WEBVTT 1 00:08:19.559 --> 00:08:26.038 Okay, good afternoon. Everyone to speed parallel computing. 2 00:08:27.088 --> 00:08:36.719 Class 21 give or take, um, April, 12 my universal question. Can you hear. 3 00:08:36.719 --> 00:08:50.609 And, see me see. Great. Thank you. So, what I did is I logged out and logged in again before the start at the class, and I got the chat window open. So. 4 00:08:50.609 --> 00:08:54.389 There's a theoretical chance we'll see questions. 5 00:08:57.749 --> 00:09:01.589 What's going on with that thing up there? 6 00:09:01.589 --> 00:09:08.668 So, do do do do do. 7 00:09:09.264 --> 00:09:12.384 But keeping stuff, we are getting late in the semester. 8 00:09:12.653 --> 00:09:24.744 So final project I mentioned in the syllabus doing something that you can argue is related to the course with a straight argue with a straight face teams of any size. 9 00:09:25.344 --> 00:09:35.153 And for in a week, I want you to give the team members and a title, and give a 1 or 2 minute proposal presentation to the class. But what you propose to do. 10 00:09:36.114 --> 00:09:36.384 Then, 11 00:09:36.384 --> 00:09:37.313 in another week, 12 00:09:38.004 --> 00:09:39.114 100 word project report, 13 00:09:39.114 --> 00:09:41.153 just to convince me that you're not waiting, 14 00:09:41.153 --> 00:09:49.823 because the due date to start work and then 10 to 15 minute presentations and the last 3 days of class again, 15 00:09:50.033 --> 00:09:52.433 I'm not going to pull out a polio off stage. 16 00:09:54.119 --> 00:09:59.129 You know, at 15 minutes and 3rd, but, you know. 17 00:09:59.129 --> 00:10:12.119 How many people there are, and how much time there are so email me with your preferred dates and probably everyone gets the 1st choice no promises but then a report doing the last day that I can require it. 18 00:10:12.119 --> 00:10:15.989 Syllabus has some more details, but that's the idea. 19 00:10:15.989 --> 00:10:25.019 So, okay, a couple of minor notes about thrust here, um. 20 00:10:25.019 --> 00:10:36.839 It does the latest version of thrust on 1 thing. I would stuff it's updating fast. A lot of the online documentation is obsolete. So the latest version of thrust. 21 00:10:36.839 --> 00:10:47.609 Is has unified memory I give you a little program that shows that I'm running on my laptop here, but it is cloned over to. 22 00:10:47.609 --> 00:10:52.649 Parallel just tiled range. 23 00:10:55.254 --> 00:11:10.134 Yeah, so the difference is to touch bigger. Maybe the differences are that we included universal letter include file. Now, my personal programming. I have little files that do a lot of this for me. 24 00:11:10.918 --> 00:11:18.928 And and then down here, instead of saying, hosted a device factor, you say universal factor. 25 00:11:18.928 --> 00:11:23.639 And it's in universal memory, which gets paged back and forth to the GPU. 26 00:11:24.563 --> 00:11:38.754 Now, my guess is, you might conceivably make this touch bigger. You might conceivably get a 2 time performance penalty at maybe not you can always test that. Of course, given how much your time is worth. 27 00:11:38.754 --> 00:11:43.614 It's probably worth it. Now, there is a question when you have something like this. 28 00:11:44.609 --> 00:11:52.859 Oh, this is a cool thing also shows my optimization of the video examples. 29 00:11:52.859 --> 00:11:59.399 So the gather takes the vector of data and a vector of indices, and it goes and. 30 00:11:59.399 --> 00:12:13.979 Randomly reads from random positions in the thing and so I use placeholder rotation and so on. And this is going to do something like this up here. Just repeat it. Okay so how to do things fast now. 31 00:12:14.364 --> 00:12:24.833 You can specify particularly where this gets executed on with an optional 1st argument. I mentioned it down here and the documentation talks. 32 00:12:24.833 --> 00:12:35.244 This is also from actually to execute on it and there's also compilers, which is just so, when you say execute on the device. Well, what's the device. 33 00:12:38.369 --> 00:12:49.553 And compilers time, it could be single threaded on the Intel using open MP multi skirted on the Intel using threading building blocks on the agile or on the gpo. And you could write your own back end. 34 00:12:49.583 --> 00:13:04.403 If you want, the theory is that the source code chain is to say, when you add compilers, which is about theory versus practice. Okay. So NVIDIA has not various tools. We've seen open thrust. Good. 35 00:13:04.884 --> 00:13:12.803 C plus plus 17 has parallelization tools in the C. C. plus plus language, and as a number of interesting blogs. 36 00:13:14.484 --> 00:13:29.124 And C, plus, plus, 17 is the easiest to use perhaps as the greatest potential but I'm worried that it's too new and it's not mature enough. Yet. I have a bias against using a tool that's less than 10 years old, 10 years. 37 00:13:29.543 --> 00:13:32.094 And see, if also 17 is not 10 years old yet. 38 00:13:33.389 --> 00:13:39.389 But there are examples they have a number of pages I've listed 1 or 2. 39 00:13:39.389 --> 00:13:49.528 Bigger for you. Yeah these are called execution policies and you specify them as an optional 1st argument. 40 00:13:49.528 --> 00:13:55.229 And, like, here, you'd see it optional. 1st, argument says what to do. 41 00:13:55.229 --> 00:14:07.828 Okay, and it's dispatch to compile time using using function overloading and C. plus plus. Okay. So it talks about it here and this other pages. So on about it. So. 42 00:14:08.693 --> 00:14:17.573 And actually, if you're basically writing a single threaded program, but you got a big sort, as I mentioned a while back, it's worth your time to do the sorting on the GPU. 43 00:14:17.573 --> 00:14:31.014 If it's if the keys are something simple, like integers and floats, because it'll use a Radix sort and it will take time to copy the data back and forth. However, the time you say for the parallel start will pay for it. 44 00:14:31.318 --> 00:14:35.879 Any case so they talk about it here. 45 00:14:35.879 --> 00:14:47.489 Okay, not a nice page and I just listed 2 of them. There's more pages here. Well, here, this example, they talk about different things here. 46 00:14:47.489 --> 00:14:52.078 So, okay, and you can have fun with that. 47 00:14:52.078 --> 00:14:58.078 Okay, another thing with NVIDIA is they have the GPU technology conference. 48 00:14:58.344 --> 00:15:08.394 And it is today and Jensen, who I see. Oh, his keynote actually was an hour ago. I haven't didn't have time to watch it, but it is free. 49 00:15:08.573 --> 00:15:16.943 So if you have free time, ha, you want to see more stuff watch his keynote and browse around there. 50 00:15:16.943 --> 00:15:30.024 Probably be hundreds of talks, so be advertising some of them and a lot of the talks videos a lot of the talks will have the slides online also like PowerPoint and PDF. So you can browse your way around, give you ideas for the term project. 51 00:15:30.024 --> 00:15:32.333 Also here, browse around here. 52 00:15:32.609 --> 00:15:46.798 Okay, good. My parallel research is to write down. I do parallel geometry of a competitive design here. Yes and I've used thrust and so on open MP for parallel some of the parallel algorithms. 53 00:15:48.234 --> 00:16:02.183 Examples to find close points in 3 D. or Here's a nice 1. we like overlaying to triangulated Paulie heater to find all the intersecting pieces to find the overlaid triangulation in 3 D using big rational risk specifics. 54 00:16:02.183 --> 00:16:06.323 So, there's no roundoff errors and it's something called simulation of simplicity to. 55 00:16:07.019 --> 00:16:16.798 And the generic cases, like a point exactly. On a line and so on. Okay. So moving on to quantum computing. 56 00:16:16.798 --> 00:16:21.599 Which I introduced it as a module in this course, like, a year or 2 ago. 57 00:16:21.599 --> 00:16:25.798 And then I started a course last year. 58 00:16:25.798 --> 00:16:35.759 Um, 2 years as a topic scores, and which I gave this fall, what I'm giving you now is a condensed introduction to the next. 59 00:16:35.759 --> 00:16:50.249 2 weeks of quantum computing, there's piles and piles and I'll show you some videos on this piles of quantum computing stuff online. If you want to learn more. For example, Duke has a virtual summer school in quantum computing. 60 00:16:50.249 --> 00:16:57.058 And they have lecture notes from PV. I haven't had time to look at their lecture notes from last time, but. 61 00:16:57.923 --> 00:17:12.503 In any case, you can have fun if you have time, I would encourage you, it's in 2 months a month and a half or other to go and register for this. The registration is actually Thursday. 62 00:17:12.778 --> 00:17:26.064 So, it's something to think about if you want to learn more about this, the summer schools are like, week, long, short courses, and they, they're all over the place, but they can bring in some quite prominent people. So, is this a chance what's this virtual now? 63 00:17:26.453 --> 00:17:31.134 So you don't get to have breakfast and lunch with the guy or gal, but you can. 64 00:17:31.798 --> 00:17:39.959 Virtually at least if you have time recommend thinking of something I've gone to a number of summer schools and different topics, and they've been excellent. 65 00:17:39.959 --> 00:17:49.229 Okay, and just random press releases to show a quantum computer. I just something I just saw this morning, a new type of hardware, and whatever. 66 00:17:49.229 --> 00:17:57.298 Oh, okay so now, so I've distilled um, my, um. 67 00:17:59.608 --> 00:18:04.409 I've distilled my quantum notes into a. 68 00:18:04.409 --> 00:18:11.398 Like, a talk here and I keep updating it to that date. There is obsolete. Now. 69 00:18:11.398 --> 00:18:22.528 And what I'm going to give you today, is this, but it has a lot of links. So I'm going to expand this out by going through some of the videos. And so, like, 5 minutes long. And so. 70 00:18:22.528 --> 00:18:26.999 You can just check something here. 71 00:18:28.679 --> 00:18:33.269 At his work yeah. And show you a few short videos and so on. 72 00:18:33.269 --> 00:18:39.118 And what is so I'd like to lecture from a blog not from slides. 73 00:18:39.118 --> 00:18:42.239 But I'll give you a feeling for quantum computing with some. 74 00:18:42.239 --> 00:18:48.598 Things so I'll go through some of the theoretical introduction, some different types of hardware algorithms and so on. 75 00:18:49.679 --> 00:19:00.328 Okay, and I've made an honest effort here, but I don't know everything yet. It's actually a difficult topic. So, and I think it's an unbiased summary. 76 00:19:00.328 --> 00:19:10.138 And guide to quantum computing for 3 years ago, the wired guide. 77 00:19:11.398 --> 00:19:14.634 Basic, well, I have to tell you what quantum mechanics is. I'll have a little video. 78 00:19:15.144 --> 00:19:27.233 So so, engineering and science you can't it's a joke that some noble winning laureate said predicting predictions are difficult, especially of the future and. 79 00:19:27.509 --> 00:19:39.269 So, in some topics, the engineering people do things 1st, the hackers and the White hacker sense and then later on that their additions come in and. 80 00:19:39.473 --> 00:19:53.903 Rationalize what the hackers did that's 1 way. Things operate an opposite way. That things operate is that the sit back and think and say from theoretical 1st principles. 81 00:19:53.903 --> 00:19:56.334 I see something interesting that we might do. 82 00:19:57.058 --> 00:20:02.548 And then they throw money and sell it the problem and then they do it. 83 00:20:02.548 --> 00:20:14.398 But the example, being the atomic bomb, or the irritation saw the possibility of nuclear fission and and then they spent billions of dollars and did it. 84 00:20:14.398 --> 00:20:21.179 And this is, and I think quantum computing is like, the physicists have done it again. The last time. 85 00:20:21.179 --> 00:20:34.499 With the atomic bomb now it's quantum computing you can argue about the benefits of society of either 1 but I think quantum computing might be a breakout thing in the next 10 years or so. 86 00:20:34.499 --> 00:20:38.878 Okay, so the theory is 40 years ago. Now, a physicist. 87 00:20:38.878 --> 00:20:45.449 Um, well, quantum mechanics those back 100 years I'll show a little video, but what quantum mechanics is. 88 00:20:45.449 --> 00:20:50.638 Because you've got varying backgrounds in the class, but so quantum mechanics. 89 00:20:50.638 --> 00:20:55.348 A lot of it was worked out 100 years ago. 90 00:20:55.348 --> 00:20:59.638 Early principles of that quantums exist more. 91 00:20:59.638 --> 00:21:02.669 Go back to Einstein and before. 92 00:21:02.669 --> 00:21:09.778 1900 timeframe, but this is so physicist Benny offset quantum mechanics might be used to do computation. 93 00:21:09.778 --> 00:21:14.788 And then fine men, most of you have heard of. 94 00:21:14.788 --> 00:21:18.929 You did theory he did practice he investigated the. 95 00:21:18.929 --> 00:21:24.509 Space shuttle Challenger disaster and so on and. 96 00:21:24.509 --> 00:21:27.868 He then time to term quantum computer. 97 00:21:27.868 --> 00:21:32.638 And, and then a few years later who David. 98 00:21:32.638 --> 00:21:39.719 Then started working out theoretically the details of what how the quantum computer could operate now. 99 00:21:39.719 --> 00:21:42.868 Nothing has been built here. Oh, this is all theory. 100 00:21:43.344 --> 00:21:53.634 But if I could do it aside the theory for computing computers is that there were a special purpose computers going back to the 19th century, 101 00:21:53.634 --> 00:21:54.263 or whatever there, 102 00:21:54.864 --> 00:22:07.134 whatever there were computers that calculated tide tables they did 12 order for a series for tide tables as mechanical computers involving gears and pulleys I've seen 1 of them. 103 00:22:07.888 --> 00:22:12.659 And and so the. 104 00:22:14.249 --> 00:22:23.003 You know, they did some of the theory theory before the practice. So I went to the special purpose computers, like, for tide cables for gallery and so on. 105 00:22:23.544 --> 00:22:33.864 And then in the 19 thirties magicians came along and said, okay, these are special purpose computers. But could we have a general computer that you could program to do? 106 00:22:33.864 --> 00:22:39.564 Anything hadn't invented the word programming yet and in the thirties started looking at. 107 00:22:40.318 --> 00:22:44.308 Ways to the general concept of computation. 108 00:22:44.844 --> 00:22:59.094 And church was 1 of them Lambda notation or both correspondence form those you had theory class there was a theoretical model of a particular computer called the turning machine 109 00:23:00.054 --> 00:23:00.563 called island, 110 00:23:00.563 --> 00:23:01.884 tearing some of you have heard of. 111 00:23:02.159 --> 00:23:13.019 Everything's ironic and what it was, it wasn't something you would build, except here in computer science class, it was a theoretical model. 112 00:23:13.019 --> 00:23:26.003 Of a computer, and you could build touring machines to do different things like, add numbers. I'd say factor, whatever factor numbers, compute leap years and then tearing had the idea of a general purpose. 113 00:23:26.064 --> 00:23:36.894 A universal turning machine and universal turning machine would take a description of any other Turing machine and its input and emulate it. So, as a theoretical concept that. 114 00:23:37.169 --> 00:23:43.019 You could have a general purpose computer and so the partitions worked it out before they built. 115 00:23:43.019 --> 00:23:57.413 Computer, so so any computer could do anything if you ignore resource limitations. Okay. So that was classical computers, thirties, forties. So, the quantum computers, they're working out in theory. How they might operate, come up with the idea. 116 00:23:57.413 --> 00:24:05.304 Hey, this might exist. And then how it might operate, and we're not getting eighties now into the 9 days. Peter sure. 117 00:24:05.578 --> 00:24:10.858 I figured out how you might factor an inter, ensure. 118 00:24:11.364 --> 00:24:25.854 On a quantum computer, and do it faster than a classical computer. And this is practically important because a major class of public key relies on the assumption that you cannot factor large managers who are not economically large. 119 00:24:25.854 --> 00:24:28.044 I mean, say a 1000 or something. 120 00:24:28.318 --> 00:24:31.858 Hasn't computers haven't been built yet? Okay. 121 00:24:31.858 --> 00:24:38.038 And now we start in the last 20 years of actually building computers and there are several major. 122 00:24:38.038 --> 00:24:46.588 Types of hardware again, it's it's early days. The field is not converged the on the best type of hardware. It's. 123 00:24:48.473 --> 00:24:57.894 So, there's several competing ideas, just like, you look at this started the automobile industry late, 19 century. There were gasoline cars diesel cars are electric cars. 124 00:24:57.894 --> 00:25:12.384 There were steam cars, the Stanley steamer and then it started converged on internal combustion, gasoline cars for a long time. Turned out to be the winning technology now where are more than 100 years later 130 years later. That consensus is starting to fall apart. 125 00:25:13.979 --> 00:25:19.709 Electric cars becoming useful again, diesel came and went because it turns out. 126 00:25:19.709 --> 00:25:22.828 The viability of diesel cards rested on a fraud. 127 00:25:22.828 --> 00:25:28.828 I'm serious you do honest calculations that are not economical and. 128 00:25:30.388 --> 00:25:33.898 Volkswagon paid more than 10Billion dollars. 129 00:25:33.898 --> 00:25:37.318 For that fraud. Okay so. 130 00:25:38.423 --> 00:25:52.794 Any case, so, you see at the start of a new type of engineering, there's all these different ideas that are competing with each other. Then a winner comes along quantum computing. We're at the stage of a lot of competing technology. There's something called. There's something called quantum and kneeling. 131 00:25:52.794 --> 00:25:54.084 We'll talk about that a little. 132 00:25:54.358 --> 00:26:08.939 And then IBM uses something called trends Mon, cube bits and talk with joses. When junctions talk about that, there's a 3rd technology called trapped ions that little press release. I showed you is a force technology. 133 00:26:08.939 --> 00:26:21.148 And so on, so we're at the stage now, we're competing technologies are getting rolled out and it's engineering right now to build better quantum computers because I haven't told you what a quantum computer is yet. 134 00:26:21.148 --> 00:26:29.608 So, I want to since I've been giving you a manager's level view right now, without talking any actual engineering. 135 00:26:29.608 --> 00:26:33.659 So, I want to for a few show, a few things of these. 136 00:26:33.659 --> 00:26:39.838 A couple of slides, because I have some people would think 5 minutes, a better lecturer than me. 137 00:26:39.838 --> 00:26:42.959 So, if I can run this video. 138 00:26:42.959 --> 00:26:46.499 4 minutes long, it's an extract from an hour long thing. 139 00:26:46.499 --> 00:26:50.219 And we'll see if I can get it to work and. 140 00:26:51.388 --> 00:26:55.199 So, what I'll do is I want to make it full screen. 141 00:26:55.199 --> 00:27:01.499 So, I'll start and we'll see if we can hear it and then, but because once I make it full screen, I. 142 00:27:02.548 --> 00:27:07.108 Can't see, oops. 143 00:29:03.479 --> 00:29:07.378 Silence. 144 00:31:06.568 --> 00:31:13.318 Okay, so 4 minutes a little there um. 145 00:31:13.318 --> 00:31:25.739 I want to now, I'll show you an 8 minute thing by Neil Cohen hoping at Delta Delta has a major quantum research group. Why is the quantum? So strange. 146 00:31:25.739 --> 00:31:29.249 And a few beginners things, because again. 147 00:31:30.358 --> 00:31:38.489 It's, they're better speakers than me, and they bring in videos and stuff. So let's just say. 148 00:31:39.689 --> 00:31:43.378 See, what not to maybe. 149 00:31:43.378 --> 00:31:46.469 Why is the quantum so strange? 150 00:31:51.838 --> 00:32:07.259 Silence. 151 00:32:07.259 --> 00:32:10.888 Professor, we don't have audio. 152 00:32:13.138 --> 00:32:19.229 She does. 153 00:32:22.858 --> 00:32:26.788 Silence. 154 00:32:26.788 --> 00:32:30.058 Silence. 155 00:32:30.058 --> 00:32:33.088 Professor, we can't hear the audio. 156 00:32:33.088 --> 00:32:38.638 Okay, could you hear the last 1. 157 00:32:38.638 --> 00:32:42.298 We tried to reach out to you in chat a little. 158 00:32:42.298 --> 00:32:45.719 Oh, sorry about that subtitles. 159 00:32:46.223 --> 00:32:59.483 Okay, well, maybe I don't show you the videos then. I'm, this is why, you know, I can hear the audio fine. 160 00:32:59.483 --> 00:33:01.403 You cannot hear the audio. 161 00:33:01.679 --> 00:33:12.449 And I don't want to spend the rest of the class debugging it. So I'll tell you what I'll do. I'll surrender on showing you the videos. You can see some of them here. 162 00:33:12.449 --> 00:33:16.078 Beginner's guide and so on. 163 00:33:16.078 --> 00:33:20.219 I'll go through what I see if I can. 164 00:33:20.219 --> 00:33:23.278 How ID bugs that event. 165 00:33:25.169 --> 00:33:32.848 Any case this is okay, so you can browse through some of this. 166 00:33:34.888 --> 00:33:38.729 And that may, okay, let me go down to a more engineering detail that. 167 00:33:38.729 --> 00:33:50.398 Okay, okay and maybe I'll show some videos Thursday. I'll go through my text thing. At least there's no audio here. 168 00:33:50.398 --> 00:34:00.564 So this, so now we're down at the math class, your computer, and you got fits. Okay in a bit has 0 or 1, and 8 fits, make a bite and bite his 256 values. 169 00:34:00.564 --> 00:34:10.824 And you use gates that Nan Gates nor Gates, and so on and gage. So generally destroy information, you cannot run them backwards in most cases. Okay. 170 00:34:10.853 --> 00:34:23.454 And they increase entropy in most cases and you build these things up to make half adders and full adders. And so on there, I just gave you. 171 00:34:25.648 --> 00:34:29.128 The summary of computer organizational logic design of okay. 172 00:34:29.128 --> 00:34:42.358 You all are familiar with that. I think if you're not then ask quantum computation, you've got bedside. Cubital IBM used to say, so a cube at. 173 00:34:42.358 --> 00:34:55.378 Um, it state, it's not a bit as a state of 1 cubic is a linear combination of 2 basis States. So, 1 cubic. 174 00:34:55.378 --> 00:35:07.708 Can star vector sort of it is 1 degree of freedom. So you've got 2 basis States and the written was this odd notation vertical bar 0 angle and so on. So. 175 00:35:07.708 --> 00:35:17.219 There's 2 basis States for a cube at 0 and 1. and if you think of say spinning electrons or. 176 00:35:17.219 --> 00:35:27.208 And say, quantum physics, it could spin up, or could spend down. So you've got 2 basis States. Okay. And. 177 00:35:27.208 --> 00:35:30.449 A cube 1 Cupid. 178 00:35:30.449 --> 00:35:39.208 At state is a linear combo of those 2 base estates. We write it as Q equals. 179 00:35:39.208 --> 00:35:46.318 To wait a, and B, complex numbers and the magnitude of the factor a B is 1. 180 00:35:46.318 --> 00:35:52.949 So that you'd right the so, the 1 cube that has this stay here. 181 00:35:53.753 --> 00:36:06.744 As a vector a B, so it's a linear combo, 2, possible basis States 0 and 1. now what? The actual physical basis States are depends on the particular technology you're using. If you're thinking of electrons, it'd be spin up and spin down. Let's say. 182 00:36:08.278 --> 00:36:11.489 Okay, so. 183 00:36:11.489 --> 00:36:14.818 And that's 1 Cuban now. 184 00:36:14.818 --> 00:36:25.318 1 way to look at that, is that the cube bed is as is it state is a superposition of those 2 basis States with those weights. So. 185 00:36:25.318 --> 00:36:37.289 A good way to think of the cube bet is that it is similar in those 2 beta States with those, those 2 weights. And that's the state of the cube. 186 00:36:37.289 --> 00:36:42.179 It's similar in both states now. 187 00:36:42.179 --> 00:36:47.489 I want to shoot down a major potential policy. 188 00:36:47.489 --> 00:36:56.548 Some people say that the underlying philosophy is that the queue is really in 1 of those 2 States, but we don't actually know which 1. 189 00:36:56.548 --> 00:37:01.708 And that's called the hidden variable theory, and it's been proven to be false. 190 00:37:01.708 --> 00:37:09.389 So, Q is not really in 1 of those 2 States. It is really simultaneously in both. 191 00:37:09.983 --> 00:37:24.923 States then give you a classical way to think of it. Let's imagine that you have a violin string. Okay. And is vibrating and it's got a fundamental, let's say, 1 kilohertz and the 1st time Onyx 2 kilohertz and 3. kilohertz and 4. 192 00:37:25.224 --> 00:37:35.034 so the violin string could be similar vibrating in several of those basis stage. So the violin string state can be a superposition. 193 00:37:35.844 --> 00:37:47.994 All these basis, so the basis States are 1 kilohertz colored kilohertz and so on. And so the violin string can be similar in several of those states at different amplitude. 194 00:37:47.994 --> 00:37:53.423 So, the violin string is a classical way to show superposition of a number of states. 195 00:37:54.688 --> 00:38:03.329 The violin string is really in the violent string really is vibrating at those several frequencies simultaneously. 196 00:38:03.329 --> 00:38:08.789 And the cubic queue really is in those 2 States. 197 00:38:08.789 --> 00:38:15.329 But now here's a difference, though, with the violin string you can observe it you can. 198 00:38:15.329 --> 00:38:27.510 The amplitude and and the frequencies and the amplitude, the queue, but you cannot. And this is really important that you bet is simultaneously in those 2 States with waits a, and B. 199 00:38:27.775 --> 00:38:42.565 But you cannot observe them and again, this is a very strong statement I'm making and even in principle, if you believe the quantum physics is correct and it's got a lot of things, arguments, observation, substantiating it. 200 00:38:43.284 --> 00:38:46.554 Then it is in principle impossible to observe its state. 201 00:38:46.860 --> 00:38:50.460 What you can do is measure the state. 202 00:38:50.460 --> 00:38:59.429 With annual applying what's called a measurement operator and the measurement operator projects it down to 1 of the basis States. 203 00:38:59.429 --> 00:39:03.030 And then you can observe which state it's in. 204 00:39:03.030 --> 00:39:08.190 And so now you can observe it when it's in 1 of the basis States, but you changed it. 205 00:39:08.190 --> 00:39:15.750 And the probability of it going to, which of those 2 basis States depends on those 2 weights. 206 00:39:15.750 --> 00:39:28.889 So, you observe it with a measurement operator, which is a projection operation and this is all mathematics. So we'll talk about late and I hope you'll likely near algebra. 207 00:39:28.889 --> 00:39:38.789 And if you don't like your or you're going to be, you got to be insane in 2 weeks. I'm exaggerating. 208 00:39:38.789 --> 00:39:42.630 I think, okay now. 209 00:39:42.630 --> 00:39:48.900 So, let me go back to so you projected it goes down to 1 of the 2 basis States. 210 00:39:48.900 --> 00:39:53.849 But you've now changed it, you've destroyed something. Okay. 211 00:39:55.079 --> 00:40:03.000 And then now, the other thing, these weights are complex. Every number I'm talking about it the rest of the course will be a complex number. Oops, I'm sorry. 212 00:40:03.000 --> 00:40:16.500 Okay, okay so the measurement changes it now, since it's a waiting of I'm trying to center what I'm talking about. Okay so it's. 213 00:40:16.500 --> 00:40:30.420 It's a way to some of the 2 bases that you can write it as that you can write it as a vector. A. B, so the state of Q is a 2 vector. It's a vector of 2 complex numbers. And the length of this factor is 1. 214 00:40:30.420 --> 00:40:35.219 Okay. 215 00:40:36.389 --> 00:40:41.309 You operate on cube was matrix. Multiplication. So queue is a 2 vector. 216 00:40:41.309 --> 00:40:50.460 And you apply 2 by 2 matrix to it complex and you get a new cube bit and the matrix has restrictions. It's. 217 00:40:50.460 --> 00:40:55.710 It's got various turns on normal and so on. It's. 218 00:40:55.710 --> 00:41:01.824 Somewhat similar to our rotation naturally identical door rotation I guess so, 219 00:41:01.824 --> 00:41:06.414 you operate some mathematically you operate on the cube and transform it to a new cube, 220 00:41:06.414 --> 00:41:09.445 but physically there are physical operations, 221 00:41:09.775 --> 00:41:10.974 which do the same thing. 222 00:41:10.974 --> 00:41:24.625 There are physical. This is why it's engineering. It's not just mathematics. There are physical things you can do to the cube, but that will transform it to another cube it. And the, the physical things can be modeled as matrix modification. 223 00:41:24.929 --> 00:41:29.670 Now, this thing. 224 00:41:29.670 --> 00:41:43.079 These physical operations, they change the actual cube, but they don't create a new, but they change the cube bit. You're operating on the old. Cupid is not there anymore. And its place is a new cube. 225 00:41:44.760 --> 00:41:47.820 You don't have the old cube anymore. 226 00:41:47.820 --> 00:41:56.635 And so this is important, you cannot copy a cube, but you can move it. You cannot copy it. No cloning. This is another very important thing. 227 00:41:57.054 --> 00:42:08.155 So he's seen a couple of important things here where the quantum computation is radically different than the classical 1. you can't observe the internal state. You cannot copy a cube. 228 00:42:08.579 --> 00:42:12.630 Um, can't clone it. 229 00:42:12.630 --> 00:42:16.050 And this has a lot of major implications. 230 00:42:16.050 --> 00:42:19.289 To the lifecycle of a cube bit. 231 00:42:19.974 --> 00:42:34.914 Is you create a classical band or Cuban classical bed? It's just a classical 1 of the 0 or 1. you operate on it with matrices and now it becomes a superposition of various states and then you transform it back to 0 or 1 and read it. 232 00:42:34.945 --> 00:42:36.625 Well, that's not very powerful. 233 00:42:36.900 --> 00:42:43.349 Yet it's about to get powerful root. Let's talk about 2 cube bits. 234 00:42:43.349 --> 00:42:46.619 Oh, by the way again, just to. 235 00:42:46.619 --> 00:42:51.030 Tie you down to reallocate the way this is worth. 236 00:42:53.219 --> 00:43:01.320 Talk spending your time on this is because this is how the world actually operates these things are real, and not just mathematical constructs. 237 00:43:01.320 --> 00:43:05.099 I got a question here from Jack about the. 238 00:43:05.099 --> 00:43:08.130 2 slit experiment. 239 00:43:09.750 --> 00:43:18.809 Yeah, the double slit experiment. Yeah, you want to tell us how it helps you understand things, Jack or. 240 00:43:18.809 --> 00:43:23.010 No, it was a few minutes ago. I didn't see it. Oh, okay. 241 00:43:23.010 --> 00:43:26.940 For those who don't understand continued. 242 00:43:26.940 --> 00:43:32.880 Yes, hi. Yeah, I can I can talk about it briefly if anyone here. Okay. Yeah. Go ahead. 243 00:43:32.880 --> 00:43:42.960 Yeah, so I had typed that in when you were talking about how a cubic isn't really in any 1 state. It's kind of like a combination of both. 244 00:43:42.960 --> 00:43:45.960 So, basically, like, the double slit experiment is. 245 00:43:45.960 --> 00:43:49.230 You shoot an electron through 2 slits. 246 00:43:49.230 --> 00:43:55.559 And there's a board at the other end and what you'll see is an interference pattern that. 247 00:43:55.559 --> 00:44:01.380 Would only be drawn if, if you were to shoot a wave through the double slit. So. 248 00:44:01.380 --> 00:44:04.650 What it means is when you send the electron through. 249 00:44:04.650 --> 00:44:09.300 The slit, it really is a a wave, so. 250 00:44:09.300 --> 00:44:15.989 It's in a multitude of it's not in any 1 position. It's in, like, a combination of all of them. 251 00:44:15.989 --> 00:44:21.599 Which is how it, which is why yeah, it's not in any 1 state. It's really in all of them, but. 252 00:44:21.599 --> 00:44:31.769 If you were to try to observe it, then you would only see it in 1 place because it needs to collapse. Exactly. Yeah. And that works even if you're sending 1 electron at a time. 253 00:44:32.849 --> 00:44:38.940 Right, yes, because it can through a wave I can go through both slits and create the right. 254 00:44:38.940 --> 00:44:49.920 Yeah, weird. And Isaac can 2 beds can be well, you can you can apply the operations Isaac. Yeah. And I think you could create 2 cube bits. 255 00:44:49.920 --> 00:44:55.349 Yeah, you do the same operations on a classical bed. I could be wrong, but I think that works. Yeah. 256 00:44:57.119 --> 00:45:06.599 The thing is, when you take those 2 separate Cubics and you measure them, they could measure differently because the measurements, this probabilistic process. 257 00:45:06.599 --> 00:45:15.059 Okay, so life is about to get exponentially harder now and I'm using exponential in the literal correct sense. 258 00:45:15.059 --> 00:45:18.090 Okay, 2. 259 00:45:18.090 --> 00:45:21.809 Um, so now with 2 events. 260 00:45:21.809 --> 00:45:23.755 The queue is a linear combo, 261 00:45:23.784 --> 00:45:24.985 4 basis factors, 262 00:45:24.985 --> 00:45:26.454 because each of the separate Cubics, 263 00:45:26.724 --> 00:45:28.614 the basis is 0 or 1, 264 00:45:29.125 --> 00:45:38.125 the basis space for the 2 beds is the exterior product of those 4 K of those 2 cases and it's 000110 or 11. 265 00:45:38.125 --> 00:45:40.494 so cues a linear combo of 4 basis values. 266 00:45:43.110 --> 00:45:49.949 And again, the magnitude of that factor has to be 1. so represented as this. 267 00:45:49.949 --> 00:45:56.039 Use your combo and the way tap to add to 1. so there's really 3 degrees of freedom there. 268 00:45:56.039 --> 00:46:06.449 Okay now, so queue exists in all 4 States simultaneously, and you'd have Pi and measurement operator. So Q is a 4 vector for complex numbers. 269 00:46:06.449 --> 00:46:13.920 Is 1, and a measurement is going to be 4 by 4 major you can apply 4 by 4 matrices and multiply it. 270 00:46:13.920 --> 00:46:19.530 Okay, and Q is in all 4 States simultaneously until you measure it. 271 00:46:19.530 --> 00:46:32.579 You got N cube beds if you got whatever you call a queue bite, let's say, with a cube, the cube bite has 256 coefficients, 2 and 55 degrees of freedom actually. So the Q bite. 272 00:46:32.579 --> 00:46:38.099 As, um, is a superposition of 256, different states. 273 00:46:39.300 --> 00:46:47.460 And this is why quantum mechanics is powerful is 1 of the reasons it's so powerful is that the amount of information. 274 00:46:47.460 --> 00:46:56.880 You can process grows exponentially with the number of Cubics so the queue bite has 256 States. 275 00:46:56.880 --> 00:47:00.269 And you can operate on them. 276 00:47:00.269 --> 00:47:07.409 With an 8 by 8 matrix so they, they can influence each other. This is what makes it interesting. 277 00:47:07.409 --> 00:47:17.699 Few bits, and the few bite were all separate and didn't talk to each other. That would not be interesting but in fact, you can operate on them. You can. 278 00:47:17.699 --> 00:47:22.650 Do you traditional logic, operation and modified so they are reversible. 279 00:47:22.650 --> 00:47:28.260 And so on, and this is important. So the amount of information grows exponentially. 280 00:47:28.260 --> 00:47:34.469 With the number of Cubics and the Cubans can interact with each other. 281 00:47:34.469 --> 00:47:47.250 And so measurement operator, same thing, it projects down to 1 of the, it rotates it projects down to 1 of the bases and which 1 it is depends on the probabilities, which are the. 282 00:47:47.250 --> 00:47:55.530 Complex magnitude. So again, today, AI is a complex number. This is means times it's complex. Conjugate. 283 00:47:55.530 --> 00:48:04.380 Okay, and operators are 4 by 4 matrices, which are the 4 by 4 matrices like. 284 00:48:04.380 --> 00:48:08.519 They like rotations they're in, they're. 285 00:48:08.519 --> 00:48:20.610 Department won etc, etc. Okay. And they all leave the magnitude of them as rotations. They risk basic needs a cube magnitude being 1. 286 00:48:20.610 --> 00:48:29.610 Okay, now how you Initialized the 2 cubic system, as you said, each cube bit separately to 0 or 1. 287 00:48:29.610 --> 00:48:36.989 Depending on how the hardware and then, so it would count too fast. A Q1 is a 1 yeah. 288 00:48:36.989 --> 00:48:46.230 This is, Q2 is a 2 Q2 and the combo the Super it has the 4. I hear the cube at. 289 00:48:46.230 --> 00:48:56.489 The 2 cubic system, it's the product of the 2 separate 1 cube systems. You call it an exterior product, whatever this different terms in the near algebra. 290 00:48:57.539 --> 00:49:05.519 Okay, but my point 15 is important. Okay. 291 00:49:05.519 --> 00:49:12.449 And again, by point 19, here in quantum computation information is not destroyed. 292 00:49:12.449 --> 00:49:25.710 Okay, measuring now there's some stuff here. I'm a little weak on myself and the philosophers argue, they argue that this consciousness involved shrugging your cat. 293 00:49:25.710 --> 00:49:40.554 Thing or something that things collapse when somebody with consciousness observes it. I think the collapse is because the measurement basically interacts your system with the outside universe. So some information flows in that. 294 00:49:42.900 --> 00:49:48.539 Okay, I'm okay now my point 23 is another big, deep topic. 295 00:49:48.539 --> 00:49:52.440 I showed you for the 2 queue bits. Let me. 296 00:49:52.440 --> 00:49:56.579 Scroll back up, if I'm not making you see sick, you do. 297 00:49:56.579 --> 00:50:00.690 Point 13 here we created the 2 cubic system as this. 298 00:50:00.690 --> 00:50:10.320 Product of the 2 Q1 best systems and to this particular system you could decompose it again into the project of the 2 separate cube. Now. 299 00:50:10.320 --> 00:50:22.769 After you've done assorted operations on it, like multiplying and transformations. It is possible that Q can no longer be separated into 2 separate cube. 300 00:50:22.769 --> 00:50:31.559 Initially, it could be separated after you multiplied by matrices perhaps it cannot be separated. 301 00:50:31.559 --> 00:50:41.099 If the queue cannot be any longer separated into the 2 separate cube, the system is called entangled. 302 00:50:41.099 --> 00:50:46.889 And and and the entanglement. 303 00:50:46.889 --> 00:50:55.320 Of the 2, and individually is very powerful and that is why quantum computation. 304 00:50:55.320 --> 00:51:01.199 Is powerful and. 305 00:51:04.409 --> 00:51:11.880 And this is and what this means is, and if you measure 1 cubic. 306 00:51:11.880 --> 00:51:15.630 Then that restricts what you might see. 307 00:51:15.630 --> 00:51:24.780 When you measure the other cube bit, let me give you an example here. 308 00:51:27.900 --> 00:51:33.030 Need to do. 309 00:51:34.829 --> 00:51:41.789 Yeah, again I can never tell what you see here, but you might see me holding up an envelope. 310 00:51:41.789 --> 00:51:47.670 Um, and I carried the envelope in 2. 311 00:51:47.670 --> 00:51:56.130 And then I put half of it in a larger envelope and mail it to do to Australia. 312 00:51:56.130 --> 00:52:01.139 And I put the other half in another envelope, whatever, and mail it to Greenland. 313 00:52:01.139 --> 00:52:05.909 Now, those 2 halves of the envelope. 314 00:52:05.909 --> 00:52:10.289 Are of the small envelope are entangled with each other. 315 00:52:10.289 --> 00:52:14.969 Okay, so here's what I mailed to Australia. 316 00:52:14.969 --> 00:52:21.719 And the outer envelope is sealed. 317 00:52:21.719 --> 00:52:26.369 Don't know what's inside the Australian. 318 00:52:26.369 --> 00:52:33.389 Opens it up he sees this. It's the right half of the smaller piece of paper. 319 00:52:33.389 --> 00:52:45.690 So now the Australian E now's, no, now knows what the Greenland will see when the green lander opens up his envelope. The Australian now knows that the green lander. 320 00:52:45.690 --> 00:52:50.820 Well, we'll see this other half. Okay. These 2 halves are entangled. 321 00:52:51.960 --> 00:52:57.030 But the thing is that until the Australian opened up his own. 322 00:52:57.030 --> 00:53:00.510 You might say the 2 things. The 2 has were super post. 323 00:53:00.510 --> 00:53:07.619 You didn't know what the child would see, but the Australians opening his own envelope. 324 00:53:07.619 --> 00:53:13.110 Has now controlled what the Greenland will see when he opens his own below. 325 00:53:14.250 --> 00:53:18.090 Or if the green lander opened his on below 1st, and saw this. 326 00:53:18.090 --> 00:53:22.860 We now know what the failed and would see so that you see, things are entangled. 327 00:53:22.860 --> 00:53:32.280 And in the quantum sense, you can do that, you can create 2 entangled cube and you can transform them. 328 00:53:32.280 --> 00:53:37.469 So, they're entangled, but they also have some complex their state. 329 00:53:37.469 --> 00:53:45.929 Has not been observed yet is a superposition, but we can send the cube. It's a 1000 miles apart. Now. This has actually been done. 330 00:53:45.929 --> 00:53:50.070 So, you move the 2 entangled cubital 1000 miles apart. 331 00:53:50.070 --> 00:54:01.409 Keeping them still at a temperature of 20 s of 1, Kelvin or whatever, depending on your technology and now, when you observe the 1 cube. 332 00:54:01.409 --> 00:54:05.579 You now know what the observer on the other cubic will see. 333 00:54:05.579 --> 00:54:12.360 And if you do this a 1000 times, and you see different thing every time, because of the probability. 334 00:54:12.360 --> 00:54:22.739 And each time, you know what the green lander will see those 2 each time, those 1000 pairs of few. But each case, the Tokyo butts in the pair are entangled to each other. 335 00:54:23.784 --> 00:54:38.155 However, this does not let you communicate. This is an important thing with my green lander and my Australian there is the fact that their 2 envelope haves are entangled does not let them to send information to each other. 336 00:54:38.155 --> 00:54:39.684 And this might take you some thinking. 337 00:54:40.199 --> 00:54:51.119 And did with the cubic thing, which has actually been done, they have created 2 entangled cube bits and I think moved them 1500 miles apart. 338 00:54:51.119 --> 00:54:58.349 Being very carefully keeping them cold and so on. And when they observed 1, it absolutely controls what you see when you observe the other. 339 00:55:00.269 --> 00:55:10.679 But it does not let you communicate, which is good because if it like you communicate, then it'd be some causality issues with relativity. 340 00:55:11.760 --> 00:55:20.579 Okay, okay, so we've seen the superposition. We've seen this entanglement. We're seeing the building blocks. 341 00:55:20.579 --> 00:55:31.170 Okay, good, but quantum computing for computer scientists 1st edition. So the way quantum algorithms work um. 342 00:55:31.170 --> 00:55:36.929 You know, you've had some classical bits and basically create quantum bits from them. 343 00:55:36.929 --> 00:55:45.570 Then do the soft matrix multiplication and now they're in superposition. 2 various things and measure them. 344 00:55:45.570 --> 00:55:50.460 And and then you've accomplished the some operations. 345 00:55:50.460 --> 00:55:54.659 And I'll talk about some of the operations. 346 00:55:54.659 --> 00:55:59.190 What the matrix qualifications often do is. 347 00:55:59.190 --> 00:56:06.840 They modify the relevant probabilities and they amplify probability, which is interest, which is, is. 348 00:56:06.840 --> 00:56:10.260 Useful for what you're trying to do, so. 349 00:56:10.260 --> 00:56:15.300 Um, quantum computers are very good for searching problems. 350 00:56:15.300 --> 00:56:20.400 And you're searching for a solution and. 351 00:56:20.400 --> 00:56:28.619 Factoring and 1 would be factoring a large enricher. And each possible factor would be 1 of the various. 352 00:56:28.619 --> 00:56:32.730 Basis some states and. 353 00:56:32.730 --> 00:56:36.000 The aptitude might be the probability. 354 00:56:36.000 --> 00:56:46.380 If you can talk about probability, but factor that this integer is a factor and the various operations increase the probability of the actual tact or decrease the probability. The others. 355 00:56:46.380 --> 00:56:54.269 Or you imagine you're searching for buried gold or something very treasure. Each possible. Location is a basis state. 356 00:56:54.269 --> 00:57:01.500 And so if there's a post acute by, then it's 256 possible locations and you do various. 357 00:57:01.500 --> 00:57:05.730 Things that increase the probability of what turns out to me the actual place. 358 00:57:05.730 --> 00:57:09.449 Okay. 359 00:57:10.590 --> 00:57:15.989 And again, measurements a complicated idea. I'm trying to understand it myself somewhat. 360 00:57:15.989 --> 00:57:20.849 So, it's an operator represented by Matrix and. 361 00:57:20.849 --> 00:57:23.849 It's effectively a rotation and. 362 00:57:23.849 --> 00:57:28.829 And for physical systems, and operator might be. 363 00:57:28.829 --> 00:57:32.699 Computing moment position, energy momentum or something. 364 00:57:32.699 --> 00:57:40.199 Yeah, okay. And the fact that the observation is probabilistic. 365 00:57:40.199 --> 00:57:43.530 The result of the measurement is probabilistic. This relates to. 366 00:57:43.530 --> 00:57:52.110 If the things about constant and uncertainty and position versus momentum, and so on these ideas are related. 367 00:57:53.130 --> 00:57:58.590 Okay um, so basically. 368 00:57:58.590 --> 00:58:02.250 You have a computer with some cube bits. 369 00:58:02.250 --> 00:58:08.070 And and you do modify an observation to a measurement. 370 00:58:08.070 --> 00:58:14.699 Now, the problem is, the measurement is probably is probabilistic. So, the operation is and now you see. 371 00:58:14.699 --> 00:58:29.250 So you want to factor a beginner chair, then it doesn't it'll give you, it'll tell you what this is probably the factor and you repeat your computation a 1000 times or something, and you probably fail to start converging. 372 00:58:29.250 --> 00:58:33.000 Now. 373 00:58:33.000 --> 00:58:37.289 The current machines might have say. 374 00:58:37.289 --> 00:58:40.920 50 cube, or whatever the. 375 00:58:41.184 --> 00:58:55.974 Ibm has ones with, like, 10 cube it's available for free actually on the web. I think it's 53 Cupid genius. You stories about, like, 53 cubic machines that sort of idea D wave has ones with more cube, but they're doing a different sort of thing. Okay. 376 00:58:58.650 --> 00:59:05.519 And as a way to represent a cube bed as a point on a sphere okay. Okay. 377 00:59:05.519 --> 00:59:18.480 So, we've seen cube beds, so just basis state and the state is a superposition of basis States and the component bits of acute byte that same might be entangled. 378 00:59:19.500 --> 00:59:22.679 And I set an operation is a matrix multiply. 379 00:59:24.989 --> 00:59:30.780 So, what are some of these operations? Wikipedia has a nice. 380 00:59:30.780 --> 00:59:37.320 Summary and well. 381 00:59:37.974 --> 00:59:52.855 And typically, these are working on systems of 2, maybe 3 cube, and he might swap the 2 cube, which you might do a control not a controlled not well invert 1 cube based the other cube is 1. let's say. 382 00:59:53.130 --> 00:59:58.380 Which is. 383 01:00:00.059 --> 01:00:09.750 You know, in a classical sense, you could imagine a control not. Okay. It's got 2 inputs X and Y, axis 1. why it gets complimented. 384 01:00:10.920 --> 01:00:21.239 And if it also is 2, outputs, X, Prime, and wide Prime, then no information got destroyed. Okay. So the classical see, not. 385 01:00:21.239 --> 01:00:26.969 If 0, why goes through effects is 1 wise complemented. Okay. 386 01:00:26.969 --> 01:00:35.820 Now, look at the quantum thing. So, X is a superposition of 0 and 1. so now why it becomes a superposition. 387 01:00:35.820 --> 01:00:38.820 Of why? And why not. Okay. 388 01:00:38.820 --> 01:00:42.900 So this starts, you know, a little more sophisticated than you might think. 389 01:00:45.059 --> 01:00:52.679 There's things that will effectively do a rotation of the 2 classical things and make a superposition and. 390 01:00:52.679 --> 01:00:58.500 It should let me go to media for a few minutes. 391 01:00:58.500 --> 01:01:02.309 Hello. 392 01:01:02.309 --> 01:01:13.710 Yeah, so this is a table of common ones here. They're all 2 by 2 major cities. Polly X is a compliment. So. 393 01:01:13.710 --> 01:01:19.170 If it's class, if the cube it is not super imposes classical thing. Otherwise it. 394 01:01:19.170 --> 01:01:27.929 But it does this up matrix and this is the, that you can do circuits of metal logic, diagrams, graphs of. 395 01:01:27.929 --> 01:01:31.469 For quantum, just like for classic I'll just as a symbol for. 396 01:01:31.469 --> 01:01:37.050 Compliment Polly Y, and Z are touch more complicated. 397 01:01:37.050 --> 01:01:40.889 Had a marred is a very powerful 1. 398 01:01:40.889 --> 01:01:43.980 What does is if you input. 399 01:01:43.980 --> 01:01:48.030 A classical cube bit, not super impose the output. 400 01:01:49.199 --> 01:01:56.880 Is 2 superimposed cube and the output is 0 and 1 superimposed 50, 50. 401 01:01:56.880 --> 01:02:09.360 So you start with classical cute to say 2, classical Q bits and you immediately apply a header Mark gate in many cases and now you have it to superimposed. 402 01:02:09.360 --> 01:02:21.960 So this is our applied to 1 these things so far applied to 1 queue but I'm sorry so you had Omar, you apply a classical cube, but that's not superimposed in the output. 403 01:02:21.960 --> 01:02:31.889 Is it's now superimposed? Okay these phase sayings, considering the cube bed as a point in a sphere to a rotation. 404 01:02:31.889 --> 01:02:40.260 The controlled not takes 2 cube, which is important to ice output. And again. 405 01:02:40.260 --> 01:02:43.500 If column X and Y. 406 01:02:43.500 --> 01:02:52.349 Effects is 1 why gets complimented? And this is the matrix here. Nice and simple but in fact. 407 01:02:52.349 --> 01:02:57.420 Effects is a superposition then why it becomes a position of it's to. 408 01:02:57.420 --> 01:03:01.500 Original value, because why it could be a superposition also. 409 01:03:03.630 --> 01:03:14.159 Control Z, it takes the quality Z at the top here and if axis 1, then the, why has the control the applied to it? 410 01:03:15.840 --> 01:03:19.469 Swap. 411 01:03:19.469 --> 01:03:24.690 The top Holy gate is used a lot has 3 coming in. 412 01:03:24.690 --> 01:03:28.829 And what it does is a comp set column X Y, and Z. 413 01:03:28.829 --> 01:03:33.539 It compliments Z if, and only if both X and Y are true. 414 01:03:33.539 --> 01:03:36.539 That's the classical version of it. 415 01:03:36.539 --> 01:03:41.099 The quantum content version of it has this 8 by 8 matrix. 416 01:03:41.099 --> 01:03:47.940 And it's when X and Y, or Z superposition funny things happen to Z. 417 01:03:47.940 --> 01:03:59.969 Okay, and by the way some of these gates can also get the can I also have a kickback property or what you think are the input bits also get modified. So. 418 01:04:01.019 --> 01:04:08.519 Okay, see these examples of quantum Gates, and you build them up to make circuits. Okay. Notable examples. 419 01:04:08.519 --> 01:04:13.530 Watson now, just like with classical logic and navigate can. 420 01:04:13.530 --> 01:04:16.650 You can build up navigates to do everything. 421 01:04:16.650 --> 01:04:19.829 There's some universal Gates here, so they talk about. 422 01:04:19.829 --> 01:04:26.789 Some of them here. Oh, okay. Oh, this is cool. So the not gate. 423 01:04:26.789 --> 01:04:35.219 Compliments it's in the square root of not gate is a square root of a compliment. So. 424 01:04:35.219 --> 01:04:39.719 It's like, I think of just complex numbers. 425 01:04:39.719 --> 01:04:54.690 Minus 1 and a number what's the square root of minus? 1 is I. so this matrix here is a complement is a square root of an arcade in the sense that you apply it twice. You get a not. 426 01:04:56.489 --> 01:04:59.730 A shift gauge an arbitrary pace shift. 427 01:04:59.730 --> 01:05:06.539 How you an arbitrary thing. So, in technology called TransAm on cube bits. 428 01:05:07.860 --> 01:05:12.570 They got various isolations and. 429 01:05:12.570 --> 01:05:22.679 You can change a phase, the relative phase of 2 isolation you can change you did by tickling it with a microwave and the 5 gigahertz range. 430 01:05:22.679 --> 01:05:28.230 And this would be and how the more you take a look more at rotate send this is a page. 431 01:05:28.230 --> 01:05:34.019 Control pay shift only if due to due to swap Tyson sample. 432 01:05:34.019 --> 01:05:40.199 Oh, this is crazy. So, swap swaps to cube square root of swap. 433 01:05:40.199 --> 01:05:45.960 What is half a swap? I don't know intuitively what half a swap is. 434 01:05:45.960 --> 01:05:51.179 But whatever it is, if you do it twice, you now have a swap. 435 01:05:51.179 --> 01:05:55.380 Okay, and this is a square root of a swap. 436 01:05:55.380 --> 01:06:02.309 You do it twice. You do it swap. Now you do it once you do the square root of a swap once. 437 01:06:02.309 --> 01:06:05.909 Those 2 out those 2 bits are are now and tangled. 438 01:06:05.909 --> 01:06:09.090 And they're in something called a bell state. 439 01:06:10.289 --> 01:06:15.000 So the square root of swap well, entangled 2 cube. 440 01:06:17.010 --> 01:06:20.460 Ended to do a controlled things. 441 01:06:23.429 --> 01:06:29.340 I showed you this 1. 442 01:06:30.570 --> 01:06:34.320 This is another common 1. 443 01:06:34.320 --> 01:06:39.659 So, the top Holy was controlled not this is a controlled swap. 444 01:06:41.610 --> 01:06:47.010 So 3 inputs X Y, and Z effects is 1, it swaps Y and Z. 445 01:06:47.010 --> 01:06:52.110 That's the classical version for the quantum version. 446 01:06:52.110 --> 01:06:55.980 X is not 0 and want us to superposition and. 447 01:06:55.980 --> 01:06:59.550 So, what happens this matrix. 448 01:06:59.550 --> 01:07:05.639 So, um. 449 01:07:07.230 --> 01:07:14.460 Since I mentioned in quantum computer, that's another technology they're ions that are trapped in the sort of magnetic trap. 450 01:07:14.460 --> 01:07:19.860 And they can be have rotations and so on that's another. 451 01:07:19.860 --> 01:07:31.050 Being built, um, other other things, and this is what it would look like you build up a circuit with several Gates and so on. 452 01:07:33.900 --> 01:07:43.199 Circuit composition, you even build them up and IBM had so you can actually do it and also have a simulator. So. 453 01:07:43.199 --> 01:07:49.739 Adam are transform mom if you got 2 cube bets, and you had to more transform the. 454 01:07:49.739 --> 01:07:55.980 To cube separately and you've now and can, and you have something. 455 01:07:57.150 --> 01:08:06.300 Now, got a full state browse, so it's a way. 456 01:08:06.300 --> 01:08:18.000 To make this superposition kind of. 457 01:08:23.010 --> 01:09:06.899 Site 458 01:09:06.895 --> 01:09:08.545 can browse it and so on. 459 01:09:15.180 --> 01:09:21.329 Yeah, so you put in. 460 01:09:21.329 --> 01:09:25.649 Well, this show here you put in and 2 bits that are all 0. 461 01:09:25.649 --> 01:09:29.430 Let's say, and you applied had a gate to each of them. 462 01:09:29.430 --> 01:09:34.649 You've now got this equal superposition of the 2 to the end possible States. 463 01:09:34.649 --> 01:09:43.050 Altogether the now all together. So, and now you apply some operator on each 2 to the end. 464 01:09:49.140 --> 01:11:37.229 Silence. 465 01:11:37.229 --> 01:11:49.710 This is a choice I made and I got to made it since it's my course I created. So it was difficult. Finding literature aimed at computer scientist in this book is 1 of them. 466 01:11:49.710 --> 01:11:57.960 So, the thing is, what some of the algorithms are is a quite different. 467 01:11:59.100 --> 01:12:03.539 From classical algorithms, the, um. 468 01:12:04.890 --> 01:12:12.840 The speeter short algorithm to factor and manager is not related to the classical algorithms a totally different idea. 469 01:12:12.840 --> 01:12:20.039 Okay, and current research now we'll give some examples here of what you can do faster. 470 01:12:20.039 --> 01:12:25.590 Or, by the way any function can, I said quantum computing. 471 01:12:25.590 --> 01:12:32.939 The matrices are vertable and you can make what would look like a non vertical matrix vertable by. 472 01:12:32.939 --> 01:12:36.270 Adding some extra controlled bits to it. So. 473 01:12:37.529 --> 01:12:42.479 Major types of quantum algorithms. 474 01:12:42.479 --> 01:12:46.859 It could be has to say. 475 01:12:51.810 --> 01:12:55.319 You can browse it on your own and so on. 476 01:12:58.020 --> 01:13:01.289 Oh, just to the lecture from the table of contents here. 477 01:13:01.289 --> 01:13:15.840 Quantum algorithms, most of them, they're searching algorithms there. You're trying to find an answer to something and if you have a possible answer, it's easy to test it. 478 01:13:15.840 --> 01:13:26.640 The problem is finding it, like, factoring a number optimization things you're trying to. This is the big thing, the D wave company does they quantum annealing? 479 01:13:26.640 --> 01:13:31.409 So, it's trying to search it's trying to find a. 480 01:13:31.409 --> 01:13:37.529 You know, to optimize the values of variables will optimize some objective function. 481 01:13:37.529 --> 01:13:46.680 And another example would be a simple thing you have, and fits. 482 01:13:46.680 --> 01:13:55.470 And inputs to your black box, and 1 of the inputs is 1 and minus 1 of them are 0 and you want to find which 1 is 1. 483 01:13:55.470 --> 01:13:59.670 Classically takes and time, and you got to check each input. 484 01:13:59.670 --> 01:14:03.060 quantumly, it's faster. 485 01:14:04.109 --> 01:14:07.739 Searching things machine learning. 486 01:14:10.050 --> 01:14:20.364 Computational biology, and so on anything involving proteins, you're trying to fold the protein and different proteins, these long, thin molecules. 487 01:14:20.635 --> 01:14:30.715 You can fold them different ways and the energy and if different parts get close to each other at lower, they attract or they were palette. It changes the potential energy, the resulting molecule. 488 01:14:30.989 --> 01:14:38.250 And they prefer to end up in a state where where they minimize the potential energy. So they're folded. So. 489 01:14:38.250 --> 01:14:43.229 Things match up nicely and, for example, for drugs. 490 01:14:43.229 --> 01:14:48.539 This affects what the drug does it affects, whether a protein. 491 01:14:48.539 --> 01:14:56.279 Does something and so computing how molecules fold is important. 492 01:14:56.279 --> 01:15:00.029 In biology and quantum computing. 493 01:15:00.029 --> 01:15:03.539 Again, it's searching searching stuff works. 494 01:15:03.539 --> 01:15:16.890 So, cryptography searching for a key. Well, that's like, searching for a factor of an energy. These are the sorts of things. Quantum computing does fast. 495 01:15:16.890 --> 01:15:25.500 Machine learning, the quantum supremacy is that can a quantum computer do it faster than a classical computer. 496 01:15:25.500 --> 01:15:30.060 And I are quantum computers actually useful for anything yet? 497 01:15:30.060 --> 01:15:38.699 Some people say they found quantum cases where the quantum computer is faster. Other people argue about it. 498 01:15:39.720 --> 01:15:47.399 Like, a year ago, there was an example found, it was it was an artificial problem that was created that could be done faster on a quantum computer. 499 01:15:47.399 --> 01:15:57.420 And I think the state of the thing is people admit, yeah, this artificial problem can be done faster but it's so artificial. It's not interesting. 500 01:15:57.420 --> 01:16:08.699 The rebuttal to that is that this is how these things progress 1st, you do an artificial thing faster, and then next year you do a more useful thing faster. So, I don't know. 501 01:16:10.079 --> 01:16:24.840 Quantum de coherence. Well, that's where these quantum computers break down. So you're at IBM. The thing is, you got these Cubics expressed as isolations and these circuits involving Joseph junctions. 502 01:16:24.840 --> 01:16:32.909 And they're down at 1, twentieth of a Calvin, and they kept isolated from the real world except when you're tickling it deliberately with a microwave. 503 01:16:34.710 --> 01:16:40.050 Well, they don't say isolated forever and this is called quantum DCO here. It's in this limits. 504 01:16:40.050 --> 01:16:43.470 How much work you can get done in the quantum computer you can only. 505 01:16:43.470 --> 01:16:47.699 Do successive operations until it DCO hears. 506 01:16:47.699 --> 01:16:52.800 Is it a we'll see. Okay, so. 507 01:16:54.239 --> 01:17:02.520 Nice summary there. So algorithms. Okay classical computing you've got your. 508 01:17:02.520 --> 01:17:08.310 You know, you're non polynomial algorithms, which again they're classical searching algorithms. 509 01:17:08.310 --> 01:17:17.010 Where there's no known way to, in searching for a solution. Like, you're, you've got a. 510 01:17:17.010 --> 01:17:20.039 Well, the predicate and you're trying to find values for. 511 01:17:20.039 --> 01:17:24.569 For the variables that make the predicate true satisfy ability problem. 512 01:17:24.569 --> 01:17:29.819 Have you had a possible and so you could check it really fast. 513 01:17:30.895 --> 01:17:42.234 But, you know, you got to try every possible answer, basically, or the square root of every possible answer perhaps. And these are called problems, non deterministic polynomial type. 514 01:17:42.475 --> 01:17:46.045 If you ran lots of machines in parallel, you could solve it and follow mealtime. 515 01:17:46.319 --> 01:17:49.920 And then there's the N P complete class. 516 01:17:49.920 --> 01:18:02.850 Where there's a strong relation between every different non Paulo meal problem, not a temporary call. No problem which, if you could do any of them fat. So, the big question unsolved question in theoretical computer sciences. 517 01:18:04.229 --> 01:18:11.399 Can you in fact, solve these problems and polynomial time when a deterministic computer and it's not known. 518 01:18:11.399 --> 01:18:19.739 But there are some NP complete problems and their problem is that if you could do them faster, you could do every NP problem past. 519 01:18:21.000 --> 01:18:30.600 That's the deterministic quantum. They got to be QB bounded air quantum polynomial time. So, again, these quantum computers. 520 01:18:30.600 --> 01:18:36.149 They produce an answer was a, with an arrow to the probability being wrong. 521 01:18:36.149 --> 01:18:46.710 In classical things, there are algorithms that will test for a number and a test of a natural number is prime. 522 01:18:46.710 --> 01:18:50.729 But the thing is that they have a chance of being wrong. 523 01:18:50.729 --> 01:18:54.270 And so you run, em, 100 times. 524 01:18:56.340 --> 01:19:00.960 Well, quantum algorithm is the same thing. They have a chance of being wrong and. 525 01:19:00.960 --> 01:19:08.850 Might be quite high might be a 3rd gets up to 50% and you don't have any information content to say it's a 3rd. 526 01:19:08.850 --> 01:19:16.439 And so they look at this called bounded error where the error is actually small enough that you can get useful out useful work out of it. Like. 527 01:19:16.439 --> 01:19:23.880 Interchangeable factors it discrete logs another important thing. It's useful in some cryptography algorithms. 528 01:19:24.930 --> 01:19:29.010 Find the square root the end through essentially of an integer. 529 01:19:29.010 --> 01:19:37.140 Launch something big, so there are algorithms that are in and how it's ready to N. P. is unknown. 530 01:19:37.140 --> 01:19:41.130 Searching thing searching is a big thing. 531 01:19:42.359 --> 01:19:47.130 Now, the thing is, the quantum competition can do some searching problems faster. 532 01:19:47.130 --> 01:19:50.970 And it's researches, can they do a new ones faster? So. 533 01:19:53.670 --> 01:20:02.430 Any case it's probabilistic so you run the thing a 1000 times, perhaps until the arrows acceptably small. 534 01:20:05.189 --> 01:20:09.510 And 1 way to look at this is. 535 01:20:10.800 --> 01:20:21.960 You start with and cubax, they're all 0 You had a they're now in tangled on a superposition. You operate on each cube in parallel to try to. 536 01:20:21.960 --> 01:20:27.989 Increase the amplitude of the of the state, which corresponds to the problem you're trying to solve. 537 01:20:27.989 --> 01:20:33.810 And you separate it out and I mentioned grover's algorithm. 538 01:20:35.909 --> 01:20:40.920 A black box with and inputs in 1 output. 1 input makes the output 1. 539 01:20:40.920 --> 01:20:51.810 This is not quite you what I described as a different thing here, based the same thing. 1 input makes the output. 1. which input is that possibly try every input. 540 01:20:51.810 --> 01:20:57.600 quantumly, you can do it in square root event, time, probabilistic things and it actually is real examples here. 541 01:20:57.600 --> 01:21:04.680 And is approved, you cannot do faster than the square root of end time. So. 542 01:21:04.680 --> 01:21:08.520 Shores algorithm to factor and. 543 01:21:08.520 --> 01:21:16.770 The largest 1 I could find was a factor of 5 digit integer so we're not going to break here public key system this year. 544 01:21:16.770 --> 01:21:23.340 Next year maybe. Okay, so this was I'll stop here at the end of my section 3. 545 01:21:23.340 --> 01:21:31.079 Maybe I'll see if I can get the video working and show some interesting videos. 546 01:21:31.079 --> 01:21:41.100 And any case, so I was giving you my version of an introduction to quantum computing. There's other versions online if you, you might prefer to me. 547 01:21:41.100 --> 01:21:48.569 There's tech stuff, there's a lot of videos online. There are YouTube channels and so on. I'll show you later. 548 01:21:49.590 --> 01:21:58.649 But what Thursday we will start drilling down to more technical details on some of the algorithms and. 549 01:21:58.649 --> 01:22:05.069 We'll get more details and at some point, if I go back to my table of contents here. 550 01:22:06.210 --> 01:22:20.189 Algorithm details, we'll revisit some of the properties and talk about some technologies and I'll get into some of the main companies IBM and so on talk about some of the companies. 551 01:22:20.574 --> 01:22:35.095 And then I'll tell if you want to run real quantum computing, IBM, and Microsoft and cloud computing will give you access to real quantum computers there, batch computers and not interactive. You submit a job and they run. 552 01:22:36.265 --> 01:22:50.515 And then 1 of the current active areas is what I call middle where they are tools using the salt level quantum things. Ibm also has a, they have a number of quantum computers, 10 or 20. 553 01:22:50.515 --> 01:22:55.255 they're older ones are online for free and they have a. 554 01:22:56.670 --> 01:23:06.989 A quick thing, they have a, um, an interface that graphically lets you build quantum computers. 555 01:23:06.989 --> 01:23:15.779 And and there is an emulator on top, and you can also submit you see, you can run. 556 01:23:15.779 --> 01:23:26.430 You can emulate them on your machine, maybe up to 5 minutes or so is where we've got this exponential speed up and, or you can run them on IBM, Israel, computer. 557 01:23:26.430 --> 01:23:31.020 So, okay, so. 558 01:23:31.020 --> 01:23:36.689 That's what enough stuff for it today if there's questions no. 559 01:23:36.689 --> 01:23:43.859 Other than that see, you guys Thursday. Oh, and remember. 560 01:23:43.859 --> 01:23:50.369 Your big task doable now is back up 1. 561 01:23:53.970 --> 01:23:58.050 Is I had to do is class 21. 562 01:23:58.050 --> 01:24:05.939 Final projects. Okay. Okay. So. 563 01:24:07.619 --> 01:24:14.399 If there's questions, if not questions, let's all go get lunch. 564 01:24:14.399 --> 01:24:18.300 Silence. 565 01:24:19.590 --> 01:24:23.520 Okay.