1 00:00:01,133 --> 00:00:04,133 Let's go for 2 00:00:05,266 --> 00:00:08,266 super 820. 3 00:00:10,133 --> 00:00:11,533 Thank you for the introduction. 4 00:00:11,533 --> 00:00:14,733 And, it's a talk such I want to, show 5 00:00:14,966 --> 00:00:18,133 how to work on quantum computers and more concrete. 6 00:00:18,133 --> 00:00:21,133 First, I want to show what you need. 7 00:00:21,266 --> 00:00:24,133 What ingredients, how it's, 8 00:00:24,133 --> 00:00:26,400 mentally realized. 9 00:00:26,400 --> 00:00:27,866 And one example. 10 00:00:27,866 --> 00:00:32,033 And then, finally, how you can run programs and algorithms 11 00:00:32,033 --> 00:00:33,266 on the quantum computer. 12 00:00:33,266 --> 00:00:37,033 And there's an especially the last step is very exciting to me 13 00:00:37,066 --> 00:00:41,800 because as a theorist, I, most of the time I'm sitting in the office. 14 00:00:41,800 --> 00:00:47,866 And so I have at least sometimes elevation that I can work on an experiment 15 00:00:47,966 --> 00:00:50,966 and see what comes up. 16 00:00:51,900 --> 00:00:52,200 Before 17 00:00:52,200 --> 00:00:56,000 I want to dive into, these topics, I want to show, 18 00:00:57,000 --> 00:00:59,433 possible implications for quantum computers. 19 00:00:59,433 --> 00:01:02,533 I mean, the most fleshy one, most of you know, is, 20 00:01:03,266 --> 00:01:07,700 I have at least heard of is, concerning prime factorization. 21 00:01:08,133 --> 00:01:12,133 Using Shor's algorithm, the idea is that this is an algorithm which, 22 00:01:13,200 --> 00:01:15,000 factorize prime numbers 23 00:01:15,000 --> 00:01:19,000 exponentially, faster than any known classical algorithm. 24 00:01:19,066 --> 00:01:22,666 And it's, it's the reason why, for example, the military is interested 25 00:01:22,666 --> 00:01:25,666 in quantum computers, and the funding is quite high in this field. 26 00:01:26,766 --> 00:01:29,433 But, because the quantum 27 00:01:29,433 --> 00:01:33,133 principle break, public key encryptions. 28 00:01:33,733 --> 00:01:39,600 But, to be honest, this application is quite, is quite fine if you take a guess, 29 00:01:39,600 --> 00:01:42,600 it would take at least 20, one year 30 00:01:42,600 --> 00:01:45,600 or even longer until you can, 31 00:01:46,166 --> 00:01:49,100 and make real use cases. 32 00:01:49,100 --> 00:01:51,900 But this is more exciting from a physical perspective. 33 00:01:51,900 --> 00:01:55,800 And this is also like something mentioned in this talks is, 34 00:01:56,366 --> 00:01:59,433 this simulation of strongly interacting quantum systems. 35 00:01:59,800 --> 00:02:02,800 So in this cases you have of, many, 36 00:02:03,933 --> 00:02:05,700 competitive terms like 37 00:02:05,700 --> 00:02:09,033 the kinetic terms and, and, interactions. 38 00:02:09,733 --> 00:02:12,133 And so you, you will have not the dominant term 39 00:02:12,133 --> 00:02:17,666 where you can apply perturbation theory on and in this cases it's hard to, 40 00:02:18,833 --> 00:02:21,833 to, to apply classical algorithms. 41 00:02:22,133 --> 00:02:25,300 And this is, quantum computers come into play. 42 00:02:25,966 --> 00:02:28,966 One example are the strongly correlated systems. 43 00:02:29,466 --> 00:02:32,700 Took me to mention before the, the, interesting 44 00:02:32,700 --> 00:02:36,700 because one of the most, open problems 45 00:02:36,700 --> 00:02:39,866 in, in physics, like high temperature superconductivity, 46 00:02:40,500 --> 00:02:43,500 buried in this models another model, 47 00:02:43,900 --> 00:02:46,900 as I mentioned, a little bit before, is, 48 00:02:47,533 --> 00:02:50,000 concerning, quantum chemistry, 49 00:02:50,000 --> 00:02:53,900 but are also strongly, interacting. 50 00:02:54,600 --> 00:02:58,333 Let me Tyson in the hot to simulate classically but but also, 51 00:02:59,133 --> 00:03:01,800 when you consider high energy physics, 52 00:03:01,800 --> 00:03:05,333 I mean, you will have in order to understand 53 00:03:05,333 --> 00:03:09,633 this, you'll have to build, large colliders, or, 54 00:03:09,866 --> 00:03:12,633 or you can do to some very limited 55 00:03:12,633 --> 00:03:16,000 as stand some classical simulations, 56 00:03:17,000 --> 00:03:20,100 which goes then it's, let us quickly but, 57 00:03:20,500 --> 00:03:23,500 but this classical simulations, 58 00:03:23,733 --> 00:03:28,466 a very hard to realize you can only consider limited systems 59 00:03:28,466 --> 00:03:31,966 and so and have to put much effort into this. 60 00:03:33,233 --> 00:03:33,900 And it 61 00:03:33,900 --> 00:03:37,533 turns out that there are also algorithms, to, 62 00:03:37,766 --> 00:03:40,566 to simulate the standard models 63 00:03:40,566 --> 00:03:43,566 and is active work on it to realize that on quantum computers. 64 00:03:43,566 --> 00:03:47,600 And it's probably, at the long term and, and cheaper way 65 00:03:47,600 --> 00:03:50,600 than building the next largest collider. 66 00:03:52,566 --> 00:03:55,566 With this in hand, I, I want to show, 67 00:03:56,833 --> 00:03:57,800 what you need. 68 00:03:57,800 --> 00:04:02,300 And this was nicely summarized in there and consensus criteria 69 00:04:02,633 --> 00:04:06,800 roughly 25 years ago, the first thing is that you need, 70 00:04:08,966 --> 00:04:11,600 qubits or 71 00:04:11,600 --> 00:04:12,800 which are scalable. 72 00:04:12,800 --> 00:04:16,600 So it's just basically the, the building block of a quantum computer 73 00:04:16,766 --> 00:04:19,500 and it's nothing. OS then you need classical bits. 74 00:04:19,500 --> 00:04:22,366 Fine. Classical, classical computer. 75 00:04:22,366 --> 00:04:24,600 The second thing, 76 00:04:24,600 --> 00:04:27,600 is that you need long enough coherence times 77 00:04:27,833 --> 00:04:31,500 this, you need that you, that you actually can use the loss of, 78 00:04:31,866 --> 00:04:35,100 quantum mechanics to, to run algorithms which, 79 00:04:35,366 --> 00:04:38,366 which are hard to simulate in classical computers. 80 00:04:38,700 --> 00:04:42,733 And then it turns out that this is actually the the most challenging issue 81 00:04:42,733 --> 00:04:46,966 for, for, for, current realizations. 82 00:04:46,966 --> 00:04:50,333 And you probably need, quantum error correction, 83 00:04:50,333 --> 00:04:54,600 a long term statistical this challenge that, this, was also mentioned at, 84 00:04:55,633 --> 00:04:57,266 talked last year, but, by Benedict. 85 00:04:57,266 --> 00:05:01,066 So I only briefly touched this at the end of of the talk. 86 00:05:02,166 --> 00:05:06,366 Then you'll need, universal, set of quantum gates 87 00:05:06,966 --> 00:05:10,066 and for quantum computers, basically the idea is that you will, 88 00:05:11,100 --> 00:05:14,933 the algorithms, consists of unitary operations, 89 00:05:14,933 --> 00:05:17,933 and then you'll need some ingredients to realize them. 90 00:05:18,800 --> 00:05:21,300 And then it turns out that, the, the, 91 00:05:21,300 --> 00:05:26,033 that you basically need one single cubit gates, which are there other methods and, 92 00:05:26,100 --> 00:05:30,866 and, for example, a phase gate at gates here and, in the bottom, 93 00:05:31,933 --> 00:05:34,000 which I will, trade later. 94 00:05:34,000 --> 00:05:37,433 And then you need a, two qubit gates which can entangle, 95 00:05:39,233 --> 00:05:41,900 qubits, which is in this case a control, 96 00:05:41,900 --> 00:05:44,766 not operations. 97 00:05:44,766 --> 00:05:48,100 This universal set, you can, can build arbitrary unitary operations. 98 00:05:49,600 --> 00:05:51,400 And finally, to get 99 00:05:51,400 --> 00:05:54,533 also something out of your, quantum computer, you will have, 100 00:05:56,433 --> 00:05:58,033 measurements, to 101 00:05:58,033 --> 00:06:01,033 get some results and compare what the, Giving, 102 00:06:03,266 --> 00:06:03,600 Yeah. 103 00:06:03,600 --> 00:06:06,900 So in the last 20 years, there were lots of proposals 104 00:06:06,900 --> 00:06:11,466 and approaches to, to satisfy this criteria. 105 00:06:11,700 --> 00:06:16,000 I just mentioned a few, the few, probably most promising right now, 106 00:06:16,833 --> 00:06:19,833 but one, superconducting qubits, which are, 107 00:06:19,833 --> 00:06:24,600 which is a strategy, pursued by, companies like Google, IBM. 108 00:06:24,600 --> 00:06:26,700 And so here in Oxford. 109 00:06:26,700 --> 00:06:30,000 And the idea is that, basically use, 110 00:06:32,500 --> 00:06:33,433 electric, 111 00:06:33,433 --> 00:06:36,233 particularly as circuit elements involving Josephson 112 00:06:36,233 --> 00:06:40,666 junctions and encode the qubits, in this circuit elements. 113 00:06:40,666 --> 00:06:43,666 I will show this, explain this later. 114 00:06:43,866 --> 00:06:47,600 Then you can, another possibility possibilities using trapped ions, 115 00:06:48,666 --> 00:06:51,600 values, values like, 116 00:06:51,600 --> 00:06:54,300 the qubits into energy levels of 117 00:06:54,300 --> 00:06:57,300 of this ions and then apply, 118 00:06:58,333 --> 00:07:01,333 policies to manipulate this, 119 00:07:03,333 --> 00:07:05,700 this, levels 120 00:07:05,700 --> 00:07:09,233 now, there was, recently there was some announcement 121 00:07:09,233 --> 00:07:13,466 that you can use topological quantum computing by, by Microsoft, 122 00:07:14,533 --> 00:07:15,066 to not 123 00:07:15,066 --> 00:07:18,366 want to state now, that this claims are correct or not. 124 00:07:18,366 --> 00:07:23,600 But if, this are the case, this would be also quite a promising, 125 00:07:25,133 --> 00:07:27,966 realization, which is, 126 00:07:27,966 --> 00:07:30,966 is it was, to scale up, 127 00:07:31,700 --> 00:07:33,766 another possibilities. 128 00:07:33,766 --> 00:07:37,400 It's using ultracold atoms with neutral atoms in, 129 00:07:38,033 --> 00:07:41,033 contrast to the ions, which we have before. 130 00:07:41,733 --> 00:07:44,700 But, but it emerged, especially in the, 131 00:07:44,700 --> 00:07:48,966 last five years is, another competitive, player in the field. 132 00:07:50,133 --> 00:07:52,433 Now, there are lots of other approaches, 133 00:07:52,433 --> 00:07:55,433 for example, photonic quantum computers, 134 00:07:56,100 --> 00:07:59,100 attempts to use silicon, quantum computing and so on, 135 00:07:59,933 --> 00:08:03,033 that I cannot, explain all of them, 136 00:08:03,633 --> 00:08:06,166 because of lack of time and because I 137 00:08:06,166 --> 00:08:09,733 if you have the lunch served later and I was hungry. 138 00:08:10,500 --> 00:08:12,733 So I will focus, now 139 00:08:12,733 --> 00:08:15,733 on superconducting circuits, qubits. 140 00:08:16,966 --> 00:08:19,033 So here in this picture, you, 141 00:08:19,033 --> 00:08:22,033 essentially can see, for transparent qubits. 142 00:08:22,500 --> 00:08:24,933 What specifically? This cost state for. 143 00:08:25,933 --> 00:08:27,300 And when you zoom in a 144 00:08:27,300 --> 00:08:30,300 little bit, you see the order of micro, 145 00:08:31,266 --> 00:08:34,266 meter, the hundreds of micrometers, you see this cross, 146 00:08:34,500 --> 00:08:38,466 a few zoom in even more, and then you see what you actually see, 147 00:08:38,466 --> 00:08:41,700 which has the size of a few hundred nanometers, 148 00:08:43,200 --> 00:08:46,866 to, it's basically a Josephson junctions 149 00:08:47,766 --> 00:08:51,433 and across, the cross shape, this is basically a large, 150 00:08:52,500 --> 00:08:55,433 capacitor, c tens. 151 00:08:55,433 --> 00:08:58,400 And the idea is that, the Josephson functions, 152 00:08:58,400 --> 00:09:01,200 is a nonlinear, 153 00:09:01,200 --> 00:09:04,766 conductivity of your circuit, which will become later. 154 00:09:04,766 --> 00:09:07,133 And when you, when you do, 155 00:09:07,133 --> 00:09:10,133 some elementary physics and, 156 00:09:10,566 --> 00:09:12,466 for the circuits, you can quantize, say, 157 00:09:12,466 --> 00:09:15,466 Hamiltonian, corresponding to the system. 158 00:09:15,766 --> 00:09:17,933 And this has a, has basically this form. 159 00:09:17,933 --> 00:09:20,933 So the first part, corresponds to the, 160 00:09:21,500 --> 00:09:23,866 energy. 161 00:09:23,866 --> 00:09:25,366 And and 162 00:09:25,366 --> 00:09:29,700 and there's a number of, Cooper pairs, on the islands. 163 00:09:30,400 --> 00:09:35,600 And the second term is, is, is basically a term, 164 00:09:36,600 --> 00:09:37,266 coming from, 165 00:09:37,266 --> 00:09:40,566 from the Josephson current, of, of this junctions. 166 00:09:41,333 --> 00:09:45,666 But, what is very important is, when you look at this, point 167 00:09:45,666 --> 00:09:49,700 that it's not, it's not quadratic, but it's a cosine, it's a cosine, 168 00:09:51,300 --> 00:09:54,300 which is basically almost a harmonic oscillator, 169 00:09:54,833 --> 00:09:57,566 which is also important is that, the number 170 00:09:57,566 --> 00:10:01,100 of Cooper pairs and the Josephson face, the, the conjugate, the barrier. 171 00:10:01,133 --> 00:10:03,433 But it's but it's, 172 00:10:03,433 --> 00:10:06,433 you, so you get almost something as, 173 00:10:06,533 --> 00:10:09,500 the harmonic oscillator. 174 00:10:09,500 --> 00:10:12,500 Now, when you look at this model, 175 00:10:13,300 --> 00:10:17,633 and compared with a harmonic oscillator, there you have a quadratic potential. 176 00:10:17,633 --> 00:10:20,633 And as you know, from your, 177 00:10:20,800 --> 00:10:24,466 first course, as in quantum mechanics, for a quadratic potential, 178 00:10:24,466 --> 00:10:27,466 you get equidistant, level spacing. 179 00:10:28,500 --> 00:10:31,500 Now, the cosine potential looks almost, 180 00:10:31,600 --> 00:10:34,266 like this, 181 00:10:34,266 --> 00:10:36,966 harmonic potential, but, but not quite. 182 00:10:36,966 --> 00:10:39,600 So what what you see is that you have 183 00:10:39,600 --> 00:10:42,600 a slight distortions of this energy levels. 184 00:10:42,633 --> 00:10:47,566 And, the, the qubit itself, corresponds to the lowest 185 00:10:47,566 --> 00:10:52,466 two eigenstates, of, of of the, of your transition qubit. 186 00:10:54,533 --> 00:10:57,666 So with this in mind, we can, try to understand 187 00:10:57,666 --> 00:11:01,100 how you apply quantum operations on, on this level 188 00:11:02,333 --> 00:11:04,166 for this. 189 00:11:04,166 --> 00:11:06,900 I consider a single qubit operations, 190 00:11:06,900 --> 00:11:09,900 two qubit operations. 191 00:11:10,866 --> 00:11:11,833 Similar. 192 00:11:11,833 --> 00:11:14,633 Basically, what you have here is 193 00:11:14,633 --> 00:11:17,633 a is a, is is a cavity, 194 00:11:17,933 --> 00:11:20,433 and you, you copied your transplant, 195 00:11:20,433 --> 00:11:23,433 qubit to, to the, to a resonator. 196 00:11:23,933 --> 00:11:27,033 But, what happens is basically, that you get the hybridization 197 00:11:27,033 --> 00:11:30,033 between the photon and, qubit states, 198 00:11:30,300 --> 00:11:33,366 which means they are no longer independent of each other. 199 00:11:33,366 --> 00:11:37,800 So but you get this light dressing similar to this quasi particle picture. 200 00:11:37,800 --> 00:11:40,800 I don't mean to show it before at all. 201 00:11:41,733 --> 00:11:44,733 Low order approximation. 202 00:11:45,000 --> 00:11:48,133 The, you can still separate them, 203 00:11:48,133 --> 00:11:51,133 but what happens is that, 204 00:11:52,200 --> 00:11:55,366 the, the, basically by applying a photon pulse, 205 00:11:55,366 --> 00:11:59,833 you can, you can change this state as a state of the transition qubit. 206 00:11:59,833 --> 00:12:03,566 So you basically applying here microwave pulse, and then, 207 00:12:04,600 --> 00:12:06,633 introduce, 208 00:12:06,633 --> 00:12:08,533 transitions in the qubits 209 00:12:08,533 --> 00:12:11,300 you have between the first and the second state. 210 00:12:11,300 --> 00:12:12,400 Yeah. 211 00:12:12,400 --> 00:12:14,700 This is a point where this, this 212 00:12:14,700 --> 00:12:17,700 it becomes very important in the sense that, 213 00:12:18,633 --> 00:12:21,800 transitions between the lowest trying states, 214 00:12:23,366 --> 00:12:25,800 allowed, but, 215 00:12:25,800 --> 00:12:30,033 transitions to higher states, the, the slightly off 216 00:12:30,033 --> 00:12:33,166 resonance, which means that they are strongly suppressed. 217 00:12:33,466 --> 00:12:38,600 So you're, you're aware that, that you excite higher levels and, 218 00:12:38,933 --> 00:12:41,933 leak information of your qubits? 219 00:12:43,400 --> 00:12:45,866 And then you want to apply to qubit operations. 220 00:12:45,866 --> 00:12:48,666 This is it can unfortunately, is not visible here 221 00:12:48,666 --> 00:12:52,433 in this picture, but, but basically you have, you have cavities. 222 00:12:52,933 --> 00:12:55,700 Between different, different qubits. 223 00:12:55,700 --> 00:12:58,366 And then you can, also, 224 00:12:58,366 --> 00:13:01,366 you can, you can drive one qubit and 225 00:13:03,433 --> 00:13:05,166 if you, 226 00:13:05,166 --> 00:13:06,733 if you microwave pies and, 227 00:13:06,733 --> 00:13:09,833 and the effect depends then on the, on the state of the other qubit. 228 00:13:11,733 --> 00:13:14,333 Finally, we have to consider measurements for this. 229 00:13:14,333 --> 00:13:16,133 You have, 230 00:13:16,133 --> 00:13:18,633 here, this, this other resonator 231 00:13:18,633 --> 00:13:22,866 and also coupled via, via cavity to this transition qubits. 232 00:13:23,133 --> 00:13:26,333 And the other concept, this also provides, similar. 233 00:13:27,633 --> 00:13:31,333 So, because of this coupling, 234 00:13:31,333 --> 00:13:34,333 the, the states of the transmission qubits, 235 00:13:35,300 --> 00:13:39,000 no longer, completely separate of the microwave pulse. 236 00:13:39,566 --> 00:13:42,000 And on the other hand, is also, 237 00:13:42,000 --> 00:13:47,233 the eight modes of, of this resonator depend on the qubit states, 238 00:13:47,666 --> 00:13:51,666 but it explicitly means this when you look at the transmission frequency, 239 00:13:51,966 --> 00:13:54,700 of your resonator, which you can just a measure 240 00:13:54,700 --> 00:13:57,866 by applying a microwave pulse, then you see that, 241 00:13:58,400 --> 00:14:01,400 it has a different resonance, states, 242 00:14:01,966 --> 00:14:03,966 if the qubit is in state zero, 243 00:14:03,966 --> 00:14:07,466 but it's, but it's getting shifted when the qubit is in state one. 244 00:14:07,533 --> 00:14:08,533 And, basically 245 00:14:08,533 --> 00:14:12,400 by reading out the transmission frequency, you can measure the qubit and, infer in 246 00:14:12,400 --> 00:14:13,200 what state it is. 247 00:14:14,833 --> 00:14:17,833 So with this in mind, we can 248 00:14:19,800 --> 00:14:23,966 we, we have basically everything to, to, 249 00:14:25,866 --> 00:14:28,866 you have to run algorithms and, 250 00:14:29,400 --> 00:14:32,700 perform a quantum operations on your quantum computer, 251 00:14:34,866 --> 00:14:37,866 the basic operations of which you have, 252 00:14:39,000 --> 00:14:42,766 in this case, are often illustrated in circuit diagrams. 253 00:14:42,766 --> 00:14:45,766 I want to, briefly sketch how they look like, 254 00:14:46,800 --> 00:14:48,266 I mean, the. 255 00:14:48,266 --> 00:14:48,566 Yeah. 256 00:14:48,566 --> 00:14:51,566 Easiest case of in your head when you consider qubits, 257 00:14:51,766 --> 00:14:54,133 they are basically denoted by a black line. 258 00:14:54,133 --> 00:14:57,133 As you can see here above. 259 00:14:58,300 --> 00:15:00,666 When your, when you consider, 260 00:15:00,666 --> 00:15:03,433 quantum operations, they, illustrated 261 00:15:03,433 --> 00:15:07,833 by, by boxes and there you, get again the protagonist, 262 00:15:07,833 --> 00:15:10,833 which I have showed you already before at the beginning. 263 00:15:12,300 --> 00:15:13,800 All of them are unitary gates. 264 00:15:13,800 --> 00:15:16,800 But as you would expect from the laws of, 265 00:15:18,433 --> 00:15:20,333 quantum mechanics, and then this is basically 266 00:15:20,333 --> 00:15:23,666 the only restrictions you have, for this operations. 267 00:15:25,733 --> 00:15:27,866 The most illustrative one is, 268 00:15:27,866 --> 00:15:31,166 I think is the, is the not gate or the X gate. 269 00:15:31,333 --> 00:15:34,666 This is, very similar to, to what your, 270 00:15:35,000 --> 00:15:38,600 expect on, classical circuits and, basically, 271 00:15:38,766 --> 00:15:41,866 I mean, you're right, it is a matrix element, but, but this, 272 00:15:43,633 --> 00:15:47,600 operation is, doing a when, when your qubit is in state zero, 273 00:15:47,800 --> 00:15:52,366 it's, it's, it flips it to a state one and otherwise it 274 00:15:52,366 --> 00:15:55,366 flips, and vice versa. 275 00:15:56,700 --> 00:15:59,733 Then then you have Hadamard gates. 276 00:16:00,800 --> 00:16:02,900 The idea of this Hadamard gate, this, it 277 00:16:02,900 --> 00:16:07,800 looks, slightly more complicated, but, basically what it is doing when you start 278 00:16:07,800 --> 00:16:12,000 in the ground state of a qubit, after applying a gate, your, 279 00:16:12,133 --> 00:16:16,000 your will be in a, superposition between, state zero and, 280 00:16:16,533 --> 00:16:19,533 state one. 281 00:16:20,500 --> 00:16:23,500 And, what I mentioned before, 282 00:16:23,700 --> 00:16:27,133 you need some additional gates, which, which can induce 283 00:16:27,600 --> 00:16:30,833 additional phases, between the states of the qubits. 284 00:16:30,833 --> 00:16:35,233 And this is done by phase gates, specifically when you have a phase 285 00:16:35,233 --> 00:16:39,666 shift of pi four is done here and it's, it's called, T gates. 286 00:16:40,166 --> 00:16:42,100 And it turns out when you're basically, 287 00:16:43,433 --> 00:16:43,800 when you 288 00:16:43,800 --> 00:16:47,900 only apply Hadamard, gates, you can, you can create 289 00:16:47,900 --> 00:16:51,600 arbitrary one qubit rotations by sticking together, 290 00:16:52,766 --> 00:16:55,966 of, of has it has been shown roughly 30 years ago 291 00:16:57,433 --> 00:17:00,433 now, one qubit gates, 292 00:17:00,600 --> 00:17:03,600 so one qubit operations. 293 00:17:03,700 --> 00:17:06,233 I mean, the, might be interesting, but, 294 00:17:06,233 --> 00:17:09,666 you cannot do so much useful things with one qubit. 295 00:17:09,800 --> 00:17:12,466 I do not have to build a quantum computer for that. 296 00:17:12,466 --> 00:17:15,466 So you need interactions between qubits 297 00:17:15,766 --> 00:17:18,766 and it turns out that when you, 298 00:17:18,966 --> 00:17:21,966 when you have at one another gate, which is, 299 00:17:22,566 --> 00:17:26,200 a c not gate, which is shown here, which, basically, 300 00:17:27,566 --> 00:17:30,566 this cNOT gate shifts, 301 00:17:30,933 --> 00:17:33,733 induces a transition of the of the second qubit only 302 00:17:33,733 --> 00:17:37,566 if when, when the first qubit is in an excited, state 303 00:17:38,933 --> 00:17:41,433 and it turns out of, in your, at the 304 00:17:41,433 --> 00:17:47,600 si not gate to your, to your second, then this is already sufficient to, to, 305 00:17:48,566 --> 00:17:51,900 create arbitrary unitary, transformation, 306 00:17:53,000 --> 00:17:55,600 transformations with, with, an arbitrary 307 00:17:55,600 --> 00:17:58,600 number of qubits. 308 00:17:58,733 --> 00:18:01,733 And finally, as mentioned, 309 00:18:01,900 --> 00:18:04,900 you have some of which are basically, 310 00:18:05,466 --> 00:18:07,200 indicate the, 311 00:18:07,200 --> 00:18:10,200 but by this box 312 00:18:10,533 --> 00:18:16,833 now, I do not only want to implement them classically, but, but I'm also interested 313 00:18:16,833 --> 00:18:22,833 to run them on a real devices and it turns out that, and the, solution. 314 00:18:22,833 --> 00:18:26,766 So what you can do, is it it's a illustrates, 315 00:18:28,633 --> 00:18:30,066 in a, a second 316 00:18:30,066 --> 00:18:33,066 is that you can program your quantum circuits, 317 00:18:34,266 --> 00:18:37,300 with Python library, which is called Qiskit. 318 00:18:38,900 --> 00:18:42,633 And the idea is basically you construct your circuit, then, 319 00:18:42,933 --> 00:18:45,766 then you, then you, 320 00:18:45,766 --> 00:18:48,766 submitted to a compiler, which, 321 00:18:49,066 --> 00:18:51,333 translates as your circuit 322 00:18:51,333 --> 00:18:54,333 to a native gate operations of your quantum computer, 323 00:18:54,333 --> 00:18:59,333 which is very similar as you are doing for, for classical coding. And, 324 00:19:00,433 --> 00:19:00,700 yeah. 325 00:19:00,700 --> 00:19:04,533 Then, basically you can analyze this circuit or so with Qiskit, 326 00:19:04,900 --> 00:19:09,266 then you have small scale simulations with all the ten qubits. 327 00:19:09,266 --> 00:19:13,000 You can simulate it classically, which is good for debugging to see 328 00:19:13,000 --> 00:19:15,033 whether you are doing the right thing. 329 00:19:15,033 --> 00:19:18,033 But, many of the, 330 00:19:18,266 --> 00:19:21,266 of, companies, they, 331 00:19:21,466 --> 00:19:23,966 they allow access to real hardware via cloud 332 00:19:23,966 --> 00:19:28,933 services and notably, there's, a, a, s bracket, 333 00:19:29,400 --> 00:19:33,000 which allows access, for example, to Google. 334 00:19:33,000 --> 00:19:34,900 It works for, 335 00:19:34,900 --> 00:19:38,666 quantum computers, but there's less, access, to IBM quantum. 336 00:19:39,200 --> 00:19:44,200 And that's, interesting is that, you do not have to be a professional. 337 00:19:44,233 --> 00:19:48,266 In fact, everybody can can register for this service. 338 00:19:48,266 --> 00:19:50,966 And you have also, 339 00:19:50,966 --> 00:19:53,700 limited a number of, 340 00:19:53,700 --> 00:19:57,033 time to, to run operations on this quantum computers. 341 00:19:57,166 --> 00:20:00,766 So, in fact, I think I know in the case of IBM quantum, it's, 342 00:20:01,700 --> 00:20:04,666 you'll have ten minutes time of computation. 343 00:20:05,733 --> 00:20:07,133 Time per month, but, 344 00:20:07,133 --> 00:20:12,166 but this is sufficient to, to run small operations and also everything. 345 00:20:12,300 --> 00:20:16,000 What I will show later is done within a few minutes. 346 00:20:19,433 --> 00:20:21,800 When you look at the, 347 00:20:21,800 --> 00:20:24,500 quantum computers, 348 00:20:24,500 --> 00:20:27,700 well, and this is cloud services, they illustrate, 349 00:20:28,633 --> 00:20:30,266 how the qubits are connected. 350 00:20:30,266 --> 00:20:32,733 This is a this is, 351 00:20:32,733 --> 00:20:34,566 snapshot of IBM. Yes. 352 00:20:34,566 --> 00:20:36,466 Which has, 353 00:20:36,466 --> 00:20:41,033 126 or 27 qubits. 354 00:20:41,033 --> 00:20:43,666 And in principle, you can use all of them. 355 00:20:43,666 --> 00:20:46,466 And it turns out that this is already hard 356 00:20:46,466 --> 00:20:49,466 to simulate on classical devices. 357 00:20:50,600 --> 00:20:51,566 Finally, and 358 00:20:51,566 --> 00:20:54,566 I also want to advocate, you can, 359 00:20:55,733 --> 00:20:56,966 do it on your own. 360 00:20:56,966 --> 00:21:01,200 And it turns out that programing quantum computers is not that much different 361 00:21:01,433 --> 00:21:04,433 to programing classical computers 362 00:21:05,033 --> 00:21:06,500 too. So this I want to 363 00:21:06,500 --> 00:21:09,800 illustrate of, first, a very simple example, 364 00:21:11,000 --> 00:21:11,366 which is 365 00:21:11,366 --> 00:21:14,533 creating a base state, but which is basically, 366 00:21:15,366 --> 00:21:18,033 either both qubits are in state zero 367 00:21:18,033 --> 00:21:21,966 and above states, in, in state one. 368 00:21:22,200 --> 00:21:28,500 So, I mean, so, so it's not very, complex, but but but in principle, 369 00:21:29,366 --> 00:21:34,033 this, this, like, creation of such, states, 370 00:21:36,933 --> 00:21:38,100 was very important 371 00:21:38,100 --> 00:21:41,100 also to, to, to, to test 372 00:21:41,133 --> 00:21:44,300 causality of, quantum mechanics and also respected in 373 00:21:44,333 --> 00:21:47,333 and Nobel Prize a few years ago, just a few years ago, 374 00:21:48,400 --> 00:21:52,400 it turns out, when you want to run it on a quantum computer, you first, 375 00:21:52,933 --> 00:21:55,933 import, quantum circuit object. 376 00:21:56,933 --> 00:22:00,900 You, you basically import your, library 377 00:22:02,633 --> 00:22:07,166 and then you apply your gates, quite straightforward. 378 00:22:07,166 --> 00:22:10,166 So it, in order to create your by state, 379 00:22:10,333 --> 00:22:14,100 first you have to apply a Hadamard gates to a qubit zero. 380 00:22:14,100 --> 00:22:19,200 So you put it in a, the first qubit on a superposition of zero and one. 381 00:22:20,933 --> 00:22:24,000 Then you apply a control not operation, 382 00:22:24,466 --> 00:22:29,033 which basically means that the, the first qubit is then in state zero. 383 00:22:29,033 --> 00:22:32,033 Then when the finished, 384 00:22:32,533 --> 00:22:33,766 zero of qubit is in state 385 00:22:33,766 --> 00:22:36,766 zero and and vice versa. 386 00:22:37,100 --> 00:22:38,900 And then you perform 387 00:22:38,900 --> 00:22:42,933 a few, two measurements to, read out the qubits. 388 00:22:43,200 --> 00:22:46,200 That's basically it. And then your, 389 00:22:46,200 --> 00:22:49,666 you can test how, how it looks on the quantum computer. 390 00:22:49,666 --> 00:22:52,666 So it's, five lines of code. 391 00:22:53,766 --> 00:22:55,866 Now, if you want to execute this, 392 00:22:55,866 --> 00:22:58,866 I mean, you can do it in a classically simulated, 393 00:23:00,333 --> 00:23:03,766 for this, they provide classical simulators. 394 00:23:05,166 --> 00:23:07,033 If you're, 395 00:23:07,033 --> 00:23:10,333 directly go to a quantum computer, you do not have to change much. 396 00:23:10,333 --> 00:23:13,500 It's basically it's basically changing two lines of code. 397 00:23:14,966 --> 00:23:18,266 And then, the next step is what I mentioned before. 398 00:23:18,266 --> 00:23:22,366 You have to test by, like, compile your circuit for the, for this, your, 399 00:23:23,400 --> 00:23:25,800 transpile. 400 00:23:25,800 --> 00:23:28,800 Basically that, this, transpile has, 401 00:23:29,333 --> 00:23:32,400 information of, the quantum computer. 402 00:23:32,400 --> 00:23:37,366 You, you want to run your code, and it's, it translates, 403 00:23:38,133 --> 00:23:41,133 it, it translates your circuit to the native, 404 00:23:42,166 --> 00:23:45,166 gates of your quantum computer 405 00:23:45,300 --> 00:23:47,233 and then your, afterwards. 406 00:23:47,233 --> 00:23:50,766 And in this case, I have prepared this, in advance. 407 00:23:53,166 --> 00:23:54,866 This circuit looks like this. 408 00:23:54,866 --> 00:23:57,866 But what you have basically is that, 409 00:23:59,066 --> 00:24:01,400 this is not this, 410 00:24:01,400 --> 00:24:05,300 this is translated to, such a, two qubit operation, 411 00:24:05,600 --> 00:24:10,366 which is almost a C, not, apart from some additional, phase shift. 412 00:24:11,633 --> 00:24:15,333 And then this the single qubit operation is, 413 00:24:16,100 --> 00:24:19,133 is translated in a lot of, of, 414 00:24:19,600 --> 00:24:22,600 rotations and additional face gates. 415 00:24:23,400 --> 00:24:26,433 But it's also interesting is when you look at the circuit, 416 00:24:26,733 --> 00:24:29,733 there are two numbers, 49 and 50. 417 00:24:30,666 --> 00:24:32,600 And, when you look at, 418 00:24:33,766 --> 00:24:36,766 the quantum computers, I have, shown before, 419 00:24:36,900 --> 00:24:41,100 it means basically that, the circuit is run on these two qubits. 420 00:24:41,100 --> 00:24:44,100 You can see here. 421 00:24:45,933 --> 00:24:46,800 And then, 422 00:24:46,800 --> 00:24:49,800 I mean, apart from it, you basically submit your job. 423 00:24:51,133 --> 00:24:53,866 And in our case, we want to run this circuit, multiple 424 00:24:53,866 --> 00:24:57,700 times, to, get some statistics and see what, what comes out. 425 00:24:57,700 --> 00:25:00,933 And then if, retrieve the result, 426 00:25:02,100 --> 00:25:05,000 which encodes some information, what, 427 00:25:05,000 --> 00:25:08,066 what gates you used, but, but, 428 00:25:09,366 --> 00:25:11,133 of properties of the quantum device. 429 00:25:11,133 --> 00:25:11,566 But nice. 430 00:25:11,566 --> 00:25:11,733 Right? 431 00:25:11,733 --> 00:25:15,233 It's it has and also, of course, the result itself. 432 00:25:15,233 --> 00:25:18,233 And then you can show it in a histogram 433 00:25:18,733 --> 00:25:21,733 in this case, I, 434 00:25:21,900 --> 00:25:24,900 I have prepared it as I mentioned, 435 00:25:25,000 --> 00:25:27,933 when you do the classical simulations, 436 00:25:27,933 --> 00:25:30,600 you get basically this count. 437 00:25:30,600 --> 00:25:34,300 I repeated the, the simulation a thousand, 24 times. 438 00:25:34,500 --> 00:25:34,833 This, 439 00:25:36,600 --> 00:25:37,000 this is a 440 00:25:37,000 --> 00:25:40,000 basically a matter of seconds for the circuits. 441 00:25:40,533 --> 00:25:42,233 And, what what, 442 00:25:42,233 --> 00:25:45,533 what you can see is that you have, basically 443 00:25:45,566 --> 00:25:49,500 of a 520 times here at your a measured the qubit, 444 00:25:50,433 --> 00:25:54,266 both qubits and state zero and otherwise you measured in state one. 445 00:25:54,266 --> 00:25:55,566 I mean, it's not not, 446 00:25:55,566 --> 00:25:59,666 perfectly 50%, but this is basically to statistical fluctuations. 447 00:26:00,466 --> 00:26:03,800 Now, you can, do the same on, on every other device. 448 00:26:05,166 --> 00:26:07,800 And in this case, you see, 449 00:26:07,800 --> 00:26:11,233 make this observation, it looks almost the same. 450 00:26:11,233 --> 00:26:14,300 You you get almost 50% on state zero. 451 00:26:14,833 --> 00:26:18,200 Both qubits and state seal of above qubits on state one. 452 00:26:18,500 --> 00:26:21,700 But what you also see is that there's, slight deviation. 453 00:26:22,433 --> 00:26:26,333 Basically that only one qubit is in state one and one qubit, 454 00:26:27,533 --> 00:26:31,733 while the other one and this is this is basically due 455 00:26:31,733 --> 00:26:35,000 to noise and hardware errors, which is quite remarkable. 456 00:26:36,133 --> 00:26:37,233 Seen before is, 457 00:26:37,233 --> 00:26:40,666 was a very small circuit, and we have already 2% error 458 00:26:40,666 --> 00:26:43,800 rates, which gives you an impression how, how good current 459 00:26:43,800 --> 00:26:46,800 hardware is. 460 00:26:47,133 --> 00:26:50,066 So, I mean, this is basically the reason 461 00:26:50,066 --> 00:26:53,500 why we have to deal with errors, in a, in the long run. 462 00:26:54,933 --> 00:26:59,566 I mean, as I mentioned, this was very, simplistic example. 463 00:26:59,900 --> 00:27:03,800 Now, if I want to, show you something which is, 464 00:27:04,733 --> 00:27:06,866 more connected to real world, 465 00:27:06,866 --> 00:27:09,866 at least from a theorist perspective. 466 00:27:10,366 --> 00:27:13,866 This is namely, this is basically dealing with quantum dynamics, 467 00:27:15,400 --> 00:27:17,033 which is one of the most, 468 00:27:17,033 --> 00:27:19,800 promising applications, 469 00:27:19,800 --> 00:27:21,733 basically use a quantum computer 470 00:27:21,733 --> 00:27:24,733 to simulate other quantum systems. 471 00:27:24,800 --> 00:27:29,333 And the idea is that you use the trusted, decomposition. 472 00:27:29,700 --> 00:27:32,933 So you, have, usually you have a very, 473 00:27:33,500 --> 00:27:37,566 complex operator or a complex system, your molecule or you, 474 00:27:38,733 --> 00:27:41,166 your, 475 00:27:41,166 --> 00:27:44,166 strongly interacting system to has some before 476 00:27:44,466 --> 00:27:47,633 and what you can, what you can do 477 00:27:47,633 --> 00:27:51,100 is that you decompose this big block or this from a, 478 00:27:51,666 --> 00:27:56,400 in a bunch of two qubit operations, and then you have this cubit operations. 479 00:27:56,400 --> 00:27:59,400 It's in state, straightforward. 480 00:28:00,133 --> 00:28:01,400 To practice and compile. 481 00:28:01,400 --> 00:28:04,400 And then you can run this 482 00:28:04,400 --> 00:28:07,200 and this, this looks, 483 00:28:07,200 --> 00:28:08,400 quite simple. 484 00:28:08,400 --> 00:28:11,333 But, the issue is, from a classical perspective, 485 00:28:11,333 --> 00:28:15,566 the dimension of the Hilbert space scales exponentially with the number of qubits. 486 00:28:16,033 --> 00:28:20,666 And, when you want to simulate such systems, classically, 487 00:28:20,700 --> 00:28:23,733 it turns out that, you're basically 488 00:28:23,766 --> 00:28:26,766 at the limits of, 489 00:28:28,000 --> 00:28:31,500 of, state of the art classical computers. 490 00:28:31,500 --> 00:28:34,500 When you go to, to roughly set the qubits, 491 00:28:34,600 --> 00:28:37,600 or a bit more, which is, I would say, 492 00:28:38,333 --> 00:28:39,433 quite far from 493 00:28:39,433 --> 00:28:42,433 complex molecules or, interacting systems. 494 00:28:42,733 --> 00:28:44,600 So that's the reason why, this, 495 00:28:45,566 --> 00:28:46,500 this approach is 496 00:28:46,500 --> 00:28:50,266 actually used also to benchmark the performance of quantum computers. 497 00:28:50,666 --> 00:28:53,566 And then you do a few, tweaks and tricks. 498 00:28:53,566 --> 00:28:56,866 You can show already that occurring quantum computers, 499 00:28:59,166 --> 00:29:01,266 can give competitive 500 00:29:01,266 --> 00:29:04,266 results, to, to classical devices. 501 00:29:04,800 --> 00:29:07,800 How is how is this done? 502 00:29:08,033 --> 00:29:10,633 Again, using Qiskit. 503 00:29:10,633 --> 00:29:13,333 I use a very simple toy model. 504 00:29:13,333 --> 00:29:16,333 But it's straightforward to use, some, 505 00:29:16,500 --> 00:29:17,500 something more complex. 506 00:29:17,500 --> 00:29:21,100 And in fact, this case is so simple that you can solve it. 507 00:29:21,500 --> 00:29:22,733 Exactly. 508 00:29:22,733 --> 00:29:25,233 By hand. 509 00:29:25,233 --> 00:29:28,500 So you have basically you have basically an interaction between two qubits, 510 00:29:28,900 --> 00:29:32,600 by some interaction and you have some additional magnetic field, 511 00:29:34,300 --> 00:29:36,200 and then then you want to, 512 00:29:36,200 --> 00:29:39,200 to code that, Trotta evolution, 513 00:29:39,200 --> 00:29:41,833 of what you have to do is you basically create 514 00:29:41,833 --> 00:29:44,833 a trotter, a trotter gate. 515 00:29:44,866 --> 00:29:48,833 So you, create your Hamiltonian with online what they took here, but 516 00:29:48,833 --> 00:29:53,833 Hamiltonian and then this, automatically creates 517 00:29:53,833 --> 00:29:57,600 you an evolution, this, qubit evolution gate. 518 00:29:58,500 --> 00:30:01,366 And. Yeah, if you want to multiply it with the times, 519 00:30:02,366 --> 00:30:02,666 you will 520 00:30:02,666 --> 00:30:05,666 have a basically at a few lines of code which, 521 00:30:06,433 --> 00:30:09,433 apply to, gates, either to the even bonds, 522 00:30:10,200 --> 00:30:12,433 which are the first two lines, 523 00:30:12,433 --> 00:30:15,866 to, to the odd and that's basically it. So, 524 00:30:17,100 --> 00:30:20,100 I can show again when your, 525 00:30:20,166 --> 00:30:23,266 want to consider one of these trotter steps for six qubits, 526 00:30:24,300 --> 00:30:26,033 it looks like this. 527 00:30:26,033 --> 00:30:29,933 I mean, it's a it's a bit more complex than before, but, 528 00:30:30,266 --> 00:30:33,466 but when you look closely at this, then, 529 00:30:35,100 --> 00:30:37,633 this red box corresponds 530 00:30:37,633 --> 00:30:40,600 to one trotter step which I have implemented. 531 00:30:40,600 --> 00:30:43,800 And and the rest is done, is done by inference by the. 532 00:30:45,433 --> 00:30:48,433 Now you can again compare 533 00:30:48,500 --> 00:30:51,500 the time evolution, as I have done by before. 534 00:30:52,000 --> 00:30:53,966 In this case, I'm, 535 00:30:53,966 --> 00:30:56,533 I saw, to not sample 536 00:30:56,533 --> 00:30:59,366 exact strings, but, but measured in magnetization. 537 00:30:59,366 --> 00:31:03,166 So, so the, the expectation value of a set on each side. 538 00:31:04,366 --> 00:31:05,900 And you do it classically, 539 00:31:05,900 --> 00:31:08,900 on, the exact simulation on a classical computer. 540 00:31:09,833 --> 00:31:12,966 I start, with, with, 541 00:31:13,733 --> 00:31:16,733 a staggered initial state, the, 542 00:31:17,300 --> 00:31:21,166 which you, which is indicated by this pattern. 543 00:31:21,166 --> 00:31:24,666 And then you evolve in time, you see that, the, 544 00:31:25,566 --> 00:31:27,766 the system equilibria. 545 00:31:27,766 --> 00:31:31,066 But you see also this, this long term oscillations. 546 00:31:32,200 --> 00:31:35,200 Now, you can compared again with a quantum computer. 547 00:31:36,133 --> 00:31:40,500 It looks not that bad, in fact, for, especially when a, 548 00:31:40,500 --> 00:31:44,766 when you have in mind that before we have a 2% error rate per, packet. 549 00:31:45,000 --> 00:31:47,766 So you, you see, especially at the beginning, 550 00:31:47,766 --> 00:31:51,766 you, you see this oscillations there, there's spun qubits. 551 00:31:53,400 --> 00:31:55,833 This, oscillation do not, 552 00:31:55,833 --> 00:31:58,833 decay really, which indicates that probably this, 553 00:31:59,700 --> 00:32:02,700 Q qubit does not work properly. 554 00:32:02,700 --> 00:32:05,766 And, but additionally, you see that, 555 00:32:07,200 --> 00:32:10,000 that the long time values, 556 00:32:10,000 --> 00:32:13,266 it's, it seems to equilibrate, but, 557 00:32:13,500 --> 00:32:19,033 but you are not able to, to, to, to capture the oscillations, 558 00:32:19,066 --> 00:32:22,466 at least when we do it as naively as I did right now. 559 00:32:23,700 --> 00:32:26,266 But, but still, in comparison to the Bose state 560 00:32:26,266 --> 00:32:29,266 I have shown before, it seems that, especially when you look at, 561 00:32:30,900 --> 00:32:32,500 look at observables. 562 00:32:32,500 --> 00:32:37,900 So it's, performs relatively good in comparison 563 00:32:38,066 --> 00:32:40,966 of what you would naively expect from, 564 00:32:40,966 --> 00:32:43,266 from 2% errors per step. 565 00:32:43,266 --> 00:32:46,700 And this is also basically an indication that when you consider physical systems 566 00:32:46,700 --> 00:32:51,133 also, that they are basically more robust to errors than you would naively expect. 567 00:32:52,833 --> 00:32:55,800 Now, I showed you 568 00:32:55,800 --> 00:32:58,733 how how valuable the quantum computers are. 569 00:32:58,733 --> 00:33:01,733 And as you have seen, you have lots of errors. 570 00:33:01,733 --> 00:33:07,100 So I want to briefly sketch at the end of my talk how to deal with them. 571 00:33:08,266 --> 00:33:10,866 One thing, and this is 572 00:33:10,866 --> 00:33:13,566 is is basically the path to goal. 573 00:33:13,566 --> 00:33:17,900 And in the long term, then you want to run more complex algorithms. 574 00:33:17,900 --> 00:33:18,966 That's for example, 575 00:33:18,966 --> 00:33:22,100 Shor's algorithm is that you have to do phantom error correction. 576 00:33:22,700 --> 00:33:25,700 The idea is basically your, instead of using, 577 00:33:25,866 --> 00:33:30,766 qubits, your, your encode redundant, information and basically, 578 00:33:31,366 --> 00:33:35,333 repeat the information of the qubits in multiple qubits 579 00:33:35,333 --> 00:33:39,700 such, that you can detect when you have an error incorrect for it. 580 00:33:41,500 --> 00:33:44,100 And this, has, has been done. 581 00:33:44,100 --> 00:33:46,666 Has been, Pope Benedict last time, 582 00:33:46,666 --> 00:33:50,266 but this in order to do this, you basically, 583 00:33:50,733 --> 00:33:54,700 require quite small error rates and large number of qubits. 584 00:33:55,333 --> 00:33:58,300 Basically the reason is, when you increase 585 00:33:58,300 --> 00:34:02,100 the number of qubits, you also increase an error rate. 586 00:34:02,100 --> 00:34:04,800 And so you basically have to balance this. 587 00:34:04,800 --> 00:34:08,000 And, I mean, this this is an active area of research. 588 00:34:08,000 --> 00:34:11,000 This is for example, a picture of 589 00:34:12,166 --> 00:34:16,933 encoding one qubits and in terms of roughly, 590 00:34:18,466 --> 00:34:21,466 I think it's for the 50 physical qubits. 591 00:34:21,633 --> 00:34:24,066 And then detecting the errors. 592 00:34:24,066 --> 00:34:28,466 But, the point is, I think in order to get this work, 593 00:34:28,500 --> 00:34:31,500 you need at least a few more years, 594 00:34:32,733 --> 00:34:36,700 another, promising thing, which is probably more applicable. 595 00:34:36,933 --> 00:34:41,966 The in this, short term is, so-called quantum error mitigation. 596 00:34:43,166 --> 00:34:44,100 It's, 597 00:34:44,100 --> 00:34:47,400 as you will have seen before, for observables, 598 00:34:47,400 --> 00:34:51,500 it seems that we do not need the, the perfect, quantum computer. 599 00:34:52,700 --> 00:34:55,566 And the idea is that you run experiments 600 00:34:55,566 --> 00:34:58,733 to learn the noise and then do some interpolation. 601 00:34:59,033 --> 00:35:02,033 This idea is basically quite simple. 602 00:35:02,533 --> 00:35:05,900 And it's also what basically what you have, 603 00:35:05,900 --> 00:35:08,900 you start with a noise rate one which, 604 00:35:09,200 --> 00:35:12,466 corresponds to the noise you have from the actual, quantum computer. 605 00:35:12,900 --> 00:35:16,000 And then even, then you know how, 606 00:35:16,200 --> 00:35:21,200 how the errors speed up, you can basically artificially enhance 607 00:35:21,200 --> 00:35:26,133 your noise rate is done by this, red dots, red crosses. 608 00:35:26,600 --> 00:35:29,433 And then you can interpolate to zero noise 609 00:35:29,433 --> 00:35:32,433 rate and, 610 00:35:33,500 --> 00:35:35,533 it it's, 611 00:35:35,533 --> 00:35:37,466 looks a bit fishy, but it seems that 612 00:35:37,466 --> 00:35:40,466 it works pretty badly for observables. 613 00:35:40,466 --> 00:35:44,633 And when you want to be competitive with classical simulations, 614 00:35:44,633 --> 00:35:49,600 and this is the method which is done to get good results. 615 00:35:49,700 --> 00:35:51,466 Quantum computers already today. 616 00:35:53,900 --> 00:35:56,766 To, to sum up, 617 00:35:56,766 --> 00:35:59,866 well, what I wanted to highlight is that basically programing 618 00:35:59,866 --> 00:36:03,733 a quantum computer is quite simple, so everybody can do it. 619 00:36:05,133 --> 00:36:09,300 I mean, this is a kind of trotter step which is only a few lines of code, 620 00:36:09,300 --> 00:36:13,800 and then you are basically already at the forefront of research. 621 00:36:16,666 --> 00:36:19,666 The remaining main challenge you have to do is, 622 00:36:20,466 --> 00:36:24,466 is understanding the error and is where most efforts are right now. 623 00:36:24,800 --> 00:36:26,100 Thank you for your attention. 624 00:36:26,100 --> 00:36:29,100 And do it yourself. 625 00:36:39,366 --> 00:36:40,800 Okay, 626 00:36:40,800 --> 00:36:44,100 so basically the question as far as I understand 627 00:36:44,100 --> 00:36:47,166 is a possibility is, better it's 628 00:36:47,200 --> 00:36:51,600 better to think about improving quantum gates and, how fast you can run. 629 00:36:52,533 --> 00:36:54,433 Yeah. Actually, that's, that's a good point. 630 00:36:54,433 --> 00:36:58,200 And, I mean, I think that's, that's the main difference between, 631 00:36:59,400 --> 00:37:02,033 different approaches of quantum computers. 632 00:37:02,033 --> 00:37:06,633 But when you look at the, the execution times of gates in, 633 00:37:07,066 --> 00:37:11,000 in the case of superconducting qubits, 634 00:37:11,000 --> 00:37:14,000 it's of order one hundreds of nanoseconds. 635 00:37:14,100 --> 00:37:17,100 And when you use trapped ions, it's, 636 00:37:17,433 --> 00:37:20,433 it's basically three orders of magnitude larger. 637 00:37:20,700 --> 00:37:23,700 And I think one of the, 638 00:37:23,933 --> 00:37:27,333 one of the most important properties, especially when you have 639 00:37:28,000 --> 00:37:31,200 ions, has so is finding a, finding approaches 640 00:37:31,200 --> 00:37:34,200 that you can reduce, 641 00:37:34,233 --> 00:37:36,966 the, the execution time of gates. 642 00:37:36,966 --> 00:37:40,833 And this is, this is also a basically cutting edge of research, 643 00:37:40,833 --> 00:37:43,833 not for the superconducting qubits, but for other devices. 644 00:37:46,400 --> 00:37:49,400 Okay. The, 645 00:37:49,433 --> 00:37:52,266 basically everyday you have different like, 646 00:37:52,266 --> 00:37:55,266 language constructs to, to different, 647 00:37:55,666 --> 00:37:58,333 types of quantum computing. 648 00:37:58,333 --> 00:38:01,266 So far as I think 649 00:38:01,266 --> 00:38:05,933 the issue is a little bit the I mean, the quantum computers are still in 650 00:38:06,166 --> 00:38:10,800 such native stages that, I think there is so far. 651 00:38:10,833 --> 00:38:14,066 No, no need to think about my infants cases. 652 00:38:14,066 --> 00:38:17,200 I think it might be the case. I mean, your, 653 00:38:18,900 --> 00:38:19,933 regard to what 654 00:38:19,933 --> 00:38:23,033 complex algorithms and how to implement that, for example, 655 00:38:24,100 --> 00:38:26,933 proposals that instead of, 656 00:38:26,933 --> 00:38:29,366 gate operations, you only, 657 00:38:29,366 --> 00:38:31,566 perform measurements. 658 00:38:31,566 --> 00:38:33,866 And and this might be sufficient 659 00:38:33,866 --> 00:38:37,433 to, to, generate the universal quantum computers. 660 00:38:37,433 --> 00:38:40,566 So in this sense, it is thought about it. 661 00:38:41,700 --> 00:38:45,166 But in principle, it's mostly that we are only at the single qubit 662 00:38:45,166 --> 00:38:46,100 and two qubit stage. 663 00:38:46,100 --> 00:38:49,300 And so it's a bit early in many cases. 664 00:38:51,900 --> 00:38:53,800 Yeah. 665 00:38:53,800 --> 00:38:57,000 So basically the question is how does quantum error correction work. 666 00:38:57,000 --> 00:38:57,266 Yeah. 667 00:38:57,266 --> 00:39:00,866 You need physical qubits to to get the logical qubits. 668 00:39:00,866 --> 00:39:03,866 And then you run in, increasing 669 00:39:05,100 --> 00:39:06,533 required coherence times. 670 00:39:06,533 --> 00:39:07,633 How does it work. 671 00:39:07,633 --> 00:39:08,433 That's a good point. 672 00:39:08,433 --> 00:39:09,466 And that's, 673 00:39:09,466 --> 00:39:10,433 I said the issue of why 674 00:39:10,433 --> 00:39:14,166 we do not have quantum error correction right now to one point. 675 00:39:15,333 --> 00:39:18,333 The point is that, 676 00:39:18,600 --> 00:39:22,533 the, the way how it works is, when your 677 00:39:23,833 --> 00:39:27,200 have as a sufficient number of qubits, then, 678 00:39:27,733 --> 00:39:32,400 basically you can correct a small number of errors. 679 00:39:33,000 --> 00:39:37,200 So, so this helps you, but at the same time still, 680 00:39:38,533 --> 00:39:42,166 as you mentioned, you'll have increasing sources of errors. 681 00:39:42,166 --> 00:39:44,533 So you have basically two factors. 682 00:39:44,533 --> 00:39:46,566 What turns out is, 683 00:39:46,566 --> 00:39:51,500 when when your error rate of physical qubits is, is large, then 684 00:39:51,500 --> 00:39:52,500 you have no chance. 685 00:39:52,500 --> 00:39:55,800 And then trying to do, quantum error correction, 686 00:39:56,766 --> 00:39:59,200 the Q 687 00:39:59,200 --> 00:40:01,200 however, right now 688 00:40:01,200 --> 00:40:05,000 we are at the stage where basically quantum error correction of means. 689 00:40:05,000 --> 00:40:09,233 So basically by, by adding security, by adding qubits, 690 00:40:09,633 --> 00:40:12,966 you, gain as much advantage 691 00:40:13,766 --> 00:40:16,766 that, it basically, 692 00:40:17,766 --> 00:40:21,100 that it basically overtakes the disadvantage from, 693 00:40:21,966 --> 00:40:27,000 more additional physical cubits and the as a, as a, concerning 694 00:40:27,000 --> 00:40:32,666 the question how, how many physical qubits you need to protect, one logical qubit. 695 00:40:33,066 --> 00:40:33,900 So it 696 00:40:35,000 --> 00:40:36,300 basically, if 697 00:40:36,300 --> 00:40:41,500 when you are below this threshold of, logically a quantum error correction bits, 698 00:40:42,066 --> 00:40:45,533 what you can see is that, the more physical qubits 699 00:40:45,533 --> 00:40:49,333 you use, the exponentially better, becomes 700 00:40:49,866 --> 00:40:52,466 your, advantage. 701 00:40:52,466 --> 00:40:56,166 And and then it's then it's, then it's, basically 702 00:40:56,800 --> 00:41:00,366 trying to be as good as possible with the physical qubits. 703 00:41:00,366 --> 00:41:03,466 And then you it might be that you need only 704 00:41:03,466 --> 00:41:06,466 a few more, 705 00:41:06,633 --> 00:41:10,466 physical qubits, but it's, but it's still a work in progress. 706 00:41:10,466 --> 00:41:15,133 In fact, I think the, state of the art for superconducting qubits 707 00:41:15,133 --> 00:41:18,133 is that you can generate one logical qubit. 708 00:41:18,900 --> 00:41:19,133 Yeah. 709 00:41:19,133 --> 00:41:20,700 So so the question is, 710 00:41:20,700 --> 00:41:22,766 can you gain the advantage when instead of, 711 00:41:22,766 --> 00:41:27,066 using qubits with two states, whether you, can gain advantage with, 712 00:41:27,666 --> 00:41:30,166 three states rights or if more states, 713 00:41:31,766 --> 00:41:33,266 yeah, this 714 00:41:33,266 --> 00:41:37,100 is, is has been explored and there are some possibilities. 715 00:41:37,100 --> 00:41:40,233 I mean, I think, for, 716 00:41:42,000 --> 00:41:44,100 for most, 717 00:41:44,100 --> 00:41:48,300 long time approaches when you are sufficiently efficient, it, 718 00:41:48,300 --> 00:41:53,200 it will I mean, maybe make an difference of a factor. 719 00:41:53,200 --> 00:41:56,200 So, so from a, 720 00:41:56,700 --> 00:41:59,700 teaching and complexity point of view, it's not change, 721 00:41:59,933 --> 00:42:02,933 but, a is, has been explored. 722 00:42:03,333 --> 00:42:06,966 For example, when you simulate lattice gauge theory, a bit of it's is, 723 00:42:07,600 --> 00:42:10,433 which is important to study high energy physics. 724 00:42:10,433 --> 00:42:13,433 So the standard of physics of the standard models, then, 725 00:42:14,400 --> 00:42:18,500 then especially in, in trapped ion systems, 726 00:42:20,033 --> 00:42:23,033 it's easy instead of, controlling two qubits, 727 00:42:24,400 --> 00:42:27,400 to, sorry, two levels, 728 00:42:27,500 --> 00:42:30,500 controlling multiple levels up to 20 levels. 729 00:42:31,200 --> 00:42:33,533 And it turns out that in this case, 730 00:42:33,533 --> 00:42:38,300 you can gain an advantage in the length of the, of the circuits. 731 00:42:38,300 --> 00:42:39,933 And and and. 732 00:42:39,933 --> 00:42:42,566 Yeah, and get more efficient computations. 733 00:42:44,333 --> 00:42:46,166 Yeah. 734 00:42:46,166 --> 00:42:46,700 Observation. 735 00:42:46,700 --> 00:42:49,333 So the question is, 736 00:42:49,333 --> 00:42:52,333 but I just quickly pick. 737 00:42:54,666 --> 00:42:57,666 Basically I saw, I saw, results here from. 738 00:42:57,666 --> 00:42:59,233 And what about, time steps. 739 00:42:59,233 --> 00:43:02,233 How does it work when I, when I, when I measure 740 00:43:02,600 --> 00:43:04,700 the state, I actually destroy it. 741 00:43:04,700 --> 00:43:05,566 And it's a good point. 742 00:43:05,566 --> 00:43:08,733 And, the answer is that I have not run. 743 00:43:08,733 --> 00:43:13,400 You have one experiment, but 30 experiments for each different system 744 00:43:13,400 --> 00:43:16,400 size. So, 745 00:43:17,100 --> 00:43:20,100 so basically, I, I, 746 00:43:20,400 --> 00:43:24,133 in advance, I state, how many steps do I want, 747 00:43:24,133 --> 00:43:27,133 for example, for, for, 748 00:43:28,033 --> 00:43:30,700 ten steps, which corresponds to time peak for ten. 749 00:43:30,700 --> 00:43:33,700 And then I run this, this experiment, 750 00:43:34,900 --> 00:43:37,900 in this case, I run a thousand times to, to, 751 00:43:38,100 --> 00:43:41,100 collect enough statistics and then to get the measurements. 752 00:43:41,166 --> 00:43:43,366 Of course, I mean, you get the massive overhead, 753 00:43:44,933 --> 00:43:46,566 but but it's doable. 754 00:43:46,566 --> 00:43:49,566 So in principle, for one two steps, 755 00:43:49,833 --> 00:43:53,733 sorry, for one time step to, generate a thousand measurements. 756 00:43:53,766 --> 00:43:56,366 It took me, 757 00:43:56,366 --> 00:43:58,100 10s on a quantum computer. 758 00:43:58,100 --> 00:44:02,500 So I think the overall plot on the right is a matter of five minutes or something. 759 00:44:03,233 --> 00:44:03,966 Yes, exactly. 760 00:44:03,966 --> 00:44:06,500 So I think that this cube. 761 00:44:06,500 --> 00:44:09,300 Yeah, that's, and this, 762 00:44:09,300 --> 00:44:10,600 qubit does not work. 763 00:44:10,600 --> 00:44:13,600 And, actually, even when you're look, 764 00:44:14,133 --> 00:44:18,400 at, at, this IBM, quantum website, you, 765 00:44:18,666 --> 00:44:22,766 you can have access, to, to the performance of this, qubits. 766 00:44:22,766 --> 00:44:25,766 And the what you see is that, sometimes, 767 00:44:26,633 --> 00:44:31,066 they are some calibrations and not all of this connections, perfect. 768 00:44:31,233 --> 00:44:34,233 This is what, what happened here? 769 00:44:34,866 --> 00:44:35,700 Yeah. Yeah. 770 00:44:35,700 --> 00:44:39,100 So I think the the point is, I mean, yeah, it does not work for, 771 00:44:40,166 --> 00:44:42,366 extra classical encryption. 772 00:44:42,366 --> 00:44:46,466 Like, you could, you can break the as a encryption. 773 00:44:46,900 --> 00:44:49,900 But the reason why they use it right now is, 774 00:44:50,700 --> 00:44:53,700 it's because it's a relatively cheap to implement. 775 00:44:54,600 --> 00:44:58,366 Yeah, but but this current research of quantum cryptography, 776 00:44:58,633 --> 00:45:01,900 which you cannot break with quantum computers and would be, 777 00:45:03,033 --> 00:45:06,033 secure because of the physical laws of quantum mechanics. 778 00:45:06,633 --> 00:45:09,766 I mean, nevertheless, I mean, probably for most cases, 779 00:45:09,766 --> 00:45:13,166 it's too expensive, and it's like quantum computers. 780 00:45:14,900 --> 00:45:16,766 They might be useful in this field 781 00:45:16,766 --> 00:45:19,766 long time, but, but then you have, 782 00:45:20,466 --> 00:45:22,066 very sensitive information. 783 00:45:22,066 --> 00:45:24,700 You will use a different encryption. 784 00:45:24,700 --> 00:45:26,133 I'll do a certain. 785 00:45:26,133 --> 00:45:29,033 No, I think not. Mine has one. 786 00:45:29,033 --> 00:45:33,700 But I think it's it's, I think it's a reasonable concern. 787 00:45:33,700 --> 00:45:36,966 And, it's also a when you look at the research 788 00:45:36,966 --> 00:45:40,733 that it's for example, of classified and in the US. 789 00:45:40,866 --> 00:45:41,700 So, when you, 790 00:45:42,666 --> 00:45:44,166 when you travel to China and 791 00:45:44,166 --> 00:45:47,166 you are quantum research, they are very interested in you. 792 00:45:50,700 --> 00:45:51,066 Okay. 793 00:45:51,066 --> 00:45:54,100 I think the question is basically what is more important 794 00:45:54,100 --> 00:45:57,100 is that understanding, 795 00:45:57,166 --> 00:46:00,533 errors and, and try to cure them is basically, 796 00:46:01,133 --> 00:46:04,500 getting larger and better quantum computers, but it's just more important. 797 00:46:06,200 --> 00:46:09,200 The point is, when you're, 798 00:46:09,400 --> 00:46:11,800 when you consider, this error 799 00:46:11,800 --> 00:46:15,100 mitigation techniques I mentioned before, I think they hope for. 800 00:46:17,400 --> 00:46:19,800 For some cases as observables. 801 00:46:19,800 --> 00:46:24,866 But I think they they ultimately break down at some point. 802 00:46:24,866 --> 00:46:28,733 And you can it can also show that they, they will not given any cases. 803 00:46:29,100 --> 00:46:33,033 So I think in the long term run you'll always need quantum error correction. 804 00:46:33,033 --> 00:46:36,133 And but the quantum computers but 805 00:46:36,466 --> 00:46:39,466 nevertheless when you look at, 806 00:46:39,700 --> 00:46:41,633 amid near-future a 807 00:46:41,633 --> 00:46:45,466 so what what would happen is that you basically you have an interplay of, 808 00:46:46,366 --> 00:46:50,066 two approaches that error mitigation that I hope you to be a little bit better 809 00:46:51,033 --> 00:46:53,300 and then you can ever get, 810 00:46:53,300 --> 00:46:56,366 fast improvement with quantum error correction once is you. 811 00:46:58,500 --> 00:47:00,566 Okay, that's a good question. 812 00:47:00,566 --> 00:47:03,266 The question is basically, 813 00:47:03,266 --> 00:47:07,100 but, I, as a program, responsible for quantum error correction. 814 00:47:07,200 --> 00:47:10,633 It's done in the compiler or on a hardware level, I think. 815 00:47:11,400 --> 00:47:14,166 I mean, that's already shown here 816 00:47:14,166 --> 00:47:17,166 a little bit. 817 00:47:18,300 --> 00:47:19,900 But what happens this time 818 00:47:19,900 --> 00:47:22,900 instead of any of the of any of any 819 00:47:23,433 --> 00:47:26,433 if any progress in quantum computer evolves, is that, 820 00:47:28,366 --> 00:47:32,733 basically one was getting a black box, I mean, already here, I mean, you see that 821 00:47:32,766 --> 00:47:37,533 a basically creates a poly evolution gate by calling it, another comment. 822 00:47:38,700 --> 00:47:41,733 So 2 or 3 years ago, I took coded up a cipher 823 00:47:41,733 --> 00:47:44,733 and it was a bit more complex. 824 00:47:44,966 --> 00:47:47,166 But I think I saw with this, quantum 825 00:47:47,166 --> 00:47:51,100 error correction is basically you, go down 826 00:47:51,100 --> 00:47:55,500 either to the compiler or is lower to the hardware level. 827 00:47:55,933 --> 00:47:57,533 And what, whatever. I did not know exactly. 828 00:48:01,500 --> 00:48:02,033 All right. 829 00:48:02,033 --> 00:48:04,800 It looks like it's one of those questions. So let's think of it again.