0 00:00:00,000 --> 00:00:30,000 Dear viewer, these subtitles were generated by a machine via the service Trint and therefore are (very) buggy. If you are capable, please help us to create good quality subtitles: https://c3subtitles.de/talk/405 Thanks! 1 00:00:09,540 --> 00:00:11,049 So hi, everyone. 2 00:00:11,050 --> 00:00:13,289 Um, first of all, it's 3 00:00:13,290 --> 00:00:14,939 really great to be here and I mean, I was 4 00:00:14,940 --> 00:00:17,039 a bit shocked and also amazed at 5 00:00:17,040 --> 00:00:18,329 how many people seemed to be interested 6 00:00:18,330 --> 00:00:19,769 in quantum computing. 7 00:00:19,770 --> 00:00:21,809 For me, to stock is actually kind of 8 00:00:21,810 --> 00:00:24,119 special because it closes a circle. 9 00:00:24,120 --> 00:00:26,249 Um, the first time I 10 00:00:26,250 --> 00:00:28,349 was at the CCC was in 11 00:00:28,350 --> 00:00:30,479 2001, and back 12 00:00:30,480 --> 00:00:31,829 then I was still in school and I was 13 00:00:31,830 --> 00:00:34,109 coming here from my small town 14 00:00:34,110 --> 00:00:35,549 in southwest Germany. 15 00:00:35,550 --> 00:00:37,709 Um, and when I arrived here, 16 00:00:37,710 --> 00:00:39,699 this was kind of like Magic Fairyland. 17 00:00:39,700 --> 00:00:41,819 So there were people doing all kinds 18 00:00:41,820 --> 00:00:43,799 of amazing things, like playing with 19 00:00:43,800 --> 00:00:45,899 electronics, picking locks. 20 00:00:45,900 --> 00:00:48,569 And there was one presentation as well on 21 00:00:48,570 --> 00:00:49,859 a Tesla coil, so to say. 22 00:00:49,860 --> 00:00:51,969 So physics student showing around 23 00:00:51,970 --> 00:00:54,269 the Tesla, I recall that he made himself 24 00:00:54,270 --> 00:00:55,769 and like explaining the physics and how 25 00:00:55,770 --> 00:00:58,079 it worked. And this is kind of how 26 00:00:58,080 --> 00:00:59,999 I got very interested in all these kind 27 00:01:00,000 --> 00:01:01,709 of things and physics and finally took 28 00:01:01,710 --> 00:01:03,309 the decision to study that as well. 29 00:01:03,310 --> 00:01:05,488 So today, 30 00:01:05,489 --> 00:01:07,469 I hope that with my talk, I would be able 31 00:01:07,470 --> 00:01:09,689 to to like instill in some of you also 32 00:01:09,690 --> 00:01:12,149 something similar, like like an interest 33 00:01:12,150 --> 00:01:14,279 in like interest in quantum phenomena and 34 00:01:14,280 --> 00:01:16,379 quantum computing in general. 35 00:01:16,380 --> 00:01:16,859 All right. 36 00:01:16,860 --> 00:01:18,989 So as I talk with you about 37 00:01:18,990 --> 00:01:21,389 quantum computers and 38 00:01:21,390 --> 00:01:22,919 some of the results will show you a lot 39 00:01:22,920 --> 00:01:24,569 of research from different groups. 40 00:01:24,570 --> 00:01:26,879 And some of the results are from my 41 00:01:26,880 --> 00:01:29,729 PhD thesis, which I did that basically. 42 00:01:29,730 --> 00:01:31,859 So I want to just thank all of my former 43 00:01:31,860 --> 00:01:33,389 colleagues and my Ph.D. 44 00:01:33,390 --> 00:01:35,519 advisors for their support during 45 00:01:35,520 --> 00:01:36,520 that work. 46 00:01:38,930 --> 00:01:41,390 All right, so 47 00:01:44,420 --> 00:01:45,420 much of it. 48 00:01:51,690 --> 00:01:53,519 So that's kind of the motivation for me 49 00:01:53,520 --> 00:01:55,139 to give this talk, because as you 50 00:01:55,140 --> 00:01:56,669 probably all noticed, there's a lot of 51 00:01:56,670 --> 00:01:58,559 buzz about quantum computers in the 52 00:01:58,560 --> 00:02:00,659 media. So every month there is an article 53 00:02:00,660 --> 00:02:02,669 on Wired or on VentureBeat showing the 54 00:02:02,670 --> 00:02:04,949 latest results from like 55 00:02:04,950 --> 00:02:06,179 groups and quantum computing. 56 00:02:06,180 --> 00:02:07,709 And also now there was this big 57 00:02:07,710 --> 00:02:09,689 announcement that Google invests money in 58 00:02:09,690 --> 00:02:10,918 building superconducting quantum 59 00:02:10,919 --> 00:02:12,389 computers. So there's a lot of 60 00:02:12,390 --> 00:02:13,679 information floating around. 61 00:02:13,680 --> 00:02:16,199 And it all kinds of ranges between 62 00:02:16,200 --> 00:02:17,969 quantum computers were like, change 63 00:02:17,970 --> 00:02:20,309 everything for us or quantum computers 64 00:02:20,310 --> 00:02:21,869 are kind of hokum. They will never work, 65 00:02:21,870 --> 00:02:22,739 probably. 66 00:02:22,740 --> 00:02:24,449 And what I want to do this talk is 67 00:02:24,450 --> 00:02:26,699 actually to to explain 68 00:02:26,700 --> 00:02:29,369 what quantum computing is, what we wanted 69 00:02:29,370 --> 00:02:30,789 and how it works, actually. 70 00:02:30,790 --> 00:02:32,879 So the 71 00:02:32,880 --> 00:02:34,109 outline for us is to. 72 00:02:34,110 --> 00:02:35,400 Yeah, as I said. Sure. 73 00:02:36,420 --> 00:02:37,949 Why we want actually to build quantum 74 00:02:37,950 --> 00:02:40,229 computers then how 75 00:02:40,230 --> 00:02:42,839 to like solve some interesting 76 00:02:42,840 --> 00:02:44,549 problems with them, for example, cracking 77 00:02:44,550 --> 00:02:45,599 passwords. 78 00:02:45,600 --> 00:02:48,299 And afterwards I will show you how to 79 00:02:48,300 --> 00:02:49,739 build a very simple quantum computer 80 00:02:49,740 --> 00:02:51,959 quantum processor using superconductors, 81 00:02:51,960 --> 00:02:54,389 resonators and microwave signals. 82 00:02:54,390 --> 00:02:56,399 And finally, I will show you some of the 83 00:02:56,400 --> 00:02:58,020 recent progress in quantum computing. 84 00:03:00,120 --> 00:03:01,649 All right, let's get started. 85 00:03:01,650 --> 00:03:02,650 So 86 00:03:04,050 --> 00:03:05,939 what is the history of quantum computing? 87 00:03:05,940 --> 00:03:08,309 Well, the beginning can be probably 88 00:03:08,310 --> 00:03:10,589 traced back to the 80s when 89 00:03:10,590 --> 00:03:12,089 physicists were already using 90 00:03:12,090 --> 00:03:14,519 conventional or classical computers to 91 00:03:14,520 --> 00:03:17,129 help them to simulate physical systems. 92 00:03:17,130 --> 00:03:19,589 And back then, people were asking, 93 00:03:19,590 --> 00:03:21,359 they were seeing that it is actually 94 00:03:21,360 --> 00:03:23,519 pretty hard to simulate a quantum 95 00:03:23,520 --> 00:03:26,779 system with a classical computer somehow 96 00:03:26,780 --> 00:03:28,439 as soon as you like it, a little bit of 97 00:03:28,440 --> 00:03:29,939 complexity to your quantum system. 98 00:03:29,940 --> 00:03:31,409 The classical computer is no longer able 99 00:03:31,410 --> 00:03:33,059 to to kind of simulated. 100 00:03:33,060 --> 00:03:35,129 And in a famous conference in 101 00:03:35,130 --> 00:03:37,559 1981, Richard Feynman, 102 00:03:37,560 --> 00:03:39,629 physics Nobel Prize winner, gave a 103 00:03:39,630 --> 00:03:41,699 talk on exactly this subject where we 104 00:03:41,700 --> 00:03:43,559 discussed how to build a computer that 105 00:03:43,560 --> 00:03:45,029 would actually be able to simulate 106 00:03:45,030 --> 00:03:46,559 quantum mechanics. 107 00:03:46,560 --> 00:03:48,869 And this is, so to say, the birth of the 108 00:03:48,870 --> 00:03:50,459 quantum computer as a concept. 109 00:03:50,460 --> 00:03:52,589 From the beginning, it was really devised 110 00:03:52,590 --> 00:03:54,989 to help physicists to simulate 111 00:03:54,990 --> 00:03:56,309 quantum mechanical system. 112 00:03:58,230 --> 00:04:00,359 And if you now go one 113 00:04:00,360 --> 00:04:02,489 step further and you can, of course, see 114 00:04:02,490 --> 00:04:04,409 that quantum computer seems to be more 115 00:04:04,410 --> 00:04:05,819 powerful than a classical computer 116 00:04:05,820 --> 00:04:07,889 because it can simulate quantum systems. 117 00:04:07,890 --> 00:04:09,929 So maybe it can also help us to solve 118 00:04:09,930 --> 00:04:11,879 some other problems which are not of like 119 00:04:11,880 --> 00:04:13,649 physical nature, but some abstract 120 00:04:13,650 --> 00:04:15,299 mathematical things. 121 00:04:15,300 --> 00:04:17,159 And amazingly, the answer to this is 122 00:04:17,160 --> 00:04:19,289 also. Yes. And now I want to show 123 00:04:19,290 --> 00:04:21,239 you how this how this gets done, so to 124 00:04:21,240 --> 00:04:23,669 say so, to understand 125 00:04:23,670 --> 00:04:25,769 quantum computing, we first need 126 00:04:25,770 --> 00:04:28,229 to have a look at the basics of classical 127 00:04:28,230 --> 00:04:29,189 computing. 128 00:04:29,190 --> 00:04:30,749 And this will be very useful because 129 00:04:30,750 --> 00:04:32,639 later on we will use a lot of concepts 130 00:04:32,640 --> 00:04:33,779 that I will introduce to you a year or 131 00:04:33,780 --> 00:04:35,459 so. It will help you to understand how 132 00:04:35,460 --> 00:04:36,989 exactly quantum computers do what they 133 00:04:36,990 --> 00:04:37,990 do. 134 00:04:40,200 --> 00:04:42,359 So, as you probably know, 135 00:04:42,360 --> 00:04:43,360 um, 136 00:04:45,450 --> 00:04:47,759 computers use bits as the basic 137 00:04:47,760 --> 00:04:50,069 unit of information A is a 138 00:04:50,070 --> 00:04:52,559 system that has two states, zero and one, 139 00:04:52,560 --> 00:04:54,359 and it's kind of an abstract mathematical 140 00:04:54,360 --> 00:04:56,459 concept. But nowadays, if you think of 141 00:04:56,460 --> 00:04:58,559 bits, you probably think of a 142 00:04:58,560 --> 00:05:00,659 way a voltage in a wire in a circuit. 143 00:05:00,660 --> 00:05:02,849 So you could say, OK, 144 00:05:02,850 --> 00:05:04,949 stage zero, if you bid, can be defined by 145 00:05:04,950 --> 00:05:07,139 having a zero voltage as zero zero 146 00:05:07,140 --> 00:05:09,339 volt in comparison to like some ground 147 00:05:09,340 --> 00:05:11,399 state. And bit one would have, 148 00:05:11,400 --> 00:05:12,540 for example, Five-fold. 149 00:05:13,550 --> 00:05:14,550 All right. 150 00:05:15,770 --> 00:05:17,899 To do useful things with bits, we need 151 00:05:17,900 --> 00:05:19,849 many of them, so we put them in a 152 00:05:19,850 --> 00:05:21,170 so-called register. 153 00:05:22,190 --> 00:05:24,499 He had a bizarre, um, enumerated 154 00:05:24,500 --> 00:05:26,119 from top to bottom. 155 00:05:26,120 --> 00:05:28,579 So there are bits in this case. 156 00:05:28,580 --> 00:05:30,799 And if you want to write 157 00:05:30,800 --> 00:05:32,479 the state of the whole wheat register, 158 00:05:32,480 --> 00:05:34,369 you can just kind of multiply them. 159 00:05:34,370 --> 00:05:36,200 The individual is together and write them 160 00:05:38,000 --> 00:05:38,929 like this. 161 00:05:38,930 --> 00:05:41,329 And you would see that for an 162 00:05:41,330 --> 00:05:43,399 input. Bitzer You would have two to 163 00:05:43,400 --> 00:05:44,779 the N possible states. 164 00:05:44,780 --> 00:05:46,009 So it's pretty efficient way to store 165 00:05:46,010 --> 00:05:47,939 information. Definitely better than using 166 00:05:47,940 --> 00:05:48,940 Roman literals. 167 00:05:52,120 --> 00:05:53,829 All right, now, you, of course, want to 168 00:05:53,830 --> 00:05:55,840 do something with your boots, so 169 00:05:56,950 --> 00:05:59,529 you need gates and a gate is also 170 00:05:59,530 --> 00:06:01,299 a abstract concept, which 171 00:06:02,350 --> 00:06:04,749 is a function in that sense, which has 172 00:06:04,750 --> 00:06:06,819 one or several inputs 173 00:06:06,820 --> 00:06:08,919 and one or several outputs on the 174 00:06:08,920 --> 00:06:10,099 other side. 175 00:06:10,100 --> 00:06:11,439 Now, for classical computing, there are 176 00:06:11,440 --> 00:06:13,599 some circuits which 177 00:06:13,600 --> 00:06:15,729 are so-called universal gates, 178 00:06:15,730 --> 00:06:17,199 for example, the nannygate, which you see 179 00:06:17,200 --> 00:06:19,989 here, which is two inputs and 180 00:06:19,990 --> 00:06:22,089 returns, one for all the possible 181 00:06:22,090 --> 00:06:24,339 input states, except if the two input 182 00:06:24,340 --> 00:06:26,789 Bitzer one and this 183 00:06:26,790 --> 00:06:28,209 Gateson universal in the sense that you 184 00:06:28,210 --> 00:06:30,729 can construct any other logic 185 00:06:30,730 --> 00:06:32,859 from this by using combinations 186 00:06:32,860 --> 00:06:34,470 and concatenation of the single gate. 187 00:06:38,650 --> 00:06:40,209 All right, so that's basically all we 188 00:06:40,210 --> 00:06:42,789 need to get started solving 189 00:06:42,790 --> 00:06:45,479 problems of our computer. 190 00:06:45,480 --> 00:06:47,559 Now let's have a look at a fictional 191 00:06:47,560 --> 00:06:48,579 problem. 192 00:06:48,580 --> 00:06:50,170 Let's say, for example, that our, 193 00:06:51,190 --> 00:06:53,769 um, beloved leader wants to 194 00:06:53,770 --> 00:06:55,209 launch a missile. 195 00:06:55,210 --> 00:06:57,489 And of course, 196 00:06:57,490 --> 00:06:58,659 not everybody should have the right to 197 00:06:58,660 --> 00:07:00,819 launch missiles. So we need the password. 198 00:07:00,820 --> 00:07:03,309 And if you want to check 199 00:07:03,310 --> 00:07:05,499 now, if the password is correct, 200 00:07:05,500 --> 00:07:08,059 we need somehow function that 201 00:07:08,060 --> 00:07:10,119 the justice for us and this function 202 00:07:10,120 --> 00:07:11,229 which is shown here and which are called 203 00:07:11,230 --> 00:07:12,669 F.J. 204 00:07:12,670 --> 00:07:15,039 looks like this. So it has an input 205 00:07:15,040 --> 00:07:17,499 on the left and one single output 206 00:07:17,500 --> 00:07:19,269 and it returns a zero for all of the 207 00:07:19,270 --> 00:07:20,739 inputs except for the one that 208 00:07:20,740 --> 00:07:22,269 corresponds to the correct passwords. 209 00:07:24,540 --> 00:07:26,669 All right, so this means that we have 210 00:07:26,670 --> 00:07:28,949 to to the end possibilities here, and 211 00:07:28,950 --> 00:07:30,299 if you make the input register large 212 00:07:30,300 --> 00:07:32,579 enough, we can have a pretty secure 213 00:07:32,580 --> 00:07:33,580 system. 214 00:07:35,940 --> 00:07:38,039 All right, now imagine that we want 215 00:07:38,040 --> 00:07:40,119 to to correct first 216 00:07:40,120 --> 00:07:42,239 password and now 217 00:07:42,240 --> 00:07:43,199 there are several possibilities. 218 00:07:43,200 --> 00:07:44,609 We can, of course, try to reverse 219 00:07:44,610 --> 00:07:46,619 engineer the system and find out to try 220 00:07:46,620 --> 00:07:48,899 to find out how the function works. 221 00:07:48,900 --> 00:07:50,999 But now for this dog, let's assume that 222 00:07:51,000 --> 00:07:53,459 the function is secure and that we cannot 223 00:07:53,460 --> 00:07:55,079 do any kind of reverse engineering. 224 00:07:55,080 --> 00:07:57,599 So then the only way to obtain a password 225 00:07:57,600 --> 00:07:59,399 is to actually brute force it, which 226 00:07:59,400 --> 00:08:01,049 means that we have to try all the 227 00:08:01,050 --> 00:08:02,609 possible values of the password and see 228 00:08:02,610 --> 00:08:04,619 if the function returns one. 229 00:08:04,620 --> 00:08:06,749 And if you want a computer 230 00:08:06,750 --> 00:08:08,549 to do this, we have to teach him to do 231 00:08:08,550 --> 00:08:10,259 it. And for this, we use a so-called 232 00:08:10,260 --> 00:08:12,809 algorithm, which is basically a 233 00:08:12,810 --> 00:08:14,549 baking recipe that the computer can 234 00:08:14,550 --> 00:08:16,679 follow to obtain a solution. 235 00:08:16,680 --> 00:08:18,839 All right. So our algorithms, pretty 236 00:08:18,840 --> 00:08:21,029 simple, would start by setting the 237 00:08:21,030 --> 00:08:23,339 register straight to the first volume, 238 00:08:23,340 --> 00:08:25,169 which is zero zero zero zero, etc. 239 00:08:26,190 --> 00:08:27,690 Then calculate F.I. 240 00:08:28,920 --> 00:08:31,139 and check if we return, if the function 241 00:08:31,140 --> 00:08:32,129 returns of one. 242 00:08:32,130 --> 00:08:34,229 And actually for a lot of 243 00:08:34,230 --> 00:08:36,538 cases, when people choose a zero zero 244 00:08:36,539 --> 00:08:38,668 zero zero as their password, it does so. 245 00:08:38,669 --> 00:08:40,469 In this case, our algorithm is terminated 246 00:08:40,470 --> 00:08:42,569 and we can directly return the 247 00:08:42,570 --> 00:08:43,859 password that we found. 248 00:08:43,860 --> 00:08:45,539 And for some other cases, for people that 249 00:08:45,540 --> 00:08:47,069 use a more secure password, we actually 250 00:08:47,070 --> 00:08:48,719 have to to check the other values as 251 00:08:48,720 --> 00:08:50,789 well. So we go as incremental value 252 00:08:50,790 --> 00:08:52,889 by one and we go back to step two and 253 00:08:52,890 --> 00:08:54,570 repeat this until we find a password. 254 00:08:55,830 --> 00:08:58,679 All right. So now you can ask yourself 255 00:08:58,680 --> 00:09:00,319 how efficient this is actually. 256 00:09:00,320 --> 00:09:02,219 Well, it's pretty easy to answer because 257 00:09:02,220 --> 00:09:04,559 if you have an input state, 258 00:09:04,560 --> 00:09:06,539 we will probably have to check the 259 00:09:06,540 --> 00:09:08,909 password at most to function at most 260 00:09:08,910 --> 00:09:09,929 end times. 261 00:09:09,930 --> 00:09:11,399 So in the best case, we would check it 262 00:09:11,400 --> 00:09:13,079 only once and then the average case we 263 00:09:13,080 --> 00:09:14,279 would check it probably another two 264 00:09:14,280 --> 00:09:15,359 times. 265 00:09:15,360 --> 00:09:17,459 So if you plot now the 266 00:09:17,460 --> 00:09:19,859 number of evaluations of the function F 267 00:09:19,860 --> 00:09:21,929 versus the size of the search space 268 00:09:21,930 --> 00:09:24,149 and would get a linear relationship, 269 00:09:24,150 --> 00:09:26,309 so which means that if we doubled 270 00:09:26,310 --> 00:09:28,229 the size of the search space, we also 271 00:09:28,230 --> 00:09:30,509 have to double the number of function 272 00:09:30,510 --> 00:09:31,679 evaluations. 273 00:09:31,680 --> 00:09:33,779 And this is the so called time complexity 274 00:09:33,780 --> 00:09:34,829 of this algorithm. 275 00:09:34,830 --> 00:09:37,859 And the idea behind us is that, um, 276 00:09:37,860 --> 00:09:40,079 the the cost that you have 277 00:09:40,080 --> 00:09:42,389 in cracking this password is in 278 00:09:42,390 --> 00:09:43,859 calling this function F, which can be 279 00:09:43,860 --> 00:09:44,909 really complicated. 280 00:09:44,910 --> 00:09:46,649 So you really want to measure how often 281 00:09:46,650 --> 00:09:48,299 you have to call this function to obtain 282 00:09:48,300 --> 00:09:49,300 the answer you need. 283 00:09:50,370 --> 00:09:51,370 All right. So. 284 00:09:52,960 --> 00:09:54,639 Please keep this in mind for because we 285 00:09:54,640 --> 00:09:56,229 will see the graph again later in the 286 00:09:56,230 --> 00:09:57,230 talk. 287 00:09:58,550 --> 00:10:00,619 OK, so that's all 288 00:10:00,620 --> 00:10:01,729 I wanted to tell you about classical 289 00:10:01,730 --> 00:10:04,009 computing, and now we are going to 290 00:10:04,010 --> 00:10:05,660 have a look at quantum computing. 291 00:10:08,300 --> 00:10:09,709 So, again, I want to go through the 292 00:10:09,710 --> 00:10:12,679 basics of quantum computing first. 293 00:10:12,680 --> 00:10:14,749 So, um, like 294 00:10:14,750 --> 00:10:16,909 for a classical system in a quantum 295 00:10:16,910 --> 00:10:19,009 system, we have also a fundamental unit 296 00:10:19,010 --> 00:10:20,749 of information, which is called the 297 00:10:20,750 --> 00:10:22,219 quantum bit cubed. 298 00:10:22,220 --> 00:10:24,589 And as the name suggests, this 299 00:10:24,590 --> 00:10:28,009 is a quantum mechanical two-level system. 300 00:10:28,010 --> 00:10:29,299 Basically, it is also an abstract 301 00:10:29,300 --> 00:10:31,369 concept. But I find it really helps if 302 00:10:31,370 --> 00:10:33,919 you imagine it as a as an atom with 303 00:10:33,920 --> 00:10:36,379 two states, which I call zero 304 00:10:36,380 --> 00:10:37,519 and the second third one. 305 00:10:38,570 --> 00:10:40,370 And this atom 306 00:10:41,480 --> 00:10:42,949 has, of course, a quantum mechanical 307 00:10:42,950 --> 00:10:45,199 state, which I indicate by putting 308 00:10:45,200 --> 00:10:47,359 this strange vector around the one. 309 00:10:47,360 --> 00:10:49,249 So whenever you see this disembodied 310 00:10:49,250 --> 00:10:50,989 underdog, you know that I'm talking about 311 00:10:50,990 --> 00:10:51,990 a quantum state. 312 00:10:53,500 --> 00:10:55,779 All right, so now one of the 313 00:10:55,780 --> 00:10:58,089 strange things about quantum systems 314 00:10:58,090 --> 00:11:00,279 is that they can not only be 315 00:11:00,280 --> 00:11:02,379 understood zero or one, but kind 316 00:11:02,380 --> 00:11:04,149 of in both states at the same time. 317 00:11:04,150 --> 00:11:06,339 So in this case, we 318 00:11:06,340 --> 00:11:08,169 wouldn't be able to, like, ride the wave 319 00:11:08,170 --> 00:11:10,329 function of the the state as a as 320 00:11:10,330 --> 00:11:12,409 a simple zero 321 00:11:12,410 --> 00:11:14,139 or one. But we would have to write as a 322 00:11:14,140 --> 00:11:16,299 more complex function here, 323 00:11:16,300 --> 00:11:18,549 which I could say and which concert, 324 00:11:18,550 --> 00:11:20,619 which is kind of a sum of the 325 00:11:20,620 --> 00:11:22,959 state zero with some amplitude, 326 00:11:22,960 --> 00:11:25,089 a plus the 327 00:11:25,090 --> 00:11:26,919 state one, which is an amplitude one 328 00:11:26,920 --> 00:11:28,269 minus eight. 329 00:11:28,270 --> 00:11:30,759 And in addition, some phase, which 330 00:11:30,760 --> 00:11:32,829 is a complex number here in which kind of 331 00:11:32,830 --> 00:11:34,539 makes that we can only add the two states 332 00:11:34,540 --> 00:11:35,919 together, but we kind of can also 333 00:11:35,920 --> 00:11:37,599 subtract them or do more complex things 334 00:11:37,600 --> 00:11:38,949 with them. 335 00:11:38,950 --> 00:11:40,629 And now this is probably pretty hard to 336 00:11:40,630 --> 00:11:42,099 get your head around it. So at least for 337 00:11:42,100 --> 00:11:44,289 me and I find it always helps 338 00:11:44,290 --> 00:11:46,359 to imagine this 339 00:11:46,360 --> 00:11:48,849 as a particle wave. 340 00:11:48,850 --> 00:11:50,979 So, for example, here would have 341 00:11:50,980 --> 00:11:53,199 a particle or wave that comes 342 00:11:53,200 --> 00:11:54,969 from the left and this wave would 343 00:11:54,970 --> 00:11:57,089 encounter like 344 00:11:57,090 --> 00:11:59,029 a barrier of two holes in it. 345 00:11:59,030 --> 00:12:00,729 Then you would have like circular waves 346 00:12:00,730 --> 00:12:02,409 going out from these two holes. 347 00:12:02,410 --> 00:12:04,479 And here in this picture, this is 348 00:12:04,480 --> 00:12:06,369 also like a single system, but it kind of 349 00:12:06,370 --> 00:12:08,709 shows like strange interference 350 00:12:08,710 --> 00:12:10,899 effects. And the two waves 351 00:12:10,900 --> 00:12:11,589 here overlap. 352 00:12:11,590 --> 00:12:13,059 And depending on the phase of between 353 00:12:13,060 --> 00:12:14,409 them, they can kind of like 354 00:12:15,550 --> 00:12:18,369 substract or like add 355 00:12:18,370 --> 00:12:20,049 themselves up. So I think this is a 356 00:12:20,050 --> 00:12:21,279 pretty good way to think about it. 357 00:12:21,280 --> 00:12:22,499 Cubit state as well. 358 00:12:25,370 --> 00:12:27,469 All right, the second 359 00:12:27,470 --> 00:12:29,899 difference to classical bits as 360 00:12:29,900 --> 00:12:32,149 concerning some measurement of quantum 361 00:12:32,150 --> 00:12:34,849 bits, so, um, 362 00:12:34,850 --> 00:12:36,889 for classical computers, I didn't even 363 00:12:36,890 --> 00:12:39,079 mention how we measure them because 364 00:12:39,080 --> 00:12:39,769 it's really trivial. 365 00:12:39,770 --> 00:12:41,929 We can just measure the voltage of 366 00:12:41,930 --> 00:12:44,239 our wire and then we get the information 367 00:12:44,240 --> 00:12:45,709 of ground zero on the one side. 368 00:12:45,710 --> 00:12:47,269 But for quantum system, it's a bit more 369 00:12:47,270 --> 00:12:49,789 complicated because in fact, 370 00:12:49,790 --> 00:12:51,469 whenever we measure the system, we also 371 00:12:51,470 --> 00:12:52,879 change the state. 372 00:12:52,880 --> 00:12:54,409 So let's assume that we have a 373 00:12:54,410 --> 00:12:56,239 measurement apparatus here which is shown 374 00:12:56,240 --> 00:12:57,589 on the right, and we want to measure the 375 00:12:57,590 --> 00:12:59,509 state of the quantum system in the state 376 00:12:59,510 --> 00:13:00,710 011 or one. 377 00:13:02,030 --> 00:13:03,949 So what we do is that we switch on some 378 00:13:03,950 --> 00:13:05,719 kind of interaction between the two 379 00:13:05,720 --> 00:13:07,909 systems. And what will now happen 380 00:13:07,910 --> 00:13:10,129 is that we will have a so-called collapse 381 00:13:10,130 --> 00:13:12,469 of the wave function where 382 00:13:12,470 --> 00:13:14,599 the Cuban said we get projected 383 00:13:14,600 --> 00:13:16,219 either in the state zero with a 384 00:13:16,220 --> 00:13:18,349 probability that's proportional to 385 00:13:18,350 --> 00:13:20,059 the amplitude of the state zero and the 386 00:13:20,060 --> 00:13:22,189 wavefunction or into the 387 00:13:22,190 --> 00:13:24,769 state one with the complementary 388 00:13:24,770 --> 00:13:25,789 amplitude. 389 00:13:25,790 --> 00:13:28,219 So this is something that is kind of 390 00:13:28,220 --> 00:13:30,529 unique for quantum systems and 391 00:13:30,530 --> 00:13:32,719 which we will encounter later again when 392 00:13:32,720 --> 00:13:34,879 we try to to measure the results 393 00:13:34,880 --> 00:13:36,139 that we obtain using our quantum 394 00:13:36,140 --> 00:13:37,140 processor. 395 00:13:40,110 --> 00:13:42,509 All right, um, like for Classico, but 396 00:13:42,510 --> 00:13:44,909 we also need many cubits to 397 00:13:44,910 --> 00:13:47,069 perform useful operations, so we 398 00:13:47,070 --> 00:13:49,169 have a quantum register and that's 399 00:13:49,170 --> 00:13:51,389 before we order the individual cubits 400 00:13:51,390 --> 00:13:53,459 from top to bottom and right away 401 00:13:53,460 --> 00:13:54,869 functions like this. 402 00:13:54,870 --> 00:13:57,089 And now if you want to like, um, 403 00:13:57,090 --> 00:13:59,219 right. The function of the whole Cubitt 404 00:13:59,220 --> 00:14:01,259 register, we just multiply the individual 405 00:14:01,260 --> 00:14:02,879 functions together like this. 406 00:14:02,880 --> 00:14:04,949 And so since there are a lot of 407 00:14:04,950 --> 00:14:06,659 vertices there and it's kind of tedious 408 00:14:06,660 --> 00:14:09,269 to read, I will often like just ah 409 00:14:09,270 --> 00:14:11,159 put all the terms in conference and write 410 00:14:11,160 --> 00:14:13,259 it like this. So when you see a state 411 00:14:13,260 --> 00:14:14,969 like this, you know that actually you 412 00:14:14,970 --> 00:14:17,279 have a multi cubitt state where each 413 00:14:17,280 --> 00:14:18,599 individual cubit is in the state 414 00:14:18,600 --> 00:14:20,130 indicated by its letter. 415 00:14:22,090 --> 00:14:23,090 All right, 416 00:14:24,160 --> 00:14:26,379 a key resource in quantum 417 00:14:26,380 --> 00:14:28,539 computing is the 418 00:14:28,540 --> 00:14:31,149 fact that we can have so-called multi 419 00:14:31,150 --> 00:14:32,949 superposition states. 420 00:14:32,950 --> 00:14:35,499 So let's remember, again, 421 00:14:35,500 --> 00:14:37,479 the two slides ago we talked about the 422 00:14:37,480 --> 00:14:39,669 fact that a cubit can be in the state 091 423 00:14:39,670 --> 00:14:40,599 at the same time. 424 00:14:40,600 --> 00:14:42,339 So now let's imagine that we prefer a 425 00:14:42,340 --> 00:14:44,529 Cubitt registered state where 426 00:14:44,530 --> 00:14:46,599 each individual cubit is in an 427 00:14:46,600 --> 00:14:48,459 equal superposition between zero and one 428 00:14:48,460 --> 00:14:50,739 state. So this is show you like here 429 00:14:50,740 --> 00:14:52,569 and you can see the factor of zero point 430 00:14:52,570 --> 00:14:54,639 five of one or two 431 00:14:54,640 --> 00:14:56,649 is just the normalization constant. 432 00:14:56,650 --> 00:14:58,869 So now if you want to obtain the wave 433 00:14:58,870 --> 00:15:00,489 function of the whole register, I can 434 00:15:00,490 --> 00:15:02,599 again just multiply the individual 435 00:15:02,600 --> 00:15:04,839 functions. But now the difference is that 436 00:15:04,840 --> 00:15:07,209 I have kind of like a sum of 437 00:15:07,210 --> 00:15:08,109 products here. 438 00:15:08,110 --> 00:15:09,739 So if I want to, like, obtain the very 439 00:15:09,740 --> 00:15:12,249 function, I have to multiply out these 440 00:15:12,250 --> 00:15:13,539 four entities. And if I do that. 441 00:15:15,300 --> 00:15:17,399 So to the end times, if I do 442 00:15:17,400 --> 00:15:19,619 that, I will get a quantum 443 00:15:19,620 --> 00:15:21,179 state which looks like this, so you can 444 00:15:21,180 --> 00:15:23,249 see that we are fuda states, zero zero 445 00:15:23,250 --> 00:15:24,269 zero zero, etc. 446 00:15:24,270 --> 00:15:26,069 Then you have to state zero zero zero 447 00:15:26,070 --> 00:15:28,229 zero one up to the state one one 448 00:15:28,230 --> 00:15:30,479 one one one. So basically, it means 449 00:15:30,480 --> 00:15:32,549 that in this register 450 00:15:32,550 --> 00:15:34,469 we have all the possible states of the 451 00:15:34,470 --> 00:15:36,599 cubits at the same time. 452 00:15:36,600 --> 00:15:38,879 And now this is pretty, pretty exciting 453 00:15:38,880 --> 00:15:40,319 and it is kind of a key resource that we 454 00:15:40,320 --> 00:15:42,539 can make use of when making when 455 00:15:42,540 --> 00:15:43,859 using quantum computers to solve 456 00:15:43,860 --> 00:15:44,860 problems. 457 00:15:48,470 --> 00:15:50,929 All right, and you often are, 458 00:15:50,930 --> 00:15:53,239 since the terms are a bit 459 00:15:53,240 --> 00:15:54,409 tedious to readers. Well, I will just 460 00:15:54,410 --> 00:15:56,839 admit to normalization 461 00:15:56,840 --> 00:15:57,839 when I write a state. 462 00:15:57,840 --> 00:15:59,690 So you will often see them like this. 463 00:16:01,750 --> 00:16:03,849 OK, last thing we 464 00:16:03,850 --> 00:16:05,919 need to learn about for quantum computing 465 00:16:05,920 --> 00:16:08,019 is Quantum Gate, 466 00:16:08,020 --> 00:16:10,329 like classical gates, quantum gates 467 00:16:10,330 --> 00:16:12,399 take a number of input cubits and produce 468 00:16:12,400 --> 00:16:13,539 a number of output. 469 00:16:13,540 --> 00:16:14,739 Hubert's. 470 00:16:14,740 --> 00:16:16,779 The difference is, though, that now, 471 00:16:16,780 --> 00:16:18,429 since we have a quantum mechanical 472 00:16:18,430 --> 00:16:20,589 system, the Quantum Gate also needs to 473 00:16:20,590 --> 00:16:22,629 perform a quantum mechanical operation. 474 00:16:22,630 --> 00:16:25,599 And this means that some things which are 475 00:16:25,600 --> 00:16:27,279 possible in classical computing are no 476 00:16:27,280 --> 00:16:28,239 longer possible. 477 00:16:28,240 --> 00:16:30,339 And quantum computing, most notably 478 00:16:30,340 --> 00:16:32,589 copying qubits, for example. 479 00:16:32,590 --> 00:16:34,719 But still, like for classical 480 00:16:34,720 --> 00:16:36,879 computers to also exist, the concept of 481 00:16:36,880 --> 00:16:39,189 a universal gait, which 482 00:16:39,190 --> 00:16:41,349 means that we can find a set of keys that 483 00:16:41,350 --> 00:16:43,539 will allow us to to 484 00:16:43,540 --> 00:16:45,549 realize any classical gate operation with 485 00:16:45,550 --> 00:16:46,550 a quantum computer. 486 00:16:50,350 --> 00:16:52,419 OK, now, if you 487 00:16:52,420 --> 00:16:54,969 combine what we have learned about 488 00:16:54,970 --> 00:16:56,649 multi keyboard super positions and 489 00:16:56,650 --> 00:16:59,169 Quantum Gate, we can 490 00:16:59,170 --> 00:17:00,370 see that if we apply 491 00:17:01,450 --> 00:17:03,219 our quantum gate to an input state, which 492 00:17:03,220 --> 00:17:04,809 is a superposition of all the possible 493 00:17:04,810 --> 00:17:07,209 inputs, then we'll get an output state 494 00:17:07,210 --> 00:17:09,699 which contains a product 495 00:17:09,700 --> 00:17:12,338 of the input state multiplied by 496 00:17:12,339 --> 00:17:13,989 the value of the function that we want to 497 00:17:13,990 --> 00:17:16,118 calculate for all these inputs state at 498 00:17:16,119 --> 00:17:18,279 once. So this is kind of magical 499 00:17:18,280 --> 00:17:19,959 because it means that we have evaluated 500 00:17:19,960 --> 00:17:21,909 this quantum function only once, but we 501 00:17:21,910 --> 00:17:23,529 have calculated its value for all the 502 00:17:23,530 --> 00:17:25,479 possible input values. 503 00:17:25,480 --> 00:17:27,459 So when people tell you that quantum 504 00:17:27,460 --> 00:17:28,869 computers harness the power of the 505 00:17:28,870 --> 00:17:30,429 multiverse, then this is what they 506 00:17:30,430 --> 00:17:31,929 usually mean. So so-called quantum 507 00:17:31,930 --> 00:17:32,930 parallelism. 508 00:17:37,870 --> 00:17:39,969 All right, the last thing that we 509 00:17:39,970 --> 00:17:42,039 need to learn about is quantum 510 00:17:42,040 --> 00:17:44,319 entanglement, and this is a concept 511 00:17:44,320 --> 00:17:46,509 which can we understand like this so 512 00:17:46,510 --> 00:17:48,789 soon that we have to cubitt state 513 00:17:48,790 --> 00:17:50,649 where the first cubit is instead zero. 514 00:17:50,650 --> 00:17:52,569 The second Cubitt is in the state one. 515 00:17:52,570 --> 00:17:54,399 And then we take these two cubits and we 516 00:17:54,400 --> 00:17:55,899 apply some function to them, which we 517 00:17:55,900 --> 00:17:57,379 call F here again. 518 00:17:57,380 --> 00:17:59,559 Now, the effect of this function is 519 00:17:59,560 --> 00:18:01,479 to allow for this input state, which we 520 00:18:01,480 --> 00:18:03,549 have to return, and an output 521 00:18:03,550 --> 00:18:04,669 state which looks like this. 522 00:18:04,670 --> 00:18:06,969 So it's a superposition between the 523 00:18:06,970 --> 00:18:09,249 zero one state and the one zero 524 00:18:09,250 --> 00:18:10,569 state. 525 00:18:10,570 --> 00:18:12,759 And now the state looks 526 00:18:12,760 --> 00:18:13,869 pretty innocuous. 527 00:18:13,870 --> 00:18:15,939 But actually it's kind 528 00:18:15,940 --> 00:18:18,549 of weird because as you might notice, 529 00:18:18,550 --> 00:18:20,829 we can no longer write the individual 530 00:18:20,830 --> 00:18:22,959 qubits separately so we can 531 00:18:22,960 --> 00:18:25,119 no longer, like, factor out 532 00:18:25,120 --> 00:18:26,889 to the first Kuban in a second cubed. 533 00:18:26,890 --> 00:18:29,049 So somehow both of them 534 00:18:29,050 --> 00:18:31,269 are kind of kind of intertwined. 535 00:18:31,270 --> 00:18:33,159 And if you would imagine that we can 536 00:18:33,160 --> 00:18:34,509 would make a measurement or the first 537 00:18:34,510 --> 00:18:36,729 Cubitt, as we said before, the 538 00:18:36,730 --> 00:18:38,769 probability of obtaining either the value 539 00:18:38,770 --> 00:18:40,959 zero or one for the first Kupets is 50 540 00:18:40,960 --> 00:18:43,779 percent. So assuming we obtain a one 541 00:18:43,780 --> 00:18:45,939 and what is then 542 00:18:45,940 --> 00:18:48,159 then really bizarre is that we seem 543 00:18:48,160 --> 00:18:50,109 also to have changed the state of the 544 00:18:50,110 --> 00:18:51,549 second Cubitt because now it's in the 545 00:18:51,550 --> 00:18:52,569 state zero. 546 00:18:52,570 --> 00:18:53,570 So. 547 00:18:54,200 --> 00:18:57,469 This is kind of kind of really weird and 548 00:18:57,470 --> 00:18:59,909 means that somehow there is a likely, 549 00:18:59,910 --> 00:19:01,609 like ghostly interactions between the two 550 00:19:01,610 --> 00:19:03,409 cuboid, which makes that when I measure 551 00:19:03,410 --> 00:19:05,239 the first of it or do something with it, 552 00:19:05,240 --> 00:19:06,739 it also affects the state of the second 553 00:19:06,740 --> 00:19:07,740 cubitt. 554 00:19:08,390 --> 00:19:10,549 And now if you think that's weird, then 555 00:19:10,550 --> 00:19:12,889 you're in good company, because 556 00:19:12,890 --> 00:19:14,869 Albert Einstein wrote a famous paper on 557 00:19:14,870 --> 00:19:16,640 this so-called 558 00:19:17,900 --> 00:19:20,749 EPR paradox where he argued 559 00:19:20,750 --> 00:19:22,879 that this must be a reason 560 00:19:22,880 --> 00:19:25,639 why quantum mechanics is incomplete and 561 00:19:25,640 --> 00:19:27,919 in fact, is actually it's 562 00:19:27,920 --> 00:19:29,209 completely valid behavior. 563 00:19:29,210 --> 00:19:31,369 And we can use this also to speed up 564 00:19:31,370 --> 00:19:33,169 computations when we use a quantum 565 00:19:33,170 --> 00:19:34,300 computer to solve problems. 566 00:19:37,190 --> 00:19:38,209 All right, so 567 00:19:39,650 --> 00:19:41,509 this was a lot of a lot of stuff to to 568 00:19:41,510 --> 00:19:44,449 digest, so just 569 00:19:44,450 --> 00:19:46,579 to a small let's do a small recap of what 570 00:19:46,580 --> 00:19:49,129 we learned. So we saw that Hubert's are 571 00:19:49,130 --> 00:19:51,319 quantum mechanical two-level systems, 572 00:19:51,320 --> 00:19:52,819 that it can be in a superposition between 573 00:19:52,820 --> 00:19:54,979 the state zero and one that a 574 00:19:54,980 --> 00:19:56,779 measurement of Cubitt state will either 575 00:19:56,780 --> 00:19:58,759 zero one and project a cube within the 576 00:19:58,760 --> 00:20:01,009 respective state, and the Cubans 577 00:20:01,010 --> 00:20:02,660 can become entangled with other qubits. 578 00:20:05,550 --> 00:20:07,769 All right, so 579 00:20:07,770 --> 00:20:10,229 back to business, we still have to 580 00:20:10,230 --> 00:20:12,309 find the password for 581 00:20:12,310 --> 00:20:14,329 for a missile launch system. 582 00:20:14,330 --> 00:20:15,330 Now, 583 00:20:17,580 --> 00:20:19,889 let's imagine that we have a 584 00:20:19,890 --> 00:20:21,869 blueprint of the function that calculates 585 00:20:21,870 --> 00:20:23,999 the passwords and we are able to 586 00:20:24,000 --> 00:20:25,500 implement the quantum version of it. 587 00:20:26,970 --> 00:20:29,129 If we can do that, then we can, like 588 00:20:29,130 --> 00:20:31,409 before produce a superposition 589 00:20:31,410 --> 00:20:33,989 of input states, calculate 590 00:20:33,990 --> 00:20:36,029 the function operator F.J. 591 00:20:36,030 --> 00:20:38,099 and then obtain the values 592 00:20:38,100 --> 00:20:40,139 of the password hashing function for all 593 00:20:40,140 --> 00:20:41,639 possible input states. 594 00:20:41,640 --> 00:20:44,099 And amazingly, of course, 595 00:20:44,100 --> 00:20:45,869 they will also be the value of the 596 00:20:45,870 --> 00:20:47,219 correct password in there. 597 00:20:47,220 --> 00:20:49,619 So now we have kind of almost 598 00:20:49,620 --> 00:20:51,299 solve our problem because we have 599 00:20:51,300 --> 00:20:53,489 calculated all the possible outcomes 600 00:20:53,490 --> 00:20:54,569 of the consultation function. 601 00:20:54,570 --> 00:20:56,459 We have identified the state which 602 00:20:56,460 --> 00:20:58,109 contains the right password. 603 00:20:58,110 --> 00:20:59,759 Now, the only thing that remains to be 604 00:20:59,760 --> 00:21:02,609 done is to get the state out of there. 605 00:21:02,610 --> 00:21:04,739 And now what we could 606 00:21:04,740 --> 00:21:06,839 do for this is just to try 607 00:21:06,840 --> 00:21:08,399 to measure the values of the cubitt after 608 00:21:08,400 --> 00:21:09,400 applying the operator. 609 00:21:10,650 --> 00:21:13,229 But since I told you that 610 00:21:13,230 --> 00:21:15,449 a measurement were kind of changed 611 00:21:15,450 --> 00:21:18,029 to Cuban state and projected into 612 00:21:18,030 --> 00:21:20,189 one of the an arbitrary state of 613 00:21:20,190 --> 00:21:22,349 the to superposition state, that we have 614 00:21:22,350 --> 00:21:23,669 the probability that we'll actually 615 00:21:23,670 --> 00:21:25,919 measure the correct state here is only 616 00:21:25,920 --> 00:21:27,719 one over. And where is the probability 617 00:21:27,720 --> 00:21:29,339 that we will get some other state, which 618 00:21:29,340 --> 00:21:31,409 is not the solution to our problem is 619 00:21:31,410 --> 00:21:32,589 one minus one over one. 620 00:21:32,590 --> 00:21:34,769 So that's pretty bad news, 621 00:21:34,770 --> 00:21:35,809 actually. 622 00:21:35,810 --> 00:21:37,979 And this is kind of the dilemma 623 00:21:37,980 --> 00:21:39,329 of quantum mechanics or quantum 624 00:21:39,330 --> 00:21:41,279 computing, because you are able to 625 00:21:41,280 --> 00:21:43,379 evaluate a function for all possible 626 00:21:43,380 --> 00:21:45,149 input states as ones, but you are not 627 00:21:45,150 --> 00:21:47,219 able to extract that information 628 00:21:47,220 --> 00:21:48,239 from the quantum state. 629 00:21:49,880 --> 00:21:51,729 So what can we do? 630 00:21:51,730 --> 00:21:54,169 Um, actually, there's a solution for this 631 00:21:54,170 --> 00:21:56,359 and the so-called Grover algorithm, which 632 00:21:56,360 --> 00:21:58,459 was invented or discovered by Grover 633 00:21:58,460 --> 00:22:00,649 in 1996, and it gives us 634 00:22:00,650 --> 00:22:02,959 a way to extract the information 635 00:22:02,960 --> 00:22:04,489 from the quantum system. 636 00:22:04,490 --> 00:22:06,589 And the algorithm does that by applying a 637 00:22:06,590 --> 00:22:08,809 pretty complicated sequence 638 00:22:08,810 --> 00:22:10,699 of gates to the output state that we 639 00:22:10,700 --> 00:22:12,529 obtain after applying it to the function 640 00:22:12,530 --> 00:22:14,909 and then repeating this square root 641 00:22:14,910 --> 00:22:16,519 of end times. 642 00:22:16,520 --> 00:22:18,019 So after doing this, we can then. 643 00:22:19,040 --> 00:22:21,219 A performance measurement and 644 00:22:21,220 --> 00:22:23,349 what the algorithm has done is to 645 00:22:23,350 --> 00:22:25,119 transfer all the amplitude to the state, 646 00:22:25,120 --> 00:22:26,709 which corresponds to the solution of our 647 00:22:26,710 --> 00:22:28,359 search problem. So when we now make a 648 00:22:28,360 --> 00:22:29,889 measurement, we will have a probability 649 00:22:29,890 --> 00:22:31,869 of almost 100 percent to obtain the 650 00:22:31,870 --> 00:22:33,489 correct answer, which, of course, is 651 00:22:33,490 --> 00:22:34,490 great. 652 00:22:36,380 --> 00:22:38,479 All right, now, 653 00:22:38,480 --> 00:22:40,549 if you have a look at the efficiency 654 00:22:40,550 --> 00:22:42,919 of this, we can visualize 655 00:22:42,920 --> 00:22:45,049 this for the case, for example, 656 00:22:45,050 --> 00:22:46,279 of 10 cubits. 657 00:22:46,280 --> 00:22:48,469 So for 10 cubits, the search space of 658 00:22:48,470 --> 00:22:50,659 our passwords is one thousand 659 00:22:50,660 --> 00:22:52,759 twenty four. And we 660 00:22:52,760 --> 00:22:54,949 can now plot the probability of 661 00:22:54,950 --> 00:22:56,989 obtaining the correct solution after 662 00:22:56,990 --> 00:22:59,239 applying the Grover operator a number 663 00:22:59,240 --> 00:23:01,129 of times. And as you can see in the 664 00:23:01,130 --> 00:23:03,409 beginning, the probability is quite 665 00:23:03,410 --> 00:23:05,239 low. So it's less than zero point one 666 00:23:05,240 --> 00:23:07,309 percent. But as we keep applying this 667 00:23:07,310 --> 00:23:09,679 Grover operation operator, the 668 00:23:09,680 --> 00:23:11,989 probability goes up, up, up 669 00:23:11,990 --> 00:23:14,899 until it reaches almost 100 percent at 670 00:23:14,900 --> 00:23:16,729 after 25 iterations. 671 00:23:16,730 --> 00:23:18,949 And that's pretty great because it means 672 00:23:18,950 --> 00:23:20,299 that we have to evaluate a search 673 00:23:20,300 --> 00:23:21,979 function not one thousand twenty four 674 00:23:21,980 --> 00:23:24,019 times, but only 24 times to obtain the 675 00:23:24,020 --> 00:23:25,129 correct solution. 676 00:23:25,130 --> 00:23:27,229 So if we go 677 00:23:27,230 --> 00:23:29,339 back to the graph from before we apply to 678 00:23:29,340 --> 00:23:30,829 the time complexity of our classical 679 00:23:30,830 --> 00:23:33,499 algorithm, we can now compare that to the 680 00:23:33,500 --> 00:23:36,169 quantum algorithm and we can see that 681 00:23:36,170 --> 00:23:37,639 the quantum algorithm is actually much 682 00:23:37,640 --> 00:23:39,169 faster for this kind of problem because 683 00:23:39,170 --> 00:23:41,629 it only needs a square root of N 684 00:23:41,630 --> 00:23:43,609 attempts or evaluations of the function 685 00:23:43,610 --> 00:23:46,399 to to find the correct solution. 686 00:23:46,400 --> 00:23:48,589 And so when people tell you that 687 00:23:48,590 --> 00:23:49,969 quantum computers are faster than 688 00:23:49,970 --> 00:23:51,739 classical computers, what they actually 689 00:23:51,740 --> 00:23:54,169 mean is that for 690 00:23:54,170 --> 00:23:56,239 some problems, quantum 691 00:23:56,240 --> 00:23:58,249 computer exist algorithms on quantum 692 00:23:58,250 --> 00:24:00,379 computers that have a smaller 693 00:24:00,380 --> 00:24:02,029 time complexity than the best known 694 00:24:02,030 --> 00:24:03,949 algorithms for classical computers. 695 00:24:03,950 --> 00:24:05,479 And the difference between the classical 696 00:24:05,480 --> 00:24:07,009 algorithm and quantum. 697 00:24:07,010 --> 00:24:08,839 Isn't this the so-called quantum 698 00:24:08,840 --> 00:24:09,840 speed-up? 699 00:24:10,810 --> 00:24:12,459 In this case, it would be so it would be 700 00:24:12,460 --> 00:24:13,899 a quadratics beat up, as you can see. 701 00:24:16,260 --> 00:24:18,419 And now I use this example 702 00:24:18,420 --> 00:24:20,519 because it's pretty easy to 703 00:24:20,520 --> 00:24:22,619 explain, and it's also something where 704 00:24:22,620 --> 00:24:24,629 we can prove that there is no better 705 00:24:24,630 --> 00:24:25,769 classical algorithm. 706 00:24:25,770 --> 00:24:27,629 But most of you probably know quantum 707 00:24:27,630 --> 00:24:30,209 computing more from code breaking 708 00:24:30,210 --> 00:24:32,309 or from the so-called short algorithm, 709 00:24:32,310 --> 00:24:34,439 because, um, most 710 00:24:34,440 --> 00:24:36,719 classical as a metric 711 00:24:36,720 --> 00:24:38,969 krypto cryptologic methods 712 00:24:38,970 --> 00:24:41,129 are based today on 713 00:24:41,130 --> 00:24:43,529 the fact that it's pretty easy to obtain 714 00:24:43,530 --> 00:24:46,139 a number by multiplying two large numbers 715 00:24:46,140 --> 00:24:47,849 together. But it's pretty difficult, on 716 00:24:47,850 --> 00:24:49,829 the other hand, to obtain the individual 717 00:24:49,830 --> 00:24:52,139 prime factors of that number from 718 00:24:52,140 --> 00:24:53,249 the multiplied one. 719 00:24:53,250 --> 00:24:55,949 So the best classical algorithm 720 00:24:55,950 --> 00:24:58,229 for this problem is kind of exponential 721 00:24:58,230 --> 00:24:59,999 and looks like this, whereas for a 722 00:25:00,000 --> 00:25:02,039 quantum computer we have an algorithm so 723 00:25:02,040 --> 00:25:03,449 called your algorithm, which can which 724 00:25:03,450 --> 00:25:05,639 can solve the problem and logarithmic 725 00:25:05,640 --> 00:25:08,159 and to restore the power of tree time. 726 00:25:08,160 --> 00:25:09,839 And this is actually a pretty big 727 00:25:09,840 --> 00:25:12,539 difference because it can make, um, 728 00:25:12,540 --> 00:25:14,039 it can change the runtime of such an 729 00:25:14,040 --> 00:25:16,079 algorithm from millions of years to a few 730 00:25:16,080 --> 00:25:17,019 hours. 731 00:25:17,020 --> 00:25:19,439 So but contrary 732 00:25:19,440 --> 00:25:20,819 to the to the search problem that I 733 00:25:20,820 --> 00:25:22,739 showed you before, there's actually no or 734 00:25:22,740 --> 00:25:24,299 to my knowledge, there's no proof that 735 00:25:24,300 --> 00:25:26,159 for a classical computer that doesn't 736 00:25:26,160 --> 00:25:27,419 exist, a better algorithm. 737 00:25:27,420 --> 00:25:29,129 So here we cannot really say that quantum 738 00:25:29,130 --> 00:25:30,449 computers will always be faster than 739 00:25:30,450 --> 00:25:32,129 classical computers because we really 740 00:25:32,130 --> 00:25:34,229 don't know if we can find a better, 741 00:25:34,230 --> 00:25:35,939 better algorithm for classical computer 742 00:25:35,940 --> 00:25:37,880 that could solve this problem faster. 743 00:25:41,400 --> 00:25:43,769 OK, so sorry 744 00:25:43,770 --> 00:25:45,299 if this was a bit theoretical, so I 745 00:25:45,300 --> 00:25:47,789 promise no more equations in this talk. 746 00:25:47,790 --> 00:25:50,009 And now I want to, um, to show 747 00:25:50,010 --> 00:25:51,599 you how you can actually build a quantum 748 00:25:51,600 --> 00:25:52,950 processor and 749 00:25:54,630 --> 00:25:56,879 went to actually many different answers 750 00:25:56,880 --> 00:25:58,349 to this question. 751 00:25:58,350 --> 00:26:00,449 And I talked before about 752 00:26:00,450 --> 00:26:02,669 qubits as kind of atoms. 753 00:26:02,670 --> 00:26:04,209 And that's a good analogy, because there 754 00:26:04,210 --> 00:26:06,209 are actually people or research groups 755 00:26:06,210 --> 00:26:08,459 that are using atoms that are trapped 756 00:26:08,460 --> 00:26:09,929 in an electromagnetic trap, which is 757 00:26:09,930 --> 00:26:12,179 shown here and used in as cubits. 758 00:26:12,180 --> 00:26:14,489 So these are two years from the 759 00:26:14,490 --> 00:26:15,689 research group in Innsbruck. 760 00:26:15,690 --> 00:26:18,329 And what they do is that they trip 761 00:26:18,330 --> 00:26:20,999 a number of ions in a so called Paul trap 762 00:26:21,000 --> 00:26:23,279 and they can put these ions 763 00:26:23,280 --> 00:26:25,409 inside there like string pearls 764 00:26:25,410 --> 00:26:27,509 on a string and then manipulate them 765 00:26:27,510 --> 00:26:28,679 using laser light. 766 00:26:28,680 --> 00:26:30,719 And since the atoms are also coupled to 767 00:26:30,720 --> 00:26:32,999 each other, use by the vibration mode 768 00:26:33,000 --> 00:26:34,439 of the whole system, you can perform 769 00:26:34,440 --> 00:26:36,749 quantum gates between individual ions. 770 00:26:36,750 --> 00:26:39,149 And so this is a pretty successful 771 00:26:39,150 --> 00:26:40,949 and pretty nice way to perform quantum 772 00:26:40,950 --> 00:26:43,069 computing and the larger 773 00:26:43,070 --> 00:26:45,239 system that they're able to do with this 774 00:26:45,240 --> 00:26:47,549 kind of approach and compose about 775 00:26:47,550 --> 00:26:49,559 50 to even 100 cubits. 776 00:26:51,340 --> 00:26:53,619 All right, so what I want to talk 777 00:26:53,620 --> 00:26:56,169 about today, though, are superconducting 778 00:26:56,170 --> 00:26:58,299 quantum processors, like the one I showed 779 00:26:58,300 --> 00:26:59,769 here, which is from the University of 780 00:26:59,770 --> 00:27:01,899 Santa Barbara, from the research group, 781 00:27:01,900 --> 00:27:03,489 which just announced a collaboration with 782 00:27:03,490 --> 00:27:06,729 Google to build quantum processors. 783 00:27:06,730 --> 00:27:09,099 So as I said, these, 784 00:27:09,100 --> 00:27:11,499 um, um, these quantum 785 00:27:11,500 --> 00:27:14,079 processors are realized using 786 00:27:14,080 --> 00:27:16,119 thin layers of superconductors on 787 00:27:16,120 --> 00:27:17,149 microchips. 788 00:27:17,150 --> 00:27:18,609 And for those of you who don't know what 789 00:27:18,610 --> 00:27:20,799 a superconductor is, it's basically a 790 00:27:20,800 --> 00:27:22,929 metal on metal that 791 00:27:22,930 --> 00:27:25,359 loses all of its electric resistance 792 00:27:25,360 --> 00:27:27,159 at a very low temperature and which at 793 00:27:27,160 --> 00:27:29,199 that temperature also exhibits quantum 794 00:27:29,200 --> 00:27:32,289 mechanical behavior and 795 00:27:32,290 --> 00:27:34,329 superconducting quantum bits are quite 796 00:27:34,330 --> 00:27:36,429 attractive because the reasoning is 797 00:27:36,430 --> 00:27:38,499 here that if you manage to build a 798 00:27:38,500 --> 00:27:40,659 few of them and you manage to make them 799 00:27:40,660 --> 00:27:41,979 really good, it would be really easy to 800 00:27:41,980 --> 00:27:44,049 scale the number of qubits to a very 801 00:27:44,050 --> 00:27:46,479 large, large amount because 802 00:27:46,480 --> 00:27:47,979 you can just fabricate them like we 803 00:27:47,980 --> 00:27:50,579 fabricate most of the microchips today. 804 00:27:50,580 --> 00:27:53,019 So and 805 00:27:53,020 --> 00:27:53,979 of course, there are many more 806 00:27:53,980 --> 00:27:56,199 technologies that allow us to build 807 00:27:56,200 --> 00:27:57,609 quantum processors, for example, to a 808 00:27:57,610 --> 00:27:59,799 nuclear magnetic resonance, spins their 809 00:27:59,800 --> 00:28:02,199 quantum dots in both Einstein condensates 810 00:28:02,200 --> 00:28:04,479 can be used to realize quantum bits. 811 00:28:04,480 --> 00:28:06,849 So I just want you to 812 00:28:06,850 --> 00:28:09,129 take away that superconducting quantum 813 00:28:09,130 --> 00:28:10,119 processors and I interrupt. 814 00:28:10,120 --> 00:28:11,559 Quantum processors are not the only 815 00:28:11,560 --> 00:28:13,419 approaches to quantum computing. 816 00:28:15,130 --> 00:28:17,319 All right, now I want to briefly 817 00:28:17,320 --> 00:28:19,899 talk about a very simple 818 00:28:19,900 --> 00:28:22,359 answer to Qubit quantum processor 819 00:28:22,360 --> 00:28:25,239 I built during my PhD thesis 820 00:28:25,240 --> 00:28:27,069 and this process of using so-called 821 00:28:27,070 --> 00:28:29,169 transman cubits, which are an 822 00:28:29,170 --> 00:28:31,209 invention of a research group and year 823 00:28:31,210 --> 00:28:32,679 from 2004. 824 00:28:32,680 --> 00:28:36,069 And what I show you here is an electron 825 00:28:36,070 --> 00:28:39,339 microscope image of the whole Kubitschek. 826 00:28:39,340 --> 00:28:41,169 And this is actually a nice system to 827 00:28:41,170 --> 00:28:43,179 discuss the basic blocks of quantum 828 00:28:43,180 --> 00:28:44,769 processors because it contains all the 829 00:28:44,770 --> 00:28:46,179 elements that you would also need for a 830 00:28:46,180 --> 00:28:48,459 larger scale quantum processor. 831 00:28:48,460 --> 00:28:50,619 So you can see that the chip is about 20 832 00:28:50,620 --> 00:28:53,469 millimeters in size and 833 00:28:53,470 --> 00:28:55,119 it's realized in a material called 834 00:28:55,120 --> 00:28:56,769 niobium, which is a metal that also 835 00:28:56,770 --> 00:28:58,899 becomes superconducting about at about 836 00:28:58,900 --> 00:29:01,329 minus two hundred sixty four degrees. 837 00:29:01,330 --> 00:29:03,639 And on a chip you see a lot of Coplin 838 00:29:03,640 --> 00:29:05,709 a waveguide which we can 839 00:29:05,710 --> 00:29:07,779 use to send microwaves to the qubits 840 00:29:07,780 --> 00:29:09,429 and some other signal lines which we can 841 00:29:09,430 --> 00:29:11,229 use to perform other operations with 842 00:29:11,230 --> 00:29:13,179 them. And so if you ask yourself where 843 00:29:13,180 --> 00:29:15,949 the cupboards are actually on the chip, 844 00:29:15,950 --> 00:29:17,829 the answer is here in the center. 845 00:29:17,830 --> 00:29:19,479 So you can see two of them. 846 00:29:19,480 --> 00:29:21,739 And in the zoomin you can actually see 847 00:29:21,740 --> 00:29:23,799 ah, well, you can probably can't 848 00:29:23,800 --> 00:29:25,689 see very well here because the contrast 849 00:29:25,690 --> 00:29:27,819 is not very high, but it's 850 00:29:27,820 --> 00:29:29,829 a large capacitor that is realized in 851 00:29:29,830 --> 00:29:32,799 aluminum, which also is a superconductor 852 00:29:32,800 --> 00:29:34,959 and which are which 853 00:29:34,960 --> 00:29:37,029 basically acts 854 00:29:37,030 --> 00:29:39,339 as a support for a cubit and a cubit 855 00:29:39,340 --> 00:29:41,409 itself is then are 856 00:29:41,410 --> 00:29:43,029 on the top of this capacitor and 857 00:29:43,030 --> 00:29:45,069 so-called Justesen Junction, which 858 00:29:45,070 --> 00:29:47,489 basically is just an 859 00:29:47,490 --> 00:29:49,479 assistant element that consists of two 860 00:29:49,480 --> 00:29:51,879 thin layers of superconductor separated 861 00:29:51,880 --> 00:29:53,379 by an insulating barrier. 862 00:29:53,380 --> 00:29:55,479 And it's what we call a 863 00:29:55,480 --> 00:29:57,639 bed contact because under 864 00:29:57,640 --> 00:29:59,019 normal conditions, there couldn't be any 865 00:29:59,020 --> 00:30:00,769 current flowing to the system. 866 00:30:00,770 --> 00:30:02,409 But when a system becomes 867 00:30:02,410 --> 00:30:04,449 superconducting, we have a 868 00:30:04,450 --> 00:30:06,489 superconducting wave function and the 869 00:30:06,490 --> 00:30:08,439 wavefunction can somehow tunnel through 870 00:30:08,440 --> 00:30:09,999 the barrier and it can be supercurrent 871 00:30:10,000 --> 00:30:11,889 flowing between the two sides of the 872 00:30:11,890 --> 00:30:13,119 structure. 873 00:30:13,120 --> 00:30:15,669 And now the 874 00:30:15,670 --> 00:30:17,919 the cubit itself 875 00:30:17,920 --> 00:30:19,759 is realized as different states of the 876 00:30:19,760 --> 00:30:21,579 system here, which we call also an 877 00:30:21,580 --> 00:30:23,649 artificial atom, because it kind of 878 00:30:23,650 --> 00:30:25,869 has the ground state and a few excited 879 00:30:25,870 --> 00:30:28,119 states that we can can 880 00:30:28,120 --> 00:30:30,369 control using microwaves, actually. 881 00:30:30,370 --> 00:30:31,689 So the difference is here that the 882 00:30:31,690 --> 00:30:33,939 frequency of the is 883 00:30:33,940 --> 00:30:36,159 compared to an atom much lower and in the 884 00:30:36,160 --> 00:30:37,359 range of a few gigahertz. 885 00:30:38,840 --> 00:30:40,909 All right, um, yes, the first 886 00:30:40,910 --> 00:30:43,189 offense and as I said, we can 887 00:30:43,190 --> 00:30:45,619 sorry for the cheesy animation, we can 888 00:30:46,730 --> 00:30:48,979 manipulate the cubits using microwave 889 00:30:48,980 --> 00:30:51,349 signals, which we sent to them through 890 00:30:51,350 --> 00:30:53,509 this, uh, snakelike structure, 891 00:30:53,510 --> 00:30:55,399 which, in fact is a of waveguide 892 00:30:55,400 --> 00:30:56,539 resonator. 893 00:30:56,540 --> 00:30:58,699 And you can think of this probably as a 894 00:30:58,700 --> 00:31:00,919 as a guitar string, which one we 895 00:31:00,920 --> 00:31:03,479 like excited would vibrate at its own 896 00:31:03,480 --> 00:31:04,459 frequency. 897 00:31:04,460 --> 00:31:06,050 And the 898 00:31:07,130 --> 00:31:08,509 function of this resonator here in the 899 00:31:08,510 --> 00:31:11,239 cubit chip is actually twofold. 900 00:31:11,240 --> 00:31:13,129 On one hand, it isolates the Cuban from 901 00:31:13,130 --> 00:31:14,779 the environment and protects it from the 902 00:31:14,780 --> 00:31:16,279 noise that is, for example, coming from 903 00:31:16,280 --> 00:31:17,509 the input line. 904 00:31:17,510 --> 00:31:18,949 And on the other hand, it also allows us 905 00:31:18,950 --> 00:31:20,899 to measure the state of the cubit after 906 00:31:20,900 --> 00:31:22,549 we have performed some operations on it. 907 00:31:23,950 --> 00:31:26,829 All right, now, I talked about 908 00:31:26,830 --> 00:31:29,019 Tacuba decades earlier, so 909 00:31:29,020 --> 00:31:30,549 in order to do that, we need some kind of 910 00:31:30,550 --> 00:31:32,139 interaction between the two cubits. 911 00:31:32,140 --> 00:31:34,149 And what we do for that is that we put a 912 00:31:34,150 --> 00:31:36,459 very small capacitor between them. 913 00:31:36,460 --> 00:31:38,589 Which kind of couples then are 914 00:31:38,590 --> 00:31:39,639 always when they are at the same 915 00:31:39,640 --> 00:31:42,099 frequency. So that means by changing 916 00:31:42,100 --> 00:31:43,779 the frequencies of the qubits, which we 917 00:31:43,780 --> 00:31:45,009 can do by changing the current. 918 00:31:45,010 --> 00:31:47,649 And is these lines here, we can 919 00:31:47,650 --> 00:31:49,869 bring them in and out of resonance and 920 00:31:49,870 --> 00:31:51,939 realize to cubitt 921 00:31:51,940 --> 00:31:53,049 good operations with them. 922 00:31:55,830 --> 00:31:58,139 All right, so that's basically it, um, 923 00:31:58,140 --> 00:32:00,299 now to operate a chip, we 924 00:32:00,300 --> 00:32:02,519 first glued to a special microwave 925 00:32:02,520 --> 00:32:04,709 PCB, which also contains Koechlin 926 00:32:04,710 --> 00:32:06,299 and safeguards that we can hook up to our 927 00:32:06,300 --> 00:32:07,379 equipment. 928 00:32:07,380 --> 00:32:09,629 Then we take this whole thing and 929 00:32:09,630 --> 00:32:11,729 mounted in a sample holder, whose main 930 00:32:11,730 --> 00:32:13,559 function is to also protect the cubits 931 00:32:13,560 --> 00:32:15,659 from any stray electromagnetic fields 932 00:32:15,660 --> 00:32:18,179 and also to anchor it to the dilution 933 00:32:18,180 --> 00:32:20,429 that the delusion cries 934 00:32:20,430 --> 00:32:22,649 that is basically shown here. 935 00:32:22,650 --> 00:32:24,719 So the sample holder gets attached to 936 00:32:24,720 --> 00:32:26,039 the bottom of that. 937 00:32:26,040 --> 00:32:28,199 And what this thing is, is basically 938 00:32:28,200 --> 00:32:30,419 just a very fancy refrigerator 939 00:32:30,420 --> 00:32:32,699 which cools down to Cuba 940 00:32:32,700 --> 00:32:34,979 to about 20 Malicki, which is 941 00:32:34,980 --> 00:32:37,199 at minus 274 a 942 00:32:37,200 --> 00:32:39,479 degree Celsius, just slightly above 943 00:32:39,480 --> 00:32:40,769 absolute zero. 944 00:32:40,770 --> 00:32:43,049 And we have to do this because 945 00:32:43,050 --> 00:32:45,299 on one hand, the superconductors 946 00:32:45,300 --> 00:32:46,889 wouldn't be superconducting if we were at 947 00:32:46,890 --> 00:32:47,939 room temperature. 948 00:32:47,940 --> 00:32:49,619 And on the other hand, if you would 949 00:32:49,620 --> 00:32:51,299 operate our cubits at room temperature, 950 00:32:51,300 --> 00:32:53,579 we would find that the 951 00:32:53,580 --> 00:32:55,709 noise and thermal exploitations of all 952 00:32:55,710 --> 00:32:57,749 the materials that are around cubits 953 00:32:57,750 --> 00:32:59,219 would destroy the quantum state of them 954 00:32:59,220 --> 00:33:00,839 really fast. So we really, really need to 955 00:33:00,840 --> 00:33:02,369 call them down to a very low temperature 956 00:33:02,370 --> 00:33:04,409 to be able to to operate them for a 957 00:33:04,410 --> 00:33:05,519 sufficiently long time. 958 00:33:07,750 --> 00:33:09,789 All right, um, so that's the short 959 00:33:09,790 --> 00:33:11,379 version of how to build a quantum 960 00:33:11,380 --> 00:33:14,019 processor. The long version takes about 961 00:33:14,020 --> 00:33:16,209 two years and lots of, uh, microwave 962 00:33:16,210 --> 00:33:18,699 calibrations and, uh, 963 00:33:18,700 --> 00:33:20,979 chases for a superconducting leaks and so 964 00:33:20,980 --> 00:33:21,909 and stuff. 965 00:33:21,910 --> 00:33:24,159 So what I want to show you here, just 966 00:33:24,160 --> 00:33:26,469 the results of one of the experiments 967 00:33:26,470 --> 00:33:28,359 we ran with this Tsukuba processor. 968 00:33:28,360 --> 00:33:30,699 And what we basically did here is to, um, 969 00:33:30,700 --> 00:33:32,199 to run the global search algorithm, which 970 00:33:32,200 --> 00:33:34,299 I showed to you earlier, for 971 00:33:34,300 --> 00:33:35,529 the case of two cubits. 972 00:33:35,530 --> 00:33:38,049 So it's really not a practical problem 973 00:33:38,050 --> 00:33:39,939 that you want to solve, but it kind of 974 00:33:39,940 --> 00:33:41,769 demonstrates all the abilities that you 975 00:33:41,770 --> 00:33:43,509 need to build a large scale quantum 976 00:33:43,510 --> 00:33:45,549 computer because it contains single 977 00:33:45,550 --> 00:33:47,709 Kubicki. It's here, for example, for 978 00:33:47,710 --> 00:33:49,209 which we use to create input 979 00:33:49,210 --> 00:33:51,939 superposition state, and it also contains 980 00:33:51,940 --> 00:33:53,709 a multi cubed gates. 981 00:33:53,710 --> 00:33:55,929 For example, here we have the so-called 982 00:33:55,930 --> 00:33:57,909 ISO upgrade and to single Cuban 983 00:33:57,910 --> 00:34:00,439 rotations, which together implement 984 00:34:00,440 --> 00:34:01,869 the function F.J. 985 00:34:01,870 --> 00:34:03,129 that we talked about earlier. 986 00:34:03,130 --> 00:34:06,189 And in this case, uh, the function of J 987 00:34:06,190 --> 00:34:08,799 marks the state 008 as the password 988 00:34:08,800 --> 00:34:10,539 or as the solution of our problem. 989 00:34:11,870 --> 00:34:13,089 All right. 990 00:34:13,090 --> 00:34:15,459 Now for the two Cubitt case to the grower 991 00:34:15,460 --> 00:34:17,468 operator has to be applied only once to 992 00:34:17,469 --> 00:34:18,749 the state to obtain a solution. 993 00:34:18,750 --> 00:34:21,279 So these two gate operations there 994 00:34:21,280 --> 00:34:23,499 do this and afterwards we can 995 00:34:23,500 --> 00:34:25,839 just measure the Cuban state 996 00:34:25,840 --> 00:34:27,698 and see if the, uh, the algorithm has 997 00:34:27,699 --> 00:34:29,229 worked, so to say. 998 00:34:29,230 --> 00:34:31,509 Now you can see the sequence of this 999 00:34:31,510 --> 00:34:32,888 gate operation here. 1000 00:34:32,889 --> 00:34:34,509 Um, what you see there is actually the 1001 00:34:34,510 --> 00:34:37,119 time on the X axis, on the Y axis, 1002 00:34:37,120 --> 00:34:39,339 the amplitudes of the microwave signals 1003 00:34:39,340 --> 00:34:41,319 that we show that we are sent to the 1004 00:34:41,320 --> 00:34:43,329 cubits which we show in green, as well as 1005 00:34:43,330 --> 00:34:45,669 the frequency changes 1006 00:34:45,670 --> 00:34:47,408 of the cubits, which is shown red. 1007 00:34:47,409 --> 00:34:49,029 So you can see here that in the beginning 1008 00:34:49,030 --> 00:34:50,468 we have the two microwave pulses that to 1009 00:34:50,469 --> 00:34:51,759 create a superposition. 1010 00:34:51,760 --> 00:34:53,198 Then we have like an interaction between 1011 00:34:53,199 --> 00:34:54,759 the two qubits where we perform all to 1012 00:34:54,760 --> 00:34:55,658 give it good. 1013 00:34:55,659 --> 00:34:57,669 Then we separate them again, perform some 1014 00:34:57,670 --> 00:34:59,859 more face manipulations, then 1015 00:34:59,860 --> 00:35:01,479 we bring them in resonance again for 1016 00:35:01,480 --> 00:35:03,549 Grover Operator And finally we change the 1017 00:35:03,550 --> 00:35:06,609 frequency and we measure out the state. 1018 00:35:06,610 --> 00:35:07,799 All right. 1019 00:35:07,800 --> 00:35:10,359 So now we want to see how successful 1020 00:35:10,360 --> 00:35:12,069 we are actually at doing this. 1021 00:35:12,070 --> 00:35:14,259 We can run this great sequence, 1022 00:35:14,260 --> 00:35:16,719 which takes about 200 nanoseconds 1023 00:35:16,720 --> 00:35:18,789 and ever do that a lot of times, and 1024 00:35:18,790 --> 00:35:20,559 then just average the results to obtain 1025 00:35:20,560 --> 00:35:21,969 some good statistics. 1026 00:35:21,970 --> 00:35:24,129 And we have done this for the case of 1027 00:35:24,130 --> 00:35:26,109 this function of zero zero. 1028 00:35:26,110 --> 00:35:28,029 And what we see here is the success 1029 00:35:28,030 --> 00:35:29,169 probabilities are to see or the 1030 00:35:29,170 --> 00:35:31,419 probability to obtain different output 1031 00:35:31,420 --> 00:35:33,689 states as a function of the the, 1032 00:35:33,690 --> 00:35:35,079 uh, the search function that we are 1033 00:35:35,080 --> 00:35:37,059 looking for. And you can see here that 1034 00:35:37,060 --> 00:35:38,589 for this case of the functions of zero 1035 00:35:38,590 --> 00:35:40,659 zero, the success probability is about 1036 00:35:40,660 --> 00:35:43,299 sixty seven percent, which is 1037 00:35:43,300 --> 00:35:44,319 less than 100 percent. 1038 00:35:44,320 --> 00:35:45,309 What would you expect? 1039 00:35:45,310 --> 00:35:47,589 And I will explain to you why 1040 00:35:47,590 --> 00:35:48,609 later. 1041 00:35:48,610 --> 00:35:50,829 So to be 1042 00:35:50,830 --> 00:35:53,439 more scientific, we have to repeat that 1043 00:35:53,440 --> 00:35:55,659 not only for this case of the function 1044 00:35:55,660 --> 00:35:57,249 of zero zero, but also for the other 1045 00:35:57,250 --> 00:35:58,839 possible search functions. 1046 00:35:58,840 --> 00:36:00,219 So we do that and we every time we 1047 00:36:00,220 --> 00:36:01,989 calculate to success probability 1048 00:36:01,990 --> 00:36:03,369 afterwards and we see that for all the 1049 00:36:03,370 --> 00:36:05,739 four cases, we are above 52 1050 00:36:05,740 --> 00:36:07,899 percent or 50 percent. 1051 00:36:07,900 --> 00:36:10,419 Sorry. And this is pretty nice because 1052 00:36:10,420 --> 00:36:12,609 50 percent is the so-called classical 1053 00:36:12,610 --> 00:36:14,689 benchmark against which we can compare 1054 00:36:14,690 --> 00:36:16,719 or quantum processor because of you would 1055 00:36:16,720 --> 00:36:19,449 think of an algorithm, a classical one 1056 00:36:19,450 --> 00:36:21,909 that gives you a solution to your 1057 00:36:21,910 --> 00:36:23,289 two bit search problem. 1058 00:36:23,290 --> 00:36:24,879 Then you could think of an algorithm that 1059 00:36:24,880 --> 00:36:27,069 like emulates this function once, 1060 00:36:27,070 --> 00:36:29,469 which has a probability of 25 percent 1061 00:36:29,470 --> 00:36:30,729 of yielding a right answer. 1062 00:36:30,730 --> 00:36:32,359 And if it doesn't find the right answer, 1063 00:36:32,360 --> 00:36:34,989 just takes a lucky guess and 1064 00:36:34,990 --> 00:36:36,639 returns some of the other remaining three 1065 00:36:36,640 --> 00:36:38,419 states. And so this is what I call here, 1066 00:36:38,420 --> 00:36:40,629 that I'm feeling lucky bonus because the 1067 00:36:40,630 --> 00:36:42,129 success probability of this classical 1068 00:36:42,130 --> 00:36:44,019 algorithm would then be 50 percent. 1069 00:36:44,020 --> 00:36:45,489 And this is what we measure our quantum 1070 00:36:45,490 --> 00:36:46,689 processor against. 1071 00:36:46,690 --> 00:36:48,699 So we can see that for the simple case, 1072 00:36:48,700 --> 00:36:50,769 we can actually achieve quantum speed 1073 00:36:50,770 --> 00:36:53,230 up in an experimental quantum processor. 1074 00:36:55,550 --> 00:36:57,259 All right, so now you probably ask 1075 00:36:57,260 --> 00:36:59,449 yourself, why can't we just scale it up 1076 00:36:59,450 --> 00:37:01,819 and build a quantum processor with like 1077 00:37:01,820 --> 00:37:04,099 a thousand or ten thousand cubits 1078 00:37:04,100 --> 00:37:06,199 and actually have several problems which 1079 00:37:06,200 --> 00:37:07,789 keep you keep us from doing that? 1080 00:37:07,790 --> 00:37:10,129 And a few of them I listed here. 1081 00:37:10,130 --> 00:37:12,439 So the biggest one for the quantum 1082 00:37:12,440 --> 00:37:14,569 processor, which I realized I'm doing 1083 00:37:14,570 --> 00:37:17,569 my PhD, is so called decoherence 1084 00:37:17,570 --> 00:37:19,820 and decoherence means that 1085 00:37:21,050 --> 00:37:23,299 basically the cubitt is not only 1086 00:37:23,300 --> 00:37:25,459 manipulated and measured by our own 1087 00:37:25,460 --> 00:37:27,889 signals, but also by other quantum 1088 00:37:27,890 --> 00:37:29,509 systems which are in the vicinity of 1089 00:37:29,510 --> 00:37:31,699 decubitus, for example, on the chip 1090 00:37:31,700 --> 00:37:34,039 itself or in the solution. 1091 00:37:34,040 --> 00:37:36,199 Krogstad and these quantum sys 1092 00:37:36,200 --> 00:37:38,269 systems manipulate the Cubitt 1093 00:37:38,270 --> 00:37:39,739 state and also performance measurement on 1094 00:37:39,740 --> 00:37:41,959 it. And as we've learned before, 1095 00:37:41,960 --> 00:37:44,329 a measurement destroys the quantum state. 1096 00:37:44,330 --> 00:37:46,699 So what this does is basically it kills 1097 00:37:46,700 --> 00:37:48,859 the state of our cubitt in a pretty short 1098 00:37:48,860 --> 00:37:50,929 amount of time for the processor, which I 1099 00:37:50,930 --> 00:37:52,969 realized this was on the order of a few 1100 00:37:52,970 --> 00:37:53,970 hundred nanoseconds. 1101 00:37:56,110 --> 00:37:58,209 OK, then the second problem is to get 1102 00:37:58,210 --> 00:38:00,819 food allergy and acute cubitt coupling 1103 00:38:00,820 --> 00:38:02,199 for a case of Tsukuba, but it's actually 1104 00:38:02,200 --> 00:38:04,299 pretty easy to devise a coupling scheme. 1105 00:38:04,300 --> 00:38:06,609 We can perform gaits between each 1106 00:38:06,610 --> 00:38:07,989 between a different cubitt. 1107 00:38:07,990 --> 00:38:09,519 But now, as you would if you would scale 1108 00:38:09,520 --> 00:38:11,409 up the number of cubits, you would see 1109 00:38:11,410 --> 00:38:13,869 that it's pretty difficult to switch 1110 00:38:13,870 --> 00:38:15,729 on and off the interaction between two 1111 00:38:15,730 --> 00:38:18,339 individual cubits with high fidelity. 1112 00:38:18,340 --> 00:38:19,929 It's kind of like if you have like a 1113 00:38:19,930 --> 00:38:21,939 phone line of a certain frequency 1114 00:38:21,940 --> 00:38:23,859 bandwidth and you want to have, for 1115 00:38:23,860 --> 00:38:26,169 example, 100 or 1000 subscriber 1116 00:38:26,170 --> 00:38:28,629 on it. And if every subscriber 1117 00:38:28,630 --> 00:38:30,609 takes some amount of the bandwidth of the 1118 00:38:30,610 --> 00:38:32,829 line, at some point you will have no 1119 00:38:32,830 --> 00:38:34,449 bandwidth left for new subscribers. 1120 00:38:34,450 --> 00:38:36,039 And this is kind of what happens with the 1121 00:38:36,040 --> 00:38:37,179 Kubicki. Are we? 1122 00:38:37,180 --> 00:38:39,459 At a certain point, we have used 1123 00:38:39,460 --> 00:38:40,989 all our frequencies that are available 1124 00:38:40,990 --> 00:38:42,879 for the Cubans and we can no longer add 1125 00:38:42,880 --> 00:38:45,369 new Cubans without kind of interfering 1126 00:38:45,370 --> 00:38:46,370 with the other ones. 1127 00:38:47,440 --> 00:38:49,719 So the same goes also for measuring 1128 00:38:49,720 --> 00:38:52,209 the Cuban state, because in our case 1129 00:38:52,210 --> 00:38:54,399 we can perform a measurement of the cubit 1130 00:38:54,400 --> 00:38:56,499 and get the correct result 1131 00:38:56,500 --> 00:38:58,479 with the probability of about 90 percent. 1132 00:38:58,480 --> 00:39:00,219 But this means, of course, that in 10 1133 00:39:00,220 --> 00:39:02,229 percent of the cases, we cannot reliably 1134 00:39:02,230 --> 00:39:03,729 measure the state of the Cuban, which is 1135 00:39:03,730 --> 00:39:05,859 also for this kind of a system, a big 1136 00:39:05,860 --> 00:39:07,239 problem. 1137 00:39:07,240 --> 00:39:09,069 All right. And of course, there are some 1138 00:39:09,070 --> 00:39:11,139 other problems which are one talk in 1139 00:39:11,140 --> 00:39:12,549 detail here, which, for example, 1140 00:39:12,550 --> 00:39:13,959 concerned the result of the. 1141 00:39:13,960 --> 00:39:15,759 So for quantum computers, it's actually 1142 00:39:15,760 --> 00:39:18,219 pretty hard to to reset the state of your 1143 00:39:18,220 --> 00:39:19,359 machine to zero. 1144 00:39:19,360 --> 00:39:21,579 And this is also like a problem which 1145 00:39:21,580 --> 00:39:23,619 which has to be solved and which is not 1146 00:39:23,620 --> 00:39:24,960 fully solved in practice yet. 1147 00:39:26,400 --> 00:39:28,469 OK, um, so I want to 1148 00:39:28,470 --> 00:39:30,599 finish this talk with a small 1149 00:39:30,600 --> 00:39:32,669 outlook on our small summary 1150 00:39:32,670 --> 00:39:34,649 of the recent trends and superconducting 1151 00:39:34,650 --> 00:39:35,650 quantum computing. 1152 00:39:36,980 --> 00:39:39,529 And now to the several groups 1153 00:39:39,530 --> 00:39:42,049 in the world are trying to improve the 1154 00:39:42,050 --> 00:39:44,599 state of quantum processors and 1155 00:39:44,600 --> 00:39:45,979 help to really build a large scale 1156 00:39:45,980 --> 00:39:47,779 quantum quantum computer. 1157 00:39:47,780 --> 00:39:50,239 And here to show you an image of the 1158 00:39:50,240 --> 00:39:51,919 research group at the University of Santa 1159 00:39:51,920 --> 00:39:54,139 Barbara and John Martinus lab, 1160 00:39:54,140 --> 00:39:55,729 which recently partnered up with Google 1161 00:39:55,730 --> 00:39:57,559 to build quantum processors. 1162 00:39:57,560 --> 00:40:00,079 And what they are doing is basically 1163 00:40:00,080 --> 00:40:03,199 to devise new types of architectures 1164 00:40:03,200 --> 00:40:05,299 that also use transman qubits like the 1165 00:40:05,300 --> 00:40:07,729 ones I showed you before and resonators. 1166 00:40:07,730 --> 00:40:09,439 But that couple of these elements and 1167 00:40:09,440 --> 00:40:11,689 different ways that makes it easier to 1168 00:40:11,690 --> 00:40:13,189 produce a large number of qubits on the 1169 00:40:13,190 --> 00:40:15,329 same chip and actually get 1170 00:40:15,330 --> 00:40:17,479 get a real quantum computer 1171 00:40:17,480 --> 00:40:19,669 out of that. So these approaches are, for 1172 00:40:19,670 --> 00:40:21,469 example, code rescue or service code 1173 00:40:21,470 --> 00:40:22,470 architecture. 1174 00:40:24,780 --> 00:40:26,909 OK, then you can as well 1175 00:40:26,910 --> 00:40:29,189 think about improving 1176 00:40:29,190 --> 00:40:30,899 the Cubans, Cubans themselves and the 1177 00:40:30,900 --> 00:40:33,209 resonators and 1178 00:40:33,210 --> 00:40:35,819 some groups, for example, in Ireland and 1179 00:40:35,820 --> 00:40:37,139 there and in other places around the 1180 00:40:37,140 --> 00:40:39,299 world are doing this by replacing 1181 00:40:39,300 --> 00:40:40,410 these copely. Now, Waveguide got 1182 00:40:40,411 --> 00:40:42,899 resonators that you see here on the left 1183 00:40:42,900 --> 00:40:45,179 by actually treaty resonators, 1184 00:40:45,180 --> 00:40:46,979 which are boxes of aluminum, that that 1185 00:40:46,980 --> 00:40:49,259 can also resonator microwave frequencies. 1186 00:40:49,260 --> 00:40:50,969 So here, for example, we see a system 1187 00:40:50,970 --> 00:40:53,529 that has a 3D cavity resonator 1188 00:40:53,530 --> 00:40:55,829 with two cubits which are placed 1189 00:40:55,830 --> 00:40:57,719 on a SSAFA substrate. 1190 00:40:57,720 --> 00:41:00,419 And the advantage of this is that you can 1191 00:41:00,420 --> 00:41:03,209 control the environment and fabrication 1192 00:41:03,210 --> 00:41:04,889 parameters of the Cuba to a much better 1193 00:41:04,890 --> 00:41:07,739 degree than you would be able to do with 1194 00:41:07,740 --> 00:41:11,039 microchips. So decoherence times and 1195 00:41:11,040 --> 00:41:12,429 the lifetime of the resonator, the 1196 00:41:12,430 --> 00:41:13,889 quality factor of the resonator in this 1197 00:41:13,890 --> 00:41:15,989 case is much better than fodder for 1198 00:41:15,990 --> 00:41:17,910 these so-called like to decubitus. 1199 00:41:21,060 --> 00:41:23,549 All right, another thing which some 1200 00:41:23,550 --> 00:41:25,379 groups are working on is so-called 1201 00:41:25,380 --> 00:41:27,749 quantum error correction, because 1202 00:41:27,750 --> 00:41:29,849 you cannot only say, OK, 1203 00:41:29,850 --> 00:41:31,559 let's put better qubits, but you can also 1204 00:41:31,560 --> 00:41:33,719 say let's work with bad qubits, 1205 00:41:33,720 --> 00:41:35,789 but devise algorithms that can help us 1206 00:41:35,790 --> 00:41:37,739 to correct errors if they occur. 1207 00:41:37,740 --> 00:41:39,599 And amazingly, this is actually possible 1208 00:41:39,600 --> 00:41:41,309 even with quantum bits. 1209 00:41:41,310 --> 00:41:44,489 And there are several approaches where 1210 00:41:44,490 --> 00:41:46,769 groups devise quantum 1211 00:41:46,770 --> 00:41:48,869 processors that can to some 1212 00:41:48,870 --> 00:41:51,089 degree correct errors and like 1213 00:41:51,090 --> 00:41:52,529 keep the quantum state of the Cubans 1214 00:41:52,530 --> 00:41:54,569 alive for an indefinite amount of time, 1215 00:41:54,570 --> 00:41:56,579 although the results which are obtained 1216 00:41:56,580 --> 00:41:58,409 here, for example, in the Yale group are 1217 00:41:58,410 --> 00:41:59,410 not yet at this point. 1218 00:42:01,550 --> 00:42:02,550 All right, the last thing 1219 00:42:03,710 --> 00:42:06,739 is then to instead, um, 1220 00:42:06,740 --> 00:42:09,019 instead of using non as solid 1221 00:42:09,020 --> 00:42:10,999 state or superconducting cubits to use 1222 00:42:11,000 --> 00:42:13,069 different quantum systems to to store 1223 00:42:13,070 --> 00:42:14,929 or process quantum information. 1224 00:42:14,930 --> 00:42:16,489 So here, for example, I show you work 1225 00:42:16,490 --> 00:42:18,829 from the group in Suckley, 1226 00:42:18,830 --> 00:42:20,449 which is a hybrid quantum system that 1227 00:42:20,450 --> 00:42:22,939 uses a diamond with 1228 00:42:22,940 --> 00:42:25,579 so-called envy centers, which are 1229 00:42:25,580 --> 00:42:26,840 nitrogen vacancy 1230 00:42:28,010 --> 00:42:30,169 centers and Diamont, and which actually 1231 00:42:30,170 --> 00:42:32,449 are responsible for the color of this 1232 00:42:32,450 --> 00:42:34,819 diamond and which amazingly can 1233 00:42:34,820 --> 00:42:36,589 store quantum information. 1234 00:42:36,590 --> 00:42:38,449 So what you have to system is that we 1235 00:42:38,450 --> 00:42:40,579 have a cubitt. And, uh, when 1236 00:42:40,580 --> 00:42:42,049 you want to manipulate the state of 1237 00:42:42,050 --> 00:42:44,119 Tacuba to keep the state 1238 00:42:44,120 --> 00:42:46,189 on the chip, but if you want to store it, 1239 00:42:46,190 --> 00:42:48,319 you can transfer it to the to the 1240 00:42:48,320 --> 00:42:50,239 NBA center in the diamond and keep it 1241 00:42:50,240 --> 00:42:52,429 there for a long time without having an 1242 00:42:52,430 --> 00:42:53,989 interference or any decoherence in a 1243 00:42:53,990 --> 00:42:54,990 Cuban state. 1244 00:42:58,260 --> 00:42:59,339 All right, so 1245 00:43:01,620 --> 00:43:03,179 as you can see, there's a lot of research 1246 00:43:03,180 --> 00:43:05,669 going on in this domain and, 1247 00:43:05,670 --> 00:43:07,919 um, you could actually plot kind 1248 00:43:07,920 --> 00:43:10,019 of a Moore's Law for 1249 00:43:10,020 --> 00:43:12,239 quantum computers or superconducting 1250 00:43:12,240 --> 00:43:13,379 quantum computers. 1251 00:43:13,380 --> 00:43:15,119 And if you do that, you would see that 1252 00:43:15,120 --> 00:43:17,399 when we when the research started on this 1253 00:43:17,400 --> 00:43:20,009 subject in 1999, 1254 00:43:20,010 --> 00:43:21,839 decubitus that we had at the time had a 1255 00:43:21,840 --> 00:43:23,909 coherence time of less than one 1256 00:43:23,910 --> 00:43:24,999 nanoseconds. 1257 00:43:25,000 --> 00:43:27,149 So they were really, really primitive by 1258 00:43:27,150 --> 00:43:28,259 today's standards. 1259 00:43:28,260 --> 00:43:30,599 And, uh, and the reason in the 1260 00:43:30,600 --> 00:43:32,819 following years, in 2002 and 2004, 1261 00:43:32,820 --> 00:43:34,799 they were new types of cubits devised, 1262 00:43:34,800 --> 00:43:36,599 which had a much longer coherence time. 1263 00:43:36,600 --> 00:43:38,459 And actually, this trend of increasing 1264 00:43:38,460 --> 00:43:40,109 the concern with the Cubans seems to go 1265 00:43:40,110 --> 00:43:42,629 on at a similar or like a 1266 00:43:42,630 --> 00:43:44,699 pretty fast rate 1267 00:43:44,700 --> 00:43:45,449 until today. 1268 00:43:45,450 --> 00:43:47,549 So in 2013, we 1269 00:43:47,550 --> 00:43:49,049 have actually superconducting Hubert's 1270 00:43:49,050 --> 00:43:51,269 that have coherence times in the order of 1271 00:43:51,270 --> 00:43:53,369 a few hundred microseconds, 1272 00:43:53,370 --> 00:43:55,529 which is large enough to envision 1273 00:43:55,530 --> 00:43:57,599 to actually use these qubits for four 1274 00:43:57,600 --> 00:43:59,879 real quantum computing. 1275 00:43:59,880 --> 00:44:02,039 So the take away here 1276 00:44:02,040 --> 00:44:04,289 is probably that quantum computers 1277 00:44:04,290 --> 00:44:06,419 are coming, but there's still, 1278 00:44:06,420 --> 00:44:07,769 of course, many, many engineering 1279 00:44:07,770 --> 00:44:09,210 challenges that we have to overcome. 1280 00:44:10,540 --> 00:44:12,939 And maybe to end this talk in a 1281 00:44:12,940 --> 00:44:14,279 selected political way. 1282 00:44:14,280 --> 00:44:16,839 Uh, the bad news is that probably 1283 00:44:16,840 --> 00:44:19,719 the quantum computers will come 1284 00:44:19,720 --> 00:44:21,189 to the hands of all the wrong people, 1285 00:44:21,190 --> 00:44:23,049 because right now it's mostly the 1286 00:44:23,050 --> 00:44:24,879 research and quantum computing is mostly 1287 00:44:24,880 --> 00:44:26,409 funded by governments and big 1288 00:44:26,410 --> 00:44:28,959 corporations. So this technology, 1289 00:44:28,960 --> 00:44:30,129 when it will become available, will 1290 00:44:30,130 --> 00:44:32,319 definitely not be available in like 1291 00:44:32,320 --> 00:44:35,049 a democratic fashion to everybody. 1292 00:44:35,050 --> 00:44:36,050 So. 1293 00:44:36,560 --> 00:44:38,629 All right, that's basically all I wanted 1294 00:44:38,630 --> 00:44:40,789 to to say, I just wanted to point out 1295 00:44:40,790 --> 00:44:43,249 that if you're interested in 1296 00:44:43,250 --> 00:44:45,139 quantum computing and hybrid quantum 1297 00:44:45,140 --> 00:44:47,029 systems, there's a talk on it tomorrow. 1298 00:44:47,030 --> 00:44:48,409 Diamonds are quantum computers. 1299 00:44:48,410 --> 00:44:50,629 Best friend, which is at twelve forty 1300 00:44:50,630 --> 00:44:52,729 five in Hall six by 1301 00:44:52,730 --> 00:44:54,529 Nicholas. Well OK. 1302 00:44:54,530 --> 00:44:57,619 So with that I thank you and 1303 00:44:57,620 --> 00:44:58,620 question. 1304 00:45:09,230 --> 00:45:10,189 Thank you for your talk. 1305 00:45:10,190 --> 00:45:12,439 We now have 15 luxurious minutes 1306 00:45:12,440 --> 00:45:14,509 of Q&A, so please 1307 00:45:14,510 --> 00:45:16,459 line up at the mikes there, six mikes, 1308 00:45:16,460 --> 00:45:18,409 one, two, three, four, five and six in 1309 00:45:18,410 --> 00:45:19,439 the back. 1310 00:45:19,440 --> 00:45:21,529 And we also have the AC and 1311 00:45:21,530 --> 00:45:23,599 Twitter. As I said before, if 1312 00:45:23,600 --> 00:45:25,849 you're physically unable to move, as in 1313 00:45:25,850 --> 00:45:27,619 not just caffeine deprived, but actually 1314 00:45:27,620 --> 00:45:29,629 not able to stand up, then please raise 1315 00:45:29,630 --> 00:45:31,609 your hands. We have a back up mic for 1316 00:45:31,610 --> 00:45:32,610 you. 1317 00:45:33,050 --> 00:45:34,069 OK, make one. 1318 00:45:34,070 --> 00:45:35,309 Go ahead. 1319 00:45:35,310 --> 00:45:37,219 Hello. Thanks for the very interesting 1320 00:45:37,220 --> 00:45:39,859 talk. I've learned a lot 1321 00:45:39,860 --> 00:45:41,019 today, Mike. 1322 00:45:41,020 --> 00:45:42,499 No, sorry. 1323 00:45:42,500 --> 00:45:44,209 Well, first of all, thanks for the very 1324 00:45:44,210 --> 00:45:46,519 interesting talk. I've learned a lot. 1325 00:45:46,520 --> 00:45:48,409 And if I understand this correctly, 1326 00:45:48,410 --> 00:45:50,359 quantum computing is at the moment 1327 00:45:50,360 --> 00:45:52,459 limited, limited by the amount of 1328 00:45:52,460 --> 00:45:54,619 cubits you can have interact with 1329 00:45:54,620 --> 00:45:56,839 each other, plus the amount you can 1330 00:45:56,840 --> 00:45:58,609 keep to keep it stable. 1331 00:45:58,610 --> 00:46:01,579 Um, do you have any idea 1332 00:46:01,580 --> 00:46:03,859 at what amount of time and what amount 1333 00:46:03,860 --> 00:46:06,289 of Cubitt quantum computing 1334 00:46:06,290 --> 00:46:07,290 can 1335 00:46:08,480 --> 00:46:10,789 reach a level where it can actually 1336 00:46:10,790 --> 00:46:12,949 compete with normal computing 1337 00:46:12,950 --> 00:46:15,619 in, say, doing Aerotek 1338 00:46:15,620 --> 00:46:17,209 calculations, et cetera? 1339 00:46:17,210 --> 00:46:17,929 Mm hmm. 1340 00:46:17,930 --> 00:46:19,109 And it's a very good question. 1341 00:46:19,110 --> 00:46:21,199 And the answer to 1342 00:46:21,200 --> 00:46:22,639 that is a bit complicated. 1343 00:46:22,640 --> 00:46:24,529 But in fact, what you want to achieve 1344 00:46:24,530 --> 00:46:27,019 with quantum qubits is the so-called, 1345 00:46:27,020 --> 00:46:29,149 uh, error threshold, because as I 1346 00:46:29,150 --> 00:46:30,829 talked about, there is a positive 1347 00:46:30,830 --> 00:46:32,869 possibility to perform error correction 1348 00:46:32,870 --> 00:46:35,179 of Cubitt. So if you are below 1349 00:46:35,180 --> 00:46:36,889 a certain level of errors for each 1350 00:46:36,890 --> 00:46:38,349 individual operation that you perform in 1351 00:46:38,350 --> 00:46:40,099 a cupboard, you can basically correct 1352 00:46:40,100 --> 00:46:42,019 that away and have a system that works 1353 00:46:42,020 --> 00:46:44,469 perfectly under the right conditions. 1354 00:46:44,470 --> 00:46:47,029 So and for, um, 1355 00:46:47,030 --> 00:46:48,349 classical approaches, like the 1356 00:46:48,350 --> 00:46:50,689 traditional approaches to quantum 1357 00:46:50,690 --> 00:46:52,849 computing to zero threshold was pretty 1358 00:46:52,850 --> 00:46:55,369 low at the order of like a 1359 00:46:55,370 --> 00:46:57,049 few fractions of a percent. 1360 00:46:57,050 --> 00:46:58,639 But with new approaches like, for 1361 00:46:58,640 --> 00:47:00,769 example, the surface surface 1362 00:47:00,770 --> 00:47:02,959 coding approach to error thresholds 1363 00:47:02,960 --> 00:47:04,609 has actually moved up quite a bit to a 1364 00:47:04,610 --> 00:47:05,569 few percent. 1365 00:47:05,570 --> 00:47:07,279 So today it would actually be invisible 1366 00:47:07,280 --> 00:47:09,469 to 12 cubits that are good 1367 00:47:09,470 --> 00:47:11,089 enough to to build real large scale 1368 00:47:11,090 --> 00:47:11,989 quantum computers. 1369 00:47:11,990 --> 00:47:13,789 Although, as I pointed out, there are 1370 00:47:13,790 --> 00:47:15,199 still a lot of other challenges, 1371 00:47:15,200 --> 00:47:17,659 challenges which keep us from doing that. 1372 00:47:17,660 --> 00:47:19,029 Okay, so that's a question. 1373 00:47:19,030 --> 00:47:19,999 Yeah, it does. 1374 00:47:20,000 --> 00:47:20,839 Thanks. 1375 00:47:20,840 --> 00:47:22,519 Does the Internet have a question? 1376 00:47:24,020 --> 00:47:25,899 Yes, there are two questions. 1377 00:47:26,900 --> 00:47:28,729 The first question is, in your example, 1378 00:47:28,730 --> 00:47:30,049 we got the right answer with a 1379 00:47:30,050 --> 00:47:31,879 probability close to one by applying 1380 00:47:31,880 --> 00:47:32,899 Grovers algorithm. 1381 00:47:32,900 --> 00:47:35,389 Mm hmm. Is this true for other, 1382 00:47:35,390 --> 00:47:36,989 uh, quantum algorithms also? 1383 00:47:36,990 --> 00:47:38,989 Um, so there's a small probability of 1384 00:47:38,990 --> 00:47:39,990 getting wrong results 1385 00:47:41,120 --> 00:47:42,319 for most quantum algorithms. 1386 00:47:42,320 --> 00:47:44,539 Yes, this is the case because 1387 00:47:44,540 --> 00:47:46,309 most of them are so-called probabilistic 1388 00:47:46,310 --> 00:47:48,229 algorithms, which give you the right 1389 00:47:48,230 --> 00:47:49,939 answer to a problem with a certain 1390 00:47:49,940 --> 00:47:52,069 probability that is close to 100 percent, 1391 00:47:52,070 --> 00:47:54,289 but not necessarily 100 percent. 1392 00:47:54,290 --> 00:47:56,569 So in this case, it could be the case 1393 00:47:56,570 --> 00:47:59,479 that we get the wrong answer, in which 1394 00:47:59,480 --> 00:48:01,129 case we just have to to like repeat the 1395 00:48:01,130 --> 00:48:03,199 process and check again 1396 00:48:03,200 --> 00:48:05,329 a couple of times. So, yeah. 1397 00:48:05,330 --> 00:48:06,559 And I mean, there are a lot of quantum 1398 00:48:06,560 --> 00:48:08,029 algorithms and I don't know then also 1399 00:48:08,030 --> 00:48:09,289 there might be some which are more 1400 00:48:09,290 --> 00:48:10,339 deterministic in that sense. 1401 00:48:10,340 --> 00:48:12,109 But to my knowledge, most of the quantum 1402 00:48:12,110 --> 00:48:13,940 algorithms, probabilistic by nature. 1403 00:48:15,840 --> 00:48:17,909 Number six, that's you. 1404 00:48:19,400 --> 00:48:22,239 Abbi, thank you very much for your child. 1405 00:48:22,240 --> 00:48:24,569 I have a pretty lame question, 1406 00:48:24,570 --> 00:48:27,089 um, conventional 1407 00:48:27,090 --> 00:48:28,829 computing units, in order to make them 1408 00:48:28,830 --> 00:48:30,959 better. You either 1409 00:48:30,960 --> 00:48:33,059 increase the density, get more bits 1410 00:48:33,060 --> 00:48:35,489 right. Or you 1411 00:48:35,490 --> 00:48:37,829 make them faster or you eldard, 1412 00:48:37,830 --> 00:48:40,079 um, uh, instructions said in some 1413 00:48:40,080 --> 00:48:42,359 way. Which of these are, uh, 1414 00:48:42,360 --> 00:48:44,249 feasible for quantum computing? 1415 00:48:44,250 --> 00:48:46,569 I mean, you answered a bit with, 1416 00:48:46,570 --> 00:48:48,719 uh, probably 1417 00:48:48,720 --> 00:48:49,529 closer. 1418 00:48:49,530 --> 00:48:51,959 So, um, I think today, 1419 00:48:51,960 --> 00:48:53,969 um, the biggest challenge in quantum 1420 00:48:53,970 --> 00:48:56,039 computing is not like having 1421 00:48:56,040 --> 00:48:58,049 higher packing densities of qubits on a 1422 00:48:58,050 --> 00:49:00,539 chip. So I think it's really more, um, 1423 00:49:00,540 --> 00:49:02,639 having the ability to even, 1424 00:49:02,640 --> 00:49:04,859 like, produce a large number of cubits 1425 00:49:04,860 --> 00:49:06,689 regardless of the of the size of the 1426 00:49:06,690 --> 00:49:09,359 structure. So I think in that sense, 1427 00:49:09,360 --> 00:49:11,519 we wouldn't wouldn't be 1428 00:49:11,520 --> 00:49:13,989 like a very high priority to optimize to 1429 00:49:13,990 --> 00:49:16,169 the packing or like the size of the 1430 00:49:16,170 --> 00:49:18,269 individual qubits under the chip. 1431 00:49:18,270 --> 00:49:20,339 And, uh, I think it's 1432 00:49:20,340 --> 00:49:22,079 more about if you talk about, like the 1433 00:49:22,080 --> 00:49:24,239 performance, you can also, of course, 1434 00:49:24,240 --> 00:49:26,369 try to decrease the amount of time 1435 00:49:26,370 --> 00:49:28,409 you need to, for example, perform quantum 1436 00:49:28,410 --> 00:49:30,689 gates. And this can be done by 1437 00:49:30,690 --> 00:49:32,579 increasing the frequency of the cubits 1438 00:49:32,580 --> 00:49:34,589 and also increasing the coupling between 1439 00:49:34,590 --> 00:49:36,779 individual qubits, which will 1440 00:49:36,780 --> 00:49:38,909 also increase the errors because 1441 00:49:38,910 --> 00:49:40,349 they will also be errors and cured when 1442 00:49:40,350 --> 00:49:41,879 you bring decubitus in and out of 1443 00:49:41,880 --> 00:49:43,049 coupling. So it's always like a 1444 00:49:43,050 --> 00:49:45,689 compromise between speed and 1445 00:49:45,690 --> 00:49:47,049 reliability or fidelity. 1446 00:49:47,050 --> 00:49:49,019 So to say things that answer your 1447 00:49:49,020 --> 00:49:51,309 question, you think 1448 00:49:51,310 --> 00:49:53,609 be a question from a camera angle. 1449 00:49:53,610 --> 00:49:55,349 Yes, thank you. 1450 00:49:55,350 --> 00:49:57,899 What do you think about linear 1451 00:49:57,900 --> 00:49:59,999 approaches for quantum computing based on 1452 00:50:00,000 --> 00:50:01,319 linear optics? 1453 00:50:01,320 --> 00:50:03,509 So in principle, the photon 1454 00:50:03,510 --> 00:50:05,399 is a pretty nice unit because it's 1455 00:50:05,400 --> 00:50:07,649 basically free from decoherence 1456 00:50:07,650 --> 00:50:09,779 and there are a lot of approaches. 1457 00:50:09,780 --> 00:50:11,969 In 2002, with freespace optical 1458 00:50:11,970 --> 00:50:14,579 Nohria been integrated into one chip. 1459 00:50:14,580 --> 00:50:16,229 And what do you think about these 1460 00:50:16,230 --> 00:50:16,949 approaches? 1461 00:50:16,950 --> 00:50:19,029 Mm hmm. Um, I'm not, 1462 00:50:19,030 --> 00:50:20,879 uh, not an expert in optical quantum 1463 00:50:20,880 --> 00:50:23,039 computing, so I don't want to comment 1464 00:50:23,040 --> 00:50:24,419 on that too much. 1465 00:50:24,420 --> 00:50:26,249 But I mean, as I said before, there are 1466 00:50:26,250 --> 00:50:28,229 many approaches to quantum computing. 1467 00:50:28,230 --> 00:50:30,419 And as of today, the race 1468 00:50:30,420 --> 00:50:31,169 is still open. 1469 00:50:31,170 --> 00:50:32,879 And whoever built the first working 1470 00:50:32,880 --> 00:50:35,009 quantum computers and if I would have to 1471 00:50:35,010 --> 00:50:37,139 bet, I would bet on like 1472 00:50:37,140 --> 00:50:39,209 quantum computers before or like 1473 00:50:39,210 --> 00:50:41,099 superconducting qubits. 1474 00:50:41,100 --> 00:50:43,259 But of course, to the optical systems and 1475 00:50:43,260 --> 00:50:44,459 photonic cube, it's also very 1476 00:50:44,460 --> 00:50:46,319 interesting. And they could prove to be a 1477 00:50:46,320 --> 00:50:48,629 viable alternative in case we should meet 1478 00:50:48,630 --> 00:50:50,369 like a roadblock with a superconducting 1479 00:50:50,370 --> 00:50:52,049 Hubert's or another technology. 1480 00:50:52,050 --> 00:50:54,419 So I think it's yeah, every technology 1481 00:50:54,420 --> 00:50:56,129 that can realize cubits is worth checking 1482 00:50:56,130 --> 00:50:58,079 out and then you have to like, measure it 1483 00:50:58,080 --> 00:50:59,789 against like different criteria. 1484 00:50:59,790 --> 00:51:01,979 For example, how far how easy is it to 1485 00:51:01,980 --> 00:51:03,449 make a large number of qubits? 1486 00:51:03,450 --> 00:51:05,369 How easy is it a couple of cubits with 1487 00:51:05,370 --> 00:51:07,559 each other and how good is the fidelity 1488 00:51:07,560 --> 00:51:09,449 when you realize individual cubitt 1489 00:51:09,450 --> 00:51:10,979 operations? So these are really the 1490 00:51:10,980 --> 00:51:12,089 criteria that you want to measure 1491 00:51:12,090 --> 00:51:14,219 against. I think maybe we can chat about 1492 00:51:14,220 --> 00:51:15,719 this later. I'm sure you would love to 1493 00:51:15,720 --> 00:51:16,720 have. 1494 00:51:17,110 --> 00:51:18,879 Number two, please. 1495 00:51:18,880 --> 00:51:20,229 Hi. 1496 00:51:20,230 --> 00:51:22,269 When you have your interference problem 1497 00:51:22,270 --> 00:51:24,249 with the with the frequencies, isn't this 1498 00:51:24,250 --> 00:51:26,049 a question of using a more complicated 1499 00:51:26,050 --> 00:51:27,729 probability space? 1500 00:51:27,730 --> 00:51:29,169 Maybe you can get around that. 1501 00:51:29,170 --> 00:51:32,139 OK, what problem are you referring to 1502 00:51:32,140 --> 00:51:34,449 when you have you have a scaling problem 1503 00:51:34,450 --> 00:51:36,309 if you add a lot of cowbirds, the 1504 00:51:36,310 --> 00:51:37,569 frequencies for them. 1505 00:51:37,570 --> 00:51:38,739 Yes. 1506 00:51:38,740 --> 00:51:41,049 OK, now, see, I mean, the problem 1507 00:51:41,050 --> 00:51:42,879 with our Cubitt processor was that the 1508 00:51:42,880 --> 00:51:44,619 coupling scheme was really very simple, 1509 00:51:44,620 --> 00:51:46,539 as as I showed, it was just a capacitor 1510 00:51:46,540 --> 00:51:48,399 that coupled the cubits to each other 1511 00:51:48,400 --> 00:51:49,359 whenever they were at the same 1512 00:51:49,360 --> 00:51:51,219 frequencies. And these architectures, for 1513 00:51:51,220 --> 00:51:52,689 example, the one here at the University 1514 00:51:52,690 --> 00:51:55,059 of Santa Barbara, use more 1515 00:51:55,060 --> 00:51:56,919 intricate coupling schemes that rely on 1516 00:51:56,920 --> 00:51:59,199 like different qubits being isolated 1517 00:51:59,200 --> 00:52:01,669 from each other by multiple resonators. 1518 00:52:01,670 --> 00:52:03,969 So the coupling factor, um, 1519 00:52:03,970 --> 00:52:05,949 I like the coupling strings and these 1520 00:52:05,950 --> 00:52:08,199 approaches goes down much 1521 00:52:08,200 --> 00:52:09,669 faster when you change the frequencies of 1522 00:52:09,670 --> 00:52:11,049 the cubits than in our case. 1523 00:52:11,050 --> 00:52:13,239 So these approaches are kind of more 1524 00:52:13,240 --> 00:52:15,369 reliable and better suited 1525 00:52:15,370 --> 00:52:16,749 to, like, realize a large number of 1526 00:52:16,750 --> 00:52:18,009 cubits, I would say. 1527 00:52:18,010 --> 00:52:20,109 So there are definitely lots, 1528 00:52:20,110 --> 00:52:21,909 lots and lots of approaches that you can 1529 00:52:21,910 --> 00:52:23,349 can, uh, can try to. 1530 00:52:23,350 --> 00:52:24,549 Yeah. To do. 1531 00:52:24,550 --> 00:52:25,779 Why don't people use better 1532 00:52:25,780 --> 00:52:27,009 superconductors? 1533 00:52:27,010 --> 00:52:29,229 Because we can do much better than 20 amk 1534 00:52:29,230 --> 00:52:30,849 by now. Hmm. 1535 00:52:30,850 --> 00:52:32,919 I mean the the temperature is really not 1536 00:52:32,920 --> 00:52:35,049 uh not uh the worst 1537 00:52:35,050 --> 00:52:35,989 problem that we have. 1538 00:52:35,990 --> 00:52:38,289 And yet we operate at low temperatures 1539 00:52:38,290 --> 00:52:40,449 mostly because we want to 1540 00:52:40,450 --> 00:52:42,549 avoid excitation of the cubitt 1541 00:52:42,550 --> 00:52:44,859 and like noise and like changing 1542 00:52:44,860 --> 00:52:46,329 the material of the superconductor would 1543 00:52:46,330 --> 00:52:47,799 be possible. But it would also be very 1544 00:52:47,800 --> 00:52:49,929 complicated because for those 1545 00:52:49,930 --> 00:52:51,459 materials I showed you, aluminum and 1546 00:52:51,460 --> 00:52:53,379 niobium, they are actually very good 1547 00:52:53,380 --> 00:52:55,419 fabrication processes in place which have 1548 00:52:55,420 --> 00:52:57,699 been optimized for like 10, 20 years. 1549 00:52:57,700 --> 00:52:59,109 And if you would take a new material, it 1550 00:52:59,110 --> 00:53:01,089 would be probably quite tricky to get 1551 00:53:01,090 --> 00:53:03,579 like a film of the same quality 1552 00:53:03,580 --> 00:53:04,989 and, uh. 1553 00:53:04,990 --> 00:53:05,869 All right. 1554 00:53:05,870 --> 00:53:07,299 OK, OK. 1555 00:53:07,300 --> 00:53:09,339 Internet, please. 1556 00:53:09,340 --> 00:53:11,829 Um, how many cubits would be necessary 1557 00:53:11,830 --> 00:53:13,539 to crack a two thousand forty eight 1558 00:53:13,540 --> 00:53:14,239 hours? 1559 00:53:14,240 --> 00:53:16,389 Oh, that's 1560 00:53:16,390 --> 00:53:17,289 a really good question. 1561 00:53:17,290 --> 00:53:19,509 And I 1562 00:53:19,510 --> 00:53:21,579 don't want to lie to the uh to 1563 00:53:21,580 --> 00:53:23,649 you now that uh I mean to 1564 00:53:23,650 --> 00:53:25,389 my knowledge the number of qubits that 1565 00:53:25,390 --> 00:53:27,669 you need to solve this problem goes 1566 00:53:27,670 --> 00:53:28,919 linear with the problem size. 1567 00:53:28,920 --> 00:53:30,579 So you would also need of the order of 1568 00:53:30,580 --> 00:53:32,259 two thousand doesn't something. 1569 00:53:32,260 --> 00:53:34,479 But there are as many bit at least 1570 00:53:34,480 --> 00:53:36,159 as as you have Bedzin, the number that 1571 00:53:36,160 --> 00:53:37,569 you want to create. But this could, of 1572 00:53:37,570 --> 00:53:39,069 course, vary by a factor, by a constant 1573 00:53:39,070 --> 00:53:40,599 factor of two or three, depending on how 1574 00:53:40,600 --> 00:53:42,489 many more bits you need for things like 1575 00:53:42,490 --> 00:53:44,439 error, correction and other stuff. 1576 00:53:44,440 --> 00:53:46,299 So but I would have to really I can look 1577 00:53:46,300 --> 00:53:48,489 it up in the shower algorithm 1578 00:53:48,490 --> 00:53:49,929 to give you an exact answer on this. 1579 00:53:51,860 --> 00:53:53,119 Number five. 1580 00:53:54,310 --> 00:53:56,469 Um, hello, um, 1581 00:53:56,470 --> 00:53:58,589 I was wondering the, uh, 1582 00:53:58,590 --> 00:54:00,879 the talks seemed like the 1583 00:54:00,880 --> 00:54:03,309 the direction of the search is 1584 00:54:03,310 --> 00:54:05,979 how we can use quantum computers, 1585 00:54:05,980 --> 00:54:08,079 how to solve the problems 1586 00:54:08,080 --> 00:54:10,929 that we have with normal computers today. 1587 00:54:10,930 --> 00:54:13,179 Um, but the but the the 1588 00:54:13,180 --> 00:54:15,299 thing that, uh, white crypto 1589 00:54:15,300 --> 00:54:17,469 was doing usually is to 1590 00:54:17,470 --> 00:54:19,569 create problems that 1591 00:54:19,570 --> 00:54:21,819 are hard to solve as they are 1592 00:54:21,820 --> 00:54:24,279 research in that direction to 1593 00:54:24,280 --> 00:54:24,579 uh. 1594 00:54:24,580 --> 00:54:27,669 Yeah, of course. I mean, uh, the basic 1595 00:54:27,670 --> 00:54:29,769 thing about quantum computing is that, as 1596 00:54:29,770 --> 00:54:31,059 I said, with the quantum computers, we 1597 00:54:31,060 --> 00:54:32,559 are able to solve some of the hard 1598 00:54:32,560 --> 00:54:34,959 problems that we use for cryptography 1599 00:54:34,960 --> 00:54:36,459 today, much faster than with the 1600 00:54:36,460 --> 00:54:37,659 classical computers. 1601 00:54:37,660 --> 00:54:39,429 So this kind of eliminates the security 1602 00:54:39,430 --> 00:54:41,319 we have in these methods. And, uh, there 1603 00:54:41,320 --> 00:54:43,689 is some a lot of research, actually, on 1604 00:54:43,690 --> 00:54:45,109 quantum cryptography. 1605 00:54:45,110 --> 00:54:46,689 I mean, I think there was a talk here on 1606 00:54:46,690 --> 00:54:48,399 those as well. But I'm really not an 1607 00:54:48,400 --> 00:54:50,859 expert in that subject and I wouldn't 1608 00:54:50,860 --> 00:54:52,119 like to comment on that now. 1609 00:54:52,120 --> 00:54:54,219 So but yeah, definitely there's a lot 1610 00:54:54,220 --> 00:54:56,079 of, uh, a lot of going on also when it 1611 00:54:56,080 --> 00:54:57,960 comes to the quantum cryptography itself. 1612 00:54:59,270 --> 00:55:00,169 OK, thank you. 1613 00:55:00,170 --> 00:55:02,529 Mm hmm. Number four. 1614 00:55:02,530 --> 00:55:04,879 Hi, um, I'm curious 1615 00:55:04,880 --> 00:55:06,949 to know what your thoughts are 1616 00:55:06,950 --> 00:55:09,109 on in the future in a world where 1617 00:55:09,110 --> 00:55:10,819 a lot of these hurdles have been removed, 1618 00:55:10,820 --> 00:55:13,039 where we have quantum computers that 1619 00:55:13,040 --> 00:55:15,109 can work with meaningful numbers of 1620 00:55:15,110 --> 00:55:17,809 qubits and relatively widespread 1621 00:55:17,810 --> 00:55:19,939 access to this technology. 1622 00:55:19,940 --> 00:55:21,529 What do you think? 1623 00:55:21,530 --> 00:55:24,709 Um, you know, some of the most promising 1624 00:55:24,710 --> 00:55:26,989 applications of this technology would be. 1625 00:55:28,370 --> 00:55:30,619 So for me personally, um, I don't think 1626 00:55:30,620 --> 00:55:32,809 that cracking passwords or reading 1627 00:55:32,810 --> 00:55:34,739 people's email is like the the thing 1628 00:55:34,740 --> 00:55:36,289 where we should build quantum computers. 1629 00:55:36,290 --> 00:55:38,119 Right. Um, for me, it's mostly the 1630 00:55:38,120 --> 00:55:40,069 ability to simulate quantum systems, 1631 00:55:40,070 --> 00:55:41,809 because even if you look today at 1632 00:55:41,810 --> 00:55:43,939 conventional electronics, um, 1633 00:55:43,940 --> 00:55:45,469 for example, a processor, you would see 1634 00:55:45,470 --> 00:55:48,019 that the size of individual transistors 1635 00:55:48,020 --> 00:55:50,269 comes down really 1636 00:55:50,270 --> 00:55:52,339 fast and approaches the limit where we 1637 00:55:52,340 --> 00:55:54,019 actually have a transistor that would 1638 00:55:54,020 --> 00:55:55,549 consist only of a few atoms. 1639 00:55:55,550 --> 00:55:57,769 So such a system would would by 1640 00:55:57,770 --> 00:55:59,719 definition have quantum mechanical 1641 00:55:59,720 --> 00:56:01,519 behavior. And if you want to understand 1642 00:56:01,520 --> 00:56:03,349 and simulate the systems, we would 1643 00:56:03,350 --> 00:56:04,909 definitely need quantum computers to do 1644 00:56:04,910 --> 00:56:06,319 that. So there are many other 1645 00:56:06,320 --> 00:56:07,849 applications and for example, protein 1646 00:56:07,850 --> 00:56:10,309 folding and like biology, genetics, 1647 00:56:10,310 --> 00:56:12,619 etc., which would require a profit 1648 00:56:12,620 --> 00:56:13,719 from this kind of computer. 1649 00:56:13,720 --> 00:56:15,319 So it's for me, it's really not about 1650 00:56:15,320 --> 00:56:16,879 cracking codes, but about like doing 1651 00:56:16,880 --> 00:56:18,459 science with that. 1652 00:56:18,460 --> 00:56:19,460 Yeah, thank you. 1653 00:56:20,650 --> 00:56:23,329 Number one one one 1654 00:56:23,330 --> 00:56:24,330 oh, thank you. 1655 00:56:25,240 --> 00:56:28,289 What I would like to know is you 1656 00:56:28,290 --> 00:56:30,309 in the popular press, I've always heard 1657 00:56:30,310 --> 00:56:33,179 that scaling to a larger number of bits 1658 00:56:33,180 --> 00:56:35,319 is hard. And I assumed that this was 1659 00:56:35,320 --> 00:56:37,419 because when you get too big, that they 1660 00:56:37,420 --> 00:56:40,509 don't interfere with each other anymore. 1661 00:56:40,510 --> 00:56:42,639 Today, I'm taking away that 1662 00:56:42,640 --> 00:56:44,749 the the arrows, 1663 00:56:44,750 --> 00:56:47,169 the noise is a big problem and 1664 00:56:47,170 --> 00:56:49,420 that the retention is a big problem. 1665 00:56:50,590 --> 00:56:52,149 And in the beginning, you mentioned that 1666 00:56:52,150 --> 00:56:54,759 the iron trap has up to 100 1667 00:56:54,760 --> 00:56:56,199 cubits already. 1668 00:56:56,200 --> 00:56:57,879 Can you say more about this iron trap 1669 00:56:57,880 --> 00:57:00,069 thing and what its parameters are 1670 00:57:00,070 --> 00:57:02,139 and why you're going in this way if 1671 00:57:02,140 --> 00:57:03,909 the other one is already so far? 1672 00:57:03,910 --> 00:57:06,099 So, yeah, as I said, I'm not an expert 1673 00:57:06,100 --> 00:57:08,259 on quantum computing, but the 1674 00:57:08,260 --> 00:57:10,869 qubits, which they have there are 1675 00:57:10,870 --> 00:57:13,269 really very good quality because the 1676 00:57:13,270 --> 00:57:15,069 coherence time can be in the range of 1677 00:57:15,070 --> 00:57:17,379 seconds and the speed 1678 00:57:17,380 --> 00:57:19,059 of operation can also be comparable to 1679 00:57:19,060 --> 00:57:20,309 that of superconducting qubits. 1680 00:57:20,310 --> 00:57:22,149 So you can have gaits which operate in 1681 00:57:22,150 --> 00:57:24,249 like nanoseconds on microseconds and 1682 00:57:24,250 --> 00:57:26,269 you can also have a readout fidelities. 1683 00:57:26,270 --> 00:57:28,509 So to sort of say the success 1684 00:57:28,510 --> 00:57:30,579 probability when you reload, given Cubitt 1685 00:57:30,580 --> 00:57:33,039 state, which approaches like 100 1686 00:57:33,040 --> 00:57:35,289 percent by like several 1687 00:57:35,290 --> 00:57:37,689 like six digits or so. 1688 00:57:37,690 --> 00:57:39,819 So this systems definitely seem 1689 00:57:39,820 --> 00:57:41,069 to be very promising. 1690 00:57:41,070 --> 00:57:43,359 Um, what kind of 1691 00:57:43,360 --> 00:57:44,829 could be a problem is probably the 1692 00:57:44,830 --> 00:57:46,959 scaling, because if you go 1693 00:57:46,960 --> 00:57:48,369 to a very large number of qubits, you 1694 00:57:48,370 --> 00:57:50,439 would have to somehow accommodate them 1695 00:57:50,440 --> 00:57:52,719 inside a trap, inside a magnetic 1696 00:57:52,720 --> 00:57:54,729 trap, which would which could be tricky. 1697 00:57:54,730 --> 00:57:56,049 But also for this problem, there are 1698 00:57:56,050 --> 00:57:57,159 solutions devised today. 1699 00:57:57,160 --> 00:57:58,860 For example, you have like R 1700 00:57:59,980 --> 00:58:01,959 atom traps, which are on a ship. 1701 00:58:01,960 --> 00:58:04,059 So we can really take individual cubits 1702 00:58:04,060 --> 00:58:05,529 or atoms or ions, if you like. 1703 00:58:05,530 --> 00:58:06,999 They can shuffle them around on a chip 1704 00:58:07,000 --> 00:58:09,159 and transport them to to to other other 1705 00:58:09,160 --> 00:58:11,079 sides and like that like isolate them 1706 00:58:11,080 --> 00:58:13,149 from each other. So as I said, for 1707 00:58:13,150 --> 00:58:14,409 me, the rest is completely open. 1708 00:58:14,410 --> 00:58:16,539 And right now I am computing 1709 00:58:16,540 --> 00:58:17,709 seems to be ahead. 1710 00:58:17,710 --> 00:58:19,839 But this could change, of course, if we 1711 00:58:19,840 --> 00:58:22,059 keep improving the superconducting qubits 1712 00:58:22,060 --> 00:58:23,829 like we did in the last 10 years. 1713 00:58:23,830 --> 00:58:24,830 So. 1714 00:58:26,880 --> 00:58:27,880 No. 1715 00:58:29,540 --> 00:58:30,540 Number six. 1716 00:58:31,620 --> 00:58:33,839 Hey, as it all at the moment, 1717 00:58:33,840 --> 00:58:36,119 we still use the binary system 1718 00:58:36,120 --> 00:58:38,819 with two systems, but we are not, 1719 00:58:38,820 --> 00:58:41,159 um, we can use higher level systems. 1720 00:58:41,160 --> 00:58:43,349 Are there any thought experiments 1721 00:58:43,350 --> 00:58:45,509 to overcome 1722 00:58:45,510 --> 00:58:47,669 the binary system with higher level 1723 00:58:47,670 --> 00:58:48,979 systems? 1724 00:58:48,980 --> 00:58:50,639 Um, yeah. You could, of course, do that. 1725 00:58:50,640 --> 00:58:52,829 And in fact, uh, 1726 00:58:52,830 --> 00:58:54,659 we did experiments where we used the 1727 00:58:54,660 --> 00:58:56,789 second and the third, uh, energy state of 1728 00:58:56,790 --> 00:58:59,099 Tacuba to have like a like a higher order 1729 00:58:59,100 --> 00:59:01,109 base for our calculations. 1730 00:59:01,110 --> 00:59:03,359 Um, but this is usually not done 1731 00:59:03,360 --> 00:59:05,459 because, uh, the speed up or 1732 00:59:05,460 --> 00:59:07,979 like to to gain information that you 1733 00:59:07,980 --> 00:59:09,359 that you achieved there is not 1734 00:59:09,360 --> 00:59:10,409 exponential. 1735 00:59:10,410 --> 00:59:12,029 So you could say that if you have lower, 1736 00:59:12,030 --> 00:59:13,829 for example, a quantum system of three 1737 00:59:13,830 --> 00:59:15,939 states, you would have a state 1738 00:59:15,940 --> 00:59:18,209 space, which is true to the power of four 1739 00:59:18,210 --> 00:59:20,249 and cubits, whereas for the cubic state 1740 00:59:20,250 --> 00:59:21,449 it would be two to the power of. 1741 00:59:21,450 --> 00:59:23,009 And so it's still a big difference. 1742 00:59:23,010 --> 00:59:25,019 But it's not going like like it's not the 1743 00:59:25,020 --> 00:59:26,579 number that that we change is not in the 1744 00:59:26,580 --> 00:59:27,539 exponent, so to say. 1745 00:59:27,540 --> 00:59:29,759 So, um, that's kind of the kind 1746 00:59:29,760 --> 00:59:31,239 of way most people don't do it. 1747 00:59:31,240 --> 00:59:32,240 OK, thanks. 1748 00:59:33,520 --> 00:59:35,099 OK, we are out of time. 1749 00:59:35,100 --> 00:59:37,259 I'm very sorry but I'm sure you can find 1750 00:59:37,260 --> 00:59:39,699 a dress outside of Nater thinking 1751 00:59:39,700 --> 00:59:40,700 like place.