect interpretation. Instead the uncertainty is due to genuine lack of
the particle having precise properties. It is not the measurement that
cuases the problem, rather the precise properties don't exist.
|
Error p118 (Simon Johnson) - Thursday, January 10, 2008
Thanks very much for making this very helpful resource available. I very
much appreciated this because I am finding Nielsen and Chuang's book rather
hard going.
I do though have a minor correction that you might like to attend to:
Page 118 Global Phase Example appears to be wrong because -i x -i = -i not
i. This affects the second formula for psi as well as the text.
|
Error p31 (James Hollis) - Monday, August 06, 2007
At 2.6.6 you introduce reversible logic, including the Toffoli gate and the Fredkin gate. You claim a combination of Toffoli gates can simulate a Fredkin gate, which is true. You also claim a combination of Fredkin gates can simulate a Toffoli gate, which is not quite true. The Toffoli gate can alter the number of ones and zeros in the computer's memory. The Fredkin gate cannot do this, it can only swap them around.
|
Comment/Error p65 (Nick Oosterhof) - Sunday, January 21, 2007
You give the examples of [0> and [1>. This confused me, because I didn't see the logic behind these examples. Only further in the document it became clear to me that these are actually /definitions/, i.e. that [0> is a short way of writing the vector (1,0) and [1> is a short way of writing (0,1). Maybe you could make this clearer in a new version.
|
Comment (Rad Radish) - Sunday, November 05, 2006
Please, add bookmarks to pdf. It will be much easier to jump across all the material.
|
Error p77, p93, and p96 (Karol Bartkiewicz) - Tuesday, October 31, 2006
p77: In the example on this page you wrote that the expansion of X equals:
1/2[<0|0>+<0|1>+<1|0>+<1|1>]-1/2[<0|0>-<0|1>-<1|0>+<1|1>]=1/2[1+0+0+1]-1/2[1-0-0+1]=0
I think that you meant:
1/2[|0><0|+|0><1|+|1><0|+|1><1|]-1/2[|0><0|-|0><1|-|1><0|+|1><1|]=1/2[2|0><1|+2|1><0|]=|0><1|+|1><0|
p93: We don't put the degree symbol by the K, but we write simply e.g. 273K. I think that you used an older notation that is no longer in use.
p96: Planck's constant should be writen in MKS system,for instance (with a little more accuracy) :
h=0.00000000000000000000000000000000066260688[Js]=6.66260688x10^(-34)[Js]
|
Error p58 (Karol Bartkiewicz) - Thursday, October 19, 2006
sqrt(1/3)|0>+sqrt(2/3)|1> doesn't equal 1, but (sqrt(1/3)<0|+sqrt(2/3)<1|)x(sqrt(1/3)|0>+sqrt(2/3)|1>) does.
|
Error p32 and p46 (Karol Bartkiewicz) - Sunday, October 15, 2006
(p46) You should ommit 'i' by the sqared theta.
Secondly, the last sentence in the quotation of Searle in the section 2.7.1 (p32) seems to be a little unclear (there is no embedded subject).
|
Error p81 (Robin Kothari) - Sunday, September 24, 2006
Equation 3.181 also seems to have an error... The right-hand side of the equation doesnt contain B. Shouldnt the last term be B|v> ?
|
Error p69 (Robin Kothari) - Wednesday, September 20, 2006
I seem to have found an error.
Equation 3.105 seems to be wrong.. Eqn. 3.110 also contradicts this.
|
Error p147 (Varun Vaidya) - Saturday, August 26, 2006
I spotted an error on pg 147 in the your explanation of the teleportation circuit. In step 1, Alice and Bob are supposed to have the pair |B_00> but later in the same step, they are said to have 1/sqrt(2)(|00> -- |11>). Isn't the |B_00> pair 1/sqrt(2)(|00> + |11>) and not 1/sqrt(2)(|00> -- |11>).
|
Error p145 (Varun Vaidya) - Thursday, August 17, 2006
In your explanation of superdense coding you say that Alice has the bolded qubit of (1/sqrt(2))*(| 00>+|11>) and Bob has the bolded qubit of (1/sqrt(2))*(|00> --| 11>). From this it seems that Alice and Bob have two different pairs of qubits i.e . Alice has |B_00> and Bob has |B_11>. Shouldnt they both have the same EPR pair? I believe Andreas Gunnarson pointed this out in v1.0. You probably forgot to fix it in v1.1
|
Error p134 (Varun Vaidya) - Sunday, August 06, 2006
I've been reading your book and I believe I spotted a mistake on page 134. When you describe the Hadamard gate, you forgot to multiply the matrix by a factor of 1/sqrt(2).
Correct - thanks... An important find.
|
|
|
|
|
Comments and Corrections (Version 1.0)
|
Question p154 (Andreas Gunnarsson)
On page 154 you give an example of C^4 as |1> + |2> + |3> + |4>,
shouldn't all that be multiplied by 1/2? Or are the vectors not unit
vectors? Or is it OK to ignore the norming factor? Omitting the
norming factor and do normalisation at the end seems very convenient and
I can't see how it could cause any problems, could it?
|
Error (Andreas Gunnarsson)
You mention Shannon's "A Mathematical Theory of Communication" but I
couldn't find a link in the bibliography, the paper can be found at
http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html
On the other hand it's a little tangential to your book which is
probably why you left it out.
Yes, this should be referenced directly.
|
Error p161 (Andreas Gunnarsson)
On page 161 (6.5) says:
H(S) <= Lmin(S) <= H(S)+1
Shouldn't that be ... < H(S)+1?
|
Error p162 (Andreas Gunnarsson)
On page 162:
always comes up heads or tails
I first read that as it never lands on the edge, perhaps it could be
rephrased as "...that always comes up the same way"
Stricltly speaking, yes - this could be clarified a little better.
|
Error p163 (Andreas Gunnarsson)
Section 6.5.2 (page 163) did get me stuck for a while, I get the
impression that the underlying details are explained later (although I
haven't read that yet). Also, I wasn't able to immediately understand
exactly what was meant by "quantum coin toss", I could either imagine a
superposition of the states |0> and (|0> + |1>)/sqrt(2) or two qubits of
which one was randomly chosen (with a classic coin toss). I believe it
would either be good to have this section after von Neumann entropy has
been introduced (at least I believe that's what this is about) or
mention in 6.5.2 that the details will be explained in 6.5.4 (assuming
that it is; I haven't read that far yet).
Well said, this is confusing
|
Comment p152 (Andreas Gunnarsson)
On page 152 you mention qutrits. Mathematically it makes sense, but
what is the physical representation? I can imagine either an atom in
three different states or two qubits where one combination is not used,
but I'm not sure the latter would work.
I don't know much about qutrits but a quick google yields a nice paper entitled "Qutrit State Engineering with Biphotons" @ http://qopt.phys.msu.su/kulik/Papers/PRL_engineering.pdf
|
Error p145-146 Superdense Coding (Andreas Gunnarsson)
I don't understand where alpha and beta come from in steps 2 to 5.
They come from another dimension! :) I wish they'd go back there
(i.e. they are a mistake - they should not be there)..
In the last case when Alice wants to send 11, shouldn't step 2 be:
|11> --> XZ --> 1/sqrt(2) (a|01> - b|10>)?
Yes, correct. Combine this with your first observation and it should read:
|11> --> XZ --> 1/sqrt(2) (|01> - |10>)
I believe that the first case in step 4:
1/sqrt(2) (a|00> + b|11>) -> CNOT -> 1/sqrt(2) (a|00> + b|11>)
should be ... CNOT -> 1/sqrt(2) (a|00> + b|10>)
Correct again.
Aren't the second and third lines in step 2 swapped?
Yes, Z should follow X.
|
Error p 152 (Andreas Gunnarsson)
the example just under (5.86):
vectoe -> vector
Correct
|
Error p 145 (Andreas Gunnarsson)
In the "superdense encoding" example you say that we start with b_00 but then you say that Alice has the leftmost qubit in 1/sqrt(2)(|00> -
|11>),
shouldn't that be 1/sqrt(2)(|00> + |11>) according to the previous
section? I first thought it was just a typo, but you say the same thing
in the "teleportation circuit" example.
Hey, you are right. This should indeed be 1/sqrt(2)(|00> +
|11>). As you may have guessed - the reason it appears in two sections
is that it is a "cut and paste" error. Well done.
|
Error p 145 (Andreas Gunnarsson)
Andreas has raised concerns about the following daigram:
|a> -- H --.-- |a>
|
|
|b> ------(+)- |b (+) a>
It should actually look like
this:
|a> -- H --.--
|
| |Bxx>
|
|b> ------(+)-
where |Bxx> is a Bell state.
|
Error p146 (Riley Perry)
The 1st two CNOTs have incorrect components.
|
Error 4.1.4, p 95 (Andreas Gunnarsson)
Second paragrah in 'Black Body Radiaion':
'the frequency gets longer' -> 'the frequency gets higher'
Correct!
|
Error 4.1.5, p 96 (Andreas Gunnarsson)
...electromagnetic theory. Which...
->
...electromagnetic theory, which...
Yes, the sentence(s) need a rewrite.
|
Error 4.1.7, p101 (Andreas Gunnarsson)
Just above (4.6):
...and the excited state at n>1...
->
...and the excited states at n>1...
On the other hand, that covers all the states which contradicts that
they are of particular interest. Are you perhaps referring to a
particular excited state? Also, it isn't explained why these states are
of particular interest.
Yes, this is unclear and needs rewriting. This refers to storing a bit information. E.g. the ground state (n=1) could be 0 and in this case, the excited state (n>1) would represent 1.
|
Error 4.1.8, p103 (Andreas Gunnarsson)
...as Einstein: he had indeed, assumed
the comma should probably not be there.
Yes, the comma should not be there.
|
Error 4.1.8, p104 (Andreas Gunnarsson)
Later, We...
Should be lower case 'w'
As Homer Simpson would say... Doh! - thanks.
|
Error 4.1.8, p104 (Andreas Gunnarsson)
The electron's position is mentioned as (x,y,x) twice, shouldn't that be
(x,y,z)? Perhaps it isn't needed at all since other coordinate systems
are equally valid
Thanks, it should read (x,y,z)
|
Error 5.1.3, p116 (Andreas Gunnarsson)
(5.5): |0> + |0> should be |0> + |1>
(5.5): |0> - |0> should be |0> - |1>
Correct.
|
Error 5.1.3, p127 (Andreas Gunnarsson)
"All probabilities some to 1"
should probably be
"All probabilities sum to 1" or "The sum of all probabilities is 1" or
something like that?
Ahhh yes, "some" should read "sum".
|
Error 5.1.3, p120 (Andreas Gunnarsson)
Note: An applet ... the Bloch sphere which is available at ...
First I read that to mean that the Bloch sphere is available at that web
site, but it probably refers to the applet. I'd suggest rewriting it to
something like:
Note: The images of the Bloch sphere were generated by an applet
available at http://... which was written by Jose Castro.
Ok, I agree.
|
Error 5.1.5, p129 (Andreas Gunnarsson)
The first two sentences in 5.1.5 should probably be one sentence.
Yes, the full stop should be removed and the "T" in "The" made lowercase.
|
Error 5.1.5, p139 (Andreas Gunnarsson)
(5.68)
(a|0> + b|1>)|1> -> CNOT -> a|00> + b|10>
shouldn't that be:
(a|0> + b|1>)|1> -> CNOT -> a|01> + b|10>
?
Also, (5.68), (5.69) and (5.70) all have an extra right parenthesis.
And in the following example there is an extra right parenthesis in the
first line and a missing left parenthesis on the next line.
All correct :) - Thanks again Andreas.
|
Error 5.2.1, p144 (Andreas Gunnarsson)
Is the first diagram correct? It seems to imply that b is forgotten. I
would have expected |b> to be |0>.
Correct, this should read |0> in the diagram, not |b>.
|
Error p217 (By an AC on Slashdot) - Friday, February 25, 2005
The second step of the continued fractions example on page 207 (217 of the PDF). 1 + 2/9 is not equal to 1 + 1/2/9.
Yes, it should read: 1 + 1/9/2.
|
Error p27 (by an AC on Slashdot)
The fast particles end up on the left hand side, the slow on the right. The demon make a temperature difference without doing any work (which violates [the] second law of thermodynamics).
Should read: "slow particles on the right", make should become "makes" and "which violates the second law of thermodynamics"
|
Error 3.6 and general issues (s/nemesis from Slashdot)
You discuss how fo fine sin(x) in 3.4.1 which is fine, i would not have, its a bit trivial, but then when you were discussing complex numbers in 3.6, you didn't discuss the rather troublesome third quadrant, and show z* and e^i(pi) in like one line, right after a shaded box at the bottom of the page, asking for students to read over it without absorbing them. also there are no self test questions, no example questions, nothing. this book needs work, but is an awesome start.
Agreed, the section on complex numbers needs expanding. Also, self test questions and example questions will probably appear in v2.0 (The next version is v1.1).
|
Error p94 (James Hari)
On page 94: you have a table that shows amplitude and frequency for three waves.
I would like to point out that as shown by the diagrams, 0.5sin has a frequency of 2, not 1/2 and 2sin has a frequency of 1/2 not 2. Effectively these two results were inverted...
Yes, thanks James - that's correct. Btw - it seems there is a problem with the reference also.
|
Error 2.4.2, p18 (Xerxes Ranby)
ƒ = OR( AND(a,b), AND(NOT(b),c)).
comment: missing last ")" in original formula
figure 2.7 should be moved to 2.4.3 or else the formula under the figure (ƒ = …) describes wrong circuit.
Yes, a ) needs to be added at the end.
|
Error p45 (James Hari)
On page 45 a minor grammatical mistake. You stated, "The maths we need to handle this includes:".
Thanks, this should be changed.
|
Error p172 (Xerxes Ranby)
In the Example box,
should be… 111 -> 0,110 -> 0,101 -> 0,011 -> 1
Yes, we should also make those 0s before the commas into 1s -> 1,110 -> 1,101 -> 1,011
|
Error 2.3.2, p11 (Birdie 1013 from Slashdot, Xerxes Ranby, & Andreas Gunnarsson)
The example says "001 -> 100" which should be "001 -> 110" (or "011 ->
100").
Correct!
|
Error 3.8.11, p60 (Andreas Gunnarsson)
Under "Properties", 3.81 says:
For all |u> that belong to R and <u|u> >= 0
I believe it should be:
<u|u> >= 0 for all |u> that belong to R^n
Hmmm, yes - there is something wrong with this property. I'll get back to you on this one.
|
Error 3.8.17, p67 (Andreas Gunnarsson)
In the last example "Representing operators X and Z..."
The |0><0| example is wrong; the first expression shows |1><1| although
the result is correct.
Correct
|
Error 3.8.9, p58 (Andreas Gunnarsson)
The reference for tensor products is pointing to 3.8.29, but there is no
such section; tensor products are covered in 3.8.28.
Correct!
|
Error 3.8.22, p75 (Andreas Gunnarsson)
3.141 refes to spectral decomposition in 3.8.28, but the section for
spectral decomposition is 3.8.27.
Correct
|
Error 3.8.20, p72 (Andreas Gunnarsson)
Property 3.118 is wrong. Perhaps you want
tr(a(A+B)) = a tr(A) + a tr(B)
or
tr(aA + bB) = a tr(A) + b tr(B)
Correct
|
Error 3.8.19, p71 (Andreas Gunnarsson)
In the example on the line above "We get a = -b" the LHS is wrong; it
should be [b a]^T instead of [a b]^T.
Yes, there is something missing. I'll redo this example and send it to you. I'm unhappy with the whole section on eigenvectors and eigenvalues. E.g. In that example I should also show the normalisation step. Thanks.
|
Error 3.8.18, p69 (Andreas Gunnarsson)
In the example, A is shown for A+|u> instead of the adjoint.
Correct
|
Error 3.8.15, p64 (Andreas Gunnarsson)
In the example, the kets are written as row vectors, they should either
be written out as column vectors or a superscripted 'T' should be added
to show that it should be transposed.
Yes, this is confusing. It also relates to an earlier error. The answer is actually as follows:
First, a definition:
A vector u in C^n can be written in horizontal notation,
u=(u_1,u_2,...,u_n)
or in matrix notation,
u =
|u_1|
|u_2|
|...| (... is a vertical ellipsis)
|u_n|
As a ket is a "normal" vector it can be written both ways. A row vector uses a square bracket [ rather than a curved bracket ( - What i've done is mixed up horizontal and row notation. Well spotted, horizontal notation is not defined anywhere in the book.
|
Error 3.8.5, p56 (Andreas Gunnarsson)
In the example, the final expression for (u| is written as a column
vector while it should be a row vector.
Correct!
|
Error 3.7.1, p48 (Andreas Gunnarsson)
There are a few typos in "Basic Matrix Arithmetic":
(a+b)O = aO + aO
(a-b)O = aO - aO
One alpha should be replaced with beta in both those equations.
Correct!
|
Error 3.6, p42 (Andreas Gunnarsson)
The multiplication example is missing an "i":
5(-4) + 5(3) + 2(-4)i + (2)(3)i^2
Correct!
|
Errors, 2.3.1, p6 and 2.3.2, p10 (Andreas Gunnarsson)
It is mentioned that a Turing machine only use the symbols 0, 1 and
blank. I do believe that a standard Turing machine can use any (finite)
number of symbols, at least I have not seen the restriction of only 0, 1
and blank before. I haven't read the original Turing paper though, so I
may be wrong.
Correct (at least to my knowledge). I quote:
Without loss of generality, the symbol set can be limited to
just "0" and "1"
http://dictionary.reference.com/search?q=turing%20machine
I should say that the alphabet is 'usually' {0,1,blank}. Thanks for pointing this out, it also led me to finding another error on the same page.
|
Error - 2.2, p5 (Andreas Gunnarsson)
"Gordon Moore proposed Moore's law in 1965, which originally stated that
processor power and speed would double in size every eighteen months
(this was later revised to two years)."
Gordon Moore's observation was actually that "The complexity for minimum
component cost has increased at a rate of roughly a factor two per year"
The paper is available at:
ftp://download.intel.com/research/silicon/moorespaper.pdf
Doubling of other properties such as speed was as far as I can tell not
mentioned in the original statement. Also, I think the most common
version of Moore's law is that it (for various definitions of "it")
doubles every 18 months.
Yes, a few people have mentioned this. Agreed, it should be fixed.
|
|
|
|
|
Feature - The Chinese Room
|
Riley and Andreas discuss the Chinese Room.
I don't agree with some of the things (e.g. the Chinese Room argument) but that's probably out of the scope of proof reading comments. :)
Perhaps I don't understand what he's getting at (Searle), but it seems to me that there are a few problems with the argument:
In the Chinese room argument it is implied that it's not a problem to construct the rule book. Your comment about a case statement highlights this. It is actually very difficult; AI research has been trying to do this for a long time. It's not just a matter of answering simple questions, it must be possible to keep a conversation going and fool a judge. The conversation depends on what has been said previously so some kind of state has to be kept. Knowledge about the world is required. So, if someone actually manages to create such a rule book I'll be happy to listen to their objections to the Turing test, but until then the Chinese room is a hypothetical argument.
Good point. It may not be possible to build a rule book.
Here's my response:
Suppose we simplify the model and allow only a limited number of words to be used in a conversation and a limited sentence size. Also, any state information (current knowledge of the world) could be encoded in the case statement. Let's say we start with an "ignorant" machine (case statement) that does not know much about the world. Given a few select topics and a few select words and sentences the machine could pass a very limited Turing test.
Now, add in some more case statement patterns to mimic a retention of "current state" (you'd have to think of them beforehand). The machine can now pass a slightly less limited Turing test, with the ability to "remember" a thread of conversation.
Given these elements, my argument is that by sheer brute force you could add more and more to this case statement to make the machine appear more and more human.
But the devil is in the detail. Is it really possible to get to this point? Does the brute force approach have complexity limitations? I agree with you, until we have a rule book that can pass the test it is unlikely that we can prove (or disprove) anything.
If Searle manages to pass the Turing test with the help of the rule book then it's not Searle but the rule book that can be said to be intelligent and know Chinese. Compare the case where the rule book is replaced with a person who knows Chinese; Searle receives the notes and shows it to this person who tells him which note to return. The fact that Searle doesn't know Chinese is irrelevant; it's the other person (the rule book in the original argument) that possesses the knowledge and intelligence. "What if there is not one but a number of rule books, which book is the intelligent one?" one could ask. In that case the intelligence would be a property of the collection of rule books.
Yes, now this is interesting. These rule books don't just "pop into existence" (we'll I guess they CAN but it is just very very unlikely) they are written by somebody. The rule book can be seen as an extension of the person (or people) that wrote it. I guess the same applies to a collection of rule books.
The Turing test, as far as I understand, is suggested as a method to detect/define intelligence. The Searle argument seems to imply that it's Searle - not the rule book - that should be considered intelligent and know Chinese. It is probably intuitive to associate intelligence with sentience which is why the Searle argument at a first glance seems relevant. Separate the two and the argument seems more like a non-sequiteur.
There does seem to be a semantic issue here. In the book, the terms strong AI and weak AI need to be more clearly defined. I'd always bundled sentience (consciousness) into strong AI, but i'm not quite sure why. My approach to sentience has always been a simplistic, Cartesian dualism* style approach - i.e. Most brains (animal and human) are sentient, but some brains are smarter than other brains (e.g. dogs are sentient but can't do calculus). It is almost as if sentience and intelligence are separate entities (in my opinion). * (added later) I should point out that I am actually a monist, it's just that I don't think sentience is "a complex thing", more like a switch.
There's a good article by Searle on the Chinese room and another written by two people with the opposing view in the same issue of Scientific American (jan 1990).
|
|
|
|