1 00:00:08,740 --> 00:00:15,819 Okay so it's a very happy to be here, had these excellent discussions and I see some familiar faces. 2 00:00:15,820 --> 00:00:16,630 I'm very happy to be here. 3 00:00:17,890 --> 00:00:26,049 So today I'll be telling you about why would you like to use quantum computers to simulate chemistry and the progress in a colloquium format? 4 00:00:26,050 --> 00:00:31,810 Not too many details. I'm happy to answer details at the end over the last ten years on this subject. 5 00:00:34,260 --> 00:00:35,910 And sorry, I just got the new clicker as well. 6 00:00:36,570 --> 00:00:46,230 So let's just think, first of all, simulation in general and I just want to make the argument that as soon as humans have had technology, 7 00:00:47,220 --> 00:00:51,390 they have been able to simulate their surrounding world in particular. 8 00:00:51,870 --> 00:00:55,200 The ancient Greeks had a classical technology. 9 00:00:55,410 --> 00:00:58,440 They were able to put gears together and they built this device. 10 00:00:58,440 --> 00:01:02,399 That fascinates me. This is antiquity, right. And, you know, around 200 BCE, 11 00:01:02,400 --> 00:01:07,380 they built this device that actually can predict the movement of the planets and even the next Olympia 12 00:01:08,160 --> 00:01:13,560 that needs an arrangement of gears that we build to try to understand the movement of classical objects. 13 00:01:14,220 --> 00:01:19,200 All right. And it is this classical technology that started with the gears and ended up with computing 14 00:01:19,710 --> 00:01:24,030 that allowed us to have pretty much the physical the physical world that we live on, 15 00:01:24,690 --> 00:01:31,530 actually. Peter Gleason One of my colleagues in the history of Science Department, and he's also Professor of physics, 16 00:01:32,040 --> 00:01:36,479 wrote this very beautiful book called Image and Logic about the emergence of computing 17 00:01:36,480 --> 00:01:42,720 as a further leg of science and has a beautiful chapter in which he says the following. 18 00:01:42,750 --> 00:01:47,910 He says that without computer simulation, the material culture of today, for example, 19 00:01:48,300 --> 00:01:54,690 my beloved iPhone or my laptop or my cell phone wouldn't exist, not even my computer. 20 00:01:54,690 --> 00:01:58,940 So in some sense now physical reality is inseparable from the virtual counterparts. 21 00:01:59,790 --> 00:02:04,860 And again, we're very good at designing bridges and rockets and classical computers, 22 00:02:05,520 --> 00:02:11,790 but we are still perhaps not as powerful at simulating the quantum world, quantum devices, even molecules. 23 00:02:12,390 --> 00:02:18,570 And that's why we perhaps want to do the same thing that we did with classical technology. 24 00:02:18,570 --> 00:02:22,680 Well, now using quantum technology in other worlds, using quantum technology to simulate the quantum world. 25 00:02:24,760 --> 00:02:29,350 So in particular, the field that interests me the most. I mean, the original title said Chemistry and Materials. 26 00:02:29,980 --> 00:02:38,920 And it is because in my group we are also thinking about quantum simulators for periodic systems and in general materials is to actually discover, 27 00:02:38,920 --> 00:02:47,200 for example, molecules. So many, many people always ask themselves the question, perhaps I'm partially responsible for this law that is going around, 28 00:02:47,200 --> 00:02:50,950 that if you ever have a quantum computer, it will be used to do chemistry. 29 00:02:51,490 --> 00:02:54,670 Okay. And I always am forced to answer this. 30 00:02:54,670 --> 00:03:01,990 And one of the ways to answer it is just thinking about what will be the most useful to humanity applications of a quantum device if we ever have it. 31 00:03:02,530 --> 00:03:05,590 And you might argue perhaps it's cryptography if you work at the NSA. 32 00:03:06,130 --> 00:03:09,250 What? I will argue that, for example, just the fine chemicals market, 33 00:03:09,890 --> 00:03:19,060 the market of drugs and perfumes and glues and all sorts of chemicals that are expensive with respect to their weight is $3 trillion. 34 00:03:19,630 --> 00:03:25,450 So if you have a quantum computer and you impact the design of of molecules, then you can you can enter this market. 35 00:03:25,960 --> 00:03:30,660 And of course, classical computers do a lot. And in my group we discover molecules is a big thing that we do. 36 00:03:31,210 --> 00:03:35,620 In particular, we have a scorpion. We make sure here this is not a chemistry seminar. 37 00:03:36,130 --> 00:03:43,290 But in this paper here, what we do is use the computer to simulate what we believe is the world's cheapest battery. 38 00:03:43,810 --> 00:03:50,140 Now, battery made of Quinones, which are basically these molecules that plants use to in their electron transfer chain. 39 00:03:50,260 --> 00:03:56,290 And we hack them or modify them with a computer to make them very, very good batteries, way cheaper than lithium batteries. 40 00:03:56,620 --> 00:03:59,680 And these batteries can be employed, for example, in these tanks here, 41 00:03:59,710 --> 00:04:06,940 coupled with solar cells, although this company, Volt, is already it's already bankrupt. 42 00:04:07,570 --> 00:04:13,630 And the reason renewable dismantled is because this is these tanks are actually filled with metals and the molecules that we decided are metal free, 43 00:04:14,290 --> 00:04:17,950 way cheaper than the chromium that these guys were putting in these tanks. Okay. 44 00:04:18,130 --> 00:04:24,950 So I'm very excited about applications like these. But of course, if you say, well, I want to be more fundamental, of course, 45 00:04:24,950 --> 00:04:32,690 this fundamental questions like I love this picture of of a process experiment of scanning a sealed tape and paint a scene on a surface. 46 00:04:33,560 --> 00:04:36,740 And the reason I like it, of course, is because you can pretty much see the conjugate, 47 00:04:36,750 --> 00:04:40,880 the electron cloud by this very, very delicate probe of this molecule in a solid phase. 48 00:04:41,480 --> 00:04:47,780 But also because Pantheon is a very strongly correlated molecule that has to be studied with powerful metal, 49 00:04:47,790 --> 00:04:49,910 such as density matrix or meditation group theory. 50 00:04:50,300 --> 00:04:54,440 You have to follow the best that we have with classical computers to understand electronic structure of the system. 51 00:04:55,130 --> 00:04:59,900 And, and we can do this the matrix normalisation group theory because it's a linear molecule. 52 00:05:00,530 --> 00:05:06,980 So flat Polynesians in an infinite limit, they are called graphene. 53 00:05:07,490 --> 00:05:12,920 And I'm in the physics department and I know that everybody is in love with graphene in these departments, with the chemists. 54 00:05:12,920 --> 00:05:14,840 We just call it infinite polyethylene, I guess. 55 00:05:14,840 --> 00:05:21,770 But, you know, graphene is basically an example of a system that is very interesting to simulate also with a simulator. 56 00:05:21,770 --> 00:05:28,129 So that's the target that I'm talking about. I'm arguing the quantum computers will be perhaps first employed to do this. 57 00:05:28,130 --> 00:05:34,430 And that's the subject of this talk. So now let's use them, see to see ourselves first and think, why do we really need them? 58 00:05:34,460 --> 00:05:41,330 Right. So this is my former advisor, Martin Catherwood on the UC Berkeley wrote this paper where he actually was pretty good, 59 00:05:41,330 --> 00:05:45,739 by the way, at extrapolating what will happen from different electronic structure methods. 60 00:05:45,740 --> 00:05:51,110 And it doesn't matter if you don't know this acronyms, but they are very popular chemistry methods for simulating molecules. 61 00:05:51,890 --> 00:05:58,670 What will be the power of those methods as we keep growing larger and larger supercomputers that use the same power as a small city? 62 00:05:59,230 --> 00:06:05,360 Okay. So if you go to one of the largest computers of today and we're already hearing this line on the plot of his paper, 63 00:06:05,900 --> 00:06:11,780 we perhaps can do with this the functional theory, a 10,000 or maybe even a hundred thousand atom simulation. 64 00:06:12,350 --> 00:06:19,130 The problem, of course, is that for different properties, for example, charge transfer states, definitely we have errors of order 80 or larger. 65 00:06:20,060 --> 00:06:25,310 And if you think about chemistry being at room temperature density, functional theory is not a predictive theory. 66 00:06:25,310 --> 00:06:28,370 Yet of course I use it to predict that battery. Okay. 67 00:06:28,430 --> 00:06:34,350 So obviously it's useful, but it's not. A predictive simulator is not a simulator that you can always rely on. 68 00:06:34,360 --> 00:06:36,910 You have to calibrate it and you have to do a lot of work to understand it. 69 00:06:37,840 --> 00:06:41,620 Now, if you think about exact solutions, those exact solutions have been proposed for a long time. 70 00:06:41,620 --> 00:06:43,399 I mean exact organisation, 71 00:06:43,400 --> 00:06:49,809 that's what it's called in physics of full configuration interaction which is called in chemistry is a very fine method within a basis. 72 00:06:49,810 --> 00:06:52,900 I can exactly that. I'm going to lay out a huge matrix and get the answer. 73 00:06:54,060 --> 00:06:57,060 The problem is that by the time the grandchildren of my children die, 74 00:06:57,390 --> 00:07:01,230 I won't be able to simulate, even with the largest computers in the world, ten atoms. 75 00:07:01,920 --> 00:07:03,480 So it's quite boring, you know, 76 00:07:03,750 --> 00:07:10,980 like I won't be able to really make predictive chemistry if we don't change the paradigm and switch from classical computing to quantum computing. 77 00:07:11,730 --> 00:07:14,970 So that's hopefully the argument that in matters to do what we're doing. 78 00:07:15,990 --> 00:07:19,410 So the current paradigm looks like this. So I take a molecule, this is acetone. 79 00:07:20,590 --> 00:07:26,470 I make them all the time independent, showing an equation and a muppet to a classical computer. 80 00:07:26,980 --> 00:07:35,110 Okay. By the way, this is the exact computer that was used by SF Boys for the first time here in the England for 81 00:07:35,110 --> 00:07:40,389 the first time to simulate an arbitrary molecule using a computer and then get the number, 82 00:07:40,390 --> 00:07:45,040 for example, that the energy is roughly 192 cartridge. 83 00:07:45,850 --> 00:07:51,390 If you think about it in terms of information, what we did is we took a quantum system which is intrinsically quantum mechanical. 84 00:07:51,760 --> 00:07:57,220 The firm unique motion of the electrons in the potential of these nuclei or even the quantum nuclei as well, 85 00:07:57,640 --> 00:08:01,150 and converted it to quantum, although of course, it's quantum information. 86 00:08:01,870 --> 00:08:09,310 But then we committed the scene of cramming this quantum information in this very inefficient yet powerful classical information processor. 87 00:08:09,850 --> 00:08:14,490 Okay. And finally, we obtained a classical information that's important. 88 00:08:14,890 --> 00:08:23,379 We're not after understanding every detail about the molecules we went after understanding some macroscopic property like an energy at a moment, 89 00:08:23,380 --> 00:08:29,830 the quadrupole moment, etc. And observable that I can enumerate with a polynomial number of numbers. 90 00:08:30,370 --> 00:08:35,950 Even the electron density is okay. What is not okay is to go after, for example, the entire full wave function. 91 00:08:36,460 --> 00:08:41,950 Because for those of you that know about it, it is akin to doing quantum tomography, which would be inefficient. 92 00:08:43,030 --> 00:08:50,590 So Richard Feynman in 1982 published this paper that is listed here in the talk that I was surprised to know is his most cited paper, 93 00:08:51,070 --> 00:08:54,309 the paper what he thinks about how to simulate physics with computers. 94 00:08:54,310 --> 00:09:00,850 So that paper is more cited than than than his QED work and all the works by Feynman. 95 00:09:01,450 --> 00:09:06,340 And what he proposed is very simple, and I can summarise it here in this a few equations. 96 00:09:06,970 --> 00:09:11,050 If I have the wave function of a molecule or a material or a system, I want to study. 97 00:09:11,860 --> 00:09:14,950 I want to first have to come up with a map, with a mapping. 98 00:09:17,240 --> 00:09:22,080 I first come up with a mapping that takes that wave function to the wave function of the quantum computer. 99 00:09:23,180 --> 00:09:26,690 And then let's imagine that we're interested in simulating the time evolution. 100 00:09:26,690 --> 00:09:32,180 This is the unitary term evolution operator which is generated by the exponential of the Hamiltonian. 101 00:09:32,660 --> 00:09:36,680 Well, you would have to have an uncontrollable quantum system, emulate the time evolution. 102 00:09:37,250 --> 00:09:44,030 Right. And that the simple system, that simple, simple idea tells you that if I want to evaluate an observable on this right hand side. 103 00:09:45,460 --> 00:09:49,930 Within the bases that I explained to them is this to me will be indistinguishable from a residual on this left hand side. 104 00:09:49,960 --> 00:09:54,360 Therefore, achieving the idea of quantum simulation. In other words, 105 00:09:54,360 --> 00:09:59,700 if I have this asset on molecule and I am looking at this circle with a rotating arrow 106 00:09:59,700 --> 00:10:05,370 which is representing the rotating phase associated with the particular low energy, 107 00:10:05,370 --> 00:10:10,320 I can state that I'm a state of this molecule that rotates at a speed proportional to its energy, 108 00:10:11,100 --> 00:10:16,499 and I can build an apparatus like this one that actually has the same time evolution. 109 00:10:16,500 --> 00:10:23,370 Then in principle, I achieve the goal. I can, for example, extract the energy out of that system and design a battery. 110 00:10:24,270 --> 00:10:32,700 Okay, so that's kind of like the goal. So now what we need is we map a quantum system to another quantum system, which is quantum information, right? 111 00:10:33,210 --> 00:10:38,670 And then we can actually map it to a quantum information processor and then get the same energy. 112 00:10:39,730 --> 00:10:43,450 Okay. So that's kind of like the high level picture of this whole. 113 00:10:44,630 --> 00:10:48,520 Well. It's like you wouldn't be here. Oh, yeah. So now. 114 00:10:49,860 --> 00:10:54,030 This is not exactly that. I read what a museum in Japan asked me the following question. 115 00:10:54,870 --> 00:11:01,440 Me and my student, James Whitfield, they asked us, you know, just imagine that there is a Moore's Law for qubits. 116 00:11:02,310 --> 00:11:06,720 Okay. When will the qubits will be a classical computer? 117 00:11:06,730 --> 00:11:10,290 And of course, we don't know. I mean, it depends on my experimental colleagues here. 118 00:11:10,290 --> 00:11:15,540 I'm going to knock on and so on and say when you have your fourth and source ready and, you know, it's it's beyond my control. 119 00:11:15,550 --> 00:11:17,879 But what I can say is the following what is true? 120 00:11:17,880 --> 00:11:24,810 And I can tell my chemistry colleagues or anybody that the simulation is that because these algorithms are polynomials scaling, 121 00:11:24,810 --> 00:11:28,140 no matter what is a polynomial power, which is basically the slope of this here. 122 00:11:28,920 --> 00:11:32,250 And I just started here this random this cube here. All right. 123 00:11:32,400 --> 00:11:38,460 Eventually, this here will cross copper cluster, which is a very powerful metal, and just disappeared from the face of existence. 124 00:11:38,760 --> 00:11:42,990 So if you're a scholar of the copper cluster metal, you could retire or study using quantum computers. 125 00:11:43,350 --> 00:11:46,300 Right? And then it then it will do secondary perturbation theory. 126 00:11:46,320 --> 00:11:51,059 Maybe one day we get away with DFT, because I argue that if you have a quantum computer, that sort of things. 127 00:11:51,060 --> 00:11:54,360 Exactly. Obviously, you will not want to do these methods. 128 00:11:54,430 --> 00:11:58,230 Okay. So this will be a predictive or an explanatory simulation of matter. 129 00:11:58,950 --> 00:12:03,680 And the other argument, I think this is a word of the year of the quantum computing people. 130 00:12:04,050 --> 00:12:09,480 I cannot believe how many times I have heard my quantum computing colleagues call talk about quantum supremacy. 131 00:12:09,840 --> 00:12:15,420 And if you haven't heard about this, you hang out with the quantum computing people and they will be telling you what quantum supremacy. 132 00:12:15,780 --> 00:12:20,819 All our community, the community that I live on in quantum computing is really thinking about the moment. 133 00:12:20,820 --> 00:12:25,050 What a quantum salivating about the moment when a quantum computer will be faster than a classical one. 134 00:12:25,590 --> 00:12:33,870 Okay. I argue that simulation of chemistry perhaps is also an experiment that can that can be one of the first ones to do quantum supremacy, 135 00:12:33,870 --> 00:12:37,830 if not the first one. Okay. And that will be exactly the moment where we just crosses the exact line. 136 00:12:38,220 --> 00:12:41,940 So we don't we don't need to go very far to achieve quantum supremacy. 137 00:12:44,220 --> 00:12:49,709 So there's a little animation problem, but I won't try to tell anybody here that doesn't know what is a quantum computer? 138 00:12:49,710 --> 00:12:56,700 What is it in three slides? So those of you that know forgive me and those of you that don't know also forgive me because it might be too stupid. 139 00:12:57,060 --> 00:12:59,490 But let's start with the classical bit. Right. 140 00:12:59,940 --> 00:13:07,110 There's currently no current of Magnetisation or no Magnetisation or up or down any type of amount of one of ones and zeros. 141 00:13:07,110 --> 00:13:14,200 That will be basically classical information. Quantum information is a generalisation to the fact that I might have two states, for example, 142 00:13:14,200 --> 00:13:17,980 around an excited state or superconducting current going to the left or to the right, 143 00:13:18,580 --> 00:13:26,660 or a particular hyper fine state of anatomy or whatever I want to use as as as a place to store information. 144 00:13:26,980 --> 00:13:33,340 But what I can do in quantum mechanics that I cannot do in classical mechanics is actually generate the superposition. 145 00:13:34,270 --> 00:13:39,370 A very cool way of visualising this is already alluded to here is basically this idea of a block sphere. 146 00:13:40,390 --> 00:13:47,200 The only thing I did is I took these two complex numbers and factories them in this way because I assume this wave function 147 00:13:47,200 --> 00:13:53,110 is normalised so I can factories them as a little point in the sphere where C2 is in the top and one is in the bottom. 148 00:13:53,530 --> 00:13:58,030 And my cubit, for example, will be in a superposition between zero and one if it's in the equator, 149 00:13:58,510 --> 00:14:02,560 but it will be either a C2 or one if it's on the, on the, on the poles. 150 00:14:03,160 --> 00:14:12,550 Note that we also have a complex phase that we can use when we when we actually move around these this direction. 151 00:14:13,420 --> 00:14:16,120 So basically that's how I like to represent them graphically. 152 00:14:16,120 --> 00:14:27,790 I show them to you a couple of times and then the power of superposition entanglement is what allows us to to have more powerful computation. 153 00:14:28,780 --> 00:14:32,380 We have some things that we have to worry about. Of course, we collapse in wave function. We will measure it. 154 00:14:33,130 --> 00:14:38,080 And what is a quantum computer in three lines is a collection of controllable and addressable qubits. 155 00:14:38,380 --> 00:14:46,530 Okay. And if we didn't have the most important result, I think of all the field is the results of error correction. 156 00:14:47,160 --> 00:14:54,420 Okay. The same way that we can correct errors in classical computing, we can correct errors in quantum in quantum information processing. 157 00:14:54,990 --> 00:15:03,060 And I think that is the most important result in the field, because if we didn't have the ability to actually build error correcting devices, 158 00:15:03,360 --> 00:15:06,490 you know, at least theoretically, they're going to be built experimentally, hopefully very soon. 159 00:15:06,510 --> 00:15:13,440 Larger and larger ones then. Then there is no hope of really having a quantum computer because the coherence eventually will take over. 160 00:15:15,300 --> 00:15:18,840 So I won't talk too much about error correction, except for a couple of points about it. 161 00:15:20,070 --> 00:15:25,470 So okay. So now this is our second slide about quantum computation, just the general graphical picture of it. 162 00:15:25,920 --> 00:15:30,450 You will initialise a quantum state, usually in a classical state, but not necessarily in this case. 163 00:15:30,810 --> 00:15:34,290 I initialise this three bits in the zero zero configuration. 164 00:15:34,290 --> 00:15:40,079 For example, imagine that you have speeds and you polarise them along a particular direction or you have molecules and 165 00:15:40,080 --> 00:15:43,710 put them all in the ground state or whatever is going to be a quantum information processing system. 166 00:15:44,610 --> 00:15:48,540 And by the application of these quantum operations, that will tell you in the first slide, 167 00:15:49,320 --> 00:15:52,980 I can prepare different arbitrary superpositions of this system. 168 00:15:54,240 --> 00:16:00,300 Which I'm going to call all the procedure. Quantum algorithms generate superposition, entanglement over all these quantum states. 169 00:16:00,570 --> 00:16:07,880 And then I will apply a measurement that will select the states according to the square of their amplitude. 170 00:16:07,890 --> 00:16:14,610 So hopefully my quantum algorithm is very smart and concentrates my answer around a number so I can do a bunch of measurements, 171 00:16:14,610 --> 00:16:20,310 calculate an expectation value. So repeating the quantum theory many times and you get a classical information out of it. 172 00:16:20,700 --> 00:16:25,800 Hence the reason that I was telling you at the beginning that I am after classical information of molecules. 173 00:16:26,310 --> 00:16:31,380 So my job has been to think about what's the best quantum algorithm, how to implement it for molecules. 174 00:16:32,410 --> 00:16:40,450 Okay. So that is a story. So a little bit more details about how to think about this because I'll be telling you about council gates and stuff. 175 00:16:41,000 --> 00:16:44,380 A gate is nothing more like an operation like in classical computing. 176 00:16:44,680 --> 00:16:50,470 In this particular case, I want to think about operations that rotate along those three different axis of the sphere X, Y and Z. 177 00:16:51,250 --> 00:16:56,680 The policy moment. This is an example of a gate that we talk a lot about in quantum information. 178 00:16:56,680 --> 00:17:00,570 Processing is a or gate. Note that this is kind of like music. 179 00:17:00,580 --> 00:17:03,040 You start on the left and move to the right, passing by the gate. 180 00:17:03,430 --> 00:17:09,130 So if I have a qubit that is represented by this line, I apply this to our operation and what I do. 181 00:17:09,160 --> 00:17:12,940 It would take my block sphere, say you was on zero and take it to the equator. 182 00:17:13,630 --> 00:17:16,960 So that's a gate. I can also talk with gates. 183 00:17:17,260 --> 00:17:20,590 The simplest one is the control gate entangles two cubits. 184 00:17:20,980 --> 00:17:25,780 And if you want to think about the classical truth table of this gate, it says that if this first Q with is one, 185 00:17:26,710 --> 00:17:31,600 then you flip the sign of the second Q rate and if it settle, you do nothing and that is enough. 186 00:17:31,600 --> 00:17:35,510 Turns out to have this set of gates to actually universally compute anything you want. 187 00:17:35,530 --> 00:17:42,370 You can play Mario Brothers on a quantum computer. With this, you can simulate the molecule or you can, I don't know, play Angry Birds. 188 00:17:42,820 --> 00:17:49,210 Okay, but. What is important is that we also have a concept of subroutines or parts of algorithms. 189 00:17:49,220 --> 00:17:54,010 For example, a very powerful one I will be using and is efficient, is important to know. 190 00:17:54,010 --> 00:17:56,050 That is to calculate the future, transform. 191 00:17:56,110 --> 00:18:03,159 You can calculate the full transform or the inverse of it by actually applying this sequence of gates that again read like music. 192 00:18:03,160 --> 00:18:09,370 I apply the same output. You know what it is now I apply controls, which is the particular control rotation. 193 00:18:09,370 --> 00:18:16,209 So it's kind of like a hybrid of one of these. And these guys between these two qubits then apply a controlled T within these two cubits and so on. 194 00:18:16,210 --> 00:18:22,570 And this is a swap. Okay, so I apply this musical scheme to my qubits and then eventually I get a quantum for your transfer. 195 00:18:23,710 --> 00:18:31,560 Right. So you're saying that. So what? Okay. So let's just dispel a myth now that we all know what quantum computation is less this phenomenon. 196 00:18:32,490 --> 00:18:37,560 I know to me that happens always is. All quantum computers will be able to solve all the problems in computers. 197 00:18:38,160 --> 00:18:41,750 And that's not true. Okay. What does this mean? 198 00:18:41,760 --> 00:18:44,920 Quantum I would say always faster and more efficient than classical ones. And that's not true. 199 00:18:44,940 --> 00:18:48,390 There are many causes of problems that you are not going to be able to solve. 200 00:18:49,470 --> 00:18:53,350 But we have a Hall of Fame, for example, quantum search. 201 00:18:53,400 --> 00:18:57,870 Many people know that it's qualitatively faster to search and database on a quantum computer. 202 00:18:59,370 --> 00:19:05,400 You can factor with an exponential speedup, and this is basically the basis of all the interest of NSA. 203 00:19:05,790 --> 00:19:10,470 They really want to build that is emails. So then they they basically need this. 204 00:19:10,980 --> 00:19:13,080 And what we need is basically quantum simulation. 205 00:19:13,590 --> 00:19:21,270 And as many people have shown and we exploit it, you get an exponential speed of in the time evolution of any local Hamiltonian. 206 00:19:21,720 --> 00:19:28,580 Okay. So there are some restrictions. You have to be able to prepare the state that you want. 207 00:19:29,390 --> 00:19:33,500 And for that, we need to actually go and talk about the stages of quantum simulation. 208 00:19:34,590 --> 00:19:37,620 First you need to prepare the state that you want. I told you, that's kind of the piece. 209 00:19:38,550 --> 00:19:44,580 Then you need to time of it, which I already asserted to you is sufficient, and then you'll be able to wait. 210 00:19:44,700 --> 00:19:48,330 You need to be able to measure the properties which will occur to you that is sufficient. 211 00:19:49,360 --> 00:19:52,300 So computer scientist, is there any computer scientist in the room? 212 00:19:53,740 --> 00:19:58,150 Well, they are very imaginative people, computer scientists, and they have these computational classes. 213 00:19:58,750 --> 00:20:01,840 And the one that we're going to talk about involves Marilyn and Arthur. 214 00:20:02,470 --> 00:20:06,100 And I'm not kidding. It's called Quantum Merlin. Arthur. Okay. 215 00:20:06,220 --> 00:20:11,290 And in this in this game Million Arthur game Merlin is ever powerful. 216 00:20:11,290 --> 00:20:15,570 And he can create any quantum state that he wants or she wants. 217 00:20:15,580 --> 00:20:21,940 Maybe it's a female magician prepares any quantum state and can win it over to Arthur. 218 00:20:22,800 --> 00:20:26,760 Which Arthur is powerful, but not so powerful. Arthur only has a quantum computer. 219 00:20:27,330 --> 00:20:31,740 So I guess now I wish we are going to have a real full blown quantum computer. 220 00:20:32,280 --> 00:20:37,590 Well, Merlin goes and gives a quantum state to Arthur. Renato can verify you can play with it, but with a quantum state. 221 00:20:37,980 --> 00:20:42,540 Okay. And it is in that context of dividing. 222 00:20:43,200 --> 00:20:46,690 I don't know what happened with the project or somebody. Thank you. 223 00:20:46,750 --> 00:20:49,950 Me? You were blocking Arthur. Yeah. 224 00:20:49,950 --> 00:20:54,930 You were looking Arthur out for these things. Yeah. So, so? 225 00:20:54,980 --> 00:20:58,170 So. So Merlin transfers the estate to Arthur to. Not to verify. Right. 226 00:20:58,470 --> 00:21:07,560 So in that context, Quantum Million, Arthur is basically any problem that if given the solution to it, 227 00:21:08,040 --> 00:21:11,520 a quantum computer can verify if it's if the solution is true or not. 228 00:21:12,090 --> 00:21:17,130 Okay. What about the quantum polynomial? In some sense is what I can do by himself. 229 00:21:17,610 --> 00:21:21,030 Arthur says, No worry, I don't need Merlin because I can generate my own solutions. 230 00:21:21,660 --> 00:21:28,620 Okay. So if quantum simulation is involved with quantum polynomial, the whole thing preparing, evolving and measuring, we're all set. 231 00:21:28,890 --> 00:21:32,670 I can simulate all my theories in the universe and I'm all set. You will be happy and I'll be happy. 232 00:21:33,240 --> 00:21:40,260 What in your hand? If it belongs to this computational complexity class, there might be a material, most likely a very frustrated system. 233 00:21:40,800 --> 00:21:46,560 For example, a very frustrated, spinning wheel of material that is not really in integral state, 234 00:21:46,560 --> 00:21:51,390 and perhaps a quantum computer will never be able to simulate. And that is still a discussion. 235 00:21:51,890 --> 00:21:57,630 Okay. So including the preparation of molecular instances, we don't know where we are in terms of quantum simulation. 236 00:21:58,290 --> 00:22:02,580 Well, Georgia Times, what we know is it's in BQ P and these are the computational classes. 237 00:22:02,820 --> 00:22:07,530 And you may be familiar of the NP versus B situation, which is very similar. 238 00:22:07,770 --> 00:22:16,640 Basically, the analogue of QM basically needed merely for preparing some states and then modifying them or developing quantum polynomial again. 239 00:22:16,650 --> 00:22:20,610 And if there are computer scientists here or people that know more about quantum algorithms, 240 00:22:20,610 --> 00:22:24,720 remember, this is a colloquium and I'm just explaining things as best as I can. 241 00:22:25,030 --> 00:22:31,649 Hand-waving. But the point here is, I argue being a chemist, that molecules are easy to prepare. 242 00:22:31,650 --> 00:22:35,490 And this is basically like some sort of ontological or philosophical argument. 243 00:22:37,010 --> 00:22:41,540 Think of a biomolecule. It has to be prepared in the lifetime of a human. 244 00:22:42,260 --> 00:22:46,210 Okay, to be useful or think about this work here. 245 00:22:46,220 --> 00:22:50,000 Well, it was prepared in a lifetime. 246 00:22:50,000 --> 00:22:56,300 That is probably reasonable. In other words, if there is a chemical reaction that more or less results in a molecule in a reasonable amount of time, 247 00:22:56,690 --> 00:23:02,390 in principle it should be some level. Okay. So anyway, we are happy to talk to you about more about that. 248 00:23:02,750 --> 00:23:08,360 We're trying to formalise it with computer scientists. So now I'm going to tell you about quantum chemistry. 249 00:23:08,360 --> 00:23:12,860 So what is the task of a quantum chemist? Okay, this is famous. 250 00:23:13,070 --> 00:23:16,520 And the only reason I'm telling this story is because it's a British scientist, someone, 251 00:23:16,520 --> 00:23:20,810 Boyce said once he stood up in front of an audience and printed his computer program, 252 00:23:21,410 --> 00:23:25,370 which is kind of like the grandfather of the Gaussian program, I guess, in a table, 253 00:23:25,370 --> 00:23:31,550 and said that quantum chemistry is a molecular geometry interest here in my program and an energy comes out. 254 00:23:32,180 --> 00:23:34,729 Okay. That was a vision that someone voice has. 255 00:23:34,730 --> 00:23:39,400 And unfortunately, many of my colleagues still believe that the only thing that quantum chemistry is okay. 256 00:23:40,490 --> 00:23:46,640 But what quantum chemistry is then therefore is taking that input geometry for a molecule using the Oppenheimer approximation, 257 00:23:47,150 --> 00:23:51,230 doing a self-consistent solution in the local basis. We like to call them atomic orbitals. 258 00:23:51,860 --> 00:23:57,979 To obtain a solution is the localised or this local basis to obtain the so-called molecular orbitals. 259 00:23:57,980 --> 00:24:02,030 So he does water and heat out of the occupied and on occupied orbitals of water. 260 00:24:02,600 --> 00:24:07,580 Okay. And that will define the Hamiltonian of the problem I want to solve. 261 00:24:07,880 --> 00:24:11,180 So that's the mean field solution, which I'm going to assume is the reference. 262 00:24:11,450 --> 00:24:18,110 Okay. And from that I want to solve the fully correlated Hamiltonian here of these two Pauli fermion operators. 263 00:24:18,260 --> 00:24:24,499 What they do is basically scatter electrons into orbitals to two orbitals due to two Coulomb repulsion and this one 264 00:24:24,500 --> 00:24:29,210 electron terms that are hoping between orbitals due to the electron kinetic energy and electron nuclear attraction. 265 00:24:29,810 --> 00:24:33,440 Okay. So this is a sample with a polynomial number. Okay. 266 00:24:33,440 --> 00:24:36,470 Actually into the 4% square such theorems. 267 00:24:36,710 --> 00:24:39,710 So to a physicist work. Okay, this is a Hamiltonian for our fermions. 268 00:24:40,160 --> 00:24:43,790 And what we, the chemists do is calculate these very exquisite parameters here. 269 00:24:44,510 --> 00:24:49,220 Okay, using a smart basis, that's a lot of the things that we can do is just calculate those numbers. 270 00:24:50,580 --> 00:24:56,220 For all intents and purposes, except some of my more advanced algorithms, that is the input to the quantum computer. 271 00:24:56,230 --> 00:25:02,900 So now if you wonder, how do I program a quantum computer to do chemistry, I use the chemistry program to do efficiently. 272 00:25:02,910 --> 00:25:03,930 This is in polynomial time. 273 00:25:03,930 --> 00:25:11,339 I can do obtain all these numbers into the four of these numbers and in square of these numbers that fully define the computational problem, 274 00:25:11,340 --> 00:25:17,370 that defines a molecular instance. You want to change the geometry of the molecule a little bit, stretch the water molecule. 275 00:25:17,420 --> 00:25:21,170 You have to do all of this and get this different set of parameters for your quantum computer, 276 00:25:21,590 --> 00:25:24,950 which again will enter your quantum simulator as classical input. 277 00:25:25,930 --> 00:25:30,629 Okay. So and we call like we like to call these numbers the integrals. 278 00:25:30,630 --> 00:25:34,310 This is a one electron integral and this is a two electron integral. Okay. 279 00:25:34,380 --> 00:25:38,360 And I think this the same problem in most lights is ten years. So if anybody got it. 280 00:25:39,920 --> 00:25:40,430 So now. 281 00:25:41,410 --> 00:25:48,220 I want to show you I told you all of that, because it's amazing that I can show you the quantum computer simulation algorithm in half us alive. 282 00:25:48,670 --> 00:25:53,079 Here it is. Okay. This is what I do, guys. And I know that many of you. 283 00:25:53,080 --> 00:25:56,290 This is the first time I saw quantum circuits. So don't worry. 284 00:25:57,460 --> 00:26:02,800 These are harder margin. Remember what the Kalamazoo. What I did there is turned all my cubits into superposition. 285 00:26:03,820 --> 00:26:11,799 All those us do that. Okay. This issue is nothing more than the unitary term evolution of the molecular operator. 286 00:26:11,800 --> 00:26:16,360 In other words, time observing the molecule. We'll talk more about how to implement it and all the caveats. 287 00:26:16,810 --> 00:26:22,090 Well, this is the only three time evolution of this operator generated by the Hamiltonian of the molecule, 288 00:26:22,360 --> 00:26:25,810 which, by this relationship is real, is related to the energy of the molecule. 289 00:26:25,840 --> 00:26:32,620 So I choose a time t so that they have the energy t is minus two times this phase, which I will be reading. 290 00:26:32,920 --> 00:26:37,540 And that's what this other one is called, the Quantum Phase Estimation Algorithm, originally proposed by Seth Lloyd. 291 00:26:38,170 --> 00:26:45,640 So what you do is the following you time evolve system and entangle it with this set of ancillary or auxiliary qubits. 292 00:26:46,090 --> 00:26:52,030 Okay. Each one of them is entangled with a successive power of two of a unitary time evolution operator. 293 00:26:52,540 --> 00:26:55,570 And you might say, What the heck are you doing around? It's actually quite intuitive. 294 00:26:56,230 --> 00:27:03,670 I am entangling the time evolution of a system with a bit and then twice its power and the four times its power and eight times and so on. 295 00:27:04,060 --> 00:27:07,720 And what I'm doing is basically writing in binary the face. 296 00:27:08,410 --> 00:27:12,880 So the face is being written in binary. Okay. And I'm hearing the time domain. 297 00:27:12,910 --> 00:27:17,710 What happens when I play if we transform? I go from a time domain to the energy of frequency domain. 298 00:27:18,220 --> 00:27:22,870 Right. So why do I get here? The energy, the frequency of oscillation of this phase. 299 00:27:24,260 --> 00:27:28,820 And if some of you do quantum dynamics. My chemistry colleagues know that sometimes this metal is used. 300 00:27:28,970 --> 00:27:33,470 Also in classical dynamics. You propagate the way pocket-knife will transfer me to reality cycle values. 301 00:27:34,640 --> 00:27:38,420 So that's basically the basic quantum algorithm for simulating chemistry. 302 00:27:39,170 --> 00:27:47,330 And what we did in 2005 is actually proposed to use it using the chemistry integrals and still doing chemistry problems. 303 00:27:47,780 --> 00:27:51,080 Now, the problems that arise are the things that you have to worry about. 304 00:27:51,410 --> 00:27:59,770 The first one is the following. These are fermions. Electrons are fermions, but the qubits are distinguishable to single health particles. 305 00:27:59,780 --> 00:28:04,549 They are not both ones. They are being withheld particles, but they are distinguishable. 306 00:28:04,550 --> 00:28:09,350 Right. So they are also not fermions. So I know this Q with this here and obviously with this here. 307 00:28:09,680 --> 00:28:13,600 So I do have permutation and symmetry. So what do I do? 308 00:28:13,620 --> 00:28:17,040 I need to build it. And I build it with a so-called Jordan beginner transformation. 309 00:28:17,610 --> 00:28:23,550 So I need to actually transform my operators another bunch of different gates to take into account that. 310 00:28:24,790 --> 00:28:28,989 Okay. So, Bree, that probably this was the hardest lie. And I speak first. 311 00:28:28,990 --> 00:28:34,240 I'm a Spanish speaker, so hopefully us still awake or not too annoyed. 312 00:28:34,600 --> 00:28:39,460 So let's go back to a molecule. How do way make up a molecule to the quantum computer? 313 00:28:40,090 --> 00:28:44,830 I want to make this very, very simple mapping. Each qubit is going to be a spin or metre. 314 00:28:45,340 --> 00:28:48,909 In other words, every two cubits is going to be a molecular orbital, 315 00:28:48,910 --> 00:28:54,459 and the first cubit is going to be the spin up and the second cubit is going to be the spindle for the first orbital, 316 00:28:54,460 --> 00:28:59,860 and then the next cubit is going to be spin up for the next door orbital. And then I want spin down for the next orbital and you keep doing that. 317 00:29:00,370 --> 00:29:02,830 There are more other ones mappings, but this is a whole mapping. 318 00:29:03,190 --> 00:29:09,070 So in other words, I have here, for example, one one set of C2 will be the first possible state of the hydrogen molecule. 319 00:29:09,340 --> 00:29:14,830 It will be two electrons and they get other or symmetric state. And then it will have this excited state and this excited state. 320 00:29:15,070 --> 00:29:18,790 And these other states are not valid because they don't have the same particle number. 321 00:29:19,390 --> 00:29:25,299 That's one example of how to map the wave function to liquids. That is very nice because each cubic has a very nice chemical. 322 00:29:25,300 --> 00:29:31,210 Interpretation is basically the fact that every two cubits will represent one of our atomic basis functions. 323 00:29:32,110 --> 00:29:37,089 So with that I can calculate how many QE do I need to stimulate interesting molecules? 324 00:29:37,090 --> 00:29:39,640 And this is from our original paper on the subject. 325 00:29:40,060 --> 00:29:46,090 When I was supposed to look and you can see that, for example, benzene and don't worry about this basis. 326 00:29:46,160 --> 00:29:50,860 If you're a chemist, you know, there are good ways to say it's benzene, for example. You have to go to a. 327 00:29:50,920 --> 00:29:57,220 Here we're required perhaps about 250 or so quantum bits, fully exact. 328 00:29:57,860 --> 00:29:59,770 Again, these are logical quantum bits. 329 00:30:00,220 --> 00:30:07,910 Caffeine, another very important molecule, at least for theoretical chemists, requires about a hundred thousand cubits and cholesterol. 330 00:30:07,910 --> 00:30:11,680 A molecule very close to my heart requires about 3000 cubits. 331 00:30:12,010 --> 00:30:16,390 Okay. And that's very cool because that's the same number of humans you need to factor a number. 332 00:30:17,020 --> 00:30:22,629 So if I were friends of the say you build a factory and a factory molecule, I would be able to simulate the cholesterol molecule. 333 00:30:22,630 --> 00:30:30,770 Exactly. And calculate how it binds to my walls of my of my veins and maybe prevent my own heart attack from eating too many Mexican tacos. 334 00:30:30,790 --> 00:30:37,050 Okay. So my first real student, James, I gave my first to James. 335 00:30:37,240 --> 00:30:41,320 I project this is when I graduated as a puzzle book with back in 2005. 336 00:30:42,220 --> 00:30:46,390 And I told my student, Well, James, please figure out all the details. 337 00:30:46,570 --> 00:30:50,560 That's the first thing to do. A grad student, right? You're going to be figuring out all the details of my potluck. 338 00:30:51,220 --> 00:30:55,450 Okay. And six years later, we publish this paper, okay? 339 00:30:55,690 --> 00:31:01,750 With all the great sequences, all the detail of how to do all this from unique operators on a quantum computer. 340 00:31:02,680 --> 00:31:09,730 And back then not many people were interested. But it got really cool when this was used as a benchmark for computer scientists. 341 00:31:10,600 --> 00:31:14,799 There was the air fire agency decided to make it a benchmark and say a computer. 342 00:31:14,800 --> 00:31:18,400 Scientists write the compiler for Alan's 2011 paper. 343 00:31:18,850 --> 00:31:25,390 Okay. And then both of computer scientist started thinking about chemistry and started reading about I don't do which tool and stuff like that. 344 00:31:25,870 --> 00:31:32,770 Okay. And notice that in our paper there was this figure that says the problem with the lower scheme is that although efficient. 345 00:31:33,010 --> 00:31:36,010 In other words, we can simulate the molecule exactly in a quantum computer. 346 00:31:36,280 --> 00:31:42,099 It would require too many gates. So if I show this to you and the user uses quantum optics and they tell him 347 00:31:42,100 --> 00:31:46,479 that simulating cholesterol will require ten to the 17 effectively 15 gates, 348 00:31:46,480 --> 00:31:51,280 he would just tell me I'm so real and like go home. Like, you know, this is still efficient. 349 00:31:51,310 --> 00:31:54,760 But the very naive first algorithm is quite expensive. 350 00:31:55,510 --> 00:32:00,590 Okay. So that's where we are. I want to tell you how much progress has been done in the last ten years. 351 00:32:02,030 --> 00:32:10,220 One word about that correction. Even with that very, quote unquote expensive algorithm is not unreasonable to do error corrected simulations. 352 00:32:10,580 --> 00:32:14,120 The way you do error correction is very similar. The way you do classical error correction. 353 00:32:14,570 --> 00:32:19,729 You're going to encode your quantum information over many qubits and measure errors on the qubits, 354 00:32:19,730 --> 00:32:24,530 do central measurements, and figure out if they are destroyed or not. And if they are destroyed, you can correct them. 355 00:32:25,190 --> 00:32:32,209 So if you do that, you can actually show that these naive error correcting Skillings were not very naive and 356 00:32:32,210 --> 00:32:36,950 that with improvements that the Yamamoto group did in Stanford in collaboration with us, 357 00:32:37,730 --> 00:32:41,540 we found that, for example, simulating the lithium hydride molecule would require about the Honda, 358 00:32:41,540 --> 00:32:45,890 the physical cubits and, you know, ten to the seven or 10 million gates. 359 00:32:46,930 --> 00:32:51,120 So that's kind of where we were about, you know, three years ago. Okay. 360 00:32:51,640 --> 00:32:55,150 So that was kind of what we're saying. Look if you can build a machine that those larger with similar lighting. 361 00:32:55,510 --> 00:32:59,710 Exactly. Still not very exciting for our colleagues. So we have to go better than that. 362 00:33:00,610 --> 00:33:04,860 And now in the meantime, things like I needed to get in here. 363 00:33:04,870 --> 00:33:10,260 What's going on? Okay, so how can I show people that this is not pie in the sky? 364 00:33:10,270 --> 00:33:14,200 I have to do experiments, and I have to convince others to do experiments. 365 00:33:14,270 --> 00:33:19,990 Some experiments I didn't do. Some of the people did. And some of them, I'm almost like a honorary co-author, like in this one. 366 00:33:20,500 --> 00:33:24,309 But this is a list of all the experiments in all the different quantum information 367 00:33:24,310 --> 00:33:30,190 processing architectures that have simulated the molecule over the years. Notice that the number of qubits is two or three only. 368 00:33:30,580 --> 00:33:33,640 But the algorithm goes better and better. You will see. Okay. 369 00:33:33,670 --> 00:33:34,750 This is for you, scalable. 370 00:33:34,960 --> 00:33:42,340 These ones here in the bottom are fully scalable, which means that whatever we implement the there is the full algorithm with no tricks, so to speak. 371 00:33:42,910 --> 00:33:48,640 And then this paper, for example, was a very stressful paper because it came out a week after my nature chemistry paper. 372 00:33:49,720 --> 00:33:54,459 So this was in the year. So let's talk about the first system that we simulated. 373 00:33:54,460 --> 00:33:58,800 And this is Paul Dirac showing you here the symmetric and anti-Semitic 374 00:33:59,110 --> 00:34:01,960 non-metallic configurations of the hydrogen molecule that we've been mentioning. 375 00:34:03,100 --> 00:34:09,010 So we did that experiment in collaboration with my colleague Andrew White in Australia, and this is how the experiment looks like. 376 00:34:10,330 --> 00:34:12,880 Basically what you do is you take two entangled photons. 377 00:34:13,240 --> 00:34:18,940 One of them represents each one of the two by two matrices that represent the six by six Hamiltonian of the hydrogen molecule. 378 00:34:19,920 --> 00:34:24,930 And you use this device to do the most expensive drive only station of a two way two matrix ever done in history. 379 00:34:25,410 --> 00:34:31,050 Okay. Which is basically this face estimation algorithm to actually read out bit by bit. 380 00:34:31,200 --> 00:34:33,870 This is an old trick that you have to use bit by bit. 381 00:34:34,080 --> 00:34:38,820 You do the one beat and then adjust the machine and read them a little bit and adjust the displacement them a little bit. 382 00:34:40,130 --> 00:34:43,190 And obtain the potential energy surface for the hydrogen molecule. 383 00:34:44,060 --> 00:34:46,400 Points in this particular a simple system, 384 00:34:46,400 --> 00:34:51,080 we can use an error correction method that only works for small systems called majority voting error correction. 385 00:34:51,740 --> 00:34:55,760 So the curves that you see there are actually error corrected up to 20 beats of precision. 386 00:34:56,240 --> 00:35:01,520 So this this is a digital quantum. Computers are digital objects. So this is as digital as MATLAB, up to 20 bits. 387 00:35:02,270 --> 00:35:05,660 So those dots there are not just placed there. They are actually data from the quantum computer. 388 00:35:06,200 --> 00:35:09,920 Okay. Which we find pretty exciting. So that was the first experiment. 389 00:35:10,590 --> 00:35:15,890 Okay. So now can we fast forward to 2014 and go to Twitter? 390 00:35:17,180 --> 00:35:21,500 And many of you might know who is John Preskill? He's one of the top quantum information theoreticians. 391 00:35:22,040 --> 00:35:26,600 And he was addressing in Twitter what was happening that year, which was a very stressful and interesting year for us. 392 00:35:27,060 --> 00:35:28,460 Okay. So we're colleagues. 393 00:35:31,390 --> 00:35:37,480 Basically we're going to Microsoft published a paper that says that it was impossible to do quantum chemistry of quantum computer for the arguments, 394 00:35:37,480 --> 00:35:43,510 I'm telling you. And he says, well, this paper, when it's formed, which is one of the out of date, there are bigger improvements. 395 00:35:44,350 --> 00:35:47,250 And citing another paper of Microsoft. Okay. 396 00:35:48,400 --> 00:35:53,890 But he was outdated because the day before we had published a paper that had better scaling than that paper. 397 00:35:54,460 --> 00:36:00,880 This is baby, the way you're talking about the paper for Mos. That already already was better than this paper. 398 00:36:01,230 --> 00:36:04,390 You know, I hadn't even noticed. Okay, and why is that? 399 00:36:04,420 --> 00:36:09,160 Because, of course, after this paper came out, there was a race between many groups, 400 00:36:09,220 --> 00:36:13,650 but mostly the Microsoft and ours, because this is what came out in Break-Up wasn't 14. 401 00:36:13,660 --> 00:36:18,819 Okay. Based on this paper, that, again, was the first paper of this race when it appeared in the archive. 402 00:36:18,820 --> 00:36:24,129 And then about six months later on their on their on pray that if you read this, I'm not going to read to you, 403 00:36:24,130 --> 00:36:28,630 but it basically says here that we're in trouble, that, you know, 404 00:36:28,630 --> 00:36:35,080 simulating a molecule with with a with a quantum computer is impossible and so on and so on. 405 00:36:35,830 --> 00:36:41,530 Okay. Well, this is a story that was the original paper in the archive in 2014. 406 00:36:41,530 --> 00:36:44,679 Sorry, there's a typo here. Okay. December. 407 00:36:44,680 --> 00:36:48,460 If the people in the article in December 2014, then in March, 408 00:36:48,760 --> 00:36:54,370 the Microsoft team themselves improved on the way to improve the seven from 8 to 11, where they need a number of basis functions. 409 00:36:54,820 --> 00:37:01,780 And remember, this is the bound like analytical found obtained by methods of computer science on our algorithm. 410 00:37:01,810 --> 00:37:05,400 Right is the worst case scenario. June 2014. 411 00:37:05,490 --> 00:37:11,400 This is our group coming back at them and being better than them by a factor of point five and, you know, log jam. 412 00:37:11,670 --> 00:37:18,569 So we were like, yes, we got back to them in this time and then again us collaborating with them because now we're friends. 413 00:37:18,570 --> 00:37:22,860 So we've together collaborated and got a better estimate, 414 00:37:22,950 --> 00:37:27,900 which we actually looked at the scaling respect to the nuclear charge and what is that is the most important problem. 415 00:37:28,770 --> 00:37:33,990 And then we collaborated with Dominic Barry from Australia to use the sparse algorithms 416 00:37:34,740 --> 00:37:39,569 which have similar scaling but super important in terms of the number of gates, 417 00:37:39,570 --> 00:37:42,630 super important and exponential speed up in terms of accuracy. 418 00:37:43,140 --> 00:37:48,120 They gave us log one over at Epsilon instead of one over Epsilon as all this or that algorithm. 419 00:37:48,120 --> 00:37:53,189 So not only we have algorithms that actually are better in terms of scaling formally 420 00:37:53,190 --> 00:37:57,810 this is about but also are better in terms of scaling respect to precision. 421 00:37:58,590 --> 00:38:00,600 So this is incredible result in a year in the cuts. 422 00:38:00,600 --> 00:38:06,059 I'm so glad that Microsoft got into the business and and also woke us up a little bit to do a lot of work too. 423 00:38:06,060 --> 00:38:10,350 And then we all got together and, you know, beat this problem down. 424 00:38:10,620 --> 00:38:14,819 So Microsoft researchers say that calculations are they estimated that they quantities of years in 425 00:38:14,820 --> 00:38:21,300 computers and coding them more or less now take seconds in some sense by improving all these killings. 426 00:38:21,870 --> 00:38:27,780 Okay. So in other words, quantum chemistry is going really rapidly reducing the resources. 427 00:38:28,470 --> 00:38:32,480 But in the meantime, my group and I will not just be being steel. 428 00:38:33,330 --> 00:38:39,800 I want to show you basically we're going to have a guy at the quantum computer simulation that is graphical that in this paper, 429 00:38:39,810 --> 00:38:40,590 people were telling me, 430 00:38:40,590 --> 00:38:46,320 the reviewers were saying, Alan, you've been doing quantum chemistry for ten years and keep publishing and publishing the same subject. 431 00:38:47,040 --> 00:38:51,090 So I said, let's reply to reviewer number one with this graph. That's not true. 432 00:38:51,390 --> 00:38:54,690 We have proposed four different methods that are completely different to each other, 433 00:38:55,470 --> 00:38:58,980 going through all these different paths of different mathematical transformations. 434 00:38:58,980 --> 00:39:04,049 And the one I just told you right now is just this path which is using the one of a hammer approximation, 435 00:39:04,050 --> 00:39:09,570 using a second quantisation and computing integrals, all living at this formation notarisation and using quantum phase estimation. 436 00:39:09,930 --> 00:39:14,080 We propose an idea about the quantum simulation for the about the quantum devices that are universal. 437 00:39:14,550 --> 00:39:18,840 We propose that quantum dynamics method that can do scattering problems in real space. 438 00:39:19,350 --> 00:39:23,309 And the one I want to tell you about today is the one that we and many other groups are super excited about. 439 00:39:23,310 --> 00:39:25,660 It's called the variation like solver. Okay. 440 00:39:25,980 --> 00:39:32,940 And that one, I argue, is going to be probably the thing that is going to do quantum supremacy sooner, small and phase estimation. 441 00:39:32,940 --> 00:39:36,089 I'll show you some experiments, too. So that's the remainder of the talk. 442 00:39:36,090 --> 00:39:38,550 I'll tell you about the variation of like in software and when do I mean by that? 443 00:39:39,560 --> 00:39:43,940 During the course of all of this, one day we were thinking in my group, actually, 444 00:39:44,600 --> 00:39:49,400 my student John MacLean basically and myself were thinking like, what happens? 445 00:39:49,820 --> 00:39:54,260 Okay, this guy Jaro, what happens if we think about a classical computer? 446 00:39:54,260 --> 00:39:59,000 What does a classical computer do? It gets us a wave function, evaluates the energy, gets us again. 447 00:39:59,270 --> 00:40:03,410 And those is iterative system, right? This is how basically all the quantum chemistry packages work, 448 00:40:03,980 --> 00:40:08,750 including the package that is a boys develop like, you know, almost 50 years, more than 50 years ago. 449 00:40:09,200 --> 00:40:14,180 So then the question is, well, can I do the same? Can I actually get the wave function, prepare the wave function? 450 00:40:14,810 --> 00:40:18,260 Even with the energy which basically all of this process is only in a quantum device, 451 00:40:18,260 --> 00:40:25,670 you prepare and measure it and then use a classical computer as a as a co-processor to optimise the wave function in the liberation of subspace. 452 00:40:26,210 --> 00:40:29,600 So that is the meaning of the, of the variation of like in solver. Okay. 453 00:40:30,440 --> 00:40:36,410 So in the present I can solve it. I can write in three lines what's going on? You have a variation of minimisation over the energy of a Hamiltonian. 454 00:40:37,130 --> 00:40:41,810 Very importantly, note that you can write the Hamiltonian as a sum of different terms of the spin operators. 455 00:40:42,440 --> 00:40:46,669 And the only thing I'm asking my quantum computer friends to do is to calculate these 456 00:40:46,670 --> 00:40:51,079 expectation values that I can multiply by the classical parameters I got from my computer. 457 00:40:51,080 --> 00:40:55,460 I told you, which parameters are those? They are the integrals. So, okay, so I calculate my integrals. 458 00:40:55,790 --> 00:41:00,290 Do I join them in a transformation or a similar transformation? Turns out the better one is probability of. 459 00:41:01,340 --> 00:41:09,079 And I use the transformation to write down how the Hamiltonian looks like in terms of the spin operators and now any quantum computer of the world, 460 00:41:09,080 --> 00:41:15,060 the supercomputing device, the quantum optics, etc. all of them can be seen or announced trap. 461 00:41:15,110 --> 00:41:18,800 All of them can be seen as a basically as a quantum console. 462 00:41:20,330 --> 00:41:24,050 And why is this so cool? Because what quantum computers are good at is to do a measurement. 463 00:41:24,770 --> 00:41:30,680 And in the classical computer, they cannot multiply and optimise and all the things that a quantum computer cannot do very well. 464 00:41:30,890 --> 00:41:34,910 Try to write the quantum circuit for multiplication. I do in my PC. 465 00:41:35,830 --> 00:41:39,130 Okay. And that's why I believe that by issuing quantum like it's already so powerful. 466 00:41:39,840 --> 00:41:46,870 And since this has been published in 2014, there has been eight papers that actually use it for something from our group analysts. 467 00:41:47,650 --> 00:41:50,680 So with the idea of this paper, if you're not, 468 00:41:50,680 --> 00:41:55,629 is the first of two recent experimentalists and the last out of two was to publish it with an experiment at hand. 469 00:41:55,630 --> 00:42:01,630 And Jeremy O'Brien in Bristol actually built this chip, which I love is so high tech connected to low tech. 470 00:42:02,200 --> 00:42:09,850 These are heaters that change the faces in these micros microscopic, kind of smaller, 471 00:42:10,000 --> 00:42:13,930 I would say very small, like a couple of centimetres long quantum optics set up. 472 00:42:14,610 --> 00:42:18,700 Okay. And here, here, do the ones that actually do not look like that. 473 00:42:18,700 --> 00:42:24,340 They look much more advanced, by the way. But this is basically the integrated quantum photonic chip. 474 00:42:24,790 --> 00:42:28,960 One of the earlier ones there has these photos that come in from these rails, 475 00:42:29,320 --> 00:42:37,330 and you can adjust the temperature of this of these regions here to actually body the faces and basically a bunch of interferometers. 476 00:42:37,600 --> 00:42:43,790 And you have these detectors at the end. And turns out that this one can do a two by two arbitrary gate. 477 00:42:44,660 --> 00:42:49,520 So with very similar like in software, we were able to to to basically evolve from two one, 478 00:42:49,730 --> 00:42:53,330 two by two matrices to four by four matrices in four years. It's not so bad. 479 00:42:53,840 --> 00:42:57,110 Okay. So now we were able to do four by four. So what can you do? 480 00:42:57,140 --> 00:43:02,570 You can do helium hydrate. Okay. Helium hydrate plot is a four by four Hamiltonian. 481 00:43:03,170 --> 00:43:09,180 And here is the result. This is a potential energy surface as we dissociate the film hydride in physicists units. 482 00:43:09,200 --> 00:43:14,180 Okay, this is in the paper and the headed mega used for more. That's only a physicist can come up with that unit. 483 00:43:14,390 --> 00:43:20,170 Okay, maybe I use thermal. Okay, I know it's. I know it's the unit that you should be using, but you should use cartridge or something. 484 00:43:20,180 --> 00:43:24,650 A chemist like so kilocalories. But anyway, here is basically the potential sort of face. 485 00:43:24,920 --> 00:43:26,720 And notice how we don't use a lot of correction. 486 00:43:27,080 --> 00:43:32,420 And most of the error here comes due to losses and due to the fact that we are doing this this this phase shifting. 487 00:43:32,420 --> 00:43:36,170 We like this. I consider rudimentary the temperature technology. 488 00:43:36,470 --> 00:43:37,100 Well, nevertheless, 489 00:43:37,100 --> 00:43:43,190 we were able to actually use the volition eigen software and optimise the wave function and each one of these points and get the energy. 490 00:43:43,190 --> 00:43:46,640 And again, this is, again, quantum computers simulating helium hydride. Okay. 491 00:43:47,270 --> 00:43:56,820 So so far, so good. So now. Let me just tell you then the latest experiment. 492 00:43:56,850 --> 00:44:02,130 Okay. I notice that I'm wearing it, so I'm not going to be late and maybe even a bit early. 493 00:44:02,670 --> 00:44:08,909 So since then, of course, I told you so far that we have developed many algorithms with no details, 494 00:44:08,910 --> 00:44:12,750 but we can talk later that reduce the scaling of the face estimation algorithm. 495 00:44:13,530 --> 00:44:16,860 And then I told you that we've been developing this variation of quantum and solver mental. 496 00:44:18,000 --> 00:44:21,750 He already has been employed, by the way, in on drops by one of my former group members, 497 00:44:21,750 --> 00:44:28,070 Michael Young, and a collaborator whose last name is Kim at Senor University as well. 498 00:44:29,520 --> 00:44:32,910 Well, we were trying to see how far we can go. And then so we started talking to Google. 499 00:44:32,940 --> 00:44:38,639 Turns out that as many of you probably know, that Google basically Acqui hired John Martinez from the University of California, 500 00:44:38,640 --> 00:44:42,330 Santa Barbara, and his entire team is now building quantum computers for Google. 501 00:44:42,990 --> 00:44:47,850 And this is how the quantum computer looks like right now is basically nine cubits coupled to these oscillators 502 00:44:47,850 --> 00:44:54,080 for readouts and and he don't really control lines and they call this cubits X one because it looks like axis. 503 00:44:54,600 --> 00:45:02,850 Okay. And they're a very phenomenal cubits. This is another diagram of the wiring diagram of this of this cubits and another picture of five of them. 504 00:45:04,380 --> 00:45:09,030 And basically the idea is like, can we use the X months to actually do both for the first time, 505 00:45:09,180 --> 00:45:11,760 a fully scalable version of the evolution of a quantum console. 506 00:45:11,910 --> 00:45:18,480 In other words, writing down all the operators without calculating them or doing any tricks like we did in the quantum optics experiment. 507 00:45:18,750 --> 00:45:22,829 Just a full, really honest simulation and also face estimation, 508 00:45:22,830 --> 00:45:27,390 which involves many more gates and basically look how they look in a superconducting machine. 509 00:45:27,960 --> 00:45:32,310 And this was done over the span of a few months because they are very good at controlling their device. 510 00:45:32,550 --> 00:45:36,240 So it's mostly talking about the problem and interfacing with them. 511 00:45:37,350 --> 00:45:42,650 That led to this paper that was just submitted in December, where we actually have, 512 00:45:42,660 --> 00:45:46,860 in this particular case, two cubits for the controller and three for the face estimation. 513 00:45:46,860 --> 00:45:47,639 In this particular case, 514 00:45:47,640 --> 00:45:55,240 I'm showing you two and actually one of the ball sequences that was used in the superconductors that corresponds to this liquid, okay, 515 00:45:55,560 --> 00:46:01,830 to calculate the energy which we can in a very minimal basis guide as these numbers that come from 516 00:46:01,830 --> 00:46:07,950 a classical PC multiplying these correlations of the qubits and if you do enough experiments, 517 00:46:08,760 --> 00:46:15,550 measure these correlations at the most in your classical computer, optimise initial state again, you know, 518 00:46:15,660 --> 00:46:21,680 suggest that your parameter for these rotations here and this particular case is a single rotation up. 519 00:46:22,930 --> 00:46:25,870 We will get chemical accuracy in this particular case. 520 00:46:25,870 --> 00:46:30,940 For these bases, we got an accuracy of one kilocalories per month, which is extremely good for chemistry. 521 00:46:31,570 --> 00:46:35,680 So I am very excited about this experiment first because we did it very quickly. 522 00:46:36,910 --> 00:46:44,990 Notice also that the small device has more cubits and can do more gates so we can, in principle, do a larger system there, improving the coherence. 523 00:46:45,730 --> 00:46:50,710 And not only that, we could also do the phase estimation algorithm. 524 00:46:51,190 --> 00:46:58,330 Okay. Which involves characterisation over many terms of the Hamiltonian, and therefore you can see there's more error in the phase estimation. 525 00:46:58,720 --> 00:47:02,799 Okay. And you can see that the variation of quantum insoluble is actually, first of all, 526 00:47:02,800 --> 00:47:08,790 more robust to error intrinsically, but also because it employed less gates. 527 00:47:09,280 --> 00:47:12,400 Underwent less decoherence. So. 528 00:47:14,820 --> 00:47:20,070 What I'm trying to say here is that theoretically this is the best possible angle here. 529 00:47:20,820 --> 00:47:25,229 See data for this experiment and the error that we get in the experiment will be 530 00:47:25,230 --> 00:47:29,250 something like this if we place our computer at the basic theoretical angle, 531 00:47:29,940 --> 00:47:36,840 but the machine is more robust and finds an experimental angle that is slightly different and that experimental angle is actually better. 532 00:47:37,140 --> 00:47:43,710 And why is that? Because we're using the variational theorem and the original theorem allows us to compensate for errors. 533 00:47:44,220 --> 00:47:47,700 It's quite cool. So in some sense if you have a noisy quantum device, 534 00:47:47,700 --> 00:47:53,940 the additional leg and a little bit actually helps you do better than, than, than you should naively. 535 00:47:54,810 --> 00:48:00,630 So this is the last resort slide. So now I'm going to talk about a paper that just appeared in Nature Chemistry. 536 00:48:01,560 --> 00:48:10,320 This is only me and editor of of Nature. They wrote this commentary in Nature Chemistry, which is actually arguing that. 537 00:48:12,040 --> 00:48:17,230 That our our our search is chaotic and maybe, yes, I'm Spanish speaking, so maybe I'm like Quixote. 538 00:48:17,770 --> 00:48:22,149 Okay. And what she basically means is that, well, you know, maybe they would be able to do this. 539 00:48:22,150 --> 00:48:26,020 Maybe not. And the second thing that she's talking about is, well, even if they do it, 540 00:48:26,020 --> 00:48:31,540 maybe the classical computing people say the tensor networks people and all these people that are getting better and better methods. 541 00:48:31,720 --> 00:48:36,520 By the time we get our quantum computer, we already have cracked the problem. Okay, let's let's do it. 542 00:48:36,730 --> 00:48:43,990 So I went to Twitter and I bet we had a bottle of champagne that in 20 years, we want to be able to have a quantum computer do this better than her. 543 00:48:43,990 --> 00:48:51,610 So stupid. What I believe is reasonable because I believe in my experimental colleagues and here is basically revolution writing to first. 544 00:48:51,610 --> 00:48:54,790 And then we did this tabletop quantum optics experiment with them, right? 545 00:48:55,240 --> 00:49:01,780 Jeremy Brian did this experiment in an integrated photonic chip and now we're using eight superconducting qubits. 546 00:49:01,780 --> 00:49:04,060 For those of you that follow the field, this is a rapid progress. 547 00:49:04,900 --> 00:49:08,740 So I trust in my experimentalist colleagues that they helped me right on this bandwagon. 548 00:49:09,280 --> 00:49:18,010 And also there's by this time that she predicted show that we can have a quantum computer, achieve quantum supremacy for chemistry applications. 549 00:49:18,900 --> 00:49:25,520 Okay. So now let me end just briefly, briefly with the following question. 550 00:49:25,530 --> 00:49:33,870 Can we beat classical computers? Okay. So for that, we start collaborating with Intel Research, which got recently interested in quantum computing. 551 00:49:34,200 --> 00:49:37,260 And they have a massive effort now in quantum quantum computing at Intel. 552 00:49:37,710 --> 00:49:41,160 And one of the early theoreticians, Mr. Jansky, collaborated with my graduate student, 553 00:49:41,160 --> 00:49:44,610 Nicholas Away and me in building this package that we like to call. 554 00:49:44,620 --> 00:49:48,480 Q Hipster. Okay. The Quantum High Performance software testing environment. 555 00:49:49,140 --> 00:49:55,470 You just happened to be this acronym for sure, right? But Q Hipster is interesting because it was built at the Interparty Computing Lab. 556 00:49:55,770 --> 00:49:58,739 My student went there as an intern and he supposed, you know, 557 00:49:58,740 --> 00:50:06,000 it's basically built to be as far as possible and therefore allows us to to do up to 40 cubits in the in the text of stampede computer. 558 00:50:06,000 --> 00:50:13,530 Actually, although the machine can handle up to 43 and in the largest computer in the world, you probably can simulate 49 cubits. 559 00:50:14,130 --> 00:50:22,170 Okay. So really, to achieve quantum supremacy, I argue, you need to go beyond 50 logical cubits, which in terms is extended to, 560 00:50:22,620 --> 00:50:28,020 you know, perhaps $0.05 or more of physical cubits just to give you a magnitude of the problem. 561 00:50:28,410 --> 00:50:36,510 And so you have the challenge. And obviously, obviously, the classical computers would keep improving slowly in terms of qubits. 562 00:50:38,450 --> 00:50:41,120 So this is the logo for the software that we're considering. 563 00:50:41,360 --> 00:50:47,810 You can send me suggestions because if people used up all 26 of January, what I think this is going to be the logo of quantum hipster. 564 00:50:49,580 --> 00:50:56,330 And with that, I just want to try to have some time for questions and thank my research group here. 565 00:50:57,950 --> 00:51:03,380 Some of the people that it is work are already gone. But the students that are really pushing these nowadays are Yankee Village can here. 566 00:51:03,800 --> 00:51:06,950 And Jonathan Romero, this is a new blog that was doing quantum computing. 567 00:51:07,520 --> 00:51:11,540 And Giacomo Richie, which is sitting somewhere here, is already moved to Intel. 568 00:51:11,540 --> 00:51:15,020 So and also Saddam was stymied. Two of my group members really move to Intel. 569 00:51:15,530 --> 00:51:20,239 Maybe Djindjic was not there anymore. Here he's sat already had left as well. 570 00:51:20,240 --> 00:51:23,180 So. But anyway, so many, many people are also moving to industry. 571 00:51:23,780 --> 00:51:27,020 So I'm one and also with a superposition of my group in the ground in the excited state. 572 00:51:27,620 --> 00:51:30,410 And with that I open for questions. Thank you.