WEBVTT 1 00:00:15.448 --> 00:00:19.228 Silence. 2 00:00:26.399 --> 00:00:35.280 Okay, okay. It's good afternoon. Everyone. 3 00:00:35.280 --> 00:00:42.390 It's the 2nd, here. 4 00:00:48.570 --> 00:00:52.320 Silence. 5 00:00:53.789 --> 00:00:56.789 Okay. 6 00:00:59.009 --> 00:01:02.100 And people hear me. 7 00:01:04.590 --> 00:01:08.849 That's looking a little. 8 00:01:08.849 --> 00:01:14.370 Thank you and Amanda and Justin and John. Great. 9 00:01:14.370 --> 00:01:21.120 So this would be class 16 of computer programming. 10 00:01:21.120 --> 00:01:24.209 And let me pull up, pay. 11 00:01:26.790 --> 00:01:30.060 Green here. 12 00:01:32.459 --> 00:01:35.700 Silence. 13 00:01:35.700 --> 00:01:44.310 And I have a chat window open, so the theory is, if I glance over to it, I'll see if you post any questions. 14 00:01:44.310 --> 00:01:50.640 So, today it's mostly going to be about D wave. 15 00:01:50.640 --> 00:01:55.379 But 1st, Tom, if we just want to review. 16 00:01:55.379 --> 00:02:04.980 Last Thursday to give people a chance to ask any questions. So we saw something about the hardware for IBM. Skewing machine is superconducting. 17 00:02:04.980 --> 00:02:08.879 Cube, it's called cube and. 18 00:02:08.879 --> 00:02:15.810 Various videos of them and links to some other video things and then we saw the introductory. 19 00:02:15.810 --> 00:02:26.819 Some things on D, waves, which is different it solves optimization questions with an annealing process. So, does anyone have any questions from last time? You'd like to talk about. 20 00:02:28.379 --> 00:02:32.849 No, okay you can ask questions at any time, just type your. 21 00:02:32.849 --> 00:02:37.740 Commented on your microphone and so on. So what I have today. 22 00:02:37.740 --> 00:02:41.699 Hi, what we have today is. 23 00:02:41.699 --> 00:02:45.120 Various things I got some web pages. 24 00:02:45.120 --> 00:02:48.689 Which I thought might be interesting. 25 00:02:48.689 --> 00:02:56.610 The way these various machines, IBM and the others typically get cold is something called a dilution refrigerator. 26 00:02:56.610 --> 00:03:07.680 And she has a problem. Any refrigerator works on, you have some physical process that absorbs heat, turns the heat into some form of potential energy. 27 00:03:07.680 --> 00:03:14.729 And, you know, the refrigerator, Eva, taking air conditioning machine in my house, it boils the. 28 00:03:14.729 --> 00:03:22.680 Various things that used to be free on ammonia and so on and converting from the liquid to the gas absorbed Pete and so. 29 00:03:22.680 --> 00:03:36.270 The surroundings got colder, nothing boils down at the temperatures that these Cubics have to be at, but typically a 50 of a Calvin so there's a couple of different methods. 1. nice. 1. 30 00:03:36.270 --> 00:03:50.099 Is called dilution refrigerator and what they're doing is they're oversimplifying. Now there's a face diagram here. They're add they're mixing helium 3 and 2 helium 4. 31 00:03:50.099 --> 00:04:03.990 And this absorbs heat and so the process gets colder and so I've got here you can read about theory things and there's another method involving. 32 00:04:03.990 --> 00:04:10.860 Magnetic substances where if you. 33 00:04:10.860 --> 00:04:14.250 You put the kinetic field they line up. 34 00:04:14.250 --> 00:04:28.678 Are you remove them genetic fields on a line? And when they underline they absorb Pete so that's another 1. any case I have here. Wikipedia article we're not talking politics. It can be quite good. And also 1 of the. 35 00:04:29.394 --> 00:04:42.413 Companies here you can read this about so you can learn something about demolition fridges and I cut down quite cold this actually no. Real lower bound. All me. Absolutely. 0T how cold that can get. 36 00:04:42.624 --> 00:04:48.444 It's just that I'm guessing that the cost to operate them, may go exponentially with the temperature or something. 37 00:04:48.749 --> 00:04:56.608 That was 1, the 2nd, 1 is to prepare. This is just relevant since we're talking with Super conductivity. 38 00:04:57.293 --> 00:04:59.603 And doses and functions and so on, 39 00:05:00.264 --> 00:05:06.774 then a Cooper pair is electrons and this is 1 of the bases underlying Super conductivity, 40 00:05:06.774 --> 00:05:12.533 which is how it works is at very low temperatures electrons can form pairs called Cooper pairs. 41 00:05:13.103 --> 00:05:17.184 It's energetically favorable for them to go in pairs. It's quantum effect. 42 00:05:17.519 --> 00:05:21.449 So, you can read about this if you'd like. 43 00:05:21.449 --> 00:05:25.379 Okay. 44 00:05:25.379 --> 00:05:28.738 So some relevant web pages. 45 00:05:28.738 --> 00:05:39.689 So, for quantum for D wave machine oh, since I'm talking physics and so, let me go on to some enrichment. Something. I'll come back onto this. 46 00:05:39.689 --> 00:05:45.149 I mean, I just want to talk about here and then we'll go to D, wave. 47 00:05:46.918 --> 00:05:55.319 I have here to our enrichment video. You watch it if you like, you don't have to. 48 00:05:55.319 --> 00:06:00.778 Hello. 49 00:06:00.778 --> 00:06:12.264 Yes, I should explain the title here. Okay. So, Roger pen Rose has done a number of interesting things. He invented pen rose, for example, which are a periodic tiling. 50 00:06:12.264 --> 00:06:16.403 So the plane also patented them in fact and. 51 00:06:16.798 --> 00:06:21.809 He also shared this year's Nobel Prize in physics. 52 00:06:22.374 --> 00:06:31.494 So, he so, the interesting person, it's fun to watch videos having the principal people involved. 53 00:06:31.824 --> 00:06:40.134 So, payroll's irrelevant, quantum physics in some sense, and that he believes that human consciousness. 54 00:06:40.678 --> 00:06:55.283 Results from some quantum effect, which actually expresses itself in the brain. So it's expressing itself up at room temperature at makris macroscopic scales. This is a very controversial thing, but he is a very smart person. 55 00:06:55.283 --> 00:07:01.074 And if he believes something, then it's worth listening to him. So this enrichment stuff, if you like that. 56 00:07:01.348 --> 00:07:08.579 So D, wave stuff there's an hour long thing here. I won't show all of it. I'll show about half of it. 57 00:07:08.579 --> 00:07:18.269 And then you can watch your get an introduction and then we'll go through some slides and which capitulate some of the. 58 00:07:18.269 --> 00:07:24.538 Video and some other stuff, and then to see some demos and I'll introduce you to D, ways web page. 59 00:07:24.538 --> 00:07:29.218 So. 60 00:07:29.218 --> 00:07:38.399 Okay, great. So, let me introduce Joel godly. Joel John D wave in January 2016 as a senior presales analyst. 61 00:07:38.399 --> 00:07:42.899 After spending 20 years and a T amp T and a T research. 62 00:07:42.899 --> 00:07:47.069 He earned a pH D from the University of Wisconsin and Madison. 63 00:07:47.069 --> 00:07:51.059 Condense matter physics after graduating from the University of Michigan. 64 00:07:51.059 --> 00:07:59.548 A D, wave, Joel's role includes bringing new users to the quantum computer and researching basic problems would show the power of the system. 65 00:07:59.548 --> 00:08:04.108 He loves learning new subjects and new technology, and also joy's talking music. 66 00:08:04.108 --> 00:08:08.309 So, with that, I'd like to turn it over to John to get us started. 67 00:08:13.108 --> 00:08:16.528 And thanks very much. Susan. 68 00:08:16.528 --> 00:08:20.369 Welcome to starting from scratch. 69 00:08:20.369 --> 00:08:23.848 Solving a problem from end to end. 70 00:08:23.848 --> 00:08:27.449 And what we want to do today is different. 71 00:08:27.449 --> 00:08:32.249 Then a lot of the videos that you can see, but it will fit right in with them. 72 00:08:32.249 --> 00:08:37.168 As we go, you'll see why and 1st, a big shout out. 73 00:08:37.168 --> 00:08:41.908 To my colleague, Victoria lever who is in Korea at the moment. 74 00:08:41.908 --> 00:08:47.369 And wrote this talk, but isn't available to give it because it's the middle of the night. 75 00:08:47.369 --> 00:08:51.178 There and maybe some of you are in that situation as well, but. 76 00:08:51.178 --> 00:09:00.028 Thanks for listening and welcome. So what we want to do here is. 77 00:09:00.028 --> 00:09:03.269 Work through a complete problem. 78 00:09:03.269 --> 00:09:06.749 A lot of the trouble that people have to get started. 79 00:09:06.749 --> 00:09:13.259 On the D wave system is that they don't know how to take a problem that they have. 80 00:09:13.259 --> 00:09:17.129 And convert it to something that can run. 81 00:09:17.129 --> 00:09:21.778 On the machine, and I think this is true for the field in general. 82 00:09:21.778 --> 00:09:25.048 Because it's also true in the gate model architecture, you. 83 00:09:25.048 --> 00:09:28.889 You really have to know how to break a problem down. 84 00:09:28.889 --> 00:09:33.749 And translate it into something that the computer. 85 00:09:33.749 --> 00:09:37.139 Can deal with and some day in the future. 86 00:09:37.139 --> 00:09:40.139 There'll be tools that do all of this for us, but. 87 00:09:40.139 --> 00:09:43.318 Those don't exist yet and so. 88 00:09:43.318 --> 00:09:48.479 I think it's a great benefit to go through a complete problem. 89 00:09:48.479 --> 00:09:52.408 As we'll see, this problem is is a simple 1, but. 90 00:09:52.408 --> 00:09:57.028 If you think about it really carefully, almost anything you've got out there. 91 00:09:57.028 --> 00:10:01.979 Probably reduces to this, or at least a little bit of it. 92 00:10:01.979 --> 00:10:07.288 Reduced to this and 1 way or other, and I'm hoping to convince you of that by the end. 93 00:10:07.288 --> 00:10:11.639 And also hoping that you'll get interested and sign up for the. 94 00:10:11.639 --> 00:10:17.489 And contact us, and maybe let us help you solve your problem and use our. 95 00:10:17.489 --> 00:10:21.778 Machines, so what we're going to do is. 96 00:10:21.778 --> 00:10:25.918 Go over what is our problem? How do we formulate it? 97 00:10:25.918 --> 00:10:29.489 How do we write a program to do that? And then. 98 00:10:29.489 --> 00:10:35.129 How do we tune it? So 1st, what is the problem that we're going to look at? 99 00:10:36.479 --> 00:10:41.999 Let's take a group of of people that we have. 100 00:10:41.999 --> 00:10:44.999 And we wanted to divide them into 2 teams. 101 00:10:44.999 --> 00:10:49.499 And equal teams, and, um. 102 00:10:49.499 --> 00:10:53.908 People want to be on a team with their friends, so. 103 00:10:53.908 --> 00:10:57.418 I hate to bring it up, but this reminds me of childhood when. 104 00:10:57.418 --> 00:11:01.379 It was gym class and you had to sit there and be divided. 105 00:11:01.379 --> 00:11:04.528 And luckily we're not solving it in that way because. 106 00:11:04.528 --> 00:11:08.428 There's not people who are better than others, whatever sport it is. 107 00:11:08.428 --> 00:11:12.899 In this case, it's just there's going to be reds and there's going to be blues. 108 00:11:12.899 --> 00:11:16.859 And we need to divide them up into 2 teams. 109 00:11:16.859 --> 00:11:24.328 And also we want to keep people on the team with their friends much as how it was chosen. 110 00:11:24.328 --> 00:11:31.019 In childhood and the edges, in this case, the relationships are given. 111 00:11:31.019 --> 00:11:35.609 And they're drawn here in this case, you can see. 112 00:11:35.609 --> 00:11:38.969 That's there are 8 people drawn. 113 00:11:38.969 --> 00:11:44.129 And there are relationships and so what we want to do is set up. 114 00:11:44.129 --> 00:11:49.619 The reds and the glucose to follow a certain principle, which is that. 115 00:11:49.619 --> 00:11:54.359 We don't want the red and glue to have edges connecting. 116 00:11:54.359 --> 00:11:59.969 In other words, we want as few red blue connections as possible. 117 00:11:59.969 --> 00:12:05.339 So, how do we do that and taking a 30000 foot view of it? 118 00:12:05.339 --> 00:12:08.578 You start guessing red and blue here. 119 00:12:08.578 --> 00:12:12.869 And let's go through instead the logical process of. 120 00:12:12.869 --> 00:12:16.859 Mapping this problem and running it on the quantum computer. 121 00:12:16.859 --> 00:12:20.698 And again, as I said before, this is small. Yes. 122 00:12:20.698 --> 00:12:24.599 Starting out with a couple edges, et cetera, blah, blah, blah. 123 00:12:24.599 --> 00:12:32.849 But we have been releasing things if you catch up on what we've been doing, that can handle much bigger and bigger problems. 124 00:12:32.849 --> 00:12:37.918 And so underneath a much bigger problem is often principles like this. 125 00:12:37.918 --> 00:12:41.308 And that's why I'm hoping we can get you interested in this and. 126 00:12:41.308 --> 00:12:45.778 Also that you follow me, and if you don't as Susan mentioned. 127 00:12:45.778 --> 00:12:49.259 Please ask the panel I'm going to try to work this through. 128 00:12:49.259 --> 00:12:54.359 In careful detail. So here are the reds and the blues. 129 00:12:54.359 --> 00:13:03.389 And what we want to do is find a solution such that there are no lines. Or, at least that's few as possible. 130 00:13:03.389 --> 00:13:06.599 Connections between different. 131 00:13:06.599 --> 00:13:10.318 Colors, so if you can see the ones, they're like. 132 00:13:10.318 --> 00:13:13.499 Across the middle we don't want that 1. 133 00:13:13.499 --> 00:13:17.428 The 1, that's horizontal there between a blue and a red. 134 00:13:17.428 --> 00:13:21.089 But somehow we've got to allocate the reds and the blues in order to do. 135 00:13:21.089 --> 00:13:24.688 That so how do we formulate this problem? 136 00:13:26.129 --> 00:13:29.969 And we need to formulate this problem as what is called. 137 00:13:29.969 --> 00:13:33.899 Binary quadratic model or. 138 00:13:33.899 --> 00:13:38.219 Is D, wave's name for a unification? 139 00:13:38.219 --> 00:13:43.078 Of 2 different models that hopefully some of you have seen before. 140 00:13:43.078 --> 00:13:47.668 And if not, that's okay, too. 1 is called Cuba, which stands for. 141 00:13:47.668 --> 00:13:50.999 Quadratic unconstrained binary. 142 00:13:50.999 --> 00:13:56.458 Optimization and that is a quadratic equation in binary variables. 143 00:13:56.458 --> 00:14:01.109 With zeros and ones. In other words. 144 00:14:01.109 --> 00:14:05.698 We might assign blue to 1 and red to a 0T. We'll do that in a moment. 145 00:14:05.698 --> 00:14:10.979 But we will do something with binary variables in Cuba. 146 00:14:10.979 --> 00:14:14.339 Or we also could do it with binary variables. 147 00:14:14.339 --> 00:14:18.119 And what is called the model after the physicist. 148 00:14:18.119 --> 00:14:23.009 Arts icing worked out a 1 dimensional problem in the 19 twenties. 149 00:14:23.009 --> 00:14:28.649 In Europe, in that case, the variables are minus 1 and 1. 150 00:14:28.649 --> 00:14:32.129 And you can formulate them either way. 151 00:14:32.129 --> 00:14:36.269 And something that that in software sits underneath them, but. 152 00:14:36.269 --> 00:14:42.119 Conceptually solve side, not solves, but conceptually represents both. 153 00:14:42.119 --> 00:14:45.149 Speak binary quadratic model. 154 00:14:45.149 --> 00:14:51.719 So, what we want to do is code up the problem and let the quantum computer. 155 00:14:51.719 --> 00:15:01.558 Or solve, or whatever we use, find the values, the zeroes and ones or the minus ones and plus ones that will solve the problem. 156 00:15:01.558 --> 00:15:06.899 Okay, so this is why we always need to do to run a problem on the wave. 157 00:15:06.899 --> 00:15:11.038 Quantum computer so 1st. 158 00:15:11.038 --> 00:15:14.489 We're going to do in this case, we're going to pick to Cuba. 159 00:15:14.489 --> 00:15:18.359 And we'll talk about why we do that. 160 00:15:18.359 --> 00:15:21.749 Mathematically it's a little easier if you're a beginner. 161 00:15:21.749 --> 00:15:26.458 Some of you out there if you're a physicist, you've seen icing models or. 162 00:15:26.458 --> 00:15:31.739 Maybe you've seen pricing models and you're familiar with the minus 1 and 1, but. 163 00:15:31.739 --> 00:15:36.269 Bear with me, they, they transform into each other, so. 164 00:15:36.269 --> 00:15:40.678 Whichever way we do it, we do it because there's advantages to doing it this way. 165 00:15:41.879 --> 00:15:48.178 The process of developing icing or Cuba, or is as follows. 166 00:15:48.178 --> 00:15:53.548 To write out your objective and your constraints and your problem domain, whatever it is. 167 00:15:53.548 --> 00:15:57.839 You convert your objective and constraints to mass statements. 168 00:15:57.839 --> 00:16:04.048 With binary variables, you make them cuboidal appropriate. We'll talk about that coming up. 169 00:16:04.048 --> 00:16:11.969 Where there's an objective something to minimize and constraints that you want to satisfy at minimum values. 170 00:16:11.969 --> 00:16:17.158 That combine and then get it ready for the computer by writing a program. 171 00:16:17.158 --> 00:16:22.769 So a big equation, or has 2 parts. 172 00:16:22.769 --> 00:16:26.489 What are we trying to minimize the objective? 173 00:16:26.489 --> 00:16:30.989 And an example of an objective that I'm not covering today. 174 00:16:30.989 --> 00:16:37.019 It's traveling salesmen problem where the U. P. S. driver or Amazon driver. 175 00:16:37.019 --> 00:16:40.469 Wants to cover as many houses as possible on. 176 00:16:40.469 --> 00:16:46.318 Her list in a given day and cover as little distance as possible. 177 00:16:46.318 --> 00:16:49.318 During that day, so she doesn't double back and. 178 00:16:49.318 --> 00:16:55.528 The distance might be the thing we're trying to minimize. It might be the objective. 179 00:16:55.528 --> 00:16:58.739 But in this case, it's going to be. 180 00:16:58.739 --> 00:17:02.639 Minimize the number of friends that are split off. 181 00:17:02.639 --> 00:17:07.888 In other words, if they're on the same team, they don't have edges connecting them. 182 00:17:07.888 --> 00:17:10.888 But if they're on separate team. 183 00:17:10.888 --> 00:17:15.509 They've got an edge connecting them and we want to reduce down to as many. 184 00:17:15.509 --> 00:17:19.979 As few, excuse me of those connecting edges as we can. 185 00:17:19.979 --> 00:17:25.348 And the other constraint will actually the constraint that we want to satisfy is. 186 00:17:25.348 --> 00:17:29.459 The team should be the same size and again, back to that. 187 00:17:29.459 --> 00:17:35.068 Crummy childhood experience for a lot of us, unless you were 1 of the great athletes. 188 00:17:35.068 --> 00:17:38.699 The 2 teams were supposed to be the same size and. 189 00:17:38.699 --> 00:17:42.898 I always got pick last back in the day, which some of us. 190 00:17:42.898 --> 00:17:49.769 That may have happened too, so let's call the team's team 0T and team 1. 191 00:17:49.769 --> 00:17:53.009 For red and blue and. 192 00:17:53.009 --> 00:17:57.298 In this case will color the red ones and. 193 00:17:57.298 --> 00:18:02.068 For each individual that we have in this case, mark by X. 194 00:18:02.068 --> 00:18:07.888 X of 0T is person 1 That'll be 1. if it's red and blue if it's. 195 00:18:07.888 --> 00:18:13.288 If it's 0T and you get the idea here, there's X1 and so on. And so. 196 00:18:13.288 --> 00:18:18.929 Excel, so we're counting starting from 0T is a lot of programmers like the 2. 197 00:18:18.929 --> 00:18:23.578 Hopefully you get the idea now that in that way. 198 00:18:23.578 --> 00:18:26.578 Well, Mark, which on which ones on 1 team. 199 00:18:26.578 --> 00:18:33.868 And which ones on the other so, what's the objective we'll get to that? 1st, and then we'll do the constraint. 200 00:18:33.868 --> 00:18:36.959 The objective in words is. 201 00:18:36.959 --> 00:18:39.959 Minimize the friends that are split off. 202 00:18:39.959 --> 00:18:44.788 That is minimize the edges with different color and points. 203 00:18:44.788 --> 00:18:49.259 And as I mentioned at the outset, the edges are. 204 00:18:49.259 --> 00:18:54.148 The part of the problem that was given to us when we started, it was a graph. 205 00:18:54.148 --> 00:18:57.838 And it had nodes, that's the people and edges. That's the. 206 00:18:57.838 --> 00:19:01.439 Yeah, that's the lines and so we want to minimize. 207 00:19:01.439 --> 00:19:04.949 Yeah, just with different color endpoints or the. 208 00:19:04.949 --> 00:19:11.189 That is the people who are split and so as some examples here. 209 00:19:11.189 --> 00:19:17.669 This 1, if I assign the blues opposite each other, like, Victoria has shown. 210 00:19:17.669 --> 00:19:20.848 Across that 1, that's across the diagonal. 211 00:19:20.848 --> 00:19:27.568 That's good. All right, because they're both blue and then the next 1, they're, they're both read. That's good. But. 212 00:19:27.568 --> 00:19:30.598 If something like this happens, where 1 is read. 213 00:19:30.598 --> 00:19:33.959 And 1 is blue, I don't want that or at least. 214 00:19:33.959 --> 00:19:37.828 I want as few of those as I can get. 215 00:19:37.828 --> 00:19:41.638 And so the question is, how are we going to do that? 216 00:19:41.638 --> 00:19:46.108 How do I tell the quantum computer to find me solutions? 217 00:19:46.108 --> 00:19:50.578 That have that in it and so just a quick analogy. 218 00:19:50.578 --> 00:19:56.429 To this is if you are out there and you've got problems with satellites. 219 00:19:56.429 --> 00:20:00.509 That are allowed to be at certain orbits at a certain time. 220 00:20:00.509 --> 00:20:06.028 This might correspond to having 2 in the same orbit that are not allowed. 221 00:20:06.028 --> 00:20:11.009 Things like that, or you're trying to put together a stock portfolio. 222 00:20:11.009 --> 00:20:15.628 And you're only allowed to buy so many. That's what I mean, by. 223 00:20:15.628 --> 00:20:20.308 Real world problems sit on top of this kind of thinking. So. 224 00:20:20.308 --> 00:20:23.578 If I can get you to understand this, then. 225 00:20:23.578 --> 00:20:27.118 We've gone a lot of the way down what you have to do. 226 00:20:27.118 --> 00:20:30.598 Make a problem work. All right. 227 00:20:30.598 --> 00:20:35.818 How do I write this out? Mathematically? There's only 4 possibilities. 228 00:20:35.818 --> 00:20:41.398 With 2, binary variables, binary, variable representing. 229 00:20:41.398 --> 00:20:46.469 Person, I, and person Jay as the other, and you can see. 230 00:20:46.469 --> 00:20:51.028 Blue and blue blue and red, red, and blue and red, and rather for. 231 00:20:51.028 --> 00:20:54.509 And what we've written in there on the right is. 232 00:20:54.509 --> 00:20:58.709 I have the States blue and blue. 233 00:20:58.709 --> 00:21:02.759 Are good I want that and I don't want. 234 00:21:02.759 --> 00:21:09.838 The middle to the 2nd and 3rd lines. In other words, with the blue and red or red and blue. 235 00:21:09.838 --> 00:21:15.148 Both okay, and I want to penalize those. 236 00:21:15.148 --> 00:21:18.358 Somehow, and the red and red. 237 00:21:18.358 --> 00:21:26.159 Are is also good. So hopefully you've got the idea. And now what we have to do is make this mathematical. 238 00:21:26.159 --> 00:21:30.868 And the 1st step is to put in the Cuba variables. 239 00:21:30.868 --> 00:21:35.398 Zeros and ones 0T in this case. 240 00:21:35.398 --> 00:21:39.058 Corresponding to blue and red corresponding to 1 and. 241 00:21:39.058 --> 00:21:46.499 Doesn't have to be that way. That's just the step that we chose. You could do it the other way around both work. 242 00:21:46.499 --> 00:21:51.388 And then 1 more step now and this is the key here. 243 00:21:51.388 --> 00:21:54.719 Is to assign values to either 1. 244 00:21:54.719 --> 00:21:58.409 And in this case, we make just by default. 245 00:21:58.409 --> 00:22:07.648 The 0, 0T and the 1 1 solutions, make those value of 0T and make the other 2 have the value of 1. 246 00:22:07.648 --> 00:22:13.108 And why did I pick 1? I could pick a half. I could pick 74. 247 00:22:13.108 --> 00:22:18.989 I could pick whatever, but in this case, this will work. Just fine would work. 248 00:22:18.989 --> 00:22:24.419 We're going to solve this problem in I know some of you from people out there that are familiar. 249 00:22:24.419 --> 00:22:30.058 With all this, or saying oh, but the gap, what about the gap between the energy states? 250 00:22:30.058 --> 00:22:33.838 Yes, yes, indeed. In this case. 251 00:22:33.838 --> 00:22:39.659 1 is good enough in this problem and that's a whole messy, complicated topic of gap size and. 252 00:22:39.659 --> 00:22:43.648 And so forth, but we'll pass on that for now because we're just getting started. 253 00:22:43.648 --> 00:22:47.519 In this problem, the point though, is that. 254 00:22:47.519 --> 00:22:53.068 We put this in a mathematical form. So now how do we do this? 255 00:22:53.068 --> 00:22:59.159 And the equation that is where it says we need our values to fit the form. 256 00:22:59.159 --> 00:23:03.239 Where did that come from? If you look at it? 257 00:23:03.239 --> 00:23:06.239 It's the most general, Cuba. 258 00:23:06.239 --> 00:23:10.979 That you can write or an X and an X Jay. 259 00:23:10.979 --> 00:23:16.048 How do I know that? We'll look at the 1st term side. 260 00:23:16.048 --> 00:23:20.278 Is some number to call the bias. 261 00:23:20.278 --> 00:23:26.548 And it's just a linear term. The 2nd term is at some, a J. Time's X. J. 262 00:23:26.548 --> 00:23:30.509 And then we have 1 coupler between them. 263 00:23:30.509 --> 00:23:38.068 That's the quadratic term and remember, I said it was called quadratic, unconstrained binary optimization. 264 00:23:38.068 --> 00:23:42.959 You're not allowed to have Exide divide by X J. or. 265 00:23:42.959 --> 00:23:50.398 Anything like that, we only allowed these terms and then we have an overall constants. 266 00:23:50.398 --> 00:23:53.939 As well, which we will talk about or the end. 267 00:23:53.939 --> 00:23:57.568 But the main point is, there's no other possibilities now. 268 00:23:57.568 --> 00:24:02.338 Some of you are thinking, hey, wait a minute. What about excise square? 269 00:24:02.338 --> 00:24:06.028 That's a quadratic term. And you're right. 270 00:24:06.028 --> 00:24:12.509 Except that if you think about it for a 2nd X, I squared is the same as. 271 00:24:12.509 --> 00:24:19.888 Okay that you got a sense that you can watch the rest of it on your own. 272 00:24:19.888 --> 00:24:24.479 2nd, here in that case, it's minus 1 and 1 and they both. 273 00:24:24.479 --> 00:24:27.689 Yes, and in, I think it is different. 274 00:24:27.689 --> 00:24:34.499 That's the that's the video you can watch the rest if you'd like, I'll switch to the slides now. 275 00:24:34.499 --> 00:24:43.348 And so we'll get a slightly different view of the same idea. Decides are more deeper than the video actually. 276 00:24:43.348 --> 00:24:47.548 And, okay. 277 00:24:47.548 --> 00:24:51.689 There we go. 278 00:24:55.409 --> 00:24:59.278 And again feel free to. 279 00:24:59.278 --> 00:25:03.929 Ask questions by typing in the chat window, or unmuting your Mike. 280 00:25:03.929 --> 00:25:10.888 Oh, okay. So quantum annealing we saw the 2, 6 minute videos also on Thursday. 281 00:25:10.888 --> 00:25:24.778 Okay, okay so what we have here is just a summary of 3 major architecture types for quantum computers. The D wave is the quantum Manila, which tries to find. 282 00:25:24.778 --> 00:25:29.699 Center assign values to variables to find the lowest energy value. 283 00:25:29.699 --> 00:25:37.469 The IBM Q was the gate computer so they had Gates quantum analog 2. 284 00:25:37.469 --> 00:25:41.368 Classical electrical engineering Gates. 285 00:25:41.368 --> 00:25:52.378 There's a 3rd type of computer called the fault tolerant quantum computer. I may have a little on it later. The problem with the 1st, 2 is they're approximate. 286 00:25:52.378 --> 00:25:55.469 And you run them many times and you may get. 287 00:25:56.064 --> 00:26:10.824 Something closer to a correct answer. Well, for a nearly 1 of the slides will say later, you actually don't need the actual optimum answer. In many cases. If you can have something that's close to optimum. That's perfectly good enough. 288 00:26:11.578 --> 00:26:21.808 Well, if you think traveling salesmen, for example, find the optimum would be the shortest possible path. If you have a path that's 1% worse in the shortest that may be fine. 289 00:26:21.808 --> 00:26:31.798 Now, fault tolerant is another type of architecture which essentially puts error correction into the. 290 00:26:31.798 --> 00:26:35.308 Architecture, so it finds answers correctly. 291 00:26:35.308 --> 00:26:39.209 But the cost of it is a 1000 times as many cube bits. 292 00:26:40.288 --> 00:26:47.128 So, it's better asymptotically better, but we have some issues there. Any case we're talking with the D wave inhaler today. 293 00:26:47.128 --> 00:26:51.959 So, again that. 294 00:26:51.959 --> 00:27:01.439 Um, just to remind you, this is take some landscape of the Y, axis, is the energy, the X axis, independent variable, depending where it is. 295 00:27:01.439 --> 00:27:13.048 Different amounts of energy, and you would like to get the global minimum, which is here where I have this arrow curser if you can see it and not get stuck in a local minimum. 296 00:27:14.189 --> 00:27:20.699 So this is the mathematics here. I'll spend a little time on this. Okay, Tony, and just me. 297 00:27:20.699 --> 00:27:33.388 Energy okay, I'm oversimplifying things, but for our purposes, it means the energy of the system, the independent variables are positions and moment whatever and the output is the energy now. 298 00:27:33.388 --> 00:27:46.499 I thing here what the sizing was looking at issues, where you got little magnets, a lot of little magnets in a system that could be magnetic domains and some magnetic system. 299 00:27:46.499 --> 00:27:49.709 Iron or something little I got. 300 00:27:49.709 --> 00:27:53.338 Lots of little pieces of iron or whatever. 301 00:27:53.338 --> 00:28:08.189 And the interesting thing is, is you mix them all up and then they'll settle out in some local minimum that with many of them see lots little magnets. Let's say. So I was looking at a question of lots of little magnets and they'll tend to align. 302 00:28:08.189 --> 00:28:21.778 You know, nose to tail somewhat, because that's energy. They're not going to align so much nose to nose because that's going to push each other away to North bulls will push each other away. For example, you want North Pole. 303 00:28:21.778 --> 00:28:28.288 Just house poll and so on. So I was looking at stuff like that in the context of magnets. Now. 304 00:28:28.288 --> 00:28:34.439 The other thing is however, if you have a table with lots of magnets on it. 305 00:28:34.439 --> 00:28:40.409 I mean, the global optimum might be, or would be all the Magnus pointing in the same direction. 306 00:28:40.409 --> 00:28:52.439 But that probably won't happen. You'll get domains of magnets, all pointing in the same direction. The next domain over will be all the magnets in that domain pointing in a different direction. 307 00:28:52.439 --> 00:28:57.959 So it'll be the system will stick in a local optimum, not a global optimum. 308 00:28:57.959 --> 00:29:05.189 Now, 1 way you can, maybe you heat it up or something so these random motion. 309 00:29:05.189 --> 00:29:10.919 Then, as you call it down slowly, then they may settle into an optimist kneeling controversy nearly. 310 00:29:10.919 --> 00:29:22.858 And the sort of thing actually happens in things like soft iron and so on you heated up enough, it will lose all its magnetism and you slowly cool it down. There'll be different. 311 00:29:22.858 --> 00:29:31.769 Areas and the R, and will all magnetize in the same direction the next day over will be a different direction. Okay. So that's what I was looking at. 312 00:29:31.769 --> 00:29:35.278 Well, to the math here. 313 00:29:35.278 --> 00:29:45.088 And would be the number of little magnets that say, instead of maggots, it could be electrons, such electrons, have a spin and electrons are little magnets also. 314 00:29:45.088 --> 00:29:50.459 It was a major discovery and physical in fact that particles have spends. 315 00:29:50.459 --> 00:29:57.388 Okay, so we have here the Sigma, the Sigma is the span of each particle. So Sigma. 316 00:29:57.388 --> 00:30:04.618 Segments of Jay and so on. So we have here. Is it going to be the have the energy the whole system. 317 00:30:04.618 --> 00:30:09.868 There'd be an energy component, Tom, just because of how the. 318 00:30:09.868 --> 00:30:15.449 That's column electrons in this case are particles interact with each other. 319 00:30:15.449 --> 00:30:21.388 And so this is what's happening here. 320 00:30:22.074 --> 00:30:35.453 This Matrix, Jay, this is more general than saying, if you got to North Pole next to each other, they are going to repel. So, I mean, just high energy and the North Pole next to his house. Paul will attract. So that will be low energy. 321 00:30:36.203 --> 00:30:39.173 This is more general than that. There's a matrix here Jay. 322 00:30:39.449 --> 00:30:42.868 Which has so is the energy. 323 00:30:43.919 --> 00:30:47.278 Of the ice particles in jay's particle. 324 00:30:47.278 --> 00:30:51.358 And so it depends on their. 325 00:30:51.358 --> 00:31:02.969 It depends on the direction they're pointing and this is that's a Super skip Z. actually here not a 2. so they're looking to say the Z component. 326 00:31:02.969 --> 00:31:07.558 These are things in treated. They're saying the sea component is just. 327 00:31:07.558 --> 00:31:20.159 But we're saying, so, if there, so it depends how they're aligned. How does the component of this pair number item number J, electrons how their origin with respect to each other and then we have this. 328 00:31:20.159 --> 00:31:26.699 Matrix say that we'll talk about the energy of the system due to due to the interactions between every pair. 329 00:31:26.699 --> 00:31:30.598 Of every pair of. 330 00:31:30.598 --> 00:31:37.769 Of electron cells as an electron just they'll be and choose to give or take. This is component to 2 interactions. 331 00:31:37.769 --> 00:31:47.159 The next thing is that the whole thing is in some global, magnetic field, like, it's in the ears field, let's say, and things which align with yours field. 332 00:31:47.159 --> 00:31:50.638 Will be have less energy than things, which are. 333 00:31:50.638 --> 00:32:00.388 Oppose the field, so that's what's happening here. So we have the direction of the electron right here and then H is just. 334 00:32:00.388 --> 00:32:06.538 The energy, you might see the scale factor for that electron here. 335 00:32:06.538 --> 00:32:16.798 So some electrons might be more important than others in the energy components. So we've got an energy component due to pairs of electrons, interacting with each other. 336 00:32:16.798 --> 00:32:23.038 And an energy component, due to just see electrons interacting with the goal of magnetic field. 337 00:32:23.038 --> 00:32:28.019 And then we got a 3rd component, which will be used for the kneeling factor. 338 00:32:28.019 --> 00:32:31.499 And it will just be again, not dependent on the direction. 339 00:32:31.499 --> 00:32:36.179 In another direction, the X direction and but what's that? 340 00:32:36.179 --> 00:32:45.058 So, this well, I mean, the extraction, what X means is not important. The big thing is that. 341 00:32:45.058 --> 00:32:54.358 We have here this time dependent thing, gamma and Emma just says how important this whole thing is and the, this is. 342 00:32:54.358 --> 00:33:00.028 This will handle the fact that the temperature cools down as time goes on. 343 00:33:00.028 --> 00:33:04.019 And so initially gamma is very large and this component is. 344 00:33:04.019 --> 00:33:10.288 Is very large, so which means interactions we can collect on something much matter because this thing is really important. 345 00:33:10.288 --> 00:33:14.969 But does gammit get smaller? This becomes less important and these other. 346 00:33:14.969 --> 00:33:23.219 Things become more important. The idea is that if we slowly cold the temperature, then we might settle in were these 1st, 2 things. 347 00:33:23.219 --> 00:33:36.419 Become very important and will hope we may end up with some global minimal. So that's what's happening. Here. We're talking about here. We solely decrease the amplitude of the gamma here until it becomes insignificant. And then maybe these other 2. 348 00:33:36.419 --> 00:33:42.538 Well, what we're trying to do is optimize the segments. The segment is going to be chosen. 349 00:33:42.538 --> 00:33:48.419 Go optimize the free variables are the segments. It's the direction of each electron let's say. 350 00:33:48.419 --> 00:33:52.199 Okay, this is called. 351 00:33:52.199 --> 00:33:55.979 The icing model and. 352 00:33:57.443 --> 00:33:58.044 Again, 353 00:34:00.923 --> 00:34:03.594 so this is our landscape, 354 00:34:03.653 --> 00:34:05.483 and the thing is with this model, 355 00:34:05.483 --> 00:34:06.953 within a quantum sense, 356 00:34:07.223 --> 00:34:15.264 the red dot does not have to climb over the peak and down to the other side can tunnel through the mountain to the other side. 357 00:34:15.773 --> 00:34:21.023 And how that is depends on the width of the mountain, not on the height of the mountain. So. 358 00:34:21.329 --> 00:34:28.648 So, we allow some quantum tunneling to try and go to a look. So the red dots digging around and we, hopefully it ends up in the low energy thing. 359 00:34:28.648 --> 00:34:41.068 Okay, all so, just talking about it here. So we have here the electrons, whatever they're in their plus state. 360 00:34:41.068 --> 00:34:47.969 Let's say, and say the plus state is a low energy date. Let's say in the minus will be the high energy state. 361 00:34:47.969 --> 00:34:51.869 In this formulation, so if they're not. 362 00:34:51.869 --> 00:34:55.199 If their low energy there, plus we excite. 363 00:34:55.199 --> 00:34:58.708 An electron to a higher and you say it goes up into the. 364 00:34:58.708 --> 00:35:11.789 Into the minus state now, what's happening here is this let's say we're starting off with and oh energy electrons now let's suppose we add enough energy to the system. 365 00:35:11.789 --> 00:35:16.768 For 1, electron to go to a tire higher state, but only for 1 electron. 366 00:35:16.768 --> 00:35:22.318 Well, those in electrons here in any 1 of them could be in that higher state, but only 1. so it was in different. 367 00:35:22.733 --> 00:35:33.773 Ways this could happen if we had more energy, so that a 2nd, electron is going to the high energy state. So there's and choose 2 ways. We could pick the 2 electrons that are in the high energy state here. 368 00:35:34.193 --> 00:35:40.313 And what's going to happen is we start off with energy and then we graduate lower the energy and things have to go down to there. 369 00:35:41.639 --> 00:35:49.949 So, again, the optimization thing is find the directions for the electron minimize the total energy. So. 370 00:35:51.539 --> 00:35:59.518 Okay, and the hope is that if he's slower slowly lower the energy in a parallel sense, it will end quantum central end up at a minimum. 371 00:36:00.778 --> 00:36:06.268 Okay, it's called the adobatic quantum model. We've seen that equation. 372 00:36:08.784 --> 00:36:22.612 Now, a big question here is how slowly we lower the temperature to try and get to the global minimum. If we lower the temperature too quickly, the state the system will get caught in a state. That's a local minimum. 373 00:36:22.974 --> 00:36:33.293 And if we lower the temperature too slowly, we'll be waiting all day. Not have an answer yet to get an optimum cooling speed, which is called the kneeling time. That's what they're talking about here. 374 00:36:34.559 --> 00:36:39.898 And is talking about ways what they're talking about here. 375 00:36:39.898 --> 00:36:49.289 Is so worried about the, the difference between the optimum energy and the next higher energy and it's a 2nd. 376 00:36:49.289 --> 00:36:57.539 Best solution is almost as good as the best solution. You got a higher chance of ending up in the 2nd, best solution. 377 00:36:57.539 --> 00:37:05.699 And that they're talking about the difference between the 2 of the energies. So low sagon value that's the optimal energy next. I can use. 378 00:37:05.699 --> 00:37:10.498 The 2nd, best energy and so on. So they're talking here again if the. 379 00:37:10.498 --> 00:37:14.429 It's the 2nd, synergy is not much worse than the best energy. 380 00:37:14.429 --> 00:37:22.588 We got a large chance of ending up in it. Instead of the optimum. The other thing is we may not care if it's very close. 381 00:37:22.588 --> 00:37:26.668 We're using grover's algorithm in here. 382 00:37:27.838 --> 00:37:31.949 Right and it's hard to calculate some of this, but. 383 00:37:31.949 --> 00:37:36.478 I don't actually know if it's better than classical, but. 384 00:37:37.768 --> 00:37:41.009 It's a discussion about the time. 385 00:37:43.438 --> 00:37:46.829 More discussion. 386 00:37:46.829 --> 00:37:56.338 About it okay and they're also going to repeat this again and again, just like, with the quantum gate model and. 387 00:37:56.338 --> 00:38:01.829 To increase chance to get to the best answer or not to. That's not much worse than the best answer. 388 00:38:01.829 --> 00:38:06.119 Okay. 389 00:38:07.739 --> 00:38:12.900 Now, getting a little more specific, so here's our equation. 390 00:38:12.900 --> 00:38:19.289 And the programmer specifies the energy for. 391 00:38:19.289 --> 00:38:25.650 Pairs of electrons, pointing different directions. The thing is, you see different pairs of electrons. 392 00:38:25.650 --> 00:38:38.695 May have different energies if it's a pair of electrons right next to each other, then that's going to be very bad. If they're in the same direction. If they're very far apart from each other, they're not affecting each other very much. So J. J. 393 00:38:38.695 --> 00:38:41.275 will be very small in that case. So. 394 00:38:42.780 --> 00:38:47.369 And just talking about the speed and so. 395 00:38:47.369 --> 00:38:53.340 Silence. 396 00:38:53.545 --> 00:39:05.664 And what they're talking about is they build a thing in some graph, something like this. And so this would be a cube and has an edge between the Cubics and they're interacting with each other. 397 00:39:06.175 --> 00:39:10.855 And and you can, and there's some energy involved there. 398 00:39:11.099 --> 00:39:15.179 Us quite is the superconducting quantum remainder parents device. 399 00:39:15.179 --> 00:39:18.690 And again using Joseph's injections and. 400 00:39:18.690 --> 00:39:26.760 Who prepare that I pointed to, and so on, and they're going to and everything gets entangled in whatever and they're trying to. 401 00:39:26.760 --> 00:39:33.269 To my sort of thing, or in this qbr too big enough to see. So. 402 00:39:33.269 --> 00:39:39.239 Now, the thing was, this architecture is they can build. 403 00:39:39.239 --> 00:39:52.949 100 or even thousands of cute bits on the same chip and but they can each cubic can only interact with it for neighbors lives 2000 here. But but each Cuba could only interact with its 4 neighbors. 404 00:39:52.949 --> 00:40:02.610 And they're big enough to actually see so, 16 by 16 unit grid then that's 256 cube bits and so on. 405 00:40:02.610 --> 00:40:13.800 Now, this thing has to be at a very low temperature. So this is the same temperature basically, as the. 406 00:40:15.179 --> 00:40:20.519 As IBM, q1020, whatever millet, calvin's. 407 00:40:20.934 --> 00:40:33.775 And these are this and refrigerator that I just talked about to get it down there. That's a stand for all that expense. I looked them up at 10M dollars or whatever. So, on the scale of money is flowing. In this thing. That's not incredibly expensive. 408 00:40:33.775 --> 00:40:41.125 Now, what's happening here is that they are their friendships, several nested stages and only at the bottom. 409 00:40:42.570 --> 00:40:53.460 But, no, 1, Calvin here, then a further up for K that's the boiling point for helium for and so on. So there are several stages. We don't go from room temperature down to. 410 00:40:53.460 --> 00:40:58.500 10, Mila, Kelvin, we take it in stage. It's much more efficient, so. 411 00:41:01.139 --> 00:41:13.949 And the point is, I guess, many of, you know, that outer space is an effective temperature of the 3 degree of the 3 degree, black background, or radiation of the universe. 412 00:41:13.949 --> 00:41:18.239 So that's if you leave something in order space long enough to equilibrate. 413 00:41:18.239 --> 00:41:22.650 It will end up at 3 degrees. 3. Calvin. 414 00:41:24.329 --> 00:41:30.630 And what D, wave machine looks like everything's happening inside there. 415 00:41:30.630 --> 00:41:34.710 So. 416 00:41:34.710 --> 00:41:38.280 And again. 417 00:41:38.280 --> 00:41:49.800 Some points that each well, here, they each Cuba connected to 6 other cube. It's maybe not just for, but just neighbors and some obvious and certain temperature. 418 00:41:49.800 --> 00:41:56.070 We got this since the equation we're trying so the hammer Tony, this is the equation that we're trying to optimize and so on. 419 00:41:56.070 --> 00:42:01.260 And you see, you got to express your optimization problem in terms of something that looks like this. 420 00:42:03.840 --> 00:42:08.400 And the actual kneeling tough is not that large compared to all the setup time. 421 00:42:09.510 --> 00:42:17.730 And they're comparing to Google, or we'll talk about that. Okay. And the point is the. 422 00:42:18.750 --> 00:42:23.760 It's still not certain that they will be faster, but it's worth exploring this. 423 00:42:25.650 --> 00:42:29.190 So. 424 00:42:30.630 --> 00:42:39.329 And just comparing quantum annealing was and he said 3 major quantum gate that's IBM. Q. and. 425 00:42:39.329 --> 00:42:44.039 Approximate because again, you're not guaranteed to get the right answer you. 426 00:42:44.039 --> 00:42:49.949 Run a 1000 tries and do we get the answer was a high probability then and so on. 427 00:42:49.949 --> 00:43:02.880 Again, remember why that you measure a cube just rehash of measuring with the gate machine. Every measurement operator has a basis. 428 00:43:02.880 --> 00:43:17.219 Set some basis, so the cube, and you can choose the direction of the basis factors. And what the measurement does is it projects the cube down onto 1 of the axis of the basis set. 429 00:43:17.219 --> 00:43:25.829 And the probability that it will be different access to provision the probability depends on the magnitude. 430 00:43:25.829 --> 00:43:29.280 Of the of the cube bit when expressed in that. 431 00:43:29.280 --> 00:43:33.119 And that set of basis factor. So it's approximate and. 432 00:43:33.119 --> 00:43:39.719 He tried many times, so the fault tolerant. 433 00:43:39.719 --> 00:43:44.880 Which would be exact, but I don't know if they really built there much. 434 00:43:44.880 --> 00:43:49.469 More complicated a 1000 Cuba to do 1 cube in. Okay. 435 00:43:49.469 --> 00:43:55.769 Okay, so those are some slides talking about some of this. 436 00:43:59.099 --> 00:44:06.030 Is in that case, it's minus 1 and 1 and they both square to 1. 437 00:44:06.030 --> 00:44:09.659 And this oops. Okay. 438 00:44:12.150 --> 00:44:16.199 Oh, okay, so you've seen some slides so. 439 00:44:16.199 --> 00:44:20.159 I would like to show you now, are some. 440 00:44:20.159 --> 00:44:27.119 Back tutorials, and so on the D wave company has spent a lot of effort. 441 00:44:27.119 --> 00:44:31.349 On trying to help people understand stuff. That's good. 442 00:44:32.849 --> 00:44:41.579 Not some little demos here. Some of these require that you set up an account. This 1 does not. Um, so. 443 00:44:43.739 --> 00:44:51.239 Let's talk a little about factoring to how you might solve factoring as an optimization question. 444 00:44:51.239 --> 00:45:01.349 Okay, well, some of this reminds me of the prologue language of any of you are taking the programming languages course in. 445 00:45:01.349 --> 00:45:08.909 Computer Science, the Prolog 1 of the things they teach and that course is the prologue English. 446 00:45:08.909 --> 00:45:13.170 And then the prologue language again to oversimplify. 447 00:45:13.170 --> 00:45:24.420 You express something, you're trying to solve it as a formula as a logical formula and Prolog searches through and finds variable values that solve it that make the formula. 448 00:45:24.420 --> 00:45:28.679 Well, that's what's happening here so I guess it's quantum version of. 449 00:45:28.679 --> 00:45:35.670 Prologue so so this example will be how to. 450 00:45:35.670 --> 00:45:40.260 Factor numbers is an optimization problem and I'm good. I don't know. 451 00:45:41.429 --> 00:45:46.139 12 or something. 452 00:45:48.000 --> 00:45:53.159 And the idea is that classically well. 453 00:45:53.159 --> 00:46:01.409 We ignore virus, serums, formats, little therapy, and so on you just try every possible Divisor and you see which ones work. 7 was a bad 1. 454 00:46:01.409 --> 00:46:04.829 For example, we need to trial divisions. 455 00:46:04.829 --> 00:46:07.860 And you eventually find the factors. 456 00:46:10.739 --> 00:46:14.519 Now. 457 00:46:14.519 --> 00:46:19.949 So, we're going with the key ways. We're going to have a, um. 458 00:46:19.949 --> 00:46:29.579 The quantum thing, this is not chores algorithm. Okay. Just this is totally unrelated to chores algorithm. This is a method designed to. 459 00:46:29.579 --> 00:46:33.360 Show how you can do it on a D wave. Okay. So. 460 00:46:33.360 --> 00:46:37.769 Before we do factoring, we want and we want a circuit. 461 00:46:37.769 --> 00:46:47.099 To do do multiplication. So here is a logic circuit you could have in Coco or whatever, which will multiply. 462 00:46:47.099 --> 00:46:54.030 2 numbers expressed in binary as feedback number in a 2 bit number. 463 00:46:54.030 --> 00:46:57.059 And produce the output here. 464 00:46:57.059 --> 00:47:04.590 The components of the circuit are are are end Gates and here are half adders. 465 00:47:04.590 --> 00:47:17.489 And full adders, so a half outer edge 2 beds and produces swell to bid answers. Some of the full Adder that's with 3 inputs ads. 466 00:47:17.489 --> 00:47:20.880 3, bad send produces a summoned and carry out. So. 467 00:47:20.880 --> 00:47:26.880 Okay, so this is simple. 468 00:47:26.880 --> 00:47:33.719 willion circuit that, that multiplies 2 numbers and it talk about it here. 469 00:47:36.119 --> 00:47:48.869 So, so we're going to do is make this multiplication look like a constraint status vacation, problem, constraint, status, vacation satisfaction. Okay. So what that means is, you got. 470 00:47:48.869 --> 00:47:53.400 This logical expression expression. 471 00:47:53.400 --> 00:47:59.190 And you want to find value for the variables that make it true that satisfy it. 472 00:48:03.630 --> 00:48:11.789 I click on here, it just has shows how the flows through the circuit to find the answer. 473 00:48:11.789 --> 00:48:21.929 Silence. 474 00:48:25.409 --> 00:48:39.210 Okay, so here we just have the same again. They just colored things here. This is a general thing not for 3 times 4 or whatever. This is a multiplication circuit. 475 00:48:41.639 --> 00:48:49.500 Now, to anticipate a little the way they're going to make factoring a constraint satisfaction. 476 00:48:49.500 --> 00:48:54.090 Is that if you. 477 00:48:54.090 --> 00:48:58.710 Okay, we thought of as a multiplication circuit you put in. 478 00:48:58.710 --> 00:49:02.010 2 numbers on the left and you get the product out on the right. 479 00:49:02.010 --> 00:49:12.989 Another way you could look at that. The opposite way is that you could fix the answer here. You could fix the product and then you could ask. 480 00:49:12.989 --> 00:49:16.469 What possible values for the inputs. 481 00:49:16.469 --> 00:49:25.170 Will satisfy the outputs constraints, this action you want to find numbers here, which satisfy that product. 482 00:49:30.269 --> 00:49:37.500 Or here is, we're going to work up to that. Let's get really simple right now. This is an end. 483 00:49:37.500 --> 00:49:40.559 So she is 1 if both a, and B are 1. 484 00:49:42.150 --> 00:49:49.980 That that's a classical version to look at it in a quantum sense. We have 3 quantum. 485 00:49:49.980 --> 00:49:53.940 Cube bench here a B and C. 486 00:49:53.940 --> 00:49:58.469 And let's say they can be true or false. 487 00:49:58.469 --> 00:50:01.769 Position part. 488 00:50:01.769 --> 00:50:05.940 And the energy of the total system. 489 00:50:05.940 --> 00:50:10.980 Depends on the values of a B and C. 490 00:50:10.980 --> 00:50:14.670 And it's going to be energetically favorable. 491 00:50:14.670 --> 00:50:18.030 If their legal values for this and indicate. 492 00:50:18.030 --> 00:50:21.690 So, these what we want, so the 3 Cubics. 493 00:50:21.690 --> 00:50:25.289 We want values for them. 494 00:50:26.309 --> 00:50:36.960 Where, if both a, and B or true then C is also true. Otherwise C is false and now you can start taking propositions and. 495 00:50:36.960 --> 00:50:41.070 grover's and so on, so you can maybe you can now start thinking. 496 00:50:41.070 --> 00:50:46.829 How we can relate constraint satisfaction and these logic gates. 497 00:50:48.900 --> 00:50:57.960 And they're talking about that here so, and again, we might simultaneously look for all the possible solutions here. 498 00:50:58.980 --> 00:51:04.349 And there's going to be 4 possible solutions so we can. 499 00:51:04.349 --> 00:51:08.519 Every value they and be, and then whatever the legal value see is. 500 00:51:09.750 --> 00:51:16.170 But if we express it like this, we've lost this thing where time flows from the left of the right. 501 00:51:16.170 --> 00:51:22.949 I kind of more information, so we're converting digital circuits. This quantum. 502 00:51:22.949 --> 00:51:28.590 Idea so, and. 503 00:51:29.034 --> 00:51:36.744 Or another way of looking at that, we've got 8 values for any in C and for them are valid and for them are not. 504 00:51:36.744 --> 00:51:50.364 So this might remind you of 1 of the early applications in the textbook where you had a symmetric function. It was true for half of its inputs and falls for half inputs. And so on your site, we started playing with things like that. 505 00:51:50.789 --> 00:51:55.019 But any case. 506 00:51:55.019 --> 00:51:59.400 Talk about how you convert from that. 507 00:51:59.400 --> 00:52:04.079 Gate to this quantum thing where we would be. 508 00:52:04.079 --> 00:52:09.840 Trying to find a solution. 509 00:52:11.880 --> 00:52:16.829 Yeah, okay. 510 00:52:19.739 --> 00:52:27.150 This is again the optimization thing move along the X access the minimize. So why access? So that's. 511 00:52:28.829 --> 00:52:32.760 So, what we're doing here is. 512 00:52:33.684 --> 00:52:48.175 Here this is quite interesting right here where I highlighted this. Okay. So just to recap now a B and C this is the end gate and B are inputs to the end gate sees the output for the end gate. 513 00:52:49.074 --> 00:52:51.175 Instead of considering it as a gauge, 514 00:52:51.594 --> 00:52:58.315 we can instead consider it as a 3 variable function energy function and which it has say, 515 00:52:58.315 --> 00:53:04.465 right here 2 a B minus for AC my minus 4 BC plus 60 let's say. 516 00:53:05.070 --> 00:53:09.329 How they got that, I don't know, it's arbitrary just many other ones. 517 00:53:09.329 --> 00:53:13.710 But there's an interesting thing about this function here. If I scroll up. 518 00:53:16.019 --> 00:53:20.190 This is the energy function here is 0. 519 00:53:20.190 --> 00:53:25.650 In the cases where a B, and C are valid and variables. 520 00:53:25.650 --> 00:53:29.010 Valid values for the advocate. 521 00:53:29.010 --> 00:53:33.750 And it's the energy is Harold for those and for only for those. 522 00:53:34.889 --> 00:53:38.909 So here the 8 possible combos of a B and C. 523 00:53:38.909 --> 00:53:42.389 The 4, which are valid things for the end, the gate. 524 00:53:42.389 --> 00:53:57.179 Again, the output can be 1 if an old gift, both inputs are 1 and if we have this energy function here, the energy for the 8 cases for the 4, valid cases, the energy 0T for the 4 invalid a says. 525 00:53:57.179 --> 00:54:01.199 The energy is more than 0T, so. 526 00:54:01.199 --> 00:54:11.309 So, you see where this quantum and healing can do if we take this function that that I've highlighted here and for this function. 527 00:54:11.309 --> 00:54:21.360 We want to find its global minimum its level minimum will be some set of values, which is about for valid and gate. 528 00:54:22.739 --> 00:54:27.869 And just for possible, it is fair minimum for equal minimum. 529 00:54:27.869 --> 00:54:31.440 That are global are that are all the same. So it's. 530 00:54:31.440 --> 00:54:37.679 So, in parallel we might find all for. So you see what we've done is we've taken the and gate. 531 00:54:37.679 --> 00:54:41.400 And so we've implemented the end gate. 532 00:54:41.400 --> 00:54:47.699 As a, as an a function as an optimization function. 533 00:54:49.230 --> 00:54:58.019 So that's the principle. So, if we take it to a more complicated thing, we've got the multiplication circuit to the right here. 534 00:54:58.019 --> 00:55:02.789 We can express this whole thing as an optimization function. 535 00:55:02.789 --> 00:55:06.329 And the minimum. 536 00:55:06.329 --> 00:55:13.800 Will the global minimum will be valid numbers factors in a product here? 537 00:55:13.800 --> 00:55:17.880 So it will be, let's say the energy will be 0. 538 00:55:17.880 --> 00:55:23.190 For Kate, for every case where the out for these, um. 539 00:55:24.929 --> 00:55:31.949 6 bits here are the, this 6 bit binary number is a product of those 2, 3 bit numbers. 540 00:55:31.949 --> 00:55:36.090 And every case which where that is valid. 541 00:55:36.090 --> 00:55:40.829 Will be 1 of the global minimum. 542 00:55:42.360 --> 00:55:54.900 So, what this idea, this paradigm shift, what it has done is that instead of thinking of a multiplication circuit, we've turned the multiplication problem into a problem. 543 00:55:54.900 --> 00:56:01.500 Of finding of minimizing of optimizing a function. 544 00:56:03.150 --> 00:56:08.039 And if I anticipate a little more, if you so this thing. 545 00:56:08.039 --> 00:56:15.150 Oops, back here, so this function, it's a function of with 12 binary variables. 546 00:56:15.150 --> 00:56:18.780 If we fix these 6. 547 00:56:18.780 --> 00:56:21.929 And that will be some product number. 548 00:56:21.929 --> 00:56:27.449 If we fix the 6 binary variables, then optimal solutions. 549 00:56:27.449 --> 00:56:35.610 Will be factors of that binary variable cells optimizing. This binary function is bullion. 550 00:56:35.610 --> 00:56:40.619 Function will be equivalent to factoring that number. 551 00:56:40.619 --> 00:56:49.019 And every different, and this more than 1 optimal solution that are all equal energy, all equally optimal. 552 00:56:49.019 --> 00:56:53.489 Each 1 of them is a pair of factors. 553 00:56:53.489 --> 00:57:01.079 So, you see how they're thinking as they do this it's quite nice. They just change the way they're thinking. 554 00:57:03.175 --> 00:57:13.164 And again, if you have a bullion, here's a bullion function for and aggregate, you can apply the thing to all of the end Gates here, similar function. 555 00:57:13.164 --> 00:57:18.715 And then the blue boxes they have had, or the orange boxes are the full adders. 556 00:57:18.989 --> 00:57:29.760 You can find so the half Hatteras 4 variables to input to output. But input output don't matter after we convert to a function you can find a function, which is. 557 00:57:29.760 --> 00:57:40.224 If this is have adverse acting legally badly and not and positive otherwise and so the full add or there's 5 variables well, 3 input to output. 558 00:57:40.224 --> 00:57:45.204 But that doesn't matter when we convert it to a function and you want a function, which is 0. 559 00:57:45.480 --> 00:57:49.320 When it's a legal output and positive otherwise. 560 00:57:49.320 --> 00:57:53.159 Okay. 561 00:57:53.159 --> 00:57:57.570 Another thing they're going to do here, is that. 562 00:57:57.570 --> 00:58:05.760 If you got wires on what the Cubans are going to be the states of the wires. 563 00:58:05.760 --> 00:58:17.489 So, if I look here look at this, if you can see the cursor, I'm juggling around the output from this and gate is 1 of the inputs to this half add or so, that's the same cube. 564 00:58:17.489 --> 00:58:23.610 Okay, so they don't just talk about so they unified things if an output of 1. 565 00:58:23.610 --> 00:58:33.659 Gate here is the input to something else. That's the same cube. So basically each or basically exactly. Each wire in the circuit is 1. 566 00:58:34.829 --> 00:58:38.219 And you can also fan and fan out here. That's okay. 567 00:58:38.219 --> 00:58:45.360 You might occupy yourself by figuring out why fan and fan out doesn't matter here. 568 00:58:45.360 --> 00:58:54.389 Found out doesn't matter. This is a classical circuit not a quantum circuit which quantum circuit you can't lose information classical circuit. You can. 569 00:58:54.389 --> 00:59:06.300 Okay, so that's this up here. So this is the circuit here from all applying. This is the circuit that will multiply. 570 00:59:06.300 --> 00:59:09.539 Um. 571 00:59:09.539 --> 00:59:16.739 2 3 bit numbers to make a 6 bit number and it's now they've changed a viewpoint here. 572 00:59:16.739 --> 00:59:24.059 The dots are variables and the edge is. 573 00:59:24.059 --> 00:59:27.869 Our Gates, if I go back a step. 574 00:59:28.980 --> 00:59:35.579 In this circuit, the little objects are Gates. 575 00:59:35.579 --> 00:59:38.940 Okay, and then you got the wires connecting the gates. 576 00:59:38.940 --> 00:59:53.400 So, here that each wire is a variable, each wire has some value. The output of this is the input to that that wire has a value, and the dots do the little boxes and things to the operations. 577 00:59:53.400 --> 00:59:56.820 And this is the opposite view point. 578 00:59:56.820 --> 01:00:00.900 The dots have value the dots are the cube. 579 01:00:00.900 --> 01:00:05.280 And the colored edges do the operations. 580 01:00:05.280 --> 01:00:10.289 So, if I look at this here. 581 01:00:10.289 --> 01:00:14.010 This is a, um, it's a queue bit. 582 01:00:14.010 --> 01:00:19.170 And it's, it gets it's connected to the red or the 2 and Gates. 583 01:00:19.170 --> 01:00:22.980 And the green are the. 584 01:00:22.980 --> 01:00:30.119 Uncle package step read or engage blue is half had or oranges full Adder. 585 01:00:30.119 --> 01:00:35.519 So the red are end gage that got an input 2 inputs in. 586 01:00:35.519 --> 01:00:38.639 No, whatever. 587 01:00:40.260 --> 01:00:47.219 3 in general, and then then we have factories and full adders. Oh, okay. So this is a circuit here. 588 01:00:48.389 --> 01:00:54.869 Right so the dots and the cube, and then the colored edges express. 589 01:00:54.869 --> 01:01:02.309 Allocate well, how they have to be related to each other to be to be valid Gates. 590 01:01:02.309 --> 01:01:07.110 So, yeah, okay. 591 01:01:07.110 --> 01:01:11.730 And so this is doing a modification. 592 01:01:11.730 --> 01:01:16.199 Now, if we fix the output to be 12. 593 01:01:16.199 --> 01:01:19.829 In binary, and we want to find values. 594 01:01:19.829 --> 01:01:25.110 Which satisfied that the values that satisfied the circuit. 595 01:01:25.110 --> 01:01:28.920 Will be factors of health. 596 01:01:28.920 --> 01:01:33.389 There's several possible legal solutions to a pair of factors. So. 597 01:01:34.530 --> 01:01:43.559 That's what they're talking about here so returns the value. So we fixed. Some of the value is 12 binary variables. 598 01:01:43.559 --> 01:01:48.840 1M variables. We fix 6 of them. We want to find the other 6 which satisfy the. 599 01:01:48.840 --> 01:01:54.719 Which satisfy we've turned to the optimization, which optimize the complete thing. So. 600 01:01:56.369 --> 01:02:00.030 Can we can try to run it or something? 601 01:02:04.860 --> 01:02:08.489 And we got it ran at. 602 01:02:08.489 --> 01:02:11.489 Scroll down here. 603 01:02:13.349 --> 01:02:17.130 Kind of make it just a 2nd. 604 01:02:18.179 --> 01:02:24.659 Okay, so it ran at 75 times got 4 solutions here. 605 01:02:24.659 --> 01:02:28.170 As 1 is a solution 2 times 6. 606 01:02:29.489 --> 01:02:32.730 Yeah, and so on. 607 01:02:32.730 --> 01:02:35.789 Okay. 608 01:02:35.789 --> 01:02:39.210 Silence. 609 01:02:40.530 --> 01:02:45.690 Silence. 610 01:02:45.690 --> 01:02:50.789 So, it found it optimized the thing and so it's 2 and 6. so. 611 01:02:50.789 --> 01:02:54.570 And if we run it 50 times, then we'll get these 4. 612 01:02:54.570 --> 01:02:57.719 Possible and get a different answer. Every time we run it, it's. 613 01:02:57.719 --> 01:03:03.210 Probabilistic and these are the 4 ways you could factor that. So. 614 01:03:04.530 --> 01:03:08.070 So that is how they turn factoring. 615 01:03:08.070 --> 01:03:11.130 Into an optimization problem. 616 01:03:11.130 --> 01:03:15.570 Silence. 617 01:03:18.420 --> 01:03:22.679 Okay. 618 01:03:22.679 --> 01:03:34.019 This paragraph here we're seeing again, you think of multiplication it's got directions. You multiply 2 factors to find a product. 619 01:03:34.019 --> 01:03:37.860 When we turn it into an optimization circuit, there's no directionality. 620 01:03:37.860 --> 01:03:46.260 We can fix any can fix any of the variables and get an awesome solution for the others. 621 01:03:47.309 --> 01:03:58.530 You can also say that, you know, we want to find factors whose 2nd, middle bit is 1 or something. 622 01:03:58.530 --> 01:04:03.119 Or you could take some bits for the input in some bits for the output, whatever. 623 01:04:04.769 --> 01:04:12.750 Okay, give you another 1 when I tried this earlier. 624 01:04:12.750 --> 01:04:17.099 It didn't actually work necessarily, but we'll give her a try. 625 01:04:18.719 --> 01:04:22.019 More optimization problems, so. 626 01:04:24.210 --> 01:04:27.539 Hello. 627 01:04:27.539 --> 01:04:31.590 Again, it is a starting to look like edge matching and. 628 01:04:31.590 --> 01:04:36.150 Stuff like that if you're in the graph theory, but. 629 01:04:38.250 --> 01:04:47.460 We are graph coloring would be another another way to describe it. What graph coloring means is it's a classical problem. 630 01:04:47.460 --> 01:04:52.829 And you've got a graph, it's got vertices and it's got edges. 631 01:04:52.829 --> 01:05:00.840 And your problem is to color the vertices of the graph also called nodes, red or blue. 632 01:05:00.840 --> 01:05:14.190 And you want to have some rule that perhaps you want when you have an edge, you want the vertices at opposite ends of the edge to be the same color, or can be opposite colors or something like that. 633 01:05:14.190 --> 01:05:17.190 It's an exponential type problem. 634 01:05:17.190 --> 01:05:24.449 Dot com and they're going to use Romeo and Juliet the Shakespeare's play as an example here. 635 01:05:25.980 --> 01:05:31.260 So, what we have here is that. 636 01:05:32.280 --> 01:05:43.380 So, the problem in Verona is, there were a lot of fights and so this is cast of characters in the play. 637 01:05:43.380 --> 01:05:47.130 And some of them were friends, and some of them were enemies. 638 01:05:47.130 --> 01:05:54.599 And they took their enemy seriously. If you met an enemy on the street 1 of you might kill the other. 639 01:05:54.599 --> 01:06:00.690 Okay, so the green edges say that these 2 people are friends. 640 01:06:00.690 --> 01:06:08.190 Lord and lady calculate our friends, the red, I just say their enemies lady and lady calculate are enemies. 641 01:06:08.190 --> 01:06:14.099 Okay, so now what we want to do. 642 01:06:14.099 --> 01:06:17.250 Is it is the river that separates. 643 01:06:17.250 --> 01:06:23.159 The city and we want to locate these people on 1 side of the river. 644 01:06:23.159 --> 01:06:27.329 Or on the other side of the river, so that. 645 01:06:27.329 --> 01:06:30.780 People on the same side of the river are friends. 646 01:06:31.980 --> 01:06:36.929 If 2 of a pair of people are enemies who want to put them on opposite sides of the river. 647 01:06:36.929 --> 01:06:44.130 So, they are less likely to kill each other so want to divide the network into 2 separate groups. 648 01:06:44.130 --> 01:06:53.219 And make it a graph sort of well, not exact. I could get the idea. Okay. So now we got the river in the middle. 649 01:06:53.219 --> 01:06:57.420 All of the on the left all the calculates are on the right. 650 01:06:57.420 --> 01:07:02.550 And fine, every pair of enemies is separated by the river. 651 01:07:03.809 --> 01:07:07.199 Which is the goal. 652 01:07:07.199 --> 01:07:12.000 And every Kay pair of friends is on the same side, which is the 2nd goal. 653 01:07:13.289 --> 01:07:16.710 And so in call that balanced nice. 654 01:07:16.710 --> 01:07:19.980 Um, and. 655 01:07:19.980 --> 01:07:23.579 What it was doing is well, the problem is. 656 01:07:23.579 --> 01:07:31.829 Finding the assignment, so each person has we put eyes on the left to the right side of the river and so search for. 657 01:07:32.909 --> 01:07:36.690 You know, assignment. 658 01:07:36.690 --> 01:07:43.349 But then Romeo and Juliet met each other and love each other and their friends, but they're on opposite sides of the river. 659 01:07:43.349 --> 01:07:48.090 And you were like to be on the same side, which doesn't work, but. 660 01:07:48.090 --> 01:07:52.170 I supported the play. Okay. People. 661 01:07:52.170 --> 01:07:55.409 Everyone ends up dead well, not everyone, but a lot of them. 662 01:07:56.670 --> 01:08:02.519 Okay, so what we want. Okay, so there's the motivation. 663 01:08:02.519 --> 01:08:14.309 What we want to do is solve so the problem we're solving is we have to choose which side of the river to place each person on. 664 01:08:15.360 --> 01:08:19.949 So, each person is a fully invariable. 665 01:08:19.949 --> 01:08:23.609 Say true, if you're on the left false if you're on the right perhaps. 666 01:08:23.609 --> 01:08:30.539 And we want to find variable values of the variables. 667 01:08:30.774 --> 01:08:35.784 The function that we're optimizing is for the friends and enemies, 668 01:08:36.324 --> 01:08:41.604 and if 2 enemies are on the same side of the river that adds to the function, 669 01:08:42.055 --> 01:08:47.305 if 2 friends are on opposite sides of the river that also adds to the functions we want to minimize the function. 670 01:08:47.850 --> 01:08:50.909 Okay. 671 01:08:52.079 --> 01:08:57.869 And it might say real world examples. 672 01:08:59.095 --> 01:09:12.295 Well, currency in Albany, Albany and Troy is a lot of shooting is going on in Albany and Troy, and there's actually gangs and Albany and try to fight each other. So I'm not joking. So this is semi real world. 673 01:09:12.295 --> 01:09:16.074 Example, we got the Hudson River separating the Albany gangs family. 674 01:09:16.380 --> 01:09:23.279 Probably gangs, the problem is the gang members have cars some of them so they drive across the river and shoot someone else. 675 01:09:23.279 --> 01:09:28.979 Okay, for more details, read the times Union. 676 01:09:28.979 --> 01:09:32.699 Okay, I'm talking about some real data set. 677 01:09:36.869 --> 01:09:40.470 Friends and enemies and, um. 678 01:09:42.359 --> 01:09:49.829 Yeah, and just see what happens here. This is idealized, because in the real example is more than 2 sides. I gather. 679 01:09:52.020 --> 01:09:55.500 It actually worked. Okay so, um. 680 01:09:55.500 --> 01:10:00.720 Silence. 681 01:10:00.720 --> 01:10:08.159 So, in any case, so they're saying they could find some locations, or the variables would solve it. Okay. 682 01:10:08.159 --> 01:10:16.829 Tried 50 times it found 4 different possible solutions so you might not find a perfect solution. But the idea is minimally unbalanced. 683 01:10:18.390 --> 01:10:24.390 Very fast. 684 01:10:26.340 --> 01:10:30.270 So, they're trying a bigger 1. now, this is a simulation. 685 01:10:32.609 --> 01:10:35.880 So they're saying the quantum annealing time is fast. 686 01:10:37.890 --> 01:10:42.779 Okay, so they're optimizing and thing was the quantity of annealing that we were talking about earlier. So. 687 01:10:44.819 --> 01:10:50.609 And, okay, and some experimental findings. 688 01:10:50.609 --> 01:10:56.130 Any case so that is the basic idea. 689 01:10:56.130 --> 01:11:00.239 Of what is happening and in this example. 690 01:11:00.239 --> 01:11:06.390 It's a quantum annealing was much faster. I never trust these examples. You get the idea. 691 01:11:09.060 --> 01:11:18.149 Other example, this optimization with these graphs is they're taking a lot of different drugs. 692 01:11:18.149 --> 01:11:30.510 I'm an old person, I'm taking several different drugs. You don't want to take pairs of drugs that high key charger 1 drug me cancel the other drug out or the 2 drugs together. The combo might be poisonous or something. 693 01:11:30.510 --> 01:11:39.180 So, you got a choice for a given disease, you got a choice of different products you might take so you want to. 694 01:11:39.180 --> 01:11:44.039 High cholesterol, there's several different tribes you might take. 695 01:11:44.039 --> 01:11:52.829 So you pick 1 that doesn't interact with some other drug blood pressure drug or something. So, this would be an optimization issue here. 696 01:11:54.420 --> 01:12:03.149 Communication networks frequencies. 697 01:12:03.149 --> 01:12:08.189 Well, if you have WI, Fi, base station, for example. 698 01:12:09.114 --> 01:12:23.935 The 2 gigahertz not the 5 gigahertz WI. Fi. It's only got what is it? You can correct me 11 channels I think, but each channel jams, like the 2 channels and neither side of it. So you don't really have the 11 channels. You can really only use about 4 or 3 at a given time. 699 01:12:24.533 --> 01:12:26.425 So you'd want to pick channels. 700 01:12:26.699 --> 01:12:32.699 Assignment that doesn't jam the adjacent WI Fi base station. Perhaps. 701 01:12:32.699 --> 01:12:40.529 Same thing on a bigger case with cell phones so you've got conflicting things and this will be an optimization problem for Apple. 702 01:12:42.479 --> 01:12:47.460 A lot of radio transmission things are conflicting issues, but. 703 01:12:47.460 --> 01:12:55.079 You want to optimize. Okay so that was the social networks demo. 704 01:12:55.079 --> 01:13:03.779 Now, there's also notebooks, I just click on to this for. 705 01:13:03.779 --> 01:13:07.560 This 1, I have access to. 706 01:13:07.560 --> 01:13:14.310 Because I created an account and I'm signed it the, for example. 707 01:13:14.310 --> 01:13:17.579 So you can, in any case. 708 01:13:17.579 --> 01:13:25.109 So the Jupiter notebooks, interactive Python notebook here, and you can open the notebook and. 709 01:13:27.510 --> 01:13:33.149 Okay, you can go through this if you want to also. 710 01:13:33.149 --> 01:13:40.350 So, factoring is a contract as a constraint satisfaction, constraint, satisfaction problem. 711 01:13:41.550 --> 01:13:46.409 Yeah, you going to fund browsing through here if you like. 712 01:13:46.409 --> 01:13:51.989 So, again turns miserably in law. This is our end. 713 01:13:51.989 --> 01:14:00.300 Our gate, and with the constraint satisfaction what you can do. So, box here, it's life code. If I hit shift enter. 714 01:14:00.300 --> 01:14:03.569 It executes it and so on. 715 01:14:03.569 --> 01:14:08.279 So, you can have fun with that. 716 01:14:09.329 --> 01:14:13.380 Yeah, okay. 717 01:14:14.579 --> 01:14:19.979 And she sort of what you can modify it. I think you would say 1, plus 2. 718 01:14:19.979 --> 01:14:24.869 You see, it's live. 719 01:14:27.149 --> 01:14:40.319 Okay, so this is a nice Jupiter. Notebooks are cool here. So you can walk through that Jupiter notebooks and more about this. 720 01:14:40.319 --> 01:14:44.279 Okay. 721 01:14:44.279 --> 01:14:47.279 So, um. 722 01:14:47.279 --> 01:14:52.260 Quick review here what? I was doing a little. 723 01:14:53.550 --> 01:14:58.079 Okay, so. 724 01:14:58.079 --> 01:15:11.250 Some relevant web pages here and so we were seeing some D wave stuff. I started this video here here. Certainly very welcome to watch the rest of the video. I showed you the 1st, 15 minutes. 725 01:15:11.250 --> 01:15:16.680 You're welcome to go here and sign up for your own account. 726 01:15:16.680 --> 01:15:26.489 Get small amounts of computing for free look at the slide. Now, these slides here. I mean, they're not just on D waves. They're and other stuff also. 727 01:15:26.489 --> 01:15:31.109 So this is a recent so slide introduction you can have fun. 728 01:15:31.109 --> 01:15:35.430 Looking at stuff here and so on. 729 01:15:35.430 --> 01:15:40.529 Various things here I may work a little of this into. 730 01:15:42.000 --> 01:15:47.159 Classes later on, but maybe maybe not. Okay. 731 01:15:47.159 --> 01:15:52.170 And then the tutorials online on the website. 732 01:15:52.170 --> 01:15:56.039 And again, you'd like to see leaders in the field. 733 01:15:56.039 --> 01:16:00.840 I encourage you to if you had time to watch the pen rose. 734 01:16:00.840 --> 01:16:08.130 Talk again, I think it's very nice to see talks by brilliant people by the leaders in the field. So. 735 01:16:08.130 --> 01:16:20.850 And we'll just let me talk about more and Microsoft thing so we're getting into some more IBM queue. So if you don't want to follow ahead of me, you're certainly very welcome. 736 01:16:20.850 --> 01:16:31.649 To look at this stuff before the class I'm not requiring you to, but you can now, these are very deep here so I'm going to be doing a little. I'll be. 737 01:16:31.649 --> 01:16:39.510 Trying to give you a flavor of some of it and then I'll be waving my hands and so on and hoping you don't notice them skipping over stuff. 738 01:16:39.510 --> 01:16:47.159 Okay, and so that's what we're moving on to. And at some point I'll talk about. 739 01:16:47.159 --> 01:16:50.460 Google squatter machine and stuff like that. 740 01:16:50.460 --> 01:16:58.079 Coming up ahead, I guess office start talking about term projects and so on, and maybe try to bring a guest lecturer or something. 741 01:16:58.079 --> 01:17:01.229 Okay, so that was the stuff for today. 742 01:17:01.229 --> 01:17:04.979 I mean, have a good week and. 743 01:17:04.979 --> 01:17:10.920 I'll talk to you Thursday and I'll stay here. I'll stay online for. 744 01:17:10.920 --> 01:17:15.119 A few minutes in case, anyone would like to ask me a question after class. 745 01:17:18.420 --> 01:17:21.720 So that's. 746 01:17:21.720 --> 01:17:26.489 Silence. 747 01:17:31.529 --> 01:17:37.859 Silence. 748 01:17:37.859 --> 01:17:44.369 Silence. 749 01:17:47.939 --> 01:17:56.579 Silence. 750 01:17:56.579 --> 01:18:01.380 Silence. 751 01:18:12.420 --> 01:18:16.409 Okay goodbye. Okay. 752 01:18:16.409 --> 01:18:21.899 Silence.