WEBVTT

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Hey, good afternoon class as usual. I don't know if anyone is hearing me.

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So, I can hear you. Oh, well, thank you. Beautiful. Okay. And again, if you have problems, then please unmute yourself and.

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And tell me, okay, let's see here.

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So the theory is, that I'm sharing the screen, so this is the fourth class of quantum computer programming, and we're going to the moment I'm going through.

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I'm going through the book, and I have highlights I mentioned here, and I'll put stuff down on here. Okay.

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A question about video quality what motivated this is I tried to upload the video to media site and it bars, because a three hundred megabytes. This is from from Tuesday.

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So I cut the resolution down and.

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Looks reasonable to me and if you're curious how I'm doing it,

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I'm using,

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I played with various buoys and then figured it was easier just to learn a command line interface,

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which is what I'm doing and so if no one objects,

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I may even try increasing the compression,

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even more it will call is motion.

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The next thing that will go is it will cause motion artifacts, but things that are still like the had and so on. And if I project the screen, that will, that will be okay.

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So, there's also a program called hand break that you can use to help compressed video files. Yeah, I looked at that. That's one of the ones interactive ones I looked at.

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The problem is I can't go into two sixty five because media site doesn't use it and.

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Yeah, well if you think it's worth it, you think it's worth a learning curve for handbrake? I, I've installed it, but I haven't used it yet.

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Yeah, I, I really like the programs, so I would recommend. Okay, thank you. Well, this still then the next question is what forms of compression are acceptable.

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So I was playing with things like, you know, video bits per second, and so on one hundred K is too small, really bad two hundred K, the original like four hundred K. and I'm just trying to play around with options and stuff.

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I also want to do things like, you know, maybe trim off the start of the, the video. And so if you're curious what I'm doing it on, I've got a nice laptop here. So I have the description of that. So essentially might want to try something else.

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And I'm glad of that much computing power because otherwise.

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I was just trying to bring up something something else here.

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Let's see if this works,

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when I was trying to do actually was to see if I can get the.

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Chatbox up get the chatbox up in another window.

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Oh, hey, it doesn't work. Oh, well, okay. You're not going to doing the worst of all possible worlds and getting audio feedback, but no chat window.

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Okay. So.

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So, I'm not sure it works coming from too many devices here. Okay, so this is for and one. Okay.

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So, what I was doing is I wanted to mix up, as I mentioned, I was sort of mixing up chapters two and three of the Lukas Chapter two with solid math and chapter three was getting into.

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Some quantum computing stuff, but what I wanted to do was now go back and do some of the bits of chapter two that.

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That I hadn't done before and I, I kill you with page numbers here. I mean, honestly, it's as much for my uses for for your use, and just scrolling through on my copy of the book here.

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And some things that I didn't some things that I didn't mention.

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That I didn't mention last time are.

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Here well, the point again, this is, I mean, this looks like fairly simple stuff, but.

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It's good to nail down the basics otherwise they'll get lost later on. So, if we're talking about so, again, this is page fifty two and so on.

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Different basis systems, different basis, sets or whatever and in some sense, if I have a vector here, let's say.

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I mean, it has a reality that's separate from the basis system that you use to represent it with. And if I've got one basis.

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One set of basis factors like this, and like this the, and it would be represented as that and another set of basis factors like.

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Like that and like that, then it would be represented as sack and you could abstractly think it's actually the same vector.

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It's just different representations and examples again, following on my example, cryptography, there's different coordinate systems.

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For a while I mentioned that the Swiss German thing, even in two dimensions for maps, as different coordinate systems. If I'm standing on the top of Mount Marcy, let's say, you know, it's a fixed point ignoring the fact that the earth is moving.

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But if I look at it, within on an ad, twenty seven map, it's got one set of coordinates. If I look at it on a W. G. S. eighty four map, the different set of coordinates.

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If I use universal trends versus Mercator coordinates, a different set of numbers. It's all the same point. And.

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And what we have is something here, let's say where.

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We got that one point,

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it's in two different in the two different coordinate systems,

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and we could have something in this particular case if we had a hard Matrix,

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which would transform stuff from,

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from one coordinates to the others say,

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and if we had a point in.

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I don't know, let's suppose this point in the economical system was say one one and I multiply this by one one I'm going to get.

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Two zero, let's say, so.

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That's nice and simple. Just good to know that down there. Okay.

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So that's in these it'd be like, trying to this would be like a transition matrix there.

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So, where it's relevant to quantum computing is that the whole there, all the operations are condition matrices, and they could be considered to be changing your basis.

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So, you had the question back in class one, but in so it, you know, you could say it's the same quantum system we operate on it.

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In a sense, it's locating the basis. Okay.

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Now, so we have the complex vector space and again, the vector space it's an abstract idea.

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You can add two vectors and you can scale effector by escape. Okay. The next thing that we do is we bring in an inter product.

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And also say called dot product, perhaps it just another operator on two vectors and.

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It's related,

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say to the angle between the two factors,

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perhaps now the thing with the complex,

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which again,

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I'm not certain with everyone's mass background is but with complex.

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So, if it was real, the thing is, there's a conjugate going on in here.

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So,

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if we take these two factors,

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say,

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one,

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plus two I,

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and,

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I don't know,

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three plus,

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four I and we do,

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we do want to say adult product of that with five plus,

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six,

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seven plus eight what we're going to do is we do the conjugate.

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So, what this is going to be one minus two I times type plus six plus three minus four. I.

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Times seven plus eight I should be seeing what you're writing. Thank you. Yes. Just what happened. Okay. The webcam or just talk excuse me.

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I don't think we can hear you now.

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Still cannot hear you.

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I don't know if you can hear us.

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Professor, we can't hear you. Yeah. I don't think it can.

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Yeah, I don't either. It's like, we've got some kind of a vector here. Yeah, go ahead and teach. Plus you got this.

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Yeah, it looks like you messed up the hang, man drawing what appears to be on the top right hand broken the false principle.

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Yeah, it could could be a Lambda could be an interesting L could be related. It makes more sense for talking about values. I think we could be a team that could be a to yeah. Good call. Okay. We're on page two guys. We got this.

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Alright. So, does it make millions if I leave and rejoin maybe That'll work and try that.

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I think

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we've got a nice picture and Saturn,

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so at least,

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you know,

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this one.

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Yeah, I've seen that one before too.

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Remember guys it's the same education.

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Same costs, I just tried direct messaging him. So maybe that will make like a sound.

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Yeah, but his computer audio entirely dead though, I guess, which is very unfortunate. So, I don't know. Our best bet is just I'm checking. Okay there we go.

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Oh, there you get a smart.

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You should add that he can't hear us also. Like, we know that, like.

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It's just like B, role for the world's worst horror movie.

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Did he get that? Didn't hear it to see it maybe you can see that. That that would have been so genius that worked.

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I feel like you saw that because he stopped writing and I feel like he's looking at the chat now, I hope is looking at the chat and just talking through is thinking of trying to fix this but it doesn't look like it at this point.

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Yeah, I don't know that's fine on him. Like, I don't blame them. It's just oh, man but if you always maybe.

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I don't think he's solid because he wasn't tapped into the meeting. Like, he was on another tab on his browser. So I don't think even saw that.

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Awesome.

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Do you think you notice if everybody is left and then came back.

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I don't think it would if you didn't see the shared the shared screen. I don't think it's that. Yeah, that's just all I can think of that we have left to do.

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Do you think can get email notifications?

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Depends on which email client is using. I use Thunderbird so I get desktop notifications, but if you just use the browser, you know.

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Writing a letter yes.

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You guys do you agree with him? Is he spending facts right now?

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I haven't disagreed with this meeting. Yeah. Say.

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I see that sharing a screen anymore. No, since the other guy tried to turn the screen to take them. Yes.

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If we all leave and Bentley join the chat.

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I don't know, I don't know, like, I left her you and I don't think it made any noise we could try leaving or joining now everyone could just do it. Let's go for it.

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No, I didn't buy all the then of course, you just look at the products that's.

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Yeah, I don't know if you can even see when people leave that we can try it.

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I'm going on the back in a minute.

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Did we get his attention? Can you hear us? Now? We can still not here. You.

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Professor, if you can hear us, I think all of his audio is gone. We can't hear any notifications anyway.

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Yeah, I think when he, when he killed the camera programming uses or whatever from terminal, I think he killed his entire audio thing.

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At least you would see the chat,

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but he doesn't check yet because he has the tab open with the schedule on it on his Chrome when we last saw screen and he just didn't flip back over because he was using that to guide his note taking on the camera,

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so you see professors,

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I asked in Cuba,

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keep calls open.

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Oh, that's a that's a good idea.

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I think I found his phone number from an email. No, it looks like you just plugged in his phone. So if he needs that, we might be able to get audio from him. Now, he might be able to hear us at this point.

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Okay,

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but currently currently a professor,

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your phone is still muted on the WebEx application so you need that and you should be able to hear you

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still know that.

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Yeah, no, it's, it kinda looks like he's, he's got the phone in though, I don't think the phone, the mobile device with WebEx app on it was connected before, but now it's still muted. So, if you Chinese that has microphone, but it's possible, he can here at this point, we still don't have confirmation. You hear me now? Oh, yep.

134
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There we go now, we can yeah, we can hear you. Awesome. Thank you. Okay, I'm just worried it in a few seconds it's gonna start feeding back, but until that happens yeah, we lost you. Right?

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When I believe you started a page two and you started to draw, like a vector and then you talked about, like, investors. That's like, why does it stop there? My my theory is that when you killed the camera, I think that's right when it stops.

136
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So it may have been something to do with that command, but it stopped your audio. Yeah. Cause the problem is the hover cam as a microphone on it also, and.

137
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Yeah, I got a hover cam, I got a laptop and I got an iPad and I got her phone in front of me.

138
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Okay, so okay.

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So, did you hear me.

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We didn't hear anything on page two. Oh, okay. Thank you. And also.

141
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It's going on here, so so.

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Oh, okay. I can.

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Can you hear me now? Yes, yes, we can. Okay. Yeah, we can hear you just a second. I'm getting feedback.

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Okay, okay.

145
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Okay, can you hear me now? No. Yes. Oh, good. Yeah. Okay. Hey, do you do part version to be better?

146
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Okay so I was just giving an executive summary of Aiken factors and I can values and they're interesting because the Aiken values are.

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There's, there's something inherent about the matrix as an operation, the vector space, and the values are some property of the matrix. That does not depend on the representation. And that's nice and a way to see.

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And what they are is that I got here and different factors of different things happening this factor here when I applied to Matrix, Mike, it rotated a little in scale. But this factor here gets does not get rotated, just get scale.

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So,

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that,

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that factors,

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and I can factor in the scale,

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how much it scales to the Ivan value and one way to look at it nice is if you have a circle into the experience,

154
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and you'll apply the matrix to all the points on the circle,

155
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it's gonna turn into an Elipse and the,

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the act,

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the major axis of the lips are the eigen factors and how much these the direction,

158
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and the length are the.

159
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I can values. So one way to look at that. Okay. I just quickly. I mentioned her mission.

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It's a matrix who's transpose is the complex conjugate that's called the agile and it just pops up and I mentioned unitary matrix and it's a rotation matrix. Basically, it's ad joint. That's just complex. transposes. Inverse.

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So, unitary agencies are effectively complex locations and they preserve distances. And they preserve angles.

162
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So, okay, so talking about.

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Moving on chapter that was cleaning up Chapter two also mentioned we don't worry about limits and so on because these are finite dimensional.

164
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And again, the reason I explicitly say don't worry about limits when people got into infinities, infinite series.

165
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And and if it dimensional spaces, they got a lot of weird things happening and it forced the development of a new field of mathematics. People got paradoxes until they nail things down more clearly.

166
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So, I mean, you got things for example. Well, addition is committed to, but a, conditionally convergence series, and you swap around elements you change, whether or not a convergence and what it converges too. So.

167
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Okay, chapter three. Now we're doing state transitions and let me pop this up here.

168
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So, here, we got things like this, which I showed you last time. Oh, that's the classical thing here. Everything's real.

169
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The numbers on the arcs are probabilities. So you go from, say zero he fired the gun towards the doubles that experiment and fifty, fifty probability. It goes to, we either slip if it goes to, to one third probability goes to. So, these are real numbers here.

170
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And this, these are real numbers, and then this is the matrix, the transition matrix it's called doubly add joint if we, some down a row or some across, come down a column or some across a row we got one. Okay.

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That's real now, if we go to the call to the attorney and K not attorney, I'm sorry quantum case too many queues and things are things get a little different what we hear.

172
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Here's a simple matrix. So, we've got three states here and the numbers on the arcs there the complex.

173
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Wait, they're not the probabilities. So, as I over here, the, we have.

174
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Well, we will well, we will have, is that the probability is the norm of the weight on the art.

175
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So, I'm just working down into this year, so for quantum the W, stochastic matrix the, some of the norms is one. So the norms are the a number of times as complex conjugate and I'll show this.

176
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Okay,

177
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so and I just mentioned this a little example over here to show that it would a little matrix down here,

178
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which showed that it's terribly stochastic.

179
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Okay. So, in any case, we have something here we have to.

180
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Okay, so here are the transitions so the one over square root or two means it's a fifty percent chance that it goes on again. Let me just show you the page.

181
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That's the second here. What I want.

182
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Okay, so again, if if we have a way here.

183
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One over square to to so the probability is one half and so on a minus one minus I square to to it's again one half. Okay.

184
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Just to nail down the Toby simple things. Okay. Now, and we get to Jason matrix there, and again, we need some norms, not the elements that show. It's doubly stochastic. Okay.

185
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And probabilities like that. Okay. Now, now the way that we apply the matrix, that's the same way we did before here.

186
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But the States now are these super position with these various waits like here, and we apply we apply the transition matrix to it. So, what I want to do is used and the thing is that.

187
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Probabilities might go down. So what I want to do is.

188
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Say show it on the I don't know I'm going straight to the.

189
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Yeah, just a nice chance. So I think these forecasted billiard ball a quantum billiard ball. Okay. So, let's say that example.

190
00:36:31.800 --> 00:36:34.855
Three three, two and.

191
00:36:38.514 --> 00:36:42.594
Is this the interesting one? No, I want to get you the interesting one here.

192
00:36:48.625 --> 00:36:49.224
And do.

193
00:36:50.844 --> 00:36:53.244
Yeah, that's that's the one I want to do. Okay.

194
00:36:55.105 --> 00:37:07.465
So, and so initially, let's say time equals zero. We are professor, we see what you're writing there. Thank you. Yeah. Okay. Time equals zero.

195
00:37:08.005 --> 00:37:11.304
Let's suppose the stake is we're in.

196
00:37:12.925 --> 00:37:15.954
Let's say or one hundred percent.

197
00:37:17.099 --> 00:37:22.914
Let's say that's the stay here and now, say a time equals one.

198
00:37:24.684 --> 00:37:27.385
What's gonna happen is that.

199
00:37:29.275 --> 00:37:40.255
The state is going to be a one over square root of two and one and a one over square root of two in zero. That'll be okay.

200
00:37:41.994 --> 00:37:53.094
And again, so now, what we have is the Super position of two states with weights, one over square root of too. And if you observed it there with probability, fifty, fifty, it would be one or two.

201
00:37:54.659 --> 00:37:58.675
But now, let's talk about time equals two now. What's gonna happen?

202
00:38:00.355 --> 00:38:05.994
Well, state one.

203
00:38:12.744 --> 00:38:17.155
It goes, which has wait one over square root of two.

204
00:38:19.344 --> 00:38:27.960
It's going to go over to stay zero. What's going on with whenever skirted two times and state three.

205
00:38:28.494 --> 00:38:41.184
So what's gonna happen it goes to zero and the weight is going to be the way here times the transition thing of one over square root to.

206
00:38:41.519 --> 00:38:54.534
So, we're gonna get one half and it goes to three just again.

207
00:38:54.534 --> 00:39:07.614
So I'm trying to avoid writing down the whole matrix, but looks like it might be easier just to do that. Yeah, I, I'll bring up to that Pat again. Okay.

208
00:39:08.815 --> 00:39:16.764
Yeah, this is a matrix I was trying to avoid writing down, but okay, this is the main transition matrix to that graph there and.

209
00:39:17.610 --> 00:39:26.875
Okay, so I have to state one. Three forty seven is what I just wrote down here. I, here's the crazy things. Stay time two.

210
00:39:27.414 --> 00:39:35.635
We take that time one state, which is forty seven multiplied by the matrix in three, forty six.

211
00:39:35.905 --> 00:39:46.195
And what we get is that it went back to a hundred percent in stage zero and so time equals to.

212
00:39:48.655 --> 00:39:53.934
Now, basically, the state is one.

213
00:39:54.925 --> 00:40:01.525
And this is a quantum sort of thing quantum thing. It could not happen classically.

214
00:40:02.485 --> 00:40:11.514
Okay, so because because of what happened is the things canceled out.

215
00:40:13.675 --> 00:40:26.605
What I want to do now is show you the two slit experiment with this quantumly. Okay. All you know, we have.

216
00:40:27.659 --> 00:40:34.135
What's happening here is against the Charles to start stage one and two are the two slits and states.

217
00:40:34.164 --> 00:40:47.784
The three through seven are various, some possible and states and again, we have quantum again. Okay.

218
00:40:47.784 --> 00:40:49.224
These complex numbers here.

219
00:40:50.250 --> 00:40:56.605
So the probability, let's say one to three transition.

220
00:40:57.775 --> 00:41:01.315
That's gotta be minus one plus I over squared with a six.

221
00:41:02.574 --> 00:41:05.724
Times minus one minus. I, over square six.

222
00:41:06.809 --> 00:41:12.414
Which is one third.

223
00:41:14.849 --> 00:41:23.940
Okay, but now, here's the thing. Oh, that's gonna give away to one. Okay.

224
00:41:23.934 --> 00:41:31.344
That's and the, and what we want to know is the.

225
00:41:32.364 --> 00:41:42.025
Wait the superposition. So, at the end, it's gonna be stage three, four, five, six or seven and at the end. So the weight on.

226
00:41:44.250 --> 00:41:48.684
So, at the end, so, let's say, queue.

227
00:41:50.309 --> 00:41:55.405
Very cool. Say the weight on state three.

228
00:41:56.695 --> 00:42:03.804
And again, that's going to be on our square two times as one.

229
00:42:08.519 --> 00:42:22.434
Square root well, and so the problem, and it doesn't get to stay three by going to stay to. So the probability here of stay three.

230
00:42:24.684 --> 00:42:32.364
Is going to be minus one plus with Square twelve that's minus one minus. I was twelve.

231
00:42:34.074 --> 00:42:36.355
Which is one six.

232
00:42:38.340 --> 00:42:44.965
Okay, fair enough. That's what the classical thing does that make sense? Okay but now, let's look at state five.

233
00:42:47.909 --> 00:42:51.204
That's the same as before.

234
00:42:55.105 --> 00:42:59.094
Now, do the probability.

235
00:43:02.304 --> 00:43:14.815
State five. Okay. Get to five, two ways. And so when we want to wait on state five, it is going to be on our square to two times.

236
00:43:15.630 --> 00:43:19.704
One minus I, over.

237
00:43:20.670 --> 00:43:26.485
Square root of six at the six there plus one over square to two times.

238
00:43:30.804 --> 00:43:33.175
One times.

239
00:43:36.630 --> 00:43:42.324
Minus one, plus I always squared of six and what are we going to get here?

240
00:43:43.284 --> 00:43:48.534
Is zero.

241
00:43:50.094 --> 00:43:50.485
Okay,

242
00:43:53.695 --> 00:43:56.364
while in the young slip terminology,

243
00:43:56.364 --> 00:43:58.224
we got destructive interference here,

244
00:43:58.829 --> 00:44:03.505
but this is showing using quantum physics,

245
00:44:03.750 --> 00:44:05.215
the destructive interference.

246
00:44:05.215 --> 00:44:16.375
So okay,

247
00:44:17.099 --> 00:44:22.914
because deterministically deterministic case.

248
00:44:25.800 --> 00:44:36.894
The deterministic case we've got the probability was I forget what it was, but it was greater than zero here. Here. It's zero. Okay.

249
00:44:37.980 --> 00:44:43.255
So this is trying to hang on. This is hope. Sorry, this is how you can do things.

250
00:44:45.144 --> 00:44:50.755
Things get interesting there solver here.

251
00:44:56.514 --> 00:45:08.635
Okay doubles and this is getting into double slit experiment. Okay. And I talk about it there.

252
00:45:09.744 --> 00:45:14.545
Any questions or anything or is this totally trivial? You wish I was going twice as fast.

253
00:45:16.525 --> 00:45:17.425
Oh, okay.

254
00:45:52.164 --> 00:45:56.335
No oh, okay. So.

255
00:45:57.864 --> 00:46:02.155
Now, we want to move on into assembling systems. I just.

256
00:46:03.210 --> 00:46:09.775
Again, I'll just go read some good stuff by find find here.

257
00:46:10.949 --> 00:46:18.324
Okay, so what this is talking about here let me write this down. And again.

258
00:46:26.875 --> 00:46:33.775
Oh, okay, so this is section. Good point four.

259
00:46:43.644 --> 00:46:48.295
Okay, so what's happening here is that we have.

260
00:46:50.670 --> 00:46:57.804
Who's separate one? Q bet systems.

261
00:47:01.585 --> 00:47:08.695
And the idea is now, consider them together as one system.

262
00:47:17.094 --> 00:47:19.764
And there's no interactions or anything. Funny. Okay.

263
00:47:23.485 --> 00:47:26.724
Oh, interactions yet. Nice. Simple. Okay.

264
00:47:28.525 --> 00:47:37.824
So this is gonna do this will motivate why you want a exterior product Tensor product. So.

265
00:47:44.425 --> 00:47:49.554
So product, okay.

266
00:47:51.000 --> 00:48:01.554
So, if I go back me back here. Yeah. Okay.

267
00:48:06.985 --> 00:48:07.465
Okay.

268
00:48:13.525 --> 00:48:16.554
Okay, let me go back here.

269
00:48:22.105 --> 00:48:32.425
So, we've got what we're gonna have here, too unrelated systems. One is a three state system, and it's actually, here we're talking deterministic.

270
00:48:32.755 --> 00:48:46.494
So we're back in the deterministic case, not quantum three stage system red marble from stage zero could go to state one with probability. One six or sorry?

271
00:48:46.494 --> 00:48:50.545
One third or state to probably two thirds etc. Okay.

272
00:48:52.105 --> 00:48:54.835
And it's got this matrix line three, fifty, six.

273
00:48:55.769 --> 00:49:09.864
Okay, that's the, the first state, the second system is a blue marble that has a Tuesday, two possible stage. You want to call them a, and B and km a goes into be probably two thirds, et cetera and it's got this matrix.

274
00:49:10.735 --> 00:49:13.824
Okay. Now, what we want to do is.

275
00:49:15.864 --> 00:49:22.585
We want to look at these two separate systems, the red marble system, and the blue marble system together as one system.

276
00:49:24.534 --> 00:49:36.025
And nothing changed physically, it's just how we're naming things. But now, so the thing is, is the tens of product here, the red marble could be it states zero one or two.

277
00:49:36.144 --> 00:49:49.614
The blue marble could be in states or B, and so the six combinations here, it's, you know, every one of three cases for red times, every one of two cases for blue.

278
00:49:49.614 --> 00:50:03.385
So, the combo system is six states. You know, I'm thinking the probability course, like a dragon previous courses. So the blue marble on its own is matrix and line. Three, fifty eight put them all together. Here are the.

279
00:50:05.994 --> 00:50:15.355
The combo systems got the six states, and we might, this is one possible state we've got right there. Okay now.

280
00:50:16.614 --> 00:50:29.364
So the number of states Mo, reply, but this is how the tens of product operates and the matrix. Here's the tenths of product as a to a matrices. So the red matrix was three by three.

281
00:50:29.364 --> 00:50:39.324
The blue matrix was two by two for the two separate systems. Now, we get a six by six matrix or transitions for the two marble system.

282
00:50:41.275 --> 00:50:49.914
So, this, I think might motivate you the, where this product comes in. Okay.

283
00:50:51.925 --> 00:50:58.704
Oh, and we can talk about here line three, sixty two with how we transition from state to state. So.

284
00:51:00.085 --> 00:51:14.425
Again, the red and the blue marble, they don't interact with each other at all and quantum terms. They're separable but we're not considering them together. So we have to do this combo is product of everything, every red state times, every blue state.

285
00:51:14.849 --> 00:51:28.644
And so, so, things get more complicated like that. Oh, okay. And the red and the blue marble sold affect each other. Now like, I had to entanglement if they did well, then interesting marbles.

286
00:51:30.025 --> 00:51:30.625
Okay.

287
00:51:30.625 --> 00:51:41.304
So that's what's happening here now with now with quantum quantum systems,

288
00:51:41.304 --> 00:51:41.394
you,

289
00:51:41.394 --> 00:51:45.985
to the tens or product of the two separate of the States,

290
00:51:45.985 --> 00:51:47.994
and of the transition matrices just like,

291
00:51:48.054 --> 00:51:50.215
with the deterministic case itself.

292
00:51:51.264 --> 00:52:05.094
It's just in the quantum case now. Weird things start happening because you now have legal operations, which would force the two marbles to interact with each other. And that makes some.

293
00:52:05.755 --> 00:52:10.284
So, again, I'm coming out in tanglement from every different direction because it's complicated.

294
00:52:11.215 --> 00:52:13.914
Okay, and that's the point here.

295
00:52:19.199 --> 00:52:25.885
So, you and that there okay assembling systems.

296
00:52:29.215 --> 00:52:32.755
And I'm not gonna rewrite magically what they have in the book here.

297
00:52:35.094 --> 00:52:48.474
I may do an example or two next time, but that was chapter three. So questions questions.

298
00:52:51.599 --> 00:52:59.184
No, okay. What we got chapter.

299
00:53:01.739 --> 00:53:15.264
For here is getting into some history of it and so you've had that in physics quickly remember the that experiment,

300
00:53:15.295 --> 00:53:23.244
which demonstrated the wave nature of things that the interesting thing with experiment is they also demonstrated with small particles of matter.

301
00:53:23.664 --> 00:53:30.864
It's not just light. So I don't know what the electrons are, something also interfered.

302
00:53:31.469 --> 00:53:45.954
And the other thing is that you get the identical interference thing, if you send one particle through at a time. So the electrons interfering with itself, these will be the matter ways. Okay.

303
00:53:46.764 --> 00:53:49.614
Alright. And they mentioned particles here. Okay.

304
00:53:53.934 --> 00:53:59.425
So, that was evidence of wave no evidence of Quanta existing.

305
00:54:01.074 --> 00:54:09.114
It's not directly quantum computation, but history is interesting. Okay so people thought that was the wave.

306
00:54:10.014 --> 00:54:21.414
Well, you could, for example, refrec retracted evidence that the light was actually in chunks called photons.

307
00:54:22.344 --> 00:54:25.974
This is what got Einstein is Nobel prize actually not relativity.

308
00:54:27.744 --> 00:54:31.255
Is that you could.

309
00:54:33.204 --> 00:54:45.534
You could firewall, rare earth elements, and you could fire photons at them. You get electrons out or you power electrons at them. He fired light at them. You get electrons out. Are you fire electrons at them? You light out.

310
00:54:46.349 --> 00:55:00.085
Things are so, the electron default on think is that if the electron doesn't have enough energy, you get no photons at all being emitted above a threshold. You start getting photon.

311
00:55:00.085 --> 00:55:12.505
So it's like a photon needs. Photons didn't exist yet. They had been discovered yet, but below a threshold no like, was admitted once the electron energy hit a certain threshold he started getting light coming out. So.

312
00:55:14.304 --> 00:55:22.494
Suggested some had to be quantitized and reversing happening. You shine light on this.

313
00:55:22.494 --> 00:55:33.114
And again, things appear to be chopped up into Quanta and this was the proof that publicans existed and okay, so that's that.

314
00:55:36.775 --> 00:55:48.204
Yeah, if you try to observe which slip the electron or photon goes through, then you destroy the interference pattern. So quarter state collapses. That's what's happening there.

315
00:55:48.690 --> 00:56:02.215
So, yeah, and I mentioned down here, the experiment happens one full on time. You get the identical thing, and you can do it with sub atomic particles.

316
00:56:03.594 --> 00:56:08.425
Okay, that's the.

317
00:56:09.360 --> 00:56:11.065
Interesting thing there.

318
00:56:19.260 --> 00:56:23.125
What's happening here? I think I'll hit that.

319
00:56:27.925 --> 00:56:41.184
I'll hit that Monday, I think, and what I want to do for a couple of minutes and just go back to something. I did a while ago, continue to Cupid operators and I want to introduce something.

320
00:56:42.025 --> 00:56:49.255
I haven't talked about, but a blocked sphere and hey, Wikipedia not bad. So.

321
00:56:56.005 --> 00:56:58.945
So, what's happening is this is one way to represent a.

322
00:57:00.985 --> 00:57:13.494
Cubic and it's a point. This is a okay, so some of the way has to be one and oh, the sorry.

323
00:57:13.494 --> 00:57:23.304
The some of the probability says to be one and you could represent it is something on the surface of a sphere of radius one. So, it could be instate zero up at the top.

324
00:57:23.304 --> 00:57:35.425
It could be in state one, which is down at the bottom, or you apply one of these unitary matrices and you rotate you rotate the cube bit one just to show you over here. So.

325
00:57:43.554 --> 00:57:52.974
Yeah, so, you know, you've got, you know, the thing starts off one zero perhaps and you buy some matrix to it.

326
00:57:53.340 --> 00:58:08.125
You've gotta get something B or whatever, and it's essentially you're getting points on the points on the sphere and it's a rotations and that's just something. Some people like.

327
00:58:08.940 --> 00:58:15.445
Yeah, okay so to talk about that there.

328
00:58:16.885 --> 00:58:29.485
And just to remind you, I talked about the some of the gates before, and again, you apply the Adam. Are you? Fine? They had a hard matrix.

329
00:58:29.485 --> 00:58:35.965
You get a superposition between them and I went through some of this. I didn't hit all of them before. But you got to controlled swap and.

330
00:58:37.045 --> 00:58:47.905
Controlled not is something like so and you gotta get knocked out here. Let me get a controlled swap and stuff like that.

331
00:58:48.659 --> 00:59:01.554
So, and I hit the I hit the I, I hit this. Let me give you another level of.

332
00:59:03.474 --> 00:59:09.235
I'll get these more the gates cred kinda tough to fully insulin or and we start talking about kiss. Good.

333
00:59:10.315 --> 00:59:19.675
Now, I wanted you got enough now to see, maybe get a flavor of what's gonna happen with some algorithms. So.

334
00:59:22.079 --> 00:59:27.594
You have so to the end different states here, because it's an N, Cupid system.

335
00:59:28.945 --> 00:59:31.945
And you apply a then,

336
00:59:31.945 --> 00:59:32.664
maybe it's a say,

337
00:59:32.695 --> 00:59:33.534
all of equal weights,

338
00:59:33.534 --> 00:59:34.074
perhaps,

339
00:59:34.465 --> 00:59:37.195
and you apply matrix the state,

340
00:59:37.764 --> 00:59:39.474
which is the solution state,

341
00:59:39.840 --> 00:59:46.974
gets its amplitude increased and then you can detect that by,

342
00:59:47.005 --> 00:59:48.715
with my measurement operators.

343
00:59:49.170 --> 00:59:52.014
So, let me write down informally. What's happening here.

344
00:59:54.894 --> 01:00:04.344
Seven, so how the search works.

345
01:00:09.179 --> 01:00:20.485
Okay, so you got bits for the end States each state.

346
01:00:21.625 --> 01:00:23.304
Is it possible solution?

347
01:00:29.724 --> 01:00:35.934
And say, you know, and then it's all obviously, there's, you know, there's weights and so on.

348
01:00:37.344 --> 01:00:52.074
Maybe the initial weights are something like, perhaps one over square root of, and one requirement event. Something like that all equal. And you generate that with something evolving an matrix.

349
01:00:52.824 --> 01:00:58.644
And then you apply, I'm sorry again, some sort of operator.

350
01:01:04.530 --> 01:01:11.875
It will change the ways of each day.

351
01:01:15.329 --> 01:01:22.045
Depending on whether it's the correct answer if it's the.

352
01:01:22.860 --> 01:01:33.744
Correct answer so in parallel again, we've got these to the end different states.

353
01:01:34.824 --> 01:01:44.394
And one of them is the end, so we're looking for it's the, it's the value of the input, which makes the function.

354
01:01:44.394 --> 01:01:52.074
True and the searching thing solution to over simplify it. So, it's a solution we're looking for.

355
01:01:52.315 --> 01:01:59.514
So the idea what this is effectively doing, when we apply an operator, and again, it's going to act in parallel to to the States.

356
01:02:00.175 --> 01:02:12.925
And the operator in some way is going to test that state to see if it's the correct answer and it's going to change the wait of that state. Because it's what operators do they changed the weights on all the States?

357
01:02:13.585 --> 01:02:20.695
And if this is a quick answer, it's going to increase the way. If it's the wrong answer, it's going to lower the way.

358
01:02:22.164 --> 01:02:27.385
Now, if you can see what's gonna happen so we, we do this. We now have a weight factor, which is not.

359
01:02:29.125 --> 01:02:32.275
Which is not all equal. Okay the correct end. Just got to hire weight.

360
01:02:34.014 --> 01:02:41.425
And now, what we do is, we, we use a measurement operator that will project in some direction, and see what we get.

361
01:02:42.114 --> 01:02:49.735
Now, one measurement is not going to certainly fine, which is a larger weight because we can't directly observe this.

362
01:02:49.735 --> 01:03:00.054
But the the thing is that we run this experiment many times, and we measure it in different directions and we're good.

363
01:03:00.054 --> 01:03:06.565
Eventually figure out statistically, which state got its weight raised. And that will tell us the answer.

364
01:03:07.554 --> 01:03:19.945
No, I'm handwaving ignoring a lot of details, but the beginning that what I hope is here maybe beginning to get a sense of how a quantum operation works is probabilistic.

365
01:03:20.275 --> 01:03:25.375
You gotta repeat it many times, but you see, you, maybe you're getting a sense of what's happening.

366
01:03:26.545 --> 01:03:29.215
Yes, so the operator this and then you measure.

367
01:03:31.860 --> 01:03:34.585
But what you do is you repeat the experiment.

368
01:03:41.244 --> 01:03:49.434
And you manager and basically at different.

369
01:03:51.809 --> 01:03:56.034
Base different bases and.

370
01:03:57.025 --> 01:04:04.195
And you get a probabilistic sense since.

371
01:04:05.155 --> 01:04:15.835
Of the, and, you know, basically have the solution. So, is this totally crazy?

372
01:04:15.835 --> 01:04:24.894
You know, obviously, you know, this is ignoring piles of details but the concept is, you might start to get a sense of what's happening.

373
01:04:26.880 --> 01:04:39.144
So, any, any questions here or something, I idea is, you you get a sense of this.

374
01:04:44.304 --> 01:04:44.934
Okay.

375
01:04:48.090 --> 01:04:58.434
Yes, correct, exactly.

376
01:05:00.085 --> 01:05:05.335
So the thing with well, grover's algorithm is a.

377
01:05:07.494 --> 01:05:14.215
I mentioned down here, the thing, the solution we're looking for factors, there was a probabilistic that.

378
01:05:16.824 --> 01:05:30.175
Yeah, the answer could be wrong, but we would what we run the quantum computer many times, and it raises a probability that we get the right answer. So a second.

379
01:05:37.074 --> 01:05:39.775
I like to keep the blinds up as long as I can actually.

380
01:05:40.710 --> 01:05:53.065
Okay, right and if you later, when we get to using IBM queue machine or the simulator, you say how many times you want to rerun it, like a thousand times or something?

381
01:05:54.684 --> 01:06:04.164
Error rates deceptively low now. Now one point down here, as I mentioned, there are classic algorithms, which are similar down here. Okay.

382
01:06:04.949 --> 01:06:18.054
Mentioned section here. Okay there are algorithms. Well, you might say is the number of prime that's try random Divisor and see if it works.

383
01:06:18.840 --> 01:06:25.974
That's a probabilistic but really bad. There are more sophisticated prime test algorithm test up in numbers. Prime.

384
01:06:27.054 --> 01:06:39.625
And they're probably stick actually, there's some more sophisticated analogy to just trying random factors, but they're actually quite good there. Some of the best prime testing algorithms are probabilistic. Also. This isn't even quantum.

385
01:06:40.375 --> 01:06:44.934
But the quantum ones are quite complex when that's the idea. So.

386
01:06:46.110 --> 01:06:54.445
But the big thing is, and some searching algorithms go faster, not all that we know about. And this is current research.

387
01:06:55.260 --> 01:07:02.635
Because the quantum algorithm don't look anything like the classical ones, so much worse.

388
01:07:03.835 --> 01:07:15.565
Okay and this is grover's algorithm here the first interesting quantum algorithm. It was called grover's algorithm.

389
01:07:15.804 --> 01:07:26.545
We had a black box within inputs and one output, which input makes the output one. Only one of the inputs makes the output one. Which one? And there's a quantum algorithm.

390
01:07:26.545 --> 01:07:37.764
Doesn't square root event time not constant time, but still, but it's probably we'll talk about talk about that at one. And then the famous one ensures algorithm to factor in. Ended your.

391
01:07:37.764 --> 01:07:52.675
I mentioned it briefly before, but it's worth mentioned again and is this will take a while to talk about. So, people think perhaps I'm going to slowly are welcome to figure out choice algorithm on their own. Oh, okay.

392
01:07:53.965 --> 01:07:57.835
This is probably a reasonable point to stop here.

393
01:07:58.405 --> 01:08:11.394
So, what we are doing is we're now working our way and finished off chapter three, and we're working our way into chapter four and continue on that with, on Monday.

394
01:08:11.844 --> 01:08:19.795
And just let me just rehash my good questions.

395
01:08:22.914 --> 01:08:37.404
Okay, I mentioned things like, I can go use transition matrix. We have the inner product, like a dog product. The difference with complex is we don't just multiply corresponding elements. That's the conjugate. The first one times.

396
01:08:37.404 --> 01:08:51.265
The second one I can, I can vectors unitary matrices. These quantum matrices are gonna be unitary there, which means a rotation. It means they're in versus there.

397
01:08:52.765 --> 01:08:55.104
Is there a join? Basically.

398
01:08:56.399 --> 01:09:10.795
Their rotations complex, and again, the differences with the quantum transition graph complex labels on the arts and the, probably, the transition is the norm on the label.

399
01:09:10.975 --> 01:09:15.385
So the label time, the number of times it's complex. Conjugate.

400
01:09:16.675 --> 01:09:19.435
On the square of the norm match I'm sorry.

401
01:09:24.295 --> 01:09:26.215
Norm squared. Okay.

402
01:09:27.869 --> 01:09:37.914
So, you know, and mentioned these, these transition matrices, the probabilities have to add up to one. And again.

403
01:09:37.914 --> 01:09:43.885
So it's a weight on an arc is one over square two the probability of that transitioning there one half and so on.

404
01:09:47.430 --> 01:09:57.145
This gives you a simple quantum example exercise, three, three, two, and with the.

405
01:09:58.500 --> 01:10:03.114
Again, with quantum weight, what can happen is that.

406
01:10:04.375 --> 01:10:17.185
You get what? This is mathematically we're getting destructive interference. If there's two ways to get to a final state, then because of the complex number is the probability of getting.

407
01:10:18.479 --> 01:10:28.045
Don't add, it's the weights add, but the weights could cancel out the complex numbers. It's not if they're real numbers where they keep getting bigger. So there's two ways to get to a final state.

408
01:10:28.074 --> 01:10:40.975
The probability of being in that final state could be zero that says you're a destructive interference here essentially a quantum concept and then to motivate dispenser product again,

409
01:10:41.755 --> 01:10:45.385
because it's worth I like,

410
01:10:46.045 --> 01:10:48.145
come on a second.

411
01:10:52.225 --> 01:10:52.734
Here.

412
01:11:04.704 --> 01:11:06.744
I've been asked if you and I shouldn't have done that.

413
01:11:11.970 --> 01:11:13.404
I just lost that.

414
01:11:17.939 --> 01:11:29.574
Well, yeah, I, I don't want to take your time by reconnecting the hover cam and so on. But let me go through and show you here.

415
01:11:31.944 --> 01:11:36.354
Motivate the, the Tensor product to two different states.

416
01:11:38.185 --> 01:11:44.784
Oh, marble thing. Okay.

417
01:11:47.939 --> 01:11:54.805
So, we have two separate things here. We got a red marble system could be in one, three states, zero, one or two.

418
01:11:55.164 --> 01:12:08.274
We have a separate independent, unrelated, blue marble system States, or B, we want to put them together and think of them as if it was one system. So, red, marble, three cases, blue, marble, two cases.

419
01:12:08.274 --> 01:12:21.145
The com was going to have six cases, and we've up to six states that multiplies. And and then so this is the six possible States for examples airway to to be.

420
01:12:21.444 --> 01:12:34.465
And the transition matrix is going to be the exterior product, the tenser product of to buy to the three by three read matrix with the two by two blue Matrix, and gives us a six by six matrix.

421
01:12:34.944 --> 01:12:36.564
So, I think this motivates to you.

422
01:12:36.564 --> 01:12:37.104
Why we,

423
01:12:37.104 --> 01:12:44.364
this why we do this product here and the only differences in the deterministic case,

424
01:12:44.425 --> 01:12:44.755
the red,

425
01:12:44.755 --> 01:12:52.465
and the blue marbles are still separate but the physics of the quantum case is that we can rotate,

426
01:12:54.534 --> 01:13:00.984
we can rotate the vector for the system and cause the red and blue marbles to entangle with each other,

427
01:13:00.984 --> 01:13:02.154
which is something doesn't happen.

428
01:13:02.154 --> 01:13:12.595
Classically quantum. And the only way I can justify is a physical experiments, find it. It actually happens.

429
01:13:14.935 --> 01:13:25.795
What I might talk about next time is bells there and which disproves the hidden variable theory or shows that,

430
01:13:26.069 --> 01:13:26.484
you know,

431
01:13:27.774 --> 01:13:31.704
because the obvious answered do the superposition of states.

432
01:13:31.704 --> 01:13:45.954
Is that really? It's in some state. We just don't know which one it's hidden. And but if you have to hidden variable thing, you cannot explain this action at a distance where you have two entangled.

433
01:13:47.274 --> 01:13:59.784
Cube bits and you move them say a thousand miles apart and you observe one and this effects. What you see in the other than that. It's impossible to explain that. Using hidden variables.

434
01:14:00.715 --> 01:14:09.475
Part of the problem is the first cue bit. The, the person Australia can decide what measurement operator to use, like, what angle and.

435
01:14:11.935 --> 01:14:16.734
Then, that affects what the person in Greenland will see when he measures is Cupid.

436
01:14:17.814 --> 01:14:26.994
And this is impossible to explain with invariable. Yeah. Actually are entangled. Okay, so that's enough from.

437
01:14:28.319 --> 01:14:42.024
For today, like I said, Chad, we'll go through this on for, you know, work our way through things on Monday. Okay.

438
01:14:42.774 --> 01:14:45.239
Any questions.

439
01:14:49.829 --> 01:14:50.340
No.

440
01:14:58.435 --> 01:14:59.274
Okay, well.

441
01:15:05.010 --> 01:15:05.279
Hello.

442
01:15:25.859 --> 01:15:27.625
Feedback always welcome.

443
01:15:32.305 --> 01:15:44.755
Okay, okay.