WEBVTT 1 00:00:01.979 --> 00:00:08.130 So, we, in theory are recording. 2 00:00:08.130 --> 00:00:13.288 And I hope you're getting sound, you're getting video. 3 00:00:13.288 --> 00:00:28.050 Silence. 4 00:00:30.179 --> 00:00:40.170 Cool. So very okay. I'll extend homework prices to get my act together enough on that. 5 00:00:41.094 --> 00:00:50.784 Next thing, I'm arranging guest lectures. There are several faculty at in different departments who are working with quantum computing. 6 00:00:51.204 --> 00:01:05.484 Most of them are far more physically based physics then programming, which is why, when I created this course, I deliberately made the title quantum computer program to differentiate it. In any case. I want you to meet some of these other faculty. 7 00:01:06.840 --> 00:01:13.140 And I've got 3 of them so far young. She and Edwin tongue. 8 00:01:13.525 --> 00:01:28.435 We'll be giving talks from 10 minutes to half an hour or something, and various other classes. I'll be asking some other people. So this will be a chance for you to see the breadth of work occurring at in quantum computing. 9 00:01:28.739 --> 00:01:40.230 And also, since I've given you again, the computing version, these people will give you a more physics based version of it. So you'll have a chance to. 10 00:01:40.230 --> 00:01:44.670 See, what's happening here? 11 00:01:45.084 --> 00:01:57.864 Okay, so various things here will be talking about table contents, some applications and honeywell's quantum computer talk a little about that more later. 12 00:01:58.135 --> 00:02:03.834 And today I'll be giving you sort of a superficial view of a lot of things that I might in more detail. 13 00:02:04.109 --> 00:02:11.460 In the future, so there's an issue with cube with the phase of acute. 14 00:02:11.460 --> 00:02:19.830 And you cannot measure the phase of an isolated cube bit. What I mean is, if you rotate a bit. 15 00:02:19.830 --> 00:02:25.020 Then all measurement operators will give the same. 16 00:02:25.020 --> 00:02:30.689 Probability get as before the rotation. So just with 1 cube. 17 00:02:30.689 --> 00:02:34.169 There's no measurement operator, which can detect the. 18 00:02:34.169 --> 00:02:43.259 The new phase, however, with 2 cube, you can measure the relative face between them. And now this is important. 19 00:02:43.259 --> 00:02:47.759 Because algorithms usually. 20 00:02:47.759 --> 00:02:52.949 And code the answer as a pay shift of a cube, you have to measure that pay shift. 21 00:02:52.949 --> 00:03:00.539 And it gives you the answer to the problem was salt. So that's just the way they work. They work by. 22 00:03:00.539 --> 00:03:04.080 Rotating acute, which is like, the answer. 23 00:03:05.340 --> 00:03:12.810 Now, I got some links here, but there's the crazy thing happens with Cubics and phase. 24 00:03:12.810 --> 00:03:19.139 Which is the concept of you might say is a little weak. 25 00:03:19.139 --> 00:03:23.400 And if you give a. 26 00:03:23.400 --> 00:03:36.360 If you have some quantum Gates, I'll show you an example on the IBM Q. simulator in a minute controlled daughter or something words, because he goes 1 way the control bit cube. It affects. 27 00:03:36.360 --> 00:03:51.180 Possibly compliments the other Cupid if you give inputs that are had of March 2 propositions, then that can actually make the control flow the other way and the control cube. It can be changed. 28 00:03:51.180 --> 00:03:57.870 And so it's sort of weird, it's called phase kick back. What it means is that. 29 00:03:57.870 --> 00:04:02.580 Faces and 1 cube and effect spaces in another cube bit. 30 00:04:02.580 --> 00:04:08.819 And I'll show you an example here. 31 00:04:08.819 --> 00:04:14.699 On the IBM queue before and then I'll show you these other pages here. 32 00:04:16.110 --> 00:04:20.730 We have something create a new circuit. 33 00:04:22.110 --> 00:04:25.800 Okay out any 2 bits here. 34 00:04:25.800 --> 00:04:29.129 So, we'll have a control doc. 35 00:04:31.588 --> 00:04:40.079 And so again, with this output here, adults, the summary it shows the. 36 00:04:41.699 --> 00:04:49.139 The pace change so all this Nope, this is where you consider a cube to be in. I can polar coordinates effectively. 37 00:04:49.139 --> 00:04:58.709 And it's 0T, it was a 0T going in. It's a 0T coming out purity. It's not mixed in and an entangled passion. Let's say. So we've got this here. 38 00:04:58.709 --> 00:05:07.019 For fun, I'm going to compliment the target cube bit there. So, what that means is that now. 39 00:05:07.019 --> 00:05:15.778 Puts a 1 and for example, if I complimented the consista review, if I complimented the control queue bit. 40 00:05:15.778 --> 00:05:21.088 What it's going to do is just going to flip the target cube bit, because it's a controlled and now. 41 00:05:21.088 --> 00:05:28.528 Well, so 0T is a 1 because I compliment it and now Q1 0T because it's a controlled, not. 42 00:05:28.528 --> 00:05:32.009 Okay, you can see by the coloring here. 43 00:05:32.009 --> 00:05:37.619 And measurement problem, let me go from probabilities to state factors. Perhaps. 44 00:05:37.619 --> 00:05:43.738 Okay, so the, um. 45 00:05:43.738 --> 00:05:55.738 To right to left again the 1 that's 0T the right most biggest 0T and the left most patches. Cute 1. cammy kill this. And let me put in a. 46 00:05:55.738 --> 00:06:04.199 They had a martyr or something here. So now what we've done just to review, we've entangled things. 47 00:06:05.668 --> 00:06:09.689 You say the to Cuba to now and tangled. 48 00:06:09.689 --> 00:06:19.978 And if we look here, 0T probability being a 1 is 50, 50 and impurities 1 half means it's entangled in. 49 00:06:19.978 --> 00:06:29.608 Okay, this I've shown you before. So the 0T is, you know what it was set by the had. 50 00:06:29.608 --> 00:06:33.389 Oh, okay. Now, let me do this here. 51 00:06:35.428 --> 00:06:44.459 So so the change is, I put ahead gate on Q1 before. 52 00:06:44.459 --> 00:06:50.879 The controlled not, but it just did. Is it rotate? It caused 0. 53 00:06:50.879 --> 00:07:01.048 To rotate, you see the face here as pie, and you can see by the if you can see it on the screen is that little? It shows the phase here that little. 54 00:07:01.048 --> 00:07:06.869 Black line, so the only different let me take it out and watch it again. So. 55 00:07:06.869 --> 00:07:13.918 Okay, with that 2nd hand Omar gate and these things both up a phase of pie watch those little black lines here. 56 00:07:13.918 --> 00:07:22.709 Going to take this out and the black line goes to the right these phase is 0T. But the head of my gate back in. 57 00:07:22.709 --> 00:07:28.678 And the phase is 1 and the purity. 58 00:07:28.678 --> 00:07:37.468 Is 1 now it's a separate thing. So, putting Q1 the target cubital in a state of superposition. 59 00:07:37.468 --> 00:07:40.889 Affected q0T the control cube at. 60 00:07:40.889 --> 00:07:45.149 So, this weird things with quantum computing. 61 00:07:45.149 --> 00:07:52.348 And what we have down here is we got 4, it's everything is completely. 62 00:07:52.348 --> 00:07:55.348 Mixed and equal probabilities. 63 00:07:55.348 --> 00:07:59.519 And with the red coloring means is of the phase angle. 64 00:07:59.519 --> 00:08:06.928 Is pie minus so blue coloring phase angles there all the red. So, what we have is. 65 00:08:06.928 --> 00:08:17.009 4 output States, they're equally probable. Each has an aptitude to point 5 to the probability of 1 quarter. However, these 2 states have. 66 00:08:17.009 --> 00:08:29.459 A different phase angle, and this doesn't immediately affect the probabilities of these 4 possible output States. However, it will affect things later on if we continue to compute. So. 67 00:08:29.459 --> 00:08:33.719 So, what we have is this phase kick back and we have this. 68 00:08:33.719 --> 00:08:37.798 Phases rotated for some of the output States. 69 00:08:37.798 --> 00:08:43.379 Okay, so that are, um. 70 00:08:45.028 --> 00:08:50.308 Where did I put it here? This 1. 71 00:09:07.349 --> 00:09:13.769 Weird sorry the other page can't figure out where I put the. 72 00:09:13.769 --> 00:09:16.979 Okay. 73 00:09:16.979 --> 00:09:28.048 So this is this thing with phase kickback and so on and now more information about phase kickback. I've got a couple of pages here. 74 00:09:28.048 --> 00:09:32.339 This here. 75 00:09:33.418 --> 00:09:38.038 So, this I thought was an interesting description and. 76 00:09:41.099 --> 00:09:45.479 Put it again that you can rotate the pace of a cube and it's not. 77 00:09:45.479 --> 00:09:49.168 Directly measurable. 78 00:09:49.168 --> 00:10:03.509 No measure an offer to produce a difference, but if you feed in these plus and minus superposition here like this, plus and minus Gates States, which you get from the operator is using some. 79 00:10:03.509 --> 00:10:06.538 Box here things here you. 80 00:10:06.538 --> 00:10:18.149 Again, I admit, I'm waving my hands. I'll let on I'm being a touch superficial, but trying to give you, you almost might say a managerial view of things you are. We now have states that. 81 00:10:18.149 --> 00:10:22.528 Will have different results later on and. 82 00:10:22.528 --> 00:10:28.499 Also, talking about ways, you can measure in relative face, which you need to get the answer in some of these things. 83 00:10:28.499 --> 00:10:32.249 So definition to kick back here. 84 00:10:32.249 --> 00:10:36.869 The they use and sell for the other. 85 00:10:36.869 --> 00:10:40.198 And salary fit cubic here. 86 00:10:40.198 --> 00:10:51.418 So so that's like the control what I was calling the control acute, but they call the Ansel cube and the other ones that controlled. 87 00:10:51.418 --> 00:10:57.239 Bit okay, so they talk about that here. You can go through that on your own somewhat. 88 00:10:58.558 --> 00:11:03.989 And it's used, we were using it without talk. I'm talking about it earlier in some things. 89 00:11:03.989 --> 00:11:07.708 Golfers alibre something, whatever which okay. 90 00:11:09.089 --> 00:11:13.948 And they're running it here on some packages and I might run it on Monday or something. 91 00:11:13.948 --> 00:11:24.359 I can figure it out. Okay, so we've got this. There's a number of descriptions on the way. I thought this 1 is tolerable and also. 92 00:11:24.359 --> 00:11:28.619 Is the kids get documentation? 93 00:11:28.619 --> 00:11:32.759 So, they're talking about the controlled, not. 94 00:11:32.759 --> 00:11:41.009 Okay, that is cool. What's happening while you initially saw latex source and then you saw the formatted thing. 95 00:11:41.009 --> 00:11:45.958 This is the way this lay tech math interpreter works. 96 00:11:45.958 --> 00:11:49.739 It sort of cool is that the initial. 97 00:11:49.739 --> 00:11:54.778 Page the has the raw the data source. 98 00:11:54.778 --> 00:12:00.839 For the, for the equations, like this equation here. 99 00:12:00.839 --> 00:12:04.708 And then after the page is loaded with a tech source. 100 00:12:04.708 --> 00:12:08.278 It triggers a call, Jim, I'll call back. 101 00:12:08.278 --> 00:12:12.538 Or the event is that the page has been loaded, and it. 102 00:12:12.538 --> 00:12:17.938 Figures a JavaScript operation, which goes through the whole page. 103 00:12:17.938 --> 00:12:21.719 And finds instances of the latex source. 104 00:12:21.719 --> 00:12:28.078 And for each incident, for each occurrence, it executes a client's side. 105 00:12:28.078 --> 00:12:33.568 They take math interpreter, which replaces the source with the generated. 106 00:12:33.568 --> 00:12:40.019 Mathematical expression, it's quite cool. And then the thing is since a generated expression. 107 00:12:40.019 --> 00:12:44.818 Is going to take more space and the latex source it has to Reflow the page. 108 00:12:44.818 --> 00:12:53.938 And so this is using the fact that the, the page, the document object model, the. 109 00:12:54.594 --> 00:13:05.364 It's an object that you can operate on, you have, you can imagine it's an X amount, which is sort of I'll look, you can do is your JavaScript. 110 00:13:05.364 --> 00:13:12.024 It can go through that representation of the page that's being displayed and it can do anything you want to it. 111 00:13:12.269 --> 00:13:21.149 It can delete elements, it can insert create new elements. It can change attributes. And so the page is totally dynamic. 112 00:13:21.149 --> 00:13:25.438 It's really cool so not quantum computing, but it's actually quite cool. 113 00:13:25.438 --> 00:13:33.389 And so you can make stuff appear and disappear for example, by if you set an invisible attribute on an element, the attribute vanishes. 114 00:13:33.389 --> 00:13:41.938 So 1 way they get active pages dynamic pages is they put everything in the page, but they flag. Most of the stuff is being invisible. 115 00:13:41.938 --> 00:13:46.769 And it's way you can make things and expand and contract and then to make something visible. 116 00:13:46.769 --> 00:13:50.099 It changed the tag to make it visible and since it's already been. 117 00:13:50.099 --> 00:13:53.609 Mostly rendered this this has nothing more has to be downloaded. 118 00:13:53.609 --> 00:14:00.688 This thing does require that the client side that your machine be reasonably powerful. 119 00:14:00.688 --> 00:14:10.469 they used to be a web browser years ago microsoft at one point had this machine all they did was show pages but it was so under powered that if you . 120 00:14:10.469 --> 00:14:25.134 Ran a page, it's like tech math like this you could watch it happening. So also the use was quadratic and the number of mass expressions on the page. So well, the side, by the way it was 1st invented by a profit Union college, children's connectivity. 121 00:14:26.394 --> 00:14:36.984 It's been expanded now, but it's quite nice. Okay. In any case. So phase kicked back you apply the controlled not where you've got just had a March superposition. 122 00:14:37.553 --> 00:14:42.533 This is the thing I would show and this just describes that I won't go through line by line, but. 123 00:14:43.948 --> 00:14:51.178 It goes through what's happening and to the extent, you want to learn more about this. I'll leave it to you and it's open ended. So. 124 00:14:52.288 --> 00:14:55.438 You can have fun, browsing this and so on. 125 00:14:55.438 --> 00:14:59.158 Oh, this is a cool thing right here. I just I want to talk about. 126 00:15:00.298 --> 00:15:04.739 Here on the left side is a controlled, not. 127 00:15:04.739 --> 00:15:08.458 Or, or the top cube bit is the controller. 128 00:15:08.458 --> 00:15:13.499 And sorry is the target and the bottom cube bit in this case is the. 129 00:15:14.698 --> 00:15:17.788 Is a control cube bed now? 130 00:15:19.198 --> 00:15:23.249 What do we have here is we reversed the. 131 00:15:23.249 --> 00:15:28.558 Order of the controlled not by putting 4 superposition. Gates. 132 00:15:28.558 --> 00:15:34.288 Around it like this so there's a lot of these equivalence operations for. 133 00:15:34.288 --> 00:15:37.438 Cube bit for the gates that I've not talked about. 134 00:15:37.438 --> 00:15:41.609 And but this is just an example of this. 135 00:15:41.609 --> 00:15:44.788 And now you might wonder. 136 00:15:44.788 --> 00:15:48.208 Why is this useful. 137 00:15:48.208 --> 00:15:52.229 Well, with your real quantum computers. 138 00:15:52.229 --> 00:16:03.058 You have limits in the Gates, you've got limits, and the way you can connect Cubics with Gates, you don't have full conductivity. It's partial connectivity. Those a little diagrams. 139 00:16:03.058 --> 00:16:08.428 For the connectivity of the IBM queue machines, for example. 140 00:16:08.428 --> 00:16:14.399 And so if you. 141 00:16:14.399 --> 00:16:18.389 If you use the circuit designer to do some general circuit. 142 00:16:18.389 --> 00:16:21.958 It may not be directly implementable. 143 00:16:23.303 --> 00:16:28.734 So, while just affecting a compiler behind the scenes, I just alluded to it and talk about it in detail. 144 00:16:29.274 --> 00:16:41.514 But there's a compiler that which happens automatically, which takes the circuit that you have drawn, you've designed and translates it into a circuit, which can be implemented on that quantum computer. 145 00:16:42.119 --> 00:16:46.019 And this is the sort of thing it might do. If you have access. 146 00:16:46.019 --> 00:16:50.578 If 2 cubic some for some hard work type reason. 147 00:16:50.578 --> 00:17:01.859 They the control, you need a control, not gate and goes 1 way, but not the other way in the hardware, but you want the other way and this is how it can be implemented. So. 148 00:17:01.859 --> 00:17:05.338 And. 149 00:17:07.048 --> 00:17:12.209 If we just go to see examples of that. 150 00:17:13.679 --> 00:17:17.608 Silence. 151 00:17:17.608 --> 00:17:21.088 No, I don't do any good example. I was trying to find the. 152 00:17:21.088 --> 00:17:29.429 The topology, but in any case, so, this is on the kiss good page talking about these. And if we go along here. 153 00:17:32.304 --> 00:17:46.913 There was a lot of other they talk about more circuit identities. Let's talk about that at the end because, and 1 way you can see this sort of stuff is working with the matrices. I've just been going a little light on the major save, just because I don't know. 154 00:17:47.189 --> 00:17:50.999 I find a tedious to be writing for by 4 matrices. 155 00:17:50.999 --> 00:18:00.088 All the time, so would slow down the lecturing, but this would be 1 way to actually look at these things. Just look at the matrices and maybe. 156 00:18:00.088 --> 00:18:05.999 I should fire up a Mathematica session or something, and do that. That could be financially. 157 00:18:05.999 --> 00:18:14.398 In any case we go now, we got the talking about the face kit back and so on with the expressions and the matrices. 158 00:18:16.528 --> 00:18:23.068 Also, talk about things like swap Gates, you can do a controlled swap gate or something then. 159 00:18:24.598 --> 00:18:36.298 Control it, and then they can work with the matrix and so on if anyone wants, I could write down this on a pad of paper, go through it line by line but. 160 00:18:36.298 --> 00:18:42.358 Okay. Um, so fun things happening here. 161 00:18:42.358 --> 00:18:48.659 Even assign a few exercises, maybe. Okay just more circuit identities just a. 162 00:18:48.659 --> 00:18:54.148 Okay, so what's happening here is that again? 163 00:18:54.148 --> 00:19:01.259 The actual hardware available Gates may be limited and so they're talking about ways that. 164 00:19:01.259 --> 00:19:08.219 You want a controlled Z would be a controlled rotate that rotates around the access in your. 165 00:19:08.219 --> 00:19:14.159 In your phase diagram and talking about ways, you can do that and so on. 166 00:19:14.159 --> 00:19:21.628 Adam are Gates really useful and controlled sorts of things swap there. Okay so. 167 00:19:24.148 --> 00:19:33.838 Singling for I thought if you had control knots or don't have a swap now, the swap, the gauge this sort of concept is important again. 168 00:19:33.838 --> 00:19:47.278 For the following reason is that you can do a to gate operation on a real quantum computer, only for 2 gates that are connected in the plainer adjacent graph for the computer. 169 00:19:47.278 --> 00:20:00.538 And so, if you want to operate on a pair of Cubics that are not adjacent on the quantum computer, what's compiler does it does a series of swaps. 170 00:20:00.538 --> 00:20:09.239 And so it brings the 2 cube together so you can operate on them and can do the swaps. If you have. 171 00:20:09.239 --> 00:20:16.828 Enough control dots, then you can use them to do your swaps and it can bring the 2 2 bits together that you want. 172 00:20:16.828 --> 00:20:20.578 To do it to gate operation on. So. 173 00:20:20.578 --> 00:20:24.118 Okay, so that's what they're talking about here. 174 00:20:24.118 --> 00:20:38.699 And controlled rotations I've been a little light on rotations, but there is there could called the poly operations of quality matrices and you could rotate by a general data. 175 00:20:40.108 --> 00:20:43.169 The way this is done in the hardware. 176 00:20:43.169 --> 00:20:48.148 Is that the hardware to interact with the cube? 177 00:20:48.148 --> 00:20:51.449 With a microwave at about. 178 00:20:51.449 --> 00:20:57.028 From 5 gigahertz give or take, we saw some stuff on the hardware, like, a week ago. 179 00:20:57.028 --> 00:21:06.388 And what happens actually, then you might say the more you tickle the cube bit with the microwave, the more it rotates. So you can control the amount of rotation. 180 00:21:06.388 --> 00:21:11.939 By how intense for how long you tickle the cube bit with the microwave. 181 00:21:11.939 --> 00:21:15.838 So, that's what they're talking about here. 182 00:21:15.838 --> 00:21:23.278 Okay, for example, they're doing some swapping. Okay. 183 00:21:23.278 --> 00:21:26.308 So, this was talking about phase. 184 00:21:26.308 --> 00:21:29.669 Now, before we get to some applications. 185 00:21:29.669 --> 00:21:32.699 I thought I would show you another. 186 00:21:33.929 --> 00:21:39.269 And another company doing quantum computing, so we've seen IBM. 187 00:21:39.269 --> 00:21:42.419 We sing D wave. 188 00:21:43.679 --> 00:21:47.548 I'm going to talk about Google at some point. 189 00:21:47.548 --> 00:21:50.548 I'm forgetting someone and Honeywell. 190 00:21:50.548 --> 00:21:56.368 And so Honeywell is working on the thing also. Now, by the way you notice that. 191 00:21:56.368 --> 00:22:08.249 Each company has the best quantum computer in the world if you pick the right metric system. So we're seeing a classical example of picking your measurement off parade here. I guess that. 192 00:22:08.249 --> 00:22:13.199 Um, so D, wave says they got the most Gates I'm Honeywell. 193 00:22:14.278 --> 00:22:18.628 Is saying they have, um. 194 00:22:18.628 --> 00:22:21.659 They say they've got the best quantum computer. 195 00:22:21.659 --> 00:22:29.009 So now what they're measuring it, 1st is a concept of quantum volume. 196 00:22:29.009 --> 00:22:36.358 To measure the quantum computer and what you're doing here is that the idea was developed by IBM. 197 00:22:37.618 --> 00:22:43.588 And they're looking at 3 different things, and they're multiplying them to give volume and maybe clicks through to. 198 00:22:44.848 --> 00:22:53.759 Okay, so Susan, well, what it is is that they're combining 3 different things. 199 00:22:53.759 --> 00:22:57.358 I'm number 1 is how many Gates your computer has. 200 00:22:57.358 --> 00:23:09.628 A number 2 is the coherence time or the number of operations you can do. And number 3 is basically a measure of the noise on the computer. How how. 201 00:23:09.628 --> 00:23:13.949 Accurate the operations are so it's going to be inverse to the noise. 202 00:23:13.949 --> 00:23:19.499 So, the quantum volume is, it's like the number of Gates you have. 203 00:23:19.499 --> 00:23:22.828 Times how many operations you can do. 204 00:23:22.828 --> 00:23:26.159 So you may say the depth of your quantum circuit. 205 00:23:26.159 --> 00:23:30.568 Before the results stopped getting useless times. 206 00:23:30.568 --> 00:23:36.598 An inverse measurement of the error on each gait. The noise on each gate. 207 00:23:36.598 --> 00:23:40.648 Okay, so okay, so Honeywell. 208 00:23:40.648 --> 00:23:50.009 They have a gate type machine like IBM somewhat. They don't have as many cube bits, but they say they're Cubics are higher quality cube beds. 209 00:23:50.009 --> 00:23:57.959 And so here we are the same number of Cubics, the error rate. 210 00:23:57.959 --> 00:24:03.538 And the cavity. 211 00:24:03.538 --> 00:24:16.614 So well, this is slightly different than IBM constituted the depth. So, IBM is using Joseph conjunctions. Honeywell is using a different physical principle for their machine. 212 00:24:16.614 --> 00:24:23.064 I'll talk about it more later, but that allows them to connect. Don't have better conductivity in their computer. 213 00:24:24.479 --> 00:24:32.548 So, IBM, it's a plainer graph, it's limited kind of Honeywell says they've better conductivity and that's why they say there is this better. 214 00:24:32.548 --> 00:24:36.598 Any case so this is another company that. 215 00:24:36.598 --> 00:24:41.818 As a quantum computer, it's also it's getting to very cold here. 216 00:24:41.818 --> 00:24:51.989 And talking about that, so I may talk about it more later, but you're free to do this. And if I can think of a way for you to play with the computer, I may do that. 217 00:24:51.989 --> 00:25:02.548 So, what I'm trying to do is set it up so that on your resume, you can say that you actually Pro used you actually ran, say IBM Q. 218 00:25:02.548 --> 00:25:13.078 You can say that if you actually hit rotten 1 so you can say, maybe you actually ran a D wave program and then so and so this will enhance your resume. 219 00:25:13.078 --> 00:25:21.298 So, okay um, so that was the Honeywell thing more details. 220 00:25:21.298 --> 00:25:25.709 There's a different 1. 221 00:25:25.709 --> 00:25:31.769 And so they're talking about only 10 cube, which doesn't sound like much. 222 00:25:32.243 --> 00:25:44.513 But they claim that they're very low noise full conductivity, which is better higher coherence time. They've got a couple of other things. 223 00:25:45.354 --> 00:25:47.423 What does mid circuit measurement means. 224 00:25:47.729 --> 00:26:01.709 Is that you have the freedom to measure 1 cube the IBM thing you started, you do your computation and at the end of it, you measure all your cube and of course, measuring causes them to protect down to classical bets. 225 00:26:01.709 --> 00:26:07.499 The Honeywell system, you can choose to measure 1 cube. 226 00:26:07.499 --> 00:26:11.009 And leave the others still super posed. 227 00:26:11.009 --> 00:26:15.598 So, that gives you more flexibility if you wish. 228 00:26:15.598 --> 00:26:23.159 Well, 1 thing they say with the spit circuit measurement, you're going to have, like, almost a classical if gate. 229 00:26:23.159 --> 00:26:26.338 Because you can use that mid circuit measurement to. 230 00:26:26.338 --> 00:26:38.429 In fact, something later in the quantum circuit in the quantum date gate diagram. So, 1 way you can look at that is honeywell's doing a hybrid of a classical in a quantum computer. 231 00:26:38.429 --> 00:26:46.138 And the high rise rotation, so you can, it can control more precisely how they're rotating a phase. So. 232 00:26:46.138 --> 00:26:56.848 And how I haven't figured it out. I haven't asked them yet if you could use it or something but in any case. So, this is honeywell's. 233 00:26:58.588 --> 00:27:02.939 So, we should do. 234 00:27:02.939 --> 00:27:11.578 So, Z, yeah, Ziff Davis has a nice some story on this and notice the day that came out today. Okay. 235 00:27:11.578 --> 00:27:14.578 So, I'm not always giving you old stuff. 236 00:27:14.578 --> 00:27:27.509 Even the old textbook, because the theory hasn't changed. The basic theory hasn't changed since the book was written, but here's the new app. So you can so, 1 thing Honeywell is doing is they have. 237 00:27:27.509 --> 00:27:31.499 Working together with a lot of other companies such as. 238 00:27:31.499 --> 00:27:34.528 Microsoft and Cambridge systems. 239 00:27:34.528 --> 00:27:38.788 And see, you can browse this and get more information. If you like. 240 00:27:38.788 --> 00:27:45.598 So, they so Honeywell is partnered Microsoft. 241 00:27:45.598 --> 00:27:50.759 Cambridge climate and some others and there is a. 242 00:27:50.759 --> 00:27:58.888 Here's a Microsoft article on it. Okay. 243 00:28:01.019 --> 00:28:12.328 And I'm still going to fix myself. In fact, I said the CD net article just came out today. So I'm trying to learn this. And if I can work some of this into a class exercise, I will so. 244 00:28:12.328 --> 00:28:17.729 So you can say you use quantum computing with Microsoft and put that on your resume also. 245 00:28:17.729 --> 00:28:25.949 Okay, so that was Honeywell a quick introduction to Honeywell any. 246 00:28:25.949 --> 00:28:29.638 Questions comments on that. 247 00:28:30.689 --> 00:28:33.808 And he would still awake. Okay. 248 00:28:33.808 --> 00:28:39.239 So next thing I'd like to talk about is. 249 00:28:39.239 --> 00:28:42.298 Some applications. 250 00:28:43.558 --> 00:28:47.368 And. 251 00:28:47.368 --> 00:28:51.628 They just kill a few things here. My browser, it's getting crazy. 252 00:28:53.308 --> 00:28:58.318 Okay. 253 00:28:58.318 --> 00:29:02.608 Show you the back and. 254 00:29:09.058 --> 00:29:13.259 Various applications here solving linear equations now. 255 00:29:15.778 --> 00:29:21.148 Couple of points here are linear equation. Systems of equations are important. 256 00:29:22.348 --> 00:29:30.989 Couple of points everyone knows this is working with sparse systems of equations. 257 00:29:30.989 --> 00:29:37.979 So, as far system of equation, the matrix of coefficients, a, is mostly 0. 258 00:29:37.979 --> 00:29:47.909 Like, a good example, I've worked on say, solving a heat flow equation, a modified flow equation say, on a 3000 by 3000. 259 00:29:47.909 --> 00:29:52.499 Grid, so it's a version of the partial differential equation. 260 00:29:52.499 --> 00:29:58.528 So there are so each element in the grid is an unknown that would be 9M unknowns. 261 00:29:58.528 --> 00:30:03.538 So, the matrix a, is 9M by 9000000. 262 00:30:03.538 --> 00:30:16.528 So, and multiply it out, just the number of elements and the matrix. Hey, but each row of a had only 5 non 0T entries a 9M minus 5 0T. So that's very sparse system. 263 00:30:16.528 --> 00:30:20.098 And when you're solving this. 264 00:30:20.098 --> 00:30:23.249 Techniques to solve. 265 00:30:23.249 --> 00:30:26.519 The techniques for solving general. 266 00:30:26.519 --> 00:30:30.868 Systems of equations. 267 00:30:30.868 --> 00:30:35.038 The problem is that. 268 00:30:35.038 --> 00:30:49.138 Well, what they're doing is they're transforming a common method to solve this equations. You transform a, and you transform it till it becomes upper triangular and you just work to the bottom up and you can. 269 00:30:49.138 --> 00:30:52.888 Assumption it didn't find all the variables. 270 00:30:52.888 --> 00:30:56.818 So, the techniques to is to make a upper triangular. 271 00:30:56.818 --> 00:31:02.429 The problem is that if you apply these techniques to sparse matrix. 272 00:31:02.429 --> 00:31:11.999 Um, you'll fill in the 0T, so you want to keep the zeros mostly as zeros. So you cannot use general techniques on as far as system because. 273 00:31:11.999 --> 00:31:16.499 It will turn it into a dense system, but you do not want. 274 00:31:16.499 --> 00:31:30.298 So, the special techniques for solving spar systems, what I was doing also is my system was also over determined where I had more equations that I had unknowns. So I actually had to solve for at least square solution. 275 00:31:30.298 --> 00:31:34.888 Best fit any case so this. 276 00:31:34.888 --> 00:31:41.939 Quantum computing method here is working with sparse systems of layer equations. 277 00:31:41.939 --> 00:31:47.969 And it's not producing X directly. It's producing. 278 00:31:47.969 --> 00:31:54.358 What it does is it creates a state where you can apply and operator to X. 279 00:31:54.358 --> 00:31:57.419 So, the solution technique will. 280 00:31:57.419 --> 00:32:01.138 You take your, a, and B, and it and you take a, and. 281 00:32:01.138 --> 00:32:07.378 Quantum operator, and what we'll do it, and it will compute and mix for you. 282 00:32:07.378 --> 00:32:12.239 Where you don't know X. okay so that's. 283 00:32:12.239 --> 00:32:15.509 But the point of this is the. 284 00:32:15.509 --> 00:32:20.459 Best method is called the H. H. L. method. It's after the 3 inventors. 285 00:32:20.459 --> 00:32:25.528 It is not in the text box that we covered for for the 1st few weeks because this. 286 00:32:25.528 --> 00:32:29.189 The H algorithm is only about 10 years old. 287 00:32:29.189 --> 00:32:36.358 A little more and so what I've got is 2 links here to talk about this. And again, I'm just going to give you, um. 288 00:32:36.358 --> 00:32:47.878 A high level view of it. Also, the type setting in this book is atrocious. We turn on some more JavaScript so the type setting here is atrocious, but. 289 00:32:49.949 --> 00:32:55.739 Okay, so working with spar says they're talking about how much faster it is. 290 00:32:55.739 --> 00:33:01.739 Recently also want to ask them Todd experience. I gave you the example I would say playing with where. 291 00:33:01.739 --> 00:33:06.568 So, I was solving a spar system sounded democratize grid. 292 00:33:06.568 --> 00:33:11.759 See, a problem is this with normal solution techniques is that. 293 00:33:13.499 --> 00:33:17.818 And then, by end grid has N squared unknowns. 294 00:33:17.818 --> 00:33:21.898 And these standard ways to solve a linear system. 295 00:33:21.898 --> 00:33:33.179 On N squared unknown, so take time into the 6. so this is the 6 power of the resolution. Okay. So now another new idea here with some of these systems. 296 00:33:33.179 --> 00:33:36.568 So, there's different ways you can solve. 297 00:33:36.568 --> 00:33:49.409 Some of these spar systems, there's the explicit method. Like I said, well, if the den system you go through and you transform the matrix a, and you make eventually you transform it till it starts becoming upper triangular need to back salt. 298 00:33:49.409 --> 00:33:55.828 There's a direct solution techniques. There are there's another class of solution techniques, which are intuitive. 299 00:33:55.828 --> 00:34:00.028 And they approximate the answer slowly. 300 00:34:00.028 --> 00:34:07.919 So, they start with an approximation to the answer and each iteration they get closer to the answer. 301 00:34:07.919 --> 00:34:16.619 So, in this case, the time depends on the accuracy, the more accurate you want the answer the or time it takes. 302 00:34:16.619 --> 00:34:26.458 So some of these expressions for time here, so, and would be the number of unknowns s would be the number of non 0T entries in each role of a. 303 00:34:26.458 --> 00:34:29.938 Calling this far system and Epsilon here. 304 00:34:29.938 --> 00:34:43.168 Is a desired accuracy so effectively what logged 1 over Epsilon would be the number desired digits and the accuracy here. So the more digits you want, the more time it takes, so these will be the 3 parameters. 305 00:34:43.168 --> 00:34:52.228 And so this would be the classical computer might take a certain time contract. And Craig is a method where you're iterating towards the answer. 306 00:34:53.579 --> 00:35:06.239 And and a few other things I left out, but in any case, we see here, there's an end in here and here, it goes down to log in. 307 00:35:07.739 --> 00:35:11.699 So, the, that. 308 00:35:11.699 --> 00:35:15.449 Is in potentially faster. 309 00:35:15.449 --> 00:35:22.829 Than the classical method, although they haven't yet got to that point of actually solve a problem. This big enough. 310 00:35:24.329 --> 00:35:27.659 Okay. 311 00:35:27.659 --> 00:35:31.349 So that's sort of the, um. 312 00:35:31.349 --> 00:35:34.409 The landscape for H. L. 313 00:35:34.409 --> 00:35:39.628 It's a method for sparse equations that. 314 00:35:39.628 --> 00:35:44.878 And it works, it doesn't produce X directly. What it does is it. 315 00:35:44.878 --> 00:35:51.418 Takes another input, which is an operator you want to apply to X and applies the operator. There's another thing is. 316 00:35:52.619 --> 00:35:57.059 So, we have the matrix a, it has the values. 317 00:35:57.059 --> 00:36:03.509 And the distance between the largest and smallest value is relevant. 318 00:36:03.509 --> 00:36:07.588 Or just generally with the methods and. 319 00:36:07.588 --> 00:36:16.768 It's the largest tagging value is very much larger than the smallest fagen value. Then it makes the problems. They're numerically less conditioned. It becomes harder to solve them. 320 00:36:18.028 --> 00:36:26.248 There are iterative methods also that will find the largest Haagen value, which will help you find. So okay, so getting in here. 321 00:36:27.509 --> 00:36:33.088 I'm waving my hands and so on wait. Wait wait wait. Wait. Okay, but trying to give you a. 322 00:36:34.289 --> 00:36:37.798 A landscape of what's happening here. 323 00:36:39.418 --> 00:36:43.858 Another concept here haven't really hit too much register is so. 324 00:36:43.858 --> 00:36:58.469 The algorithms that we've seen somewhat well, the registers set a cube that has the input. There are also some extra registers that are effectively working registers like scratch scratch pad. You might say so, some cute bits I use as a scratch pad. 325 00:36:58.469 --> 00:37:06.628 Pretty diagram basically again, it's like some of the earlier ones we've seen. 326 00:37:06.628 --> 00:37:12.869 You got the input and they've got some other Cuba, Twitter, essentially a scratch pad and. 327 00:37:12.869 --> 00:37:16.108 What's happening? Is this step in the middle. 328 00:37:16.108 --> 00:37:22.949 It's an approximation to the answer and you repeated you get the answer more accurately so. 329 00:37:22.949 --> 00:37:31.528 Yeah, I may have to some more detail next time. I like to hit things and catering greater depth over a couple of classes. So, in any case. 330 00:37:31.528 --> 00:37:35.398 So that's what's going on here and the answer will be. 331 00:37:35.398 --> 00:37:39.298 There'll be a face rotation and you're pulling out so. 332 00:37:40.619 --> 00:37:43.768 It's not exact, it's an approximation. 333 00:37:44.969 --> 00:37:52.199 And I might hit this more detail next time. In any case. 334 00:37:52.199 --> 00:37:57.778 Um. 335 00:37:57.778 --> 00:38:05.668 Um, may talk about it a little here so writing I might write it accepts. Okay so that was this. 336 00:38:05.668 --> 00:38:12.480 Is this is the kiss? Good thing. I've found another very nice description of a child. 337 00:38:12.480 --> 00:38:17.159 So, Here's another website haven't showed you. 338 00:38:17.159 --> 00:38:21.900 A quantum computing set of examples and so on. 339 00:38:21.900 --> 00:38:29.760 And this is quite well written I think so it's got tutorials and stuff so feel free to browse through here and. 340 00:38:31.619 --> 00:38:35.760 In any case this solving this problem and. 341 00:38:37.619 --> 00:38:42.030 Okay, this is small way in, which has been in the news. 342 00:38:42.030 --> 00:38:45.090 Okay, so you can. 343 00:38:45.090 --> 00:38:48.510 Get the from here. 344 00:38:50.730 --> 00:38:54.389 Okay, that was 1 application. 345 00:38:54.389 --> 00:38:58.349 Other applications. 346 00:39:03.599 --> 00:39:07.469 Okay, Eva. 347 00:39:07.469 --> 00:39:13.170 Simulating a molecule, so this is like D wave is doing in fact. 348 00:39:13.170 --> 00:39:18.929 They're trying to find the minimum energy state for. 349 00:39:20.159 --> 00:39:24.840 Protein folding perhaps or how 2 molecules of fit together. 350 00:39:24.840 --> 00:39:32.340 And so the idea is that if you this, so you have a protein on. 351 00:39:32.340 --> 00:39:46.199 Long thin molecule, if it can wrap around itself, so to speak to fold together, then different parts of the molecule will get close to each other and they'll have a lower potential and you look attract each other. 352 00:39:46.199 --> 00:39:50.730 Exactly, and in real life, what happens? 353 00:39:50.730 --> 00:39:55.380 Is the protein bouncing around jumping around and look at a minimum energy in it? 354 00:39:55.380 --> 00:39:58.469 And then it folds up and. 355 00:39:58.469 --> 00:40:01.650 This is very important, biologically. 356 00:40:01.650 --> 00:40:05.159 Because what the protein will do. 357 00:40:05.159 --> 00:40:11.429 Its activity depends on what parts are on the outside after it folded up. 358 00:40:11.429 --> 00:40:17.190 So that if you have a potential drug, perhaps. 359 00:40:17.190 --> 00:40:27.179 And you want to know what it might do you have to know what are the active parts of this molecule? The active parts are the parts on the outside after it folded up. 360 00:40:27.179 --> 00:40:30.510 So, it's important to know how it folds up. 361 00:40:30.510 --> 00:40:34.230 And that, so it's important to know the minimum energy state. 362 00:40:35.340 --> 00:40:48.389 And also, you've got 2 molecules, you've got a drug, it's like a key fitting into a lock. Actually if the key fits into the lock correctly, it will open the lock. You've got 2 molecules and do they fit together? 363 00:40:49.945 --> 00:41:02.815 So, again, they're bouncing around in the real world and sort of searching for the 10000 megahertz, I think, is typical frequency or something. And then they get to a low energy state. They will click together. 364 00:41:02.815 --> 00:41:05.005 Well, like, 2 parts of a puzzle actually. 365 00:41:06.269 --> 00:41:19.349 And again, that determines what's going to happen chemically biologically. So you have to know how things the minimum energy state. So, this is this section of this online textbook here. 366 00:41:19.349 --> 00:41:25.739 So, it's important to find the minimum energy values. That's the minimum energy state. 367 00:41:25.739 --> 00:41:30.360 The ground state of the system. 368 00:41:30.360 --> 00:41:37.530 So, they're talking about tide here and so and so that was the I just gave you the purpose of all of this thing here. 369 00:41:37.530 --> 00:41:42.119 And they're talking about how they might try to solve it. So. 370 00:41:42.119 --> 00:41:45.360 So you can if you're interested in, say this. 371 00:41:45.360 --> 00:41:48.780 Sort of thing, you can go through this on your own somewhat. 372 00:41:49.949 --> 00:41:54.090 So so linear system of equations, simulating molecules. 373 00:41:54.090 --> 00:42:00.179 Commentary optimization. 374 00:42:01.559 --> 00:42:11.369 Again, trying to find graph universal, perhaps we traveling salesmen. 375 00:42:11.369 --> 00:42:19.530 And cut things, I'm trying to find a cut line to a graph, which cuts the fewest number of edges of the graph. Perhaps. 376 00:42:19.530 --> 00:42:24.480 Things like that and so that's the purpose of this optimization sort of thing. 377 00:42:24.480 --> 00:42:30.030 Matt Max cut. Okay, so you can browse through that. If you want I make do a bigger example. 378 00:42:30.030 --> 00:42:38.010 On Monday, so we've seen linear equations and energy optimization again. 379 00:42:38.010 --> 00:42:41.280 These common editorial optimization things. 380 00:42:41.280 --> 00:42:44.880 Satisfy ability. 381 00:42:45.804 --> 00:42:47.364 We saw some of this with the way, 382 00:42:47.364 --> 00:43:02.275 satisfy ability means you've got a bullion expression it's got variables in it and variables can each 1 can be true or false and satisfy ability question is is there a set of values for the variables that will make the whole expression 383 00:43:02.364 --> 00:43:02.815 true. 384 00:43:03.090 --> 00:43:07.679 And this is 1 of these canonical. 385 00:43:07.679 --> 00:43:17.849 And P, complete type problems I believe if you have 3 variables that takes exponential time so far as we know, and be complete. 386 00:43:17.849 --> 00:43:22.019 What empty complete means just give you a quick review of what's happening here. 387 00:43:23.519 --> 00:43:26.789 The theory have different classes. 388 00:43:26.789 --> 00:43:30.780 Of our problems and. 389 00:43:30.780 --> 00:43:38.940 Problem is 1 that would take polynomial time to solve the, the parameters of number of variables. So, polynomial time. 390 00:43:38.940 --> 00:43:45.030 In a number of variables to solve N. P. means non deterministic polynomial. 391 00:43:45.030 --> 00:43:52.500 What that means is that it's a problem where we can verify the answer in polynomial time. 392 00:43:52.500 --> 00:44:01.320 It's like, if you got buried treasure map, let's say, and it says, if you dig here in the backyard, you'll find a pot of gold. 393 00:44:03.000 --> 00:44:13.914 Well, is it, you know, do you dig at the claim? It's easy to check if it's true or not you just dig there, but if you don't have a claim solution, you'd have to dig everywhere. 394 00:44:13.914 --> 00:44:18.804 So, it's very hard to find a possible answer, but very easy to test it. 395 00:44:19.139 --> 00:44:23.159 Satisfy ability you have to effectively. 396 00:44:23.159 --> 00:44:30.960 Almost trial possible values, so the variables but if you have a claimed answer, it's really easy to test it. 397 00:44:30.960 --> 00:44:36.780 So the N. P and P means you can try all possible answers and parallel. 398 00:44:36.780 --> 00:44:40.679 And the front of them succeeds good and be complete. 399 00:44:40.679 --> 00:44:44.280 Well, that means is that. 400 00:44:45.329 --> 00:44:50.429 If you can solve, so, the big unsolved question among the. 401 00:44:50.429 --> 00:44:55.019 Is is there a fast a polynomial time way to. 402 00:44:55.019 --> 00:45:00.300 Solve these problems, or does it take exponential time? Honor. 403 00:45:00.300 --> 00:45:03.420 Normal computer classical computer, not quantum. 404 00:45:03.420 --> 00:45:10.710 It's the answer is unknown yet, but they've done some partial work, which is this. 405 00:45:10.710 --> 00:45:23.070 They do know that there are a group of problems called NP, complete problems. Now, what this means is that if you can solve and then complete problem and polynomial time. 406 00:45:23.070 --> 00:45:28.860 Then you can solve all problems in polynomial ties, all NP problems. 407 00:45:28.860 --> 00:45:36.539 Or most of them, they can be transformed into each other. So if you can solve 1 of them fast. 408 00:45:36.539 --> 00:45:39.750 That means pulling them, you can solve all of them fast. 409 00:45:39.750 --> 00:45:43.800 Quite cool. So that's what to send Pete complete thing, right here means. 410 00:45:45.059 --> 00:45:50.429 Okay, so what they're talking about here using grover's algorithm, which. 411 00:45:50.429 --> 00:45:54.329 Finds which input will make a meal. 412 00:45:54.329 --> 00:45:58.920 We'll make the function true. 413 00:45:58.920 --> 00:46:03.809 And 3 sat are these building expressions on 3 variables. 414 00:46:06.119 --> 00:46:10.440 Okay, so so they're talking about. 415 00:46:12.059 --> 00:46:17.550 There would be an example right here converting this into a. 416 00:46:17.550 --> 00:46:26.159 Again, a quantum program, and effectively you go through it in parallel to get the answer. If there is an answer. 417 00:46:26.159 --> 00:46:29.639 Now. 418 00:46:29.639 --> 00:46:33.300 So, what they're doing is that. 419 00:46:34.920 --> 00:46:39.809 They have the 3 variables. V1, V2 and v3. Fs the function. 420 00:46:39.809 --> 00:46:43.380 And some values of the variables and make it true. 421 00:46:43.380 --> 00:46:54.960 And these f, being 1, and in this case, there are 3 truths and 5 false of 8 cases and they would like to find 1 of the solutions and. 422 00:46:57.414 --> 00:47:10.855 And can you go over directly with you something? So that's what they're talking about a casket implementation of this here again I may hit it my detail later this is giving you a feeling of what's happening solving these 3 sat piece satisfy build. 423 00:47:10.855 --> 00:47:16.554 I think the 3 variables who cares but the idea is, you get the idea down and maybe you can solve it on. 424 00:47:16.829 --> 00:47:25.889 More so this is satisfy ability as a big application. And what it's doing is that. 425 00:47:25.889 --> 00:47:39.059 Iterating and we're going to get the probability of the States, which our solutions will be high. And the probability of the States, which are not solutions will be low. And every time we iterate the. 426 00:47:39.059 --> 00:47:42.840 The saddest solutions could hire. 427 00:47:42.840 --> 00:47:46.739 Yeah, okay so that's a superficial introduction to. 428 00:47:46.739 --> 00:47:54.599 Satisfy ability so. 429 00:47:54.599 --> 00:47:59.579 Hybrid neural nets. 430 00:48:01.260 --> 00:48:10.980 That's are important. They tell me I'm joking. So what they're talking about here is combining a quantum. 431 00:48:10.980 --> 00:48:18.239 Doing some of the training and kiss and then using it on a classical. 432 00:48:18.239 --> 00:48:24.090 Computer, so so combining classical with quantum. 433 00:48:24.090 --> 00:48:27.539 Do some training here, so. 434 00:48:28.344 --> 00:48:42.594 Okay, so this will be so I just again gave you the quick introduction and you can go through this in my Dubai. We're sandwich the quantum layer between 2, classical layers and again. 435 00:48:42.929 --> 00:48:51.179 Again, these nets in the real world will say, take Tesla where they've announced almost. 436 00:48:51.179 --> 00:48:57.599 Full autonomous driving and so what. 437 00:48:57.599 --> 00:49:01.079 Tesla is training their net on. 438 00:49:01.079 --> 00:49:14.820 Is basically all of the drivers would agree to let them have the video of what's happening and the training uses server farms. Basically, it's the server farms level levels of computation. 439 00:49:14.820 --> 00:49:24.480 To do the training, but once you've got the coefficients, then you can actually use the quantum computer on your end video. That's inside your Tesla. 440 00:49:24.480 --> 00:49:32.280 Well, they've gotten away from the video now they're building their own, but basically that so the training is an enormous amount. So. 441 00:49:32.280 --> 00:49:39.840 Computation so it's a server farm and you build a server farm in places where electricity is cheap. So. 442 00:49:39.840 --> 00:49:46.139 Say in the state of Washington, they build up the Columbia river near some humungous subteam chick a walk Tom. 443 00:49:47.190 --> 00:49:51.659 Take a walk hydro plant and so on. Okay. 444 00:49:54.389 --> 00:49:57.510 In any case, so that is. 445 00:49:58.650 --> 00:50:07.980 neuronet was an application, a recent quantum algorithms that are not in the books yet. 446 00:50:07.980 --> 00:50:12.630 And. 447 00:50:12.630 --> 00:50:18.539 Again, it's solving linear equations and other to solve it interactively. 448 00:50:18.539 --> 00:50:21.809 Okay, so. 449 00:50:21.809 --> 00:50:26.070 What I wanted to do today was introduce you to. 450 00:50:26.070 --> 00:50:30.119 Various some applications of quantum computing. 451 00:50:30.119 --> 00:50:34.349 I just skimmed it a little. I may hit it in more detail later, such as. 452 00:50:34.349 --> 00:50:40.619 Solving spar systems and introduce you to honeywell's quantum computer. 453 00:50:40.619 --> 00:50:48.929 And more talking more about phase 10, talked about it so much. And face is important because. 454 00:50:48.929 --> 00:51:01.409 If you feed our Gates into 1 of these controlled doc things, for example, essentially causes and control not to go in reverse and affects the phase of the control cube. 455 00:51:01.409 --> 00:51:07.590 And it's also important, because a lot of algorithms, and called the answers of, hey, shift face, rotation. 456 00:51:07.590 --> 00:51:14.130 So, we're going to have future attractions. I'll talk about these applications in more detail. 457 00:51:14.130 --> 00:51:19.650 I'll also introduce you to more. I want to give you a landscape. 458 00:51:19.650 --> 00:51:24.869 All the various companies out there doing quantum computing, it's not just IBM. 459 00:51:26.844 --> 00:51:41.815 And Google, Google, Microsoft, and again, if you would like to read ahead from me, you can read. So I'm going to. So Microsoft so these companies are trying to set up consortium form alliances and so on so that you can. 460 00:51:44.909 --> 00:51:49.199 You know, see what's going on here. 461 00:51:49.199 --> 00:51:52.260 Oh, okay. 462 00:51:52.260 --> 00:51:56.250 And you can Google and Google and see what they're doing. 463 00:51:56.250 --> 00:52:00.420 So that's enough stuff for today. 464 00:52:00.420 --> 00:52:04.349 I'll send you on with this on Monday. 465 00:52:04.349 --> 00:52:10.920 Any early today, but come, but lots of time, if anyone would like to ask questions. 466 00:52:12.150 --> 00:52:18.840 Otherwise have a good weekend, I cannot say, enjoy the good weather because it's, it's raining outside now, but. 467 00:52:20.730 --> 00:52:27.119 But and I'll work, I'll picks up homework 5 and give you more time to do it. 468 00:52:28.289 --> 00:52:34.559 What makes N. P. complete different from N. P. hard Joseph. N. P. hard. 469 00:52:34.559 --> 00:52:38.610 Is worse than N. P. complete. 470 00:52:38.610 --> 00:52:42.090 I believe now, this is not. 471 00:52:42.090 --> 00:52:49.469 My specialty, but there are problems that are worse than NP complete that. 472 00:52:49.469 --> 00:52:54.389 If you can solve an NP complete problem fast. 473 00:52:54.389 --> 00:52:59.340 Does not mean that you could solve an NP hard problem fast. 474 00:53:01.440 --> 00:53:05.309 That's what I think the answer is so, let me do a quick check. 475 00:53:07.230 --> 00:53:10.980 Silence. 476 00:53:10.980 --> 00:53:15.840 Yeah, either, at least as hard as the harder problems. 477 00:53:15.840 --> 00:53:19.260 So, we see they're outside and complete. 478 00:53:23.730 --> 00:53:28.889 And not your worst possible thing. There are things that are even worse. So. 479 00:53:31.050 --> 00:53:34.260 And, um. 480 00:53:34.260 --> 00:53:41.820 Any other questions and quantum computing is their hierarchy also so. 481 00:53:41.820 --> 00:53:47.309 Well, by the way the ID then P complete and. 482 00:53:47.309 --> 00:53:50.880 The guy you came up with it, I think, was. 483 00:53:50.880 --> 00:54:01.769 Steve corporate something, I think he had trouble getting his paper published, because he didn't actually do anything new. It proposed the classification, but it didn't solve anything. 484 00:54:01.769 --> 00:54:05.670 Examples of case at problems. 485 00:54:05.670 --> 00:54:14.760 Well, it's related to stuff and Coco. Um, I used to teach cocoa a few times also. 486 00:54:16.139 --> 00:54:21.030 So you have, it's because you got this bullion circuits I mean. 487 00:54:21.030 --> 00:54:27.360 A synchronous logic in a computer, you're Adder circuits, your half address your full adders and so on. 488 00:54:27.360 --> 00:54:34.619 They're Boolean circuits and you might like to find simple ways to implement them. 489 00:54:34.619 --> 00:54:39.960 And so we teach things like carnal maps. 490 00:54:39.960 --> 00:54:45.420 And so on, and if you've got some circuits, if you've got some outputs, you don't care about. 491 00:54:45.420 --> 00:54:52.349 Then that makes optimizing the circuit quite difficult. 492 00:54:53.519 --> 00:54:58.230 And it's important, it saves money, optimize it. It costs us money to build it. 493 00:54:58.230 --> 00:55:05.340 And, but optimizing see, so the case that thing gets into there. 494 00:55:05.340 --> 00:55:10.800 It's a brilliant circuit. 495 00:55:11.909 --> 00:55:20.820 It's I'm taking a leap here, but you have a 1B served. You're trying to find what values of variables make it. True. 496 00:55:20.820 --> 00:55:24.449 That comes in as a sub problem of trying to optimize these. 497 00:55:24.449 --> 00:55:28.380 Bullion circuits for electrical engineering problems. 498 00:55:28.380 --> 00:55:35.460 Give me a minute or 2 I could, I could think of something, but. 499 00:55:36.539 --> 00:55:41.699 It's a class of solving, you know, you'd like to solve different types of problems. You solve. 500 00:55:41.699 --> 00:55:47.460 Quadratic expressions and whatever and this is the time now, what makes these things hard. 501 00:55:48.719 --> 00:55:52.980 Because they're discrete, they're lumpy so. 502 00:55:52.980 --> 00:55:56.130 Solving equations or answers. 503 00:55:56.130 --> 00:56:00.599 Are restricted to be into jurors, or in this case binary values. 504 00:56:00.599 --> 00:56:11.340 Is harder than solving equations where the variables can be smooth, like, real rational numbers in real numbers. This is counter intuitive. 505 00:56:12.869 --> 00:56:25.500 But if the variables are real numbers, you can change smooth, you can change the value variables smoothly. Look what happens to the output as you smoothly change an input. 506 00:56:25.500 --> 00:56:37.829 If the variables are Boolean, there's 0, 1, you can't change them smoothly and you change a variable from 0T to 1. the output also jumps on smoothly. And so it's a lot harder to work with those. 507 00:56:39.420 --> 00:56:42.750 I know this sounds counterintuitive, but. 508 00:56:43.980 --> 00:56:48.300 Inner juries are harder than reels also when I can. 509 00:56:48.300 --> 00:56:51.449 Justify that statement formally. 510 00:56:51.449 --> 00:56:55.469 The 1st order predicate logic, but intuitively. 511 00:56:55.469 --> 00:57:02.250 I can give unsolved problems involving integers at an intelligent 10 year old. Might. 512 00:57:02.250 --> 00:57:05.369 Understand the problem they haven't been solved yet. 513 00:57:05.369 --> 00:57:13.380 Every even numbers system, or 2 primes, go back conjecture with the reels. There not. There's nothing like that. And the reels. 514 00:57:13.380 --> 00:57:17.880 The hard and solve problems are also hard to understand what the problem is. 515 00:57:17.880 --> 00:57:23.460 A little diversion, but you're welcome. 516 00:57:24.809 --> 00:57:28.829 Was the random questions, um, if you'd like to ask questions about. 517 00:57:30.539 --> 00:57:33.599 Spring term or something or RPI. 518 00:57:33.599 --> 00:57:39.989 No, other than that, I have a good day and like I said, we'll leave. 519 00:57:39.989 --> 00:57:43.440 Couple of minutes early now so have a good weekend. 520 00:57:55.320 --> 00:58:01.559 Silence. 521 00:58:02.880 --> 00:58:06.929 You're welcome.