and then once he told me some stuff about it, it kinda caught my interest.

@heather You American?

and then google.

My dad is an engineer and he thinks physics is a waste of time

@BernardMeurer, yep.

@BernardMeurer I'll probably have time on the weekend. Although I also have a 40 page paper to digest asap...

@BernardMeurer watch your language :p but hmm, well - at the beginning, these things are a bit of work I'd guess

@ACuriousMind what papier

@Sanya The only person who can tell me to watch my language is John Rennie because he's my virtual grandfather

or Bob

@sanya unless his teacher has an account here I don't see how it could offend anybody :p

he's your adopted grandfather

@0celo7 This one

@Sanya It's not work, it's nonsense, this shouldn't be an introductory course to chemistry

except for 0celo7, who is offended by everything.

yes

stop triggering me

@heather cool what field of engr?

@0celo7 And Bob yes, he's my adopted, wait grandfather? Who's my mother and father then?

@0celo7 lol

@vzn, electrical/optical

mainly electrical

@ACuriousMind I would find string theory so much more interesting if someone told me what $G_2$, etc. are.

@BernardMeurer yeah, you're right - physical chemistry introduction yes, general chemistry introduction no

@0celo7 It's one of the exceptional Lie groups.

@heather ah neat it is actually possible to do optical QM experiments for "not a lot" of money... did one years ago...

@Sanya On a first semester course

@vzn, oh, cool...I'll have to look into that some time

@ACuriousMind Sigh

Not that

What is it

@heather yeah basically there are some cheap detector chips that measure "quantum-ly"

don't tell me it's some damn lattice either

@BernardMeurer well, I did do schroedinger QM in first semester chemistry brag - but yeah, I'll agree with you, that's a lot to stomach right at the start :<

@Sanya Are you a physics major?

@0celo7 It's the automorphism group of the octonions :P

Because I'm a bloody computer engineer

@ACuriousMind Have you proved the automorphism group is Lie?

@BernardMeurer I started with chemistry ... but then I was like "not my thing"

ok, I see how you have a right to be annoyed :D

@BernardMeurer ask me your analysis question now

@0celo7 Ah, the one about $\bar{\mathbb R}$?

yes, which is some freaky 3rd world object

god awful notation btw

$\bar{A}$ denotes closure, but $\Bbb R$ is closed.

often it means to take +/- infty? :|

that must be some European thing

So the old man comes around and says this $\bar{\mathbb R} = \mathbb R \cup \{-\infty, +\infty\}$

@0celo7 It's a subgroup of GL(7) that can be described by equations, so applying the regular value theorem should yield that easily.

@0celo7 dunno, I don't say I approve of the notation by the way

@ACuriousMind You have to check that the group operations are smooth

That might be immediate.

No, I don't.

Is smoothness inherited?

Yes

@Sanya I don't see any reason to extend it like that.

and then he says $$-\infty, +\infty \notin \mathbb R; -\infty\neq +\infty; \forall x\in\mathbb R, -\infty < x< +\infty$$

it's not a compactification

@BernardMeurer What does $\pm\infty$ even mean?

Okay, so, quantum fourier transform:

How are they constructed?

He doesn't say!

@0celo7 You need to extend it like that to make formal statements about limits being equal to $\pm\infty$.

@ACuriousMind No.

I asked for the axiomatic construction of them and he said there was none

@0celo7 I think it's used somewhere in analysis but I don't remember what it was really used for anymore

basically the equivalent of a discrete fourier transform, but quantum-y

that they were just 'concepts'

but that doesn't mean anything!

used in shor's algorithm to determine the period of the series

Let me look at my notes.

and implemented as a quantum gate?

is that right?

if so, what is the matrix that represents it?

@BernardMeurer You don't "construct" $\pm\infty$. You just add two objects to $\mathbb{R}$ and call them $\infty$ and $-\infty$ and require that they fulfill $-\infty < x < \infty$ for all reals.

What is this nonsense?

Or, rather, you define $<$ to work like that.

@heather What do you mean implemented as a quantum gate? Is a quantum gate just like an normal logical gate ( but quantum ofc)?

$\lim_{x\to y}f(x)=\infty$ just means that $f$ is unbounded as $x\to y$.

@BernardMeurer, basically, yeah

Instead of AND and OR being the basic gates, you have single qubit gates and the cNOT

If then I'd imagine it takes more then one to make a fourier transform circuit, so implemented with quantum logic gates

yeah, cNOT and all that jazz

@BernardMeurer, yeah, I think it does, but then wouldn't there still be a matrix that represents the overall thing?

@0celo7 No, it doesn't, consider a function that oscillates infinitely often near $y$ while growing in amplitude. You wouldn't write $\lim = \infty$ for that, hopefully.

@ACuriousMind Hm, seems to lack rigor somehow

@BernardMeurer Where?

Just like a Toffoli gate can be assembled from cNOTs, Hadamards, and such, but has an overall matrix that describes it.

@ACuriousMind In your face, Hollywood

Though it would be useful to understand what gates made it up...

Wikipedia really needs to be more explanatory sometimes. =)

Seriously though, it just seems weird to me, but sure let's go with that

@ACuriousMind $\lim_{x\to y}f(x)=\infty$ means $(\forall M> 0)(\exists \delta>0):|x-y|<\delta\implies f(x)>M,$ no?

@heather I'm guessing there would yeah, but no clue

@0celo7 Yes, which is not the same as being unbounded.

@BernardMeurer, I'll ask the google

@ACuriousMind That's what I meant, sorry.

The function can be unbounded without fulfilling that.

@ACuriousMind Yes, I mistyped.

@vzn Did you see the new Google Pixel?

Ok, so please explain what this $\bar{\Bbb R}$ thing is?

is this the matrix for the qft?

referencing this pdf: www1.gantep.edu.tr/~koc/qc/chapter5.pdf

@BernardMeurer no what is it?

@ACuriousMind Do we generally require that the Frechet derivative is a bounded map?

@vzn madeby.google.com/phone

I think it is, another source references it...it seems to be the two-qubit gate.

@heather Don't know. The only person who could perhaps help you, @DanielSank, is AFK at the moment I believe

@BernardMeurer, okay, good to know, I'll keep an eye out for him in the chat room.

@ACuriousMind Oh, I guess a more natural requirement is that it's continuous (as a linear map) on $E$, which is equivalent to being bounded.

This pdf has both the matrix and a circuit representation. cs.bham.ac.uk/internal/courses/intro-mqc/current/…

@BernardMeurer very interesting. ps got an android LG phone for $10 via a loyalty deal at a supermarket ~1yr ago

the samsung VR phones are pretty way cool too, some friends have em o_O

@BernardMeurer dude ask your question

@0celo7 My question is why do we need $\bar{\mathbb R}$ to define convergence to $\pm\infty$?

You don't. @ACuriousMind should agree. But it might be convenient.

What is your definition of convergence to $\pm\infty$?

What does it mean to have a superposition over a whole series of numbers?

@BernardMeurer You don't need it to define that convergence, but using it (in particular the $-\infty < x < \infty$ part) saves you from always having to state the case $\lim = \pm\infty$ as an exception when writing down statements about limits (like $\forall n: a_n < b_n \implies \lim a_n \leq \lim b_n$).

@ACuriousMind I was told that if the series it tends to $\pm\infty$ it's just divergent. End of story.

Wow, I just figured out something really cool: for 1 qubit, the Hadamard gate is equivalent the quantum fourier transform.

It is divergent, but diverging "to $\pm \infty$" is more...controlled that just diverging.

So there are no exceptions to write down!

We only write down statements for convergent sequences.

@ACuriousMind You won't care, but: Any Banach space has a partition of unity.

@0celo7 if something asks "find the distance from the origin to the line" what is the first thing you think it's asking?

the line is a parametrized vector btw..

find the distance clearly.

@Obliv aha, life lessons time

WAIT

give me 5 minutes

@0celo7 distance from where to where

ok

@Obliv do you know what a Banach space is?

we don't even need Banach

just a normed vector space

do you know what that is?

I'm just trying to assure myself i'm not crazy. That is poor wording, isn't it? Shouldn't it be: "find the magnitude of the normal vector that extends to the origin?"

no i never got that far in d&f. stopped half way into group theory when things were getting hairy @0celo7

d&f talks about normed vector spaces?

that's (functional) analysis

it talks about everything to do with algebraic structures more or less

@Obliv "the distance" from any extended object to a point is usually meant to be the shortest distance.

@Obliv it's the infimum of distances

For a line, this shortest distance is obtained by dropping the perpendicular.

@Obliv Let $E$ be a normed vector space, $V$ an affine subspace.

@acuriousmind english isn't my first language how am i supposed to know that

@0celo7 affine?

The distance from $x\in E$ to $V$ is $\inf\{||x-v||\mid v\in V\}$.

@0celo7 You know you're not being helpful, right?

@ACuriousMind Ok, now I am confused

What's wrong with that?

also i never bothered to learn what supremum/infimum were. I don't have time for your shennanigans @0celo7 i have an exam in like 35 minutes

@Obliv Uh, I didn't say you were supposed to know that

oh crap less than that.. 25 minutes

@ACURIOUSMIND I'M NOT CRAZY

NOOOO PANIC TIME

I DIDNT LEARN ANY OF THE QUADRIC SURFACES

@Obliv $V\subset E$ is affine if $a,b\in V\implies a-b\in V$.

@0celo7 It's not wrong. But did you really think that when Obliv asked about what distance exactly is meant, he wanted to hear about normed vector spaces and affine spaces?

@ACuriousMind ...yeah, I did.

I didn't realize he had a test in 25 minutes

I thought he was asking in general

@Obliv But yeah, what ACM said. Orthogonal projections.

You can prove that using calculus.

You want a line going from the origin to the line which intersects the line orthogonally.

Then the distance will be the distance from the origin to the intersection point.

@ACuriousMind Better?

is a space curve an image of a vector function through an interval @0celo7

y/n

@0celo7 Yes.

"Space curve" is not a term I've seen in any serious mathematics text @Obliv , sorry.

ok just curve

my book says space for some reason

Space?

@ACuriousMind You never reminded me to tell you my amusing story.

Hmmm?

It's a physics group theory story

I was busy getting my life into order :P

But you can tell it now, I'll listen

It's quick

So, remember back in the day, when I was a naive boy who enjoyed physics?

yes

oh shit... i have to be able to sketch these surfaces. @0celo7 did u ever have to learn how to sketch an elliptic paraboloid?

lol

I can't even draw a proper circle :P

@Obliv nope

15 minutes until I kms.

15 minutes until I kilometers?

At least I learned a valuable lesson. Don't wait until the days before an exam to start studying :D

@ACuriousMind Ok, well, we've talked about how "group theory" in physics is not group theory, right?

yep

if only we had infinite time on the test then I could plot like 100 points.

well I was very naive

and then connect the dots

@iceL actually a few days is fine but i waited until the last day for calc since i also waited until the last 2-3 days for physics.

@ACuriousMind so I went on amazon and looked up "group theory"

and they overlapped.

I wanted to learn more about this mysterious subject

...did you buy that Zee book?

I bought two books that looked neat

@ACuriousMind ...what?

This is me 2 years ago

this is a retroactive story

(not the right word but whatever)

I own these books

They have 0 to do with the group theory in physics

@Obliv there's a couple videos that pop up in a google search that teach u how to draw elliptical paraboloids google search: google.com/…

@iceL study theory rigorously until I learned i've wasted too much time then try to cram a bunch of exercise problems. Then hope to get a C

since exams are mostly on whether or not you can solve problems rather than proving theorems/understanding the material

@ACuriousMind shitty physics terminology cost me $40

@0celo7 Yes, they look as if they don't

If you need something about finite group though

I can probably find it in there lol

I might read the left one, at least a little

in preparation for algebraic topology

@IceLord yes probably.

@heather actually i think ellipsoids and elliptic paraboloids are the only ones i think I can draw. it's the other ones that I'm going to have to improvise.

actually no i think i can do all of these

@Obliv, oh, sorry. good luck with your exam!

Well that's good

just need to use traces, setting one of the variables to 0

How is shor's algorithm implemented using quantum gates (in an ideal setting, I mean)? Even a reference that shows the diagram for this would be absolutely fabulous...

@iceL it's a college and it's in the tri-state area. I'm transferring to a university next year though actually.

For once, with shor's algorithm, google has failed me.

@ACuriousMind is this ordering better?

@0celo7 Well, that is mildly amusing, I guess ;)

@0celo7 wait what was wrong with those books?

@0celo7 I still think the Abbot book looks kinda out of place there

ACM didn't like me having a GR book for mathematicians next to Abbott

Ok let me rework it again

@Obliv: "They have 0 to do with the group theory in physics"

@0celo7 ...are you really bored, or why are you sorting your books on my behalf :D

@heather I understood that part but I'm confused what he was expecting when purchasing a book on group theory. It's a mathematical theory in the first place.

@ACuriousMind I am actually very bored right now.

Procrastinating a bunch of things.

@Obliv This was back when he wasn't a mathematician yet and had only heard of group theory in the context in which physicists use it, which is more representation theory and Lie theory to mathematicians.

I'm not a mathematician

ok how about now

oh I see. @0celo7 are you trying to build your own library

@0celo7, no, not perfect enough =)

Better

no, not better

this doesn't look right :(

wow that book on morse theory is tiny

It's like it's going from thickest to thinnest...

@heather that's my OCD

@0celo7, yeah, I can be like that, especially with my books, but then my mom wonders why I don't clean my room a lot...

@ACuriousMind What do?

Get rid of it I guess

@Obliv yes.

Aha, victory: arxiv.org/pdf/1507.08852v1.pdf

my advisor said my book collection was not good

I am fixing that

Just for factoring 15, but still, that's something, I'll keep reading

Nah, I got the last cheap copy of Beem & Ehrlich

He has to shell out $300 for a copy

but it's unfair; he has lots of out of print book from way back when

His Milnor doesn't look like a photocopy

@0celo7 I tried Springer link at uni wifi, still doesn't work

@ACuriousMind Are representations of finite groups of any use in Strings?

@BernardMeurer hmm

Tried to create an account: nothing :/

Well, then you can't get Abbott on the cheap

Oh, another reference found, on IBM's quantum experience: quantumexperience.ng.bluemix.net/qstage/#/…

Who knew user guides could actually be helpful? =)

@0celo7 Can't you get it and I pay you?

@heather User guides are an amazing resource

@BernardMeurer, some of the time; in this case, definitely.

@0celo7 Nothing springs to mind, but my overviewof what happens in string theory is woefully incomplete

@BernardMeurer I've been summoned?

@DanielSank, is the following the matrix representing a two-qubit quantum fourier transform?

Also, what exactly does it mean to have a superposition over a series of numbers?

@BernardMeurer dude I'd have to ship to the 3rd world

that would cost as much as the book

@ACuriousMind I really want to learn representation theory, and I'm debating whether to go right to Lie groups or go through finite groups first, which has profound geometric implications

@DanielSank Yes, there's a QC question for ya bro

@0celo7 Brrrr

We're NATO, we're first world

dude are you gonna ask about QM or not

@BernardMeurer Europe is 3rd world in general.

@0celo7 I need to understand schrodinger on spherical coordinates

lol wtf

I can help

do you know what polar coordinates are

do you know the multivariable chain rule?

No$^2$

I was helping Reb with this yesterday actually

@BernardMeurer oh

Did the dean ever get back to you?

Yep

He said the prof can do what he wants

And the theory classes aren't mandatory

So I can attend someone else's class if I want

do that

Which I can't because my schedule doesn't allow

oh

Yeah :/

I guess I can explain...basically all of calc 3

I'll just do magic

Ok tonight I need to prove that one can define manifolds to be separable and that this works

@heather not sure off hand.

I'm sure you can look it up though.

Having read into degenerate gases, I have to ask

Is energy continuous or discrete?

@SirCumference I'm not sure we know that yet

@BernardMeurer Well, take electron degenerate gases for example. Two electrons (opposite spins) each occupy the energy states between the lowest possible energy and the Fermi energy.

When we're talking about electrons rising to new energy levels in that sense, are we saying energy is discrete?

@SirCumference Hmm, well, isn't a quanta the discretion of energy?

@BernardMeurer Is it in that sense?

@SirCumference I think that's what it means, but I don't know a lot. @DanielSank?

I'm talking about energy levels here

For example, if two electrons occupy the same energy state, do they have the exact same energy? If they were to gain energy at all, would that necessarily put them in higher energy states?

Isn't there something about you not being able to differentiate between electrons at the same energy state? I don't know, I think it was in my chemistry notes

@DanielSank, I think I figured it out: 1. that is the matrix for 2 qubit quantum fourier transformations (and a Hadamard is the 1 qubit quantum fourier transformation) 2. A single qubit can be 0, 1, or a superposition of those two states ($\alpha |0\rangle + \beta |1\rangle$). Two qubits can be 00, 11, 01, 10, or a superposition of those four states, and so on. A quantum computer with $n$ qubits can be in a superposition of up to $2^n$ states at the same time.

Yay google!

@BernardMeurer Here's my canonical answer about that.

@DanielSank It makes me uncomfortable that one of the answers on that question says "In my opinion" twice

Here's a question I posted a while back that I haven't gotten an answer for: How does a superposition work with the cNOT quantum gate?

If anyone could help with it, that'd be great!

@SirCumference Why? Asking about the meaning of words in physics is subject to opinion.