# Talk:Quantum logic gate

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The article asserts that ${\displaystyle R(\cos ^{-1}{\begin{matrix}{\frac {3}{5}}\end{matrix}}))}$ along with a couple of other gates form a "universal" set of gates. What is the significance and/or derivation of 3/5? Would other angles work as well? What is the critical property of the particular angle? --David Battle 01:39, 18 August 2005 (UTC)

The fact that it's usable at all is due to the fact that it divided by 2pi is irrational, I believe. For all irrational numbers x all real numbers r in [0,1) and all open intervals that include r, there is an integer n such that nx mod 1 is in the interval. Why this specific angle? Well, ${\displaystyle e^{\theta i}=\cos x+i\sin x}$, so ${\displaystyle e^{\cos ^{-1}{\begin{matrix}{\frac {3}{5}}\end{matrix}}}=\cos(\cos ^{-1}{\begin{matrix}{\frac {3}{5}}\end{matrix}})+i\sin(\cos ^{-1}{\begin{matrix}{\frac {3}{5}}\end{matrix}})}$, which I believe is ${\displaystyle {\frac {3}{5}}+i{\frac {4}{5}}}$, whose absolute value is 1. The associated angle (the argument of this number) is irrational--I think. Actually, using ${\displaystyle e^{i}}$ for that term of the matrix should work as well, and it's pretty simple, too. Now my question is why an angle is being multiplied by 2pi. --Ihope127 23:10, 19 June 2007 (UTC)
You're right, multiplying an angle by 2pi in the phase gate example doesn't make sense. I have removed it. --V79 (talk) 17:15, 1 May 2009 (UTC)

## Rotating qubit

${\displaystyle R_{x}({\frac {2\pi }{n}})={\begin{bmatrix}\cos {\frac {\pi }{n}}&-i\sin {\frac {\pi }{n}}\\-i\sin {\frac {\pi }{n}}&\cos {\frac {\pi }{n}}\end{bmatrix}}}$.

${\displaystyle R_{y}({\frac {2\pi }{n}})={\begin{bmatrix}\cos {\frac {\pi }{n}}&-\sin {\frac {\pi }{n}}\\\sin {\frac {\pi }{n}}&\cos {\frac {\pi }{n}}\end{bmatrix}}}$.

${\displaystyle R_{z}({\frac {2\pi }{n}})={\begin{bmatrix}\cos {\frac {\pi }{n}}-i\sin {\frac {\pi }{n}}&0\\0&\cos {\frac {\pi }{n}}+i\sin {\frac {\pi }{n}}\end{bmatrix}}}$ .

## Quantum gate (PC game) confusion

concerning articles :1:Quantum gate, 2:Quantum Gate and 3:Quantum Gate (PC game) previously, 3 redirected to 2 which held the info about the game, which i thought was very confusing, as it was clear to me that 2 should redirect to 1, with 3 holding the information about the game, so i moved the game information from 2 to 3, and redirected 2 to one, this will be coppied on the other two articles' talk page 193.60.83.241 (talk) 11:47, 14 May 2008 (UTC)

## NAND is not unitary

The section in the article which claims to demonstrate how a NAND quantum gate could be physically realised is most strange, because the "NAND gate" produced at the end is not invertible, thus not unitary, and hence not a quantum gate at all! Indeed, if the "gate" produced existed at all, it could be used to create copies of the state of qubits, blatantly violating the no-cloning theorem. However, I'm not sufficiently versed in the electrodynamics to tell whether the whole thing is just nonsense, or perhaps rather a poorly remembered example that was really supposed to produce some other classical gate, such as CNOT. 81.170.129.141 (talk) 23:34, 1 February 2013 (UTC)

In cruder terms, I too wish to call bullshit on this section. Reading it seems to suggest you can get NAND by multiplying by a clever choice of phase shift. No citations either. Should be removed. — Preceding unsigned comment added by 71.172.178.157 (talk) 13:48, 12 October 2014 (UTC)
I'm new to quantum gates, but I think I have to agree. AFAIK all quantum gates are reversable. No matter how you look at it, AND OR NAND NOR etc. can't be implemented. Only NOT Xor Xnor. (Please correct me if I'm wrong) --User:AltruismAndCake
Yeh the section is not Quantum mechanics, the Bloch equations are obtained by taking the saddle points of the full quantum theory resolved explicitly over only product states. This is classical mechanics.

## Superpositions within Matrices

Do the logic gates allow superpositional values to act as operators or instructions? If they do, that's not really coming through in the article. If they do not, then is this a fundamental limitation of the quantum phenomena, or is it just much simpler to build a QC with "ordinary" logic gates? While the answers to these questions might turn out to be rather awkward, I think they'd go a long way to making the idea of quantum computing more accessible to a larger number of people. Thank you! -- 17:38, 22 April 2014 (UTC) — Preceding unsigned comment added by TheLastWordSword (talkcontribs)

Superpositions are those values that are not aligned perfectly along the base vectors, which represents the observable states of the variable. It is a medium-large project to 1) figure out *which* pieces of knowledge are the basics of quantum computing, and 2) to wrap the (mine/your) head around them -- so expecting it to just jump out at you and explain itself is a bit.. much to ask. Of course it would be awesome if every article was awesome that way, but we are just humans. Also, ***you*** can enhance it. 2001:2002:51E3:8007:B66D:83FF:FE0E:C298 (talk) 20:36, 7 September 2017 (UTC)

## Universality via Deutsch gates

Assume Deutsch gates are permitted to take an arbitrary rotation as parameter, e.g. set via a potentiometer-like control attached to each Deutsch gate that can be rotated smoothly about 360 degrees when manually constructing the circuit. Presumably this would permit realizing any unitary operation on n qubits with finitely many quantum gates.

As a function of n, what is the minimum number of Deutsch gates needed to be sure of being able to implement any unitary operation?

It seems likely this has already been determined. If so this section of the article should say something about it. Vaughan Pratt (talk) 18:09, 1 December 2015 (UTC)