# Talk:Quantum Computation

This is a nice introduction to a complicated subject. I am no expert, so my comments pertain only to how understandable the explanation is.

General comments:

1) Instead of referring to Pieper's MS Thesis for further references in the into paragraph, please give the essential references here.

.... RESPONSE TO COMMENT: We have addressed this points at the end of the article in the new section "Final Remarks and Further Readings."

2) The first use of |1> occur two lines before it is defined!

.... RESPONSE TO COMMENT: This was a typo, that now is corrected.

3) It seems to me that the normalization of |\psi> is more a matter of two things: (a) Quantum mechanics ls linear, and so the norm of the wave-function is not really important. But (b) if \psi is to describe a probability, then one chooses to normalize ||\psi|| = 1.

.... RESPONSE TO COMMENT: We agree with these observations. Since the article is not intended to overemphasize concepts from quantum physics, we have avoided using terms such as "wave-function." We have however emphasized on point (b), saying: *We note that quantum mechanics is inherently linear and stochastic; in particular, requiring that kets are unit vectors is just a way to normalize vectors so as to have a probabilistic interpretation.*

4) the \theta used in the definition of T(\theta) is confusing since you used it in (1) for \psi too. Can you use a different symbol?

.... RESPONSE TO COMMENT: For clarity of exposition, we have changed $\theta$ to $\alpha$.

5) The "addition mod 2" symbol \oplus, is defined in a somewhat hidden way. As this is used later, can you set it off (as an equation) and expand upon it?

.... RESPONSE TO COMMENT: To address this point, we added a new equation defining mod 2 addition, and provided an external-link to clarify this concept further.

6) In the Single-qubit Gates section it might be nice to mention that the I X and Z matrices are "Pauli matrices" which is why the are Pauil gates, I guess. Same for H, being a Hadamard matrix

.... RESPONSE TO COMMENT: We have replaced the term of "Pauli" and "Hadamard gates" to "Pauli" and "Hadamard matrices," respectively.

7) In the Multi-qubit Gates section, the CNOT gate equation is not compiled. Perhaps the blockmatrix construct is not defined for wikis?

.... RESPONSE TO COMMENT: Unfortunately, the Wiki does not recognize the LaTEX "blockmatrix" command. Because of this, we display matrices that required the use of this command now as figures.

8) In Deutsche's Algorithm, it seems that the equations for U_f|x>|y> are defined for general |y>, not just H|1>? Is this true? Then why use this specific y? If it is not true, then thus reader needs more help to understand.

.... RESPONSE TO COMMENT: The identity uses that |y>= H|1>, and we have made this now explicit in the paper by showing the main steps in the calculation.

Also: There are a number of places where it would be nice to include links to outside pages that give discussions/definitions of some topics. In particular for:

"a later section" endomorphism Hermitian operator bilinear associative

.... RESPONSE TO COMMENT: We have created links to the Wikipedia on terms like this but which are not yet part of the Scholarpedia.

The article seems to end rather abruptly. I would have liked to have seen:

A) A discussion of why Deutsch's algorithm is "faster". I didn't get it

.... RESPONSE TO COMMENT: We have clarified that Deutsch's algorithm is no necessarily "faster" however it demonstrates how one could in principle determine if $f$ is constant or not, only via the manipulation of quantum gates.

B) Where does the \sqrt{N} come in in Grover's Algorithm

.... RESPONSE TO COMMENT: We have expanded on this point, citing an identity due to Boyer et. al. (1998).

C) A final section that says: "To learn more about X, see Y, about Z see W, etc."

.... RESPONSE TO COMMENT: We have now added at the end of the article a new section entitled "Final Remarks and Further Readings."

## Modulo 2 arithmetic

There appears to be an error in the definition of the operator ⊕ in this article. Shou1dn't 1 ⊕ 1 = 0 ?

.... RESPONSE TO COMMENT: Yes, thank you! The typo has been corrected!