1 00:00:14,710 --> 00:00:18,730 So thank you. Thank you very much for the for the introduction. So, yes, exactly. 2 00:00:18,730 --> 00:00:26,650 So today I'm going to give you a non-exhaustive and perhaps a bit biased overview of the developing field of quantum simulation. 3 00:00:27,470 --> 00:00:32,110 Right. So as you would see, it is not accidental that this talk sits in between. 4 00:00:32,470 --> 00:00:39,130 After we are stuck on the relativistic heavy ion collisions and the black is stuck on quantum matter of correction. 5 00:00:39,820 --> 00:00:47,440 In fact, quantum simulation is something in between a physics experiments and and apart from computation. 6 00:00:48,160 --> 00:00:54,570 So let me. So to walk you through, walk you to the to the thoughts, the philosophy and the practice of quantum simulation. 7 00:00:55,050 --> 00:01:01,140 So let me let me start from the very basic. So science science is about making quantitative observations of phenomena, 8 00:01:01,590 --> 00:01:11,670 then formulating a theory or a mathematical model to explain these observations and making new predictions out of out of the model. 9 00:01:12,750 --> 00:01:20,490 So an important part of our job as theoretical physicists is to be able to compute the physical behaviour that results from a model. 10 00:01:21,600 --> 00:01:28,650 Okay, So usually the simplest predictions can be obtained by explicitly solving a model, right? 11 00:01:29,040 --> 00:01:36,689 However, in the general case, explicit solutions are not available and we have to resort to a cascade of less and less, 12 00:01:36,690 --> 00:01:39,910 less and less pretentious strategies to solve to solve the problem. 13 00:01:39,930 --> 00:01:46,860 For example, we can we may want to do a brute force simulation of the model, usually using a computer. 14 00:01:47,860 --> 00:01:53,980 Or we may want to resort to a controlled approximation schemes or two if none of this work. 15 00:01:54,190 --> 00:01:57,970 We can try to replace the model with some simpler phenomenological model. 16 00:01:58,660 --> 00:02:03,880 Right. So let me take a minute to remind you how this works in the context of classical classical mechanics. 17 00:02:04,750 --> 00:02:09,910 Right. So one of the early drives to develop classical mechanics was to explain planetary motion. 18 00:02:10,930 --> 00:02:16,300 Right. So. So the motion of a single planets orbiting around the sun is described by Newton's equation. 19 00:02:16,900 --> 00:02:24,040 This equation can be explicitly solved, and this exact solution tells us a great deal about the astronomical observations. 20 00:02:25,570 --> 00:02:33,940 Now, when we move to the problem of many celestial bodies, so call and call and their number we deal with and Newton equations. 21 00:02:34,900 --> 00:02:40,840 Right. We deal with anything and equations, and this problem is famously not solvable, even for an equals three. 22 00:02:41,320 --> 00:02:48,730 Right. What we can do instead is performing a brute force computation of the trajectories of the of the bodies. 23 00:02:49,000 --> 00:02:56,760 So how do we do that? Basically, we use Newton input so that the system, state of the system is described by six times ten variables. 24 00:02:56,770 --> 00:03:00,370 So all the positions and all the velocities of all the bodies. Right. 25 00:03:00,610 --> 00:03:05,469 And we use Newton Equation to update this 610 variables for the next time step. 26 00:03:05,470 --> 00:03:12,970 So for a short time step and we repeat this process over and over to obtain to compute the full trajectory. 27 00:03:13,300 --> 00:03:19,420 Now, using modern computers, this can be done very efficiently for thousands or even millions of bodies. 28 00:03:19,630 --> 00:03:22,300 Right. So it's fair to say. Sorry. 29 00:03:22,990 --> 00:03:32,350 So it's fair to say that this that this problem is said that the brute force, numerical simulations are extremely powerful in this problem. 30 00:03:32,830 --> 00:03:38,130 And here in this this animation, I hope you see it. 31 00:03:38,140 --> 00:03:45,970 Yes. You see a computer animation of a of the trajectories computed for our many by the computational problem computed using a computer. 32 00:03:47,160 --> 00:03:52,310 Okay. So this is this is the situation. Now, let's move to quantum mechanics, right? 33 00:03:52,950 --> 00:04:00,690 So quantum mechanics, the original drive to develop quantum mechanics stemmed from from the from the problem of atomic spectra, for example, hydrogen. 34 00:04:00,900 --> 00:04:05,370 Right. So we deal with the motion of a single electron orbiting around the nucleus. 35 00:04:06,400 --> 00:04:12,040 Right. And this is described by Schrodinger equation. Now, Schrodinger equation in this case is explicitly solvable. 36 00:04:12,340 --> 00:04:17,410 And the exact solution of this problem tells us a great deal about the observation of atomic spectra. 37 00:04:17,800 --> 00:04:26,560 So great. So far, so good now. And here you see the illustration of some some of the atomic orbitals the sent from the solution. 38 00:04:26,890 --> 00:04:36,310 Now problem comes when we go when we move to the problem of many, many quantum particles like for example, and problem of and electrons. 39 00:04:37,030 --> 00:04:43,540 Right. So in this case, we deal with the Schrödinger equation with the embody Schrodinger equations equation. 40 00:04:45,340 --> 00:04:49,240 And and this problem, of course, is famously not solvable even for n equals three. 41 00:04:49,270 --> 00:04:54,070 Just like in the classical case. But here there is something, something much worse happening. 42 00:04:54,970 --> 00:05:02,560 Essentially, the NYU Schrodinger equation describes the evolution in time of the embody wave function of the system, 43 00:05:02,560 --> 00:05:04,600 of the wave function of electrons. Right. 44 00:05:04,810 --> 00:05:13,690 So this wave function is nothing but a complex number assigned for every possible classical configuration for the end for the end particles. 45 00:05:14,140 --> 00:05:22,080 Right. So imagine these particles. Let's be generous and say that this particles can be in a given number of states, say ten or even five or even two. 46 00:05:22,390 --> 00:05:33,400 Right? Just every particle can be in two states. Of the number of configurations of the system is two, is two by two, by two by two, two end times. 47 00:05:33,970 --> 00:05:41,210 Right. So it's two two power and. So essentially we have the system is described by two power and numbers. 48 00:05:41,290 --> 00:05:46,120 Complex numbers. Right. And we have two. This is the the many body weight function. 49 00:05:46,600 --> 00:05:56,630 Right? Now, this this wave function, as you see the complexity of this object explodes exponentially with the number of particles. 50 00:05:57,020 --> 00:06:05,120 And I'm sure I think that in the recent pandemics, pretty much everyone got a sense of how quick and exponential growth is. 51 00:06:05,870 --> 00:06:11,630 Right. So this is a we we could try to estimate how bad this is for a real problem of interest. 52 00:06:12,680 --> 00:06:22,820 So we could try to convince ourselves. But then here I instead I reported the words from a Nobel lecture of Walter Kohn, 1999, who argued, 53 00:06:23,120 --> 00:06:30,530 even provocatively argued that the many body wave function, the quantum anybody wave function is not a legitimate scientific concept. 54 00:06:30,980 --> 00:06:39,260 So the the essential the essential point here is that the amount of information that you would need to describe the wave function of many electrons, 55 00:06:39,260 --> 00:06:44,240 for example, quickly exceeds the amount of matter in the entire universe. 56 00:06:44,330 --> 00:06:50,690 So even for a thousand, even for a thousand electrons, this would be this would exceed the amount of matter in the entire universe. 57 00:06:50,900 --> 00:06:58,090 So this is the bottom line here, is that so you may agree or not with this strong viewpoint, but that the problem is real. 58 00:06:58,340 --> 00:07:02,060 So the problem of the exponential world is real, right? 59 00:07:02,330 --> 00:07:07,340 So it's not about it's not really about technological advance advantage. 60 00:07:07,760 --> 00:07:11,180 Advance is not about building better. 61 00:07:11,930 --> 00:07:14,910 It's not about building a better and stronger supercomputer. 62 00:07:14,930 --> 00:07:21,740 So there is a fundamental limitation in the capability of computers to deal with quantum physics. 63 00:07:22,340 --> 00:07:25,370 Right. And this is something new is different from from classical mechanics. 64 00:07:28,540 --> 00:07:36,990 So I think it's fair to say that brute force numerical computations of the quantum antibody problem are fundamentally out of reach. 65 00:07:38,350 --> 00:07:46,139 Hmm. Okay. And this is actually why if you try to Google quantum, anybody physics or quantum, anybody would function as you as you could do, 66 00:07:46,140 --> 00:07:50,640 for example, for the other for the previous, in contrast with what you did with the previous images. 67 00:07:51,390 --> 00:07:57,300 Here you find just a bunch of funny and incomprehensible drawings that we theoretical physicists like. 68 00:07:58,320 --> 00:08:06,300 And this is because essentially it's very hard to even visualise this massive, huge amount of information encoded in the many body wave function. 69 00:08:07,420 --> 00:08:15,190 Okay, So basically, quantum theory calls for countless approximation schemes and phenomenological theories. 70 00:08:15,700 --> 00:08:21,070 And this includes, for example, what you I think what you have seen in the previous talk by Dr. Brewer. 71 00:08:22,410 --> 00:08:25,590 Okay, So this is this is the this is it. 72 00:08:25,950 --> 00:08:32,850 But then you may legitimately wonder at this point why Why do we even care about solving the quantum anybody problem? 73 00:08:33,060 --> 00:08:41,460 Right. So after all, for example, if football is made of many quantum particles, as far as we know, but we can predict this behaviour extremely well. 74 00:08:41,910 --> 00:08:46,800 Right. So why why do we even care about solving them? Anybody, quantum anybody problem? 75 00:08:47,610 --> 00:08:54,540 So the point here is that many important phenomena in nature are intrinsically quantum and intrinsically anybody in the 76 00:08:54,540 --> 00:09:00,680 sense of ignoring quantum effects or ignoring correlation effects between the particles is not a good idea for describing. 77 00:09:01,320 --> 00:09:01,490 Right. 78 00:09:01,560 --> 00:09:09,330 And here I will give you an exhaustive list of some some problems that would be very nice to solve if we could deal with the quantum anybody problem. 79 00:09:09,630 --> 00:09:14,820 Right. So in the domain of chemistry, for example, if we had the solution of the quantum anybody problem, 80 00:09:15,120 --> 00:09:20,459 this would give us this would allow us to perform a first principle computation of molecular structure, 81 00:09:20,460 --> 00:09:24,780 for example, or molecular reaction rates of chemical reactions. 82 00:09:25,350 --> 00:09:31,049 Or this would allow us to predict this, would allow it to give us the opportunity to predict new molecules, 83 00:09:31,050 --> 00:09:34,470 for example, with obvious applications, for example, for drug design and so on. 84 00:09:34,650 --> 00:09:37,590 So here in the illustration you see an example. 85 00:09:38,610 --> 00:09:44,249 This is basically a so-called light harvesting complex that plays a role in the process of photosynthesis. 86 00:09:44,250 --> 00:09:48,690 And it's an example of a process where quantum quantum mechanical effects are important. 87 00:09:49,830 --> 00:09:55,140 Now let's move to the domain of condensed matter physics to discuss close to what they actually do. 88 00:09:55,620 --> 00:10:02,159 Right. So here solution of the them anybody problem would give us first principle computation of the properties of materials, 89 00:10:02,160 --> 00:10:06,600 for example, of their structure, of their out of equilibrium response and so on and so forth. 90 00:10:07,110 --> 00:10:12,389 And this would give us the opportunity to predict new materials or new phases of matter. 91 00:10:12,390 --> 00:10:18,000 For example, the conditions for the for having high temperature superconductors. 92 00:10:18,000 --> 00:10:21,780 And this would obviously be extremely important for applications. 93 00:10:22,780 --> 00:10:26,500 Right. And finally, also in the context of high energy physics. 94 00:10:26,890 --> 00:10:31,150 So the solving the problem would give us first principle computation, for example, 95 00:10:31,150 --> 00:10:35,140 of a hydraulic structure or nuclear reactor or nuclear reaction rates. 96 00:10:35,470 --> 00:10:41,940 And this would give us the opportunity to predict the behaviour of matter in extreme conditions of temperature and pressure. 97 00:10:41,950 --> 00:10:50,200 For example, in the early universe dynamics or in the inner stars or in relativistic heavy collisions have, 98 00:10:50,200 --> 00:10:53,350 just as you heard in the previous stuff by by Dr. Brewer. 99 00:10:53,740 --> 00:10:57,850 So this is would obviously be extremely interesting also in this context. 100 00:10:58,270 --> 00:11:03,879 And these are all examples coming from natural sciences. But actually, there are examples that go beyond the domain of physics. 101 00:11:03,880 --> 00:11:09,370 I think Dr. Blackett will briefly touch upon this aspect in the in the next stock. 102 00:11:10,900 --> 00:11:13,600 Okay, so the summary of the situation is the following. 103 00:11:13,630 --> 00:11:22,330 So basically solving the quantum anybody problem would lead to a huge progress, to a huge leap forward along in several branches of science. 104 00:11:22,540 --> 00:11:29,980 Right. So this would be really great. However, we have said that brute force numerical computations are fundamentally impossible. 105 00:11:30,940 --> 00:11:35,290 On the other hand, controlled approximations in many cases are known to suffer badly. 106 00:11:35,710 --> 00:11:39,480 Right. Otherwise, we would have sort of all these problems. And then. 107 00:11:39,610 --> 00:11:46,120 And phenomenology is not always satisfactory for us. So this seems like a seems like a bad situation. 108 00:11:46,120 --> 00:11:50,070 So that's why our question is, is there a way out from from the simulation? 109 00:11:50,080 --> 00:11:52,360 And as you can guess from the fact that I'm giving this talk. 110 00:11:55,060 --> 00:12:04,560 The answer is a possible answer is yes, in the sense that the that there is a possibility that was suggested in the early eighties by my research. 111 00:12:04,570 --> 00:12:10,930 Richard Feynman, that is actually the contents of the stock, which is the possibility of performing quantum simulations. 112 00:12:11,320 --> 00:12:19,059 So basically the following fundamental idea is the following. So if we can't if we can't store and process in anybody, 113 00:12:19,060 --> 00:12:26,320 we function in a classical computer which is made of units that can state that can be in two states, either zero or one. 114 00:12:27,130 --> 00:12:35,590 So the point is, because this would say for the for the problem of a thousand electrons, this would require a computer as big as universe. 115 00:12:35,950 --> 00:12:43,090 But then how why don't we store and process the information contained in this way function, for example, a thousand electrons? 116 00:12:43,570 --> 00:12:48,670 Why don't we use it and process it using a processor that is made of quantum units, 117 00:12:48,940 --> 00:12:52,330 that is made of quantum particles, like, for example, a thousand atoms. 118 00:12:52,630 --> 00:12:58,680 Right? So provided we can operate with this objects, manipulate them quantum mechanically, right? 119 00:12:58,690 --> 00:13:04,360 Not classically, but quantum mechanically, then we only need a thousand particles to stimulate thousands of particles. 120 00:13:04,360 --> 00:13:07,960 We don't need something as big as bigger than the universe. Right. 121 00:13:08,170 --> 00:13:13,600 So this is this is the central idea That was central insight that was before the proposed. 122 00:13:14,580 --> 00:13:17,690 Right. And this goes under the name of of quantum simulation. 123 00:13:17,840 --> 00:13:28,790 Right. So the goal is to is to simulate quantum mechanics, Quantum anybody problems using quantum and using a controllable quantum, anybody's system. 124 00:13:29,300 --> 00:13:36,360 Right. So this is. And this looks like a strange idea. 125 00:13:36,360 --> 00:13:41,540 I just invite you to pay attention to the rest of the talk. What I try to make make it a bit bit clearer. 126 00:13:42,320 --> 00:13:49,130 So how do we how do we simulate a quantum system using a quantum machine, using a set of quantum devices? 127 00:13:49,610 --> 00:13:53,940 So the most important thing is that we need a new type of hardware, right? 128 00:13:54,860 --> 00:14:00,739 So basically what we need is a highly controllable quantum anybody system where we can access, 129 00:14:00,740 --> 00:14:05,090 control, manipulate, observe individual individual quantum particles, 130 00:14:05,390 --> 00:14:16,160 which which operates in a way that is not somehow affected or not disturbed or not destroyed by the, for example, by environmental processes. 131 00:14:17,180 --> 00:14:20,720 Right. Okay. So we need we need this kind of machine or hardware. 132 00:14:20,990 --> 00:14:23,059 Right. And suppose we are given such a machine. 133 00:14:23,060 --> 00:14:30,480 So suppose we are given a quantum antibody system that we can control, maybe not perfectly, but we have a good degree of control on. 134 00:14:31,040 --> 00:14:35,869 So what do we do with it? How do we perform a quantum simulation of our system of interest? 135 00:14:35,870 --> 00:14:42,140 For example, our favourite molecule, our favourite material or our favourite nucleus or whatever, whatever you like. 136 00:14:42,680 --> 00:14:52,130 So what do we have to do? So for first thing first you have to essentially encode the states of the system of interest in the states of your hardware. 137 00:14:52,370 --> 00:14:59,660 So you need a mapping of correspondence between the states of the system of interest and the states of your of your quantum particles. 138 00:14:59,900 --> 00:15:04,370 So this mapping can be more or less obvious, more or less direct. 139 00:15:04,610 --> 00:15:07,700 But in some cases, it's very it's very direct. 140 00:15:07,700 --> 00:15:14,300 In some cases it's very convoluted, very abstract. And you need some imagination to to to build this this correspondence. 141 00:15:14,310 --> 00:15:18,800 But it doesn't matter. You just need one correspondence between the two, between the two. 142 00:15:20,230 --> 00:15:26,320 Right. Second, we need to be able to prepare the system in the states that we need in the state that we like for. 143 00:15:26,500 --> 00:15:33,970 And this is where the control enters. Right. So we need to prepare in a wave function that represents the wave function that we care about. 144 00:15:36,400 --> 00:15:45,070 Then and this is usually the bottleneck. We need to be able to design the forces or technically the Hamiltonian that governs the system in 145 00:15:45,070 --> 00:15:51,370 a way that mimics or resembles the the forces or the actual evolution of the system of interest. 146 00:15:51,640 --> 00:15:54,220 Right. And here is where where most of the pain comes. 147 00:15:55,400 --> 00:16:01,110 Right, because it's your system has its own native infractions and doesn't want to do what you want. 148 00:16:01,170 --> 00:16:07,370 Right. So you have to be somehow drive it into into the into doing what you want. 149 00:16:07,550 --> 00:16:11,600 Right. And finally, you have to be able to measure the observable something there. 150 00:16:11,600 --> 00:16:14,180 So there is some observable that you care about in the actual system, 151 00:16:14,360 --> 00:16:19,370 and you have to be able to map it back to your hardware and be able to measure this precise quantity. 152 00:16:20,600 --> 00:16:24,889 Okay. So basically, all this set of requirements can be summarised in a single equation, 153 00:16:24,890 --> 00:16:29,050 which is the one that you find that you find in the bottom of the slides, 154 00:16:29,060 --> 00:16:33,860 which expresses the equivalence between the quantum anybody dynamics happening on one side, 155 00:16:33,860 --> 00:16:38,570 on the actual system and on the other side something in your artificial hardware. 156 00:16:39,230 --> 00:16:43,820 Right. So basically this, this correspondence is about building is about building, 157 00:16:43,940 --> 00:16:48,600 constructing a dictionary between your system of interest and your and your hardware. 158 00:16:48,620 --> 00:16:52,910 If you are able to do this, then you can perform your quantum simulation. 159 00:16:53,060 --> 00:16:55,280 And of course, this is this is not easy in general. 160 00:16:55,280 --> 00:17:02,660 And that's that's already in the in the paper by Feynman, you see a remark on how difficult this can be. 161 00:17:02,870 --> 00:17:06,690 But of course, this is one one possible way to proceed with. 162 00:17:07,370 --> 00:17:12,470 Okay. So before before going on to tell about tell you about examples. 163 00:17:13,280 --> 00:17:21,620 Right. So to tell you about where we stand in this enterprise and and what the what what can we do now, what we can hope to do next. 164 00:17:21,920 --> 00:17:29,930 Right. I want to give you a little piece of theory and draw an important distinction between two approaches to quantum simulation. 165 00:17:30,230 --> 00:17:35,120 So one that is called analogue quantum simulation and one that is called digital quantum simulation. 166 00:17:35,130 --> 00:17:38,600 So I don't know, quantum simulation is close to what I described so far. 167 00:17:38,990 --> 00:17:45,320 Right. And is actually in the examples that I would give that I will give I will talk about analogue quantum simulation. 168 00:17:45,350 --> 00:17:51,320 So analogue means essentially that your hardware, your quantum system has some native interactions. 169 00:17:51,920 --> 00:17:56,270 Right? And basically the cards that you can play, you can play two cards essentially. 170 00:17:56,270 --> 00:18:05,810 Right. So you can addition, you can use additional engineering in the system to tweak the native interactions to to take the form that you want. 171 00:18:06,830 --> 00:18:13,549 Right. Or you can be somehow device clever mapping some clever counterintuitive mappings that 172 00:18:13,550 --> 00:18:18,320 map your your native system to some system that superficially looks very different. 173 00:18:19,250 --> 00:18:23,899 But is this what you what you would like. So you can play you can play these two games essentially. 174 00:18:23,900 --> 00:18:31,310 And this is. And so basically you have your system. It functions more or less in the way it wants to function up to some up to some messaging. 175 00:18:31,790 --> 00:18:37,130 Right. This is an analogue quantum simulation. Now, digital quantum simulation is a priori something very different. 176 00:18:37,640 --> 00:18:42,530 So here the principle is different. So the idea is that you want to switch on and off. 177 00:18:43,010 --> 00:18:45,230 You want to be able to switch on and off your units, 178 00:18:45,530 --> 00:18:53,240 your your individual units of your quantum hardware such that you can address them individually and perform individual operations on them. 179 00:18:53,270 --> 00:18:57,350 So on every. On each one of them. Or maybe pairs of them. 180 00:18:57,560 --> 00:19:04,100 Right. You want to be able to perform this building block operations that we call unitary gates. 181 00:19:04,760 --> 00:19:14,270 Right. And then the idea is that an arbitrary quantum dynamics for the full system of particles can be approximated arbitrarily. 182 00:19:14,270 --> 00:19:19,380 Well, provided you are given a large enough set of of gates of any target. 183 00:19:19,520 --> 00:19:25,159 So the idea is that you have to form a set of gates that you can efficiently implement, right. 184 00:19:25,160 --> 00:19:31,040 In such a way that these gates form a universal gates set right in universal gates. 185 00:19:31,040 --> 00:19:36,110 That means that an arbitrary quantum dynamics can be approximated by a sequence of these building blocks. 186 00:19:36,440 --> 00:19:41,180 Right. So you can you can decompose it in a sequence of unitary gates. 187 00:19:41,570 --> 00:19:44,060 Right. That is also called a quantum circuits. 188 00:19:44,750 --> 00:19:51,530 So basically, you know, a lot of quantum simulation, you don't need to devise some strange or clever mappings. 189 00:19:51,830 --> 00:19:55,160 All you need to do, all you need to have is a software. Right. 190 00:19:55,190 --> 00:20:02,090 So you need a program that compiles your actual your target evolution that you want in your actual system. 191 00:20:02,360 --> 00:20:07,940 It is complicit in terms of a sequence of gates. Or a lot of circuits. 192 00:20:08,540 --> 00:20:12,649 So in this illustration, you see what the quantum circuit looks like. This is an illustration. 193 00:20:12,650 --> 00:20:16,580 So in this case, time flows from left to right. 194 00:20:17,050 --> 00:20:22,470 Right. So on the left we have our initial quantum units that are prepared in some reference state. 195 00:20:22,490 --> 00:20:26,330 Let's call it zero. Okay, so this is our initial state. 196 00:20:26,600 --> 00:20:31,880 Right. Then we have our digitised evolution. So our sequence of unitary gates. 197 00:20:32,270 --> 00:20:39,860 Right. And this is created by a software that creates it in such a way that this sequence of gates reproduces exactly the dynamics that we want. 198 00:20:40,370 --> 00:20:47,330 Right. So this funny boxes and drawings are the are drawn from some set of gates, some special set of gates. 199 00:20:47,720 --> 00:20:53,960 Right. And then at the end on the right, we measure the cubits. And the answer to our problem is encoded in this measurement. 200 00:20:55,130 --> 00:21:01,490 So you see that the the the power of the digital machine is that is hardware independent. 201 00:21:01,490 --> 00:21:06,630 Somehow it can approximate arbitrarily well any any quantum dynamics in principle. 202 00:21:06,650 --> 00:21:14,360 So it's universal in this sense. This is kind of the ultimate goal of the field of of the field of, uh, of the field. 203 00:21:14,360 --> 00:21:22,040 And this is, this is why the the analogy with of between this things and the classical computer is the reason why we call this a quantum computer. 204 00:21:22,580 --> 00:21:26,250 Right? So you will hear more about this in the talk by Dr. 205 00:21:27,530 --> 00:21:33,950 But I can let me just I can help mention in the fact that in the development of this field of universal quantum computation, 206 00:21:33,950 --> 00:21:38,510 the researchers in Oxford played really a protagonist, protagonist role. 207 00:21:38,900 --> 00:21:43,160 So, you know, it's an art record and interesting and so on and so forth. 208 00:21:44,060 --> 00:21:47,660 So this is a very important topic. What way then here in particular? 209 00:21:48,470 --> 00:21:53,420 Very good. So, right, so this is this is what we would like to do, right? 210 00:21:55,760 --> 00:22:04,040 So if you've never heard before or thought about or thought before too deeply about quantum simulation or quantum computation, 211 00:22:04,040 --> 00:22:08,090 I hope I conveyed the message that this is a very exciting theoretical idea. 212 00:22:08,300 --> 00:22:14,630 Right. But then where do we stand in the implementation, in the implementation of this idea? 213 00:22:15,050 --> 00:22:15,280 Right. 214 00:22:15,470 --> 00:22:25,850 So there are several competing experimental platforms that are participating in the race to build somehow a more and more powerful quantum machine. 215 00:22:26,130 --> 00:22:28,280 Right. So there are there are very, very many by now. 216 00:22:29,120 --> 00:22:36,599 Here I reported two pictures that illustrate to two kind of families of this of this quantum device. 217 00:22:36,600 --> 00:22:42,650 This on the left, we see the so-called Ammal family, so the atomic molecular and optical systems. 218 00:22:43,520 --> 00:22:47,720 And on the right, we see solid so-called solid state systems. 219 00:22:47,930 --> 00:22:52,130 So in the pictures give you a rough idea of what what these devices look like. 220 00:22:52,940 --> 00:23:01,470 But the important, important point to stress here is that this device are at the moment that these devices are kind of imperfect. 221 00:23:01,490 --> 00:23:07,940 So they are they are called MSC, MSC devices, meaning noisy intermediate scale quantum devices. 222 00:23:08,360 --> 00:23:12,440 And the problem is that the size of these devices is limited. 223 00:23:12,740 --> 00:23:19,010 And they the time, the coherence time. So the time where this machine works in a quantum mechanical way is also limited. 224 00:23:19,430 --> 00:23:19,670 Right. 225 00:23:19,880 --> 00:23:27,980 So, roughly speaking, you may say that the boundary, the frontier of current quantum devices is more or less at the boundary of classical computation. 226 00:23:27,990 --> 00:23:34,069 So on the task where we think whether this objects would outperform classical computers at the moment, 227 00:23:34,070 --> 00:23:37,720 they can compete with classical computers, right? 228 00:23:37,730 --> 00:23:48,590 And it's kind of a active topic of research to try to make a proof of principle experiment that that provably beats what what quantum, 229 00:23:48,590 --> 00:23:51,600 what the classical computer can do. All right. 230 00:23:51,840 --> 00:23:56,010 So this is this is the current state of the art. Of course, the Holy Grail. 231 00:23:56,040 --> 00:24:01,889 The holy grail of the field. The ultimate goal is to build a scalable and tolerant quantum computer. 232 00:24:01,890 --> 00:24:07,650 So this would give us unlimited, unlimited size and unlimited coherence time. 233 00:24:08,160 --> 00:24:12,540 Right. So really, you will hear more about this in the next talk by Dr. Plucker. 234 00:24:13,080 --> 00:24:19,200 Now, I just want to say that this, of course, many, many of us believe that this that this will come right. 235 00:24:19,200 --> 00:24:23,189 And many and huge amounts of people are working to make this possible. 236 00:24:23,190 --> 00:24:29,160 This this, of course, will need a lot of a lot of work and a lot of effort. 237 00:24:30,060 --> 00:24:37,470 Good. So so okay, So what I'm going to do in the remaining part of the talk. 238 00:24:39,530 --> 00:24:42,409 It's to essentially give you an overview, 239 00:24:42,410 --> 00:24:53,450 a selected overview of some of the some of the experimental platforms that are considered today to some of the best analogue 240 00:24:53,450 --> 00:24:59,750 quantum simulators that we use to somehow to to study quantum anybody physics and try to solve quantum anybody problems. 241 00:25:00,710 --> 00:25:03,380 And then I will describe at the end, 242 00:25:03,380 --> 00:25:12,560 I will describe one successful example of of a quantum simulation performed using this devices that is drawn by is drawn from my from my own work. 243 00:25:13,620 --> 00:25:15,479 Okay, so let's let's go there. 244 00:25:15,480 --> 00:25:23,280 So I will focus on family of quantum simulators that is called the Go under the name, of course, not on quantum simulators. 245 00:25:24,180 --> 00:25:30,540 So that all quantum simulators are essentially the effort to produce them originated from the 246 00:25:31,020 --> 00:25:37,530 from the from the effort to to produce to essentially to the efforts in low temperature physics. 247 00:25:37,530 --> 00:25:46,740 So to produce and the the coolest somehow system that that that that functions in a quantum mechanical way. 248 00:25:47,100 --> 00:25:53,370 Right. So what what they have done essentially is to isolate or to trap a gas of atoms, 249 00:25:54,180 --> 00:26:01,470 to confine them in a region of space and to cool them to extremely low temperatures in the order of nano kelvin. 250 00:26:01,650 --> 00:26:07,880 Right. Using various very experimental techniques that were developed for this purpose. 251 00:26:08,010 --> 00:26:13,710 Right. So disclaimer, I'm a theoretical physicist, so this is not what I, it is not what I do personally. 252 00:26:13,980 --> 00:26:19,740 Right. But I will, I will try to give you somehow a flavour of how these things are are done. 253 00:26:20,250 --> 00:26:26,310 So okay, so essentially these gases are trapped and cooled for extremely low temperature using several techniques. 254 00:26:26,580 --> 00:26:35,490 And in this cooling process where this is where the number of particles is extremely reduced compared to microscopic samples, 255 00:26:35,700 --> 00:26:44,220 but still it's a we obtain a very cool, a very cold gas which is still contained, which still contains a lot of atoms. 256 00:26:44,520 --> 00:26:53,030 Right. And the crucial point here is that the the the temperature is lowered to such an extent that the the the wavelength. 257 00:26:53,310 --> 00:26:57,240 Right. So the the wavelength associated with the quantum mechanical nature of the 258 00:26:57,240 --> 00:27:00,990 motion of this particles is comparable to the size of the confinement region. 259 00:27:01,230 --> 00:27:07,110 Right. So when this happens, it means that the quantum mechanical nature of these objects cannot be ignored, 260 00:27:07,170 --> 00:27:10,300 of the motion of this object cannot be ignored anymore. Right. 261 00:27:10,560 --> 00:27:15,240 And this is how people realised, for example, the first Bose-Einstein condensate. 262 00:27:16,020 --> 00:27:25,800 So the first an exotic phase of matter that was not observed so far by was not observed before by cooling and cooling this gas of bosonic atoms. 263 00:27:26,920 --> 00:27:34,330 Okay, So this is this is what you do. And then, of course, when when people successfully realised this, 264 00:27:34,870 --> 00:27:40,419 this very cold gas is then they realise that these systems somehow they have all the control techniques 265 00:27:40,420 --> 00:27:46,930 that they have developed to do this somehow could be pushed forward and maybe used to realise this. 266 00:27:46,930 --> 00:27:52,030 Feynman's dream of a fully controllable, isolated one from anybody's system. 267 00:27:52,390 --> 00:27:55,450 Right. So this is how it how it originated. Right. 268 00:27:55,750 --> 00:28:03,129 So, so people try to develop other experimental techniques to control the interactions between these particles, for example, 269 00:28:03,130 --> 00:28:10,420 the strength of the interaction between particles or the the shapes of the range of interactions or the selective 270 00:28:10,420 --> 00:28:15,610 interactions so that certain particles preferentially interact with certain others and so on and so forth. 271 00:28:15,880 --> 00:28:21,370 So all this kind of engineering can be achieved with atomic molecular optical techniques. 272 00:28:21,760 --> 00:28:28,150 Right. And this is an important step in the realisation of a of a quantum simulator, because remember what I said before, 273 00:28:28,360 --> 00:28:32,950 we have to be able to tweak the native interactions of the Hamiltonian to mimic, 274 00:28:32,950 --> 00:28:39,249 to, to, to mimic the behaviour of our, our preferred system of interest, because the atoms are just atoms, 275 00:28:39,250 --> 00:28:45,000 they don't know that they have to simulate the relativistic heavy collision. 276 00:28:45,010 --> 00:28:47,440 Right. So we have to do something for that. 277 00:28:48,160 --> 00:28:55,650 Okay, So we have we can control interactions and we also experimentalists develop very advanced imaging techniques. 278 00:28:55,660 --> 00:29:05,170 So to somehow measure remember in this list of requirements, that is also the requirements of being able to measure individual particles. 279 00:29:05,170 --> 00:29:07,920 And this is something that today people can actually do. 280 00:29:07,930 --> 00:29:19,030 So there are very advanced imaging techniques that basically give us access to two spatial, temporally resolved measurements in the in the system. 281 00:29:19,720 --> 00:29:23,520 Okay. So this is a this is the playground. Okay. 282 00:29:23,790 --> 00:29:31,500 So one one development that stemmed out of this development after this efforts is the so-called optical lattices. 283 00:29:31,740 --> 00:29:39,660 You can do optical lattices as a sort of analogue quantum simulator for condensed matter physics in the following sense. 284 00:29:39,870 --> 00:29:43,470 So condensed matter physics is about electrons moving in a solid. 285 00:29:43,560 --> 00:29:48,090 So a solid is a crystal, right? Is a periodic structure or regular structure. 286 00:29:48,240 --> 00:29:50,880 And electrons move in this periodic structure, right? 287 00:29:51,240 --> 00:30:01,890 So what people managed to to realise in the field in the context of cold atoms is essentially to realise periodic potentials by using lasers. 288 00:30:02,070 --> 00:30:06,630 Right. So basically arranging counter propagating lasers, we can form sending waves. 289 00:30:07,110 --> 00:30:11,910 Right. And extending waves generate the potential that is felt by the atoms. 290 00:30:12,240 --> 00:30:21,450 So the atoms now move periodic potential pretty similarly to what electrons do in the in materials, right, but with important differences. 291 00:30:21,660 --> 00:30:25,830 So one crucial difference is that this this is just a potential. 292 00:30:25,830 --> 00:30:29,130 So the the crystal is not dynamical itself. 293 00:30:29,160 --> 00:30:32,850 So as we say, there are no vibrations on the crystal, There are no phonons. 294 00:30:33,090 --> 00:30:36,420 And this makes our system much more coherent, much more isolated. 295 00:30:36,960 --> 00:30:40,110 Right. And second, it's there is a difference of scale. 296 00:30:40,500 --> 00:30:45,900 So electrons are tightly packed together in materials, and you can hardly imagine to visualise, 297 00:30:46,980 --> 00:30:51,540 to be to pick one single electron and control it and and visualise it. 298 00:30:51,660 --> 00:30:55,740 Right. Well here this is completely programmable. 299 00:30:55,920 --> 00:31:01,229 Right. So we can decide the, the lattice spacing of this of the system. 300 00:31:01,230 --> 00:31:08,160 Right. So we can basically realise called neutral items that are very heavy, very slow and very distant from each other. 301 00:31:08,460 --> 00:31:13,630 Right. And jump from one potential well to the next of this sort of egg box. 302 00:31:14,300 --> 00:31:17,700 Egg box. Right. And interact with each other. 303 00:31:17,790 --> 00:31:27,240 So basically and this, this is fully programmable in the sense that the geometry of this lattices is completely customisable. 304 00:31:27,840 --> 00:31:37,470 Right. As you see in this representation where people manage to trap food, to confine the atoms in an arbitrary pre-defined geometries. 305 00:31:38,020 --> 00:31:39,800 Right. Performance of these figures. 306 00:31:40,260 --> 00:31:46,830 So the Hamiltonian, the kind of the forces that govern the system, the the the native Hamiltonian takes in this form. 307 00:31:47,130 --> 00:31:49,470 So it's not important to really understand what it is. 308 00:31:49,770 --> 00:31:58,829 But what I want to stress is that this term proportional to J is associated with the tunnelling of of neutral atoms from one side of the lattice, 309 00:31:58,830 --> 00:32:07,650 so from one bottom of the well to the next, and this other instead of corresponds to the interactions when two atoms sit on the same lattice side. 310 00:32:08,040 --> 00:32:15,090 So this is kind of a simulator for is very closely resembles the kind of hamiltonians that we have in condensed matter physics. 311 00:32:15,570 --> 00:32:20,970 And this, this, this is why this created a lot of excitement because we can now simulate. 312 00:32:22,730 --> 00:32:28,280 Yeah, we can very directly simulate how many functions of interest in contacts in condensed matter physics. 313 00:32:28,550 --> 00:32:32,840 For example, the Hamiltonian that is thought to govern high temperature superconductors. 314 00:32:34,330 --> 00:32:42,069 Okay. So now there is, as I said, there is additional engineering tools that we can apply right here to the creativity of the people. 315 00:32:42,070 --> 00:32:43,960 That was really stunning, right? 316 00:32:44,170 --> 00:32:52,750 For example, we can use a speckle pattern for our lasers to create a quasi random to superimpose a quasi random potential on this lattice. 317 00:32:53,020 --> 00:32:59,530 Right. And this. This mimics the fact the behaviour moves the motion of particles of quantum particles in a disordered potentials. 318 00:32:59,800 --> 00:33:04,620 So in this way we can study phenomena like understood localisation phenomenon, right? 319 00:33:04,740 --> 00:33:12,520 That that was originally proposed for the motion of electrons in the, in the in the impurity bands of a semiconductor. 320 00:33:13,710 --> 00:33:19,470 Okay. Then the other interesting thing is that you can shake, right? 321 00:33:19,470 --> 00:33:24,510 You can periodically vary your optical lattice. Right. Just let me open it in time. 322 00:33:24,510 --> 00:33:28,440 You can shake it in a in a single direction or you can shake it circularly. 323 00:33:28,920 --> 00:33:37,320 And interestingly enough, essentially, that this periodic shaking gives rise to artificial, for example, to artificial magnetic fields. 324 00:33:37,620 --> 00:33:44,040 Now, this neutral, these atoms are neutral, so they are not sensitive to magnetic fields in the sense of orbital magnetic field. 325 00:33:44,460 --> 00:33:53,430 But you can engineer, you can engineer such artificial magnetic fields by this additional additional toolbox, essentially. 326 00:33:53,940 --> 00:34:01,700 And this this was this was realised in previous years. And finally, another example that I report is that we can use internal spin states. 327 00:34:01,710 --> 00:34:04,900 So the atoms, the atoms have internal states, right? 328 00:34:06,120 --> 00:34:10,859 And this internal states can be used to mimic an extra dimension of the system. 329 00:34:10,860 --> 00:34:12,570 So what they call a synthetic dimension. 330 00:34:12,580 --> 00:34:21,990 So we can we can confine we can basically simulate the motion of a higher dimensional system by using internal internal levels of the atoms. 331 00:34:22,290 --> 00:34:28,079 So you see that you can really play with your creativity and engineer very 332 00:34:28,080 --> 00:34:33,120 interesting mappings between your native hardware and your target point of interest, 333 00:34:33,120 --> 00:34:40,110 your target system of interest to, to to study many more or less obvious quantum anybody problems. 334 00:34:41,230 --> 00:34:48,879 Okay. And of course, as I said, one of the ultimate goals in this game is to study open products in condensed matter physics, 335 00:34:48,880 --> 00:34:52,660 for example, the elusive mechanism for high temperature superconductivity. 336 00:34:53,620 --> 00:35:00,489 Okay, So this is so, so much for optical lattice is another very interesting platform that is gaining 337 00:35:00,490 --> 00:35:04,569 a lot of traction in recent years is the so-called so neutral atom processor. 338 00:35:04,570 --> 00:35:08,160 So in particular what is called Gap memory's right. 339 00:35:08,440 --> 00:35:16,240 So here essentially we have still called reactive atoms, in particular in alkali atoms of a hydrogen like atom. 340 00:35:17,200 --> 00:35:24,820 Right. And here the particular thing here is that atoms are trapped in in what is called optical tweezers. 341 00:35:24,940 --> 00:35:29,799 So essentially very tightly focussed lasers that form micro traps for the atom. 342 00:35:29,800 --> 00:35:33,670 So basically we can we can trap individual atoms in individual traps. 343 00:35:34,090 --> 00:35:41,440 And the advantage here is that then we can move, move around these traps and fully, fully reconfigure the geometry of the system. 344 00:35:41,800 --> 00:35:48,640 So this is one. So the geometry is one piece of, of, of the analogue simulation. 345 00:35:48,640 --> 00:35:53,230 The other super important piece of this analogue simulation is essentially the 346 00:35:53,230 --> 00:36:00,040 ability to fully program the strength of interactions between these particles. 347 00:36:00,040 --> 00:36:06,070 And this is done by exciting the atoms to so-called reverse states, so highly excited with most states. 348 00:36:06,490 --> 00:36:15,070 But essentially we we program our lasers, right to drive transition between the ground state of these atoms and the very highly excited states. 349 00:36:15,670 --> 00:36:16,600 Right. What is that? 350 00:36:16,630 --> 00:36:24,730 The essentially the electron that move that orbits around the atom occupies a very a very high orbit, so a very distant orbit from the nucleus. 351 00:36:25,060 --> 00:36:28,360 Right. So this the wave function of this electron is very big. 352 00:36:28,660 --> 00:36:32,800 But the advantage of this is that the atom now has a giant polarised ability, 353 00:36:33,160 --> 00:36:37,810 so it has giant interactions that let me show you how I would type before that. 354 00:36:38,380 --> 00:36:43,330 The Hamiltonian that describes the dynamic of the system basically as these pieces. 355 00:36:43,690 --> 00:36:51,040 So this is a piece that drives the transitions, basically that the atoms are described as two level systems, the ground state and the reverse state. 356 00:36:52,170 --> 00:36:56,340 Right. And this this piece describes the transitions between the states. 357 00:36:56,730 --> 00:37:03,840 Then we have the energy difference between the two states. And then we have this interactions, which I'm going to describe. 358 00:37:04,140 --> 00:37:11,370 So these interactions are basically dipole dipole interactions or minor bars, interactions that are controlled by the distance. 359 00:37:12,220 --> 00:37:15,910 Right. And the special properties of this of the system is the following. 360 00:37:16,360 --> 00:37:21,880 Essentially, if we picture the ground states of the wave function of the electron in the ground state of this atom, 361 00:37:22,150 --> 00:37:25,480 it looks like this small blue dot, right? 362 00:37:25,690 --> 00:37:28,900 This is the the electron orbiting near the nucleus. 363 00:37:29,200 --> 00:37:35,950 Now, when the atom is excited to the red states or to a highly excited state that its wave function looks more or less like that. 364 00:37:36,580 --> 00:37:44,440 Right. So basically this is electrons is moves and forms the giant wave function and has a giant polarised ability. 365 00:37:44,830 --> 00:37:53,950 Now when we try to simultaneously excite nearby atoms for the ribbon states, the dipole dipole interaction between them is enormous. 366 00:37:54,310 --> 00:37:57,500 So this this is energetically prevented somehow. 367 00:37:57,550 --> 00:38:04,120 So we have the phenomenon of reverse blockade when where the when the these two giant functions overlap. 368 00:38:04,330 --> 00:38:08,260 Essentially it becomes impossible to simultaneously inside these two atoms. 369 00:38:08,500 --> 00:38:15,430 And this mechanism can be very efficiently exploited to entangle, to create entanglement between atoms. 370 00:38:16,420 --> 00:38:25,030 Right. And this is described by this this piece in the. So here to show you the high degree of control with the geometry, essentially, 371 00:38:25,090 --> 00:38:30,730 this is this is a movie that was created by the Mitchell looking slab in Harvard. 372 00:38:31,000 --> 00:38:35,379 Essentially, these are these are nothing but rather got them trapped in this micro, 373 00:38:35,380 --> 00:38:40,870 trapped in this optical tweezers and reconfigured to in arbitrary shapes through to create 374 00:38:41,170 --> 00:38:46,110 essentially arbitrary geometries and arbitrary animation that you see in this old video games. 375 00:38:47,220 --> 00:38:50,820 Okay. So this is another platform. And finally, another. 376 00:38:51,120 --> 00:38:56,400 Last but not least, another platform that I wanted to mention is from Niles. 377 00:38:57,300 --> 00:39:04,200 Right. This, of course, plays a special role here in Oxford, here downstairs, because building we have one of the world leading. 378 00:39:04,740 --> 00:39:08,940 What leading labs realise interrupt quantum computing. 379 00:39:09,310 --> 00:39:19,460 Right. So led by the Lukas and Fritz Balancing and also the Oxford also play a leading role in in the sort of inspiration of the of this technology. 380 00:39:19,550 --> 00:39:24,870 Right. So coming from dating back to art record and Rustin and so on. 381 00:39:24,870 --> 00:39:28,440 So this is this is really something important here here in Oxford. 382 00:39:28,770 --> 00:39:36,270 Right. So I am from that as a similar principle, except that the these are not atoms in the sense that these are ionised atoms. 383 00:39:36,270 --> 00:39:40,679 So they are, they are charged. Right. And they basically. 384 00:39:40,680 --> 00:39:48,030 Okay, let me skip the details here. But they are they are still trapped in some using some some special traps for charged particles. 385 00:39:48,330 --> 00:39:54,870 And the point is that we end up with some especially in this, uh, geometry given by the pole trap, 386 00:39:55,210 --> 00:40:03,810 we end up with a lined with a crystal one dimensional crystal of atoms of io's sorry that are trapped electromagnetically, Right. 387 00:40:03,810 --> 00:40:10,110 And the atoms, the internal. So we can use the internal levels of these atoms to store quantum information. 388 00:40:10,620 --> 00:40:14,070 Right. So these atoms can be in two states, right? 389 00:40:14,880 --> 00:40:21,000 And the these atoms are able to interact. So to talk to each other via the vibrations of this crystal. 390 00:40:21,180 --> 00:40:27,180 So this is like imagine a system that is floating in the vacuum, trapped with this electromagnetic field, right? 391 00:40:27,570 --> 00:40:30,750 Then there are some vibrations of this crystal, right? 392 00:40:30,750 --> 00:40:34,680 And this vibration coupled to the transition between the internal level of the system. 393 00:40:34,860 --> 00:40:42,780 And basically, if you go through the math, you end up with the Hamiltonian of this form, but you have some some type of easy model, right? 394 00:40:42,780 --> 00:40:46,200 With this is spin spin interactions. 395 00:40:46,200 --> 00:40:51,360 And again, this is how we view it as an analogue simulator for condensed matter models, right? 396 00:40:51,810 --> 00:40:57,060 So some, some, some sort of some sort of quantum magnets in the most obvious sense. 397 00:40:57,060 --> 00:41:00,420 In the most negative sense. Very good. 398 00:41:00,420 --> 00:41:08,219 So this is a no. This is some of the leading experimental platforms that realise analogue quantum 399 00:41:08,220 --> 00:41:11,730 simulation and also hopefully at some point digital quantum simulations. 400 00:41:14,810 --> 00:41:17,840 So in the remaining time, actually, I have less time than I thought. 401 00:41:17,840 --> 00:41:26,420 But in the remaining time I want to tell you one just one example of of how you can use this simulator, 402 00:41:26,570 --> 00:41:31,330 this quantum simulator, to realise somehow, you know, 403 00:41:31,400 --> 00:41:36,020 in a slightly non-obvious but not slightly non-obvious way to realise quantum 404 00:41:36,020 --> 00:41:40,490 simulations of problems of interest that are in other fields like in other contexts. 405 00:41:40,730 --> 00:41:47,300 So in particular, I want to present one example coming from going in the direction of high energy physics, right? 406 00:41:47,540 --> 00:41:51,259 So what I want to talk about simulating quantum field theories, right? 407 00:41:51,260 --> 00:41:56,659 Sort of like the theories of fundamental interactions using these quantum machines right now. 408 00:41:56,660 --> 00:42:00,860 This is a very, very, very difficult problem like condensed matter physics, 409 00:42:00,860 --> 00:42:06,500 where I showed you that there is a more or less direct analogy between the kind of hamiltonians 410 00:42:06,740 --> 00:42:11,270 you can realise in quantum simulators and the kind of hamiltonians you would like to realise, 411 00:42:11,780 --> 00:42:18,620 right, because they mimic the interest in quantum in high energy physics, this is much more difficult and the problem is the following. 412 00:42:18,620 --> 00:42:26,149 So there are many problems. So one is that theories of fundamental interactions have usually two two kinds, at least two kinds of particles. 413 00:42:26,150 --> 00:42:31,250 So there are the matter particles, the fermions, right? Like the quarks or the electrons. 414 00:42:31,520 --> 00:42:38,540 And then you have the degrees of freedom, like h fields, like the electromagnetic field or the the gluon field. 415 00:42:38,570 --> 00:42:44,540 Right? So we have different kinds of particles. Right? And so so we have to have different kinds of species. 416 00:42:44,560 --> 00:42:51,080 And on top of that, these particles can exist in many in many, many species of this particle exist. 417 00:42:51,080 --> 00:42:55,610 For example, they can have different charges, spin, colour, flavour and so on and so forth. 418 00:42:55,960 --> 00:43:02,240 Right. While for example, your beryllium atoms of your iron trap are all these properties are all the same. 419 00:43:03,410 --> 00:43:08,479 So you have to be able somehow to encode this thing in your, in your simulator. 420 00:43:08,480 --> 00:43:14,840 And finally, most importantly, actually the most important problem is that this method met their degrees of freedom and degrees of freedom 421 00:43:15,200 --> 00:43:21,770 interact in a very complicated way that is dictated by what particle physicists call gauge symmetry. 422 00:43:22,130 --> 00:43:31,040 Right? So there is some some local symmetry constraints that the the motion of the combined motion of matter and the edge fields have to be right. 423 00:43:31,220 --> 00:43:38,170 And of course your your poor atoms or photons or particles or whatever, they know nothing about the symmetry, right? 424 00:43:38,180 --> 00:43:47,900 They have their own Hamiltonian and you have to find a way somehow to encode this complicated interactions in your in your native hardware. 425 00:43:48,350 --> 00:43:52,549 Right. Okay. So this is, as I said, this is very difficult problem. 426 00:43:52,550 --> 00:43:56,480 This is very challenging both for analogue and digital quantum simulation. 427 00:43:58,250 --> 00:44:07,489 So what do we do? So there is there was some recent progress in one in one example which which is the example of electrodynamics, right? 428 00:44:07,490 --> 00:44:13,930 So electrodynamics is one of the one of the one of the fundamental quantum field theory is, well, 429 00:44:13,940 --> 00:44:19,610 it's not fundamental, but it's it's one of the quantum field theory you may like to realise. 430 00:44:19,730 --> 00:44:24,740 Right. So this is the the describes the theory of electrons and positrons in interact interacting with photons. 431 00:44:27,650 --> 00:44:34,129 So in particular the progress was achieved for a simplified version of one of quantum electrodynamics, 432 00:44:34,130 --> 00:44:39,080 which is fundamental dynamics in one dimension, right in one plus one spacetime dimension. 433 00:44:39,080 --> 00:44:42,890 So what goes under the name of Schwinger model, right? 434 00:44:43,100 --> 00:44:47,989 So this is of course, on the one hand, of course this is bound because it's easier, right? 435 00:44:47,990 --> 00:44:51,680 So you have to start somewhere. But actually, I think most, 436 00:44:51,770 --> 00:44:56,899 most interestingly is the fact that this simplified version of Quantum through the right mix actually 437 00:44:56,900 --> 00:45:04,219 shares some some nontrivial features that are with the higher dimensional theories of interest, 438 00:45:04,220 --> 00:45:09,260 for example, quantum dynamics, for example, the phenomenon of core confinement. 439 00:45:09,470 --> 00:45:14,750 I'm sure you've you heard it in the previous talk by a by Dr. Brewer. 440 00:45:14,780 --> 00:45:19,639 Right. So this phenomenon of poor confinement plays a crucial role in in the theories of strong interaction. 441 00:45:19,640 --> 00:45:23,780 And it is present in this lower dimensional version of quantum electrodynamics. 442 00:45:23,780 --> 00:45:29,900 So there are there are reasons why you would like to perform quantum simulations of this simplified theory, right? 443 00:45:31,420 --> 00:45:35,170 So. Okay, so the monster that you would like to simulate is the following. 444 00:45:35,530 --> 00:45:38,920 So this is the Hamiltonian of quantum electrodynamics. 445 00:45:39,150 --> 00:45:42,850 You know, one dimensional in one plus one dimensional space times. 446 00:45:43,420 --> 00:45:50,560 Right. So this this has three pieces. One piece describes the mass of the of the electrons and positrons, the mass of the fermions. 447 00:45:51,760 --> 00:45:59,230 One piece describes the invariant interaction, so the minimal coupling between the formulas and the electric field. 448 00:45:59,470 --> 00:46:02,590 Right. One dimension. We have only electric field. We don't have a magnetic field. 449 00:46:03,310 --> 00:46:06,970 And the last piece is the energy associated with the electric field. 450 00:46:07,970 --> 00:46:13,070 Plus possibly a big round, a big, round electric field. Okay, so this is the Schwinger model. 451 00:46:13,100 --> 00:46:16,220 The latest version of the Schwinger model of quantum electrodynamics. 452 00:46:16,490 --> 00:46:27,710 So we have we want to put this this complicated matter and gauge the dynamics in the in the way we want to include it in our quantum simulator. 453 00:46:27,950 --> 00:46:35,300 Right. So basically, before that, let me show you try to visualise what kind of processes happen in this, in this theory. 454 00:46:35,360 --> 00:46:41,899 So imagine we start from the vacuum, right? So there are no that are basically in the in the links of this one dimensional chain. 455 00:46:41,900 --> 00:46:43,790 We represent the fermions. Right. 456 00:46:44,470 --> 00:46:51,110 And on the sorry, on the sides of this chain, we represent the furnace and on the links of this chain, we represent the electric field. 457 00:46:51,140 --> 00:46:54,140 The electric field is like a tower can take many values. 458 00:46:54,440 --> 00:47:01,370 Right. So this is like the vacuum configuration where there are no particles and the electric field, zero is zero everywhere. 459 00:47:01,910 --> 00:47:08,600 Right. Now, one of the some some of the processes described by the dynamics of this Hamiltonian look look like the following. 460 00:47:09,020 --> 00:47:17,270 So when we act with this interactions on the on this link, basically we create a particle antiparticle pair. 461 00:47:17,300 --> 00:47:19,510 So an electron positron pair. Right. 462 00:47:19,520 --> 00:47:26,240 And the value of the electric, the electric field between these particles, the particles is correspondingly a just adjusted. 463 00:47:26,600 --> 00:47:31,310 So in such a way to respect nature in variance. So this this obeys essentially the Gauss law. 464 00:47:31,850 --> 00:47:37,730 When you when you cross a particle, the electric field changes. There is some electric field created by the particles. 465 00:47:38,300 --> 00:47:45,730 Now, we can repeat this process in other locations. For example, here on the left, we create another particle antiparticle pair you can recreate, 466 00:47:45,740 --> 00:47:52,640 and then we can annihilate this particle antiparticle pair here and create a longer string of electric field. 467 00:47:53,030 --> 00:47:59,450 Right. And we can go on and create another particle antiparticle pair, annihilate and create an even longer string. 468 00:47:59,990 --> 00:48:05,570 And then we can even create another particle antiparticle pair on top of that and raise the electric field even higher. 469 00:48:05,750 --> 00:48:11,120 And so on and so forth. So basically you should imagine the quantum anybody dynamics generated by this 470 00:48:11,120 --> 00:48:15,980 Hamiltonian as a complicated superposition of all sorts of processes of this form. 471 00:48:16,190 --> 00:48:20,240 Right. This is in a way that is described by the parameters of this Hamiltonian. 472 00:48:20,270 --> 00:48:29,900 So this is what we want to encode in our read Megatons or Trapped ions or optical lattice or whatever, whatever your imagination can can achieve. 473 00:48:30,110 --> 00:48:38,360 Right. So basically what we were able to figure out is how to encode a simplified version of this quantum nature, the dynamics using Redbook atoms. 474 00:48:38,810 --> 00:48:46,250 So I say simplified version in the sense that we allow our electric field to have to take only two values instead of infinitely many values. 475 00:48:46,280 --> 00:48:50,749 So this is kind of a, if you wish, a low energy approximation of this of this theory. 476 00:48:50,750 --> 00:48:57,920 But in the in the limit where you allow for more and more values of this electric field, you recover the full quantum electrodynamics. 477 00:48:58,460 --> 00:49:02,300 Right? So in this in this simplified case, essentially we realised. 478 00:49:03,230 --> 00:49:13,820 That you can you can map the configurations of of of particles of fields in the in this quantum link model, 479 00:49:13,820 --> 00:49:18,770 which is the name of this truncated, truncated version of quantum electrodynamics. 480 00:49:19,040 --> 00:49:24,620 You can encoded in the configurations of which we got from arrays in the blockade regime. 481 00:49:24,800 --> 00:49:30,890 So in this regime, where to to rework atoms cannot be simultaneously excited, Right? 482 00:49:31,040 --> 00:49:32,420 This is why I mentioned this before. 483 00:49:32,630 --> 00:49:41,150 And the point I want to stress here is that the symmetry constraints or the constraints that matter particles and fields should 484 00:49:41,150 --> 00:49:50,060 move together in a is mapped is exactly mapped onto the constraints the two Friedberger atoms cannot be simultaneously excited. 485 00:49:50,300 --> 00:49:53,660 So this is somehow a non-obvious mapping. 486 00:49:53,660 --> 00:49:56,810 So it's not very it's not. Somehow not. 487 00:49:57,070 --> 00:50:04,850 So another unknown logic, if you wish, as the condensed matter mappings for two optical lattices. 488 00:50:05,090 --> 00:50:12,200 Right. But it doesn't matter. It's a mapping, it works and you can map all the quantities from one side to the other and study and study dynamics. 489 00:50:12,500 --> 00:50:16,070 Quantum electrodynamics Looking at the evolution of your LEDERBERG atoms. Right. 490 00:50:16,430 --> 00:50:22,660 So here you have to believe me. There is a dictionary between the states in such a way that every possible local configuration 491 00:50:22,670 --> 00:50:27,800 from method and electric field maps to a given configuration of there is MacArthur's. 492 00:50:29,090 --> 00:50:32,870 Okay. Once you map the states, you can ask what is the corresponding Hamiltonian? 493 00:50:33,230 --> 00:50:38,270 And here we have essentially a strike of luck in the sense that the native Hamiltonian of 494 00:50:38,640 --> 00:50:43,820 the God is already what you want is already upon suitably identifying the parameters, 495 00:50:44,030 --> 00:50:50,420 is already the Hamiltonian of the quantum link model. So here, somehow we were with Lucky, right? 496 00:50:50,630 --> 00:50:53,630 So we have a mapping between the states and mapping between the forces. 497 00:50:54,830 --> 00:50:57,950 And finally, we want to be able to access the observables. Right? 498 00:50:58,210 --> 00:51:04,550 The corresponding observables. And here you can do that. So this this figure shows numerical simulations. 499 00:51:05,930 --> 00:51:09,230 Right on the left, you see the dynamics of the river. Got them. 500 00:51:09,720 --> 00:51:15,290 SHANE You see that to two bright spots can never be beside each other. 501 00:51:15,290 --> 00:51:19,549 Because. Because of the river blockade. Right. So this is the evolution. 502 00:51:19,550 --> 00:51:25,320 So horizontally you have space vertical, you have time. This is the spacetime evolution of of your river. 503 00:51:25,340 --> 00:51:33,200 Gotham chains prepared in a state that corresponds within the mapping corresponds to a uniform string of electric field. 504 00:51:33,530 --> 00:51:36,770 So in the vacuum of particles, in presence of an electric field, 505 00:51:36,920 --> 00:51:42,440 and this is the corresponding enemies mapped 1 to 1 to the dynamics of Friedberger with the guidance. 506 00:51:42,710 --> 00:51:46,910 And also here, the simulation shows the full string their models. So the truncated string, 507 00:51:46,910 --> 00:51:52,549 their model which signifies that the the the this somehow this truncated version 508 00:51:52,550 --> 00:51:56,720 is more or less doing what the full quantum electrodynamics problem would do. 509 00:51:57,350 --> 00:52:02,780 So you have in this case at least you have sort of a full dictionary, right between the Hamiltonian, 510 00:52:02,780 --> 00:52:08,570 your target Hamiltonian and your in your quantum hardware, in this case your readable gamma rays. 511 00:52:09,470 --> 00:52:13,850 Okay. So I just want to close. Can I take another minute? 512 00:52:13,940 --> 00:52:23,419 Yes. So my final slide is basically is okay now, now that you have a way to encode your your your quantum field theory, 513 00:52:23,420 --> 00:52:28,490 if you wish on on your on your reader Gotham train. 514 00:52:28,730 --> 00:52:32,210 Right. So the question is what what kind of physics can we and we simulate. 515 00:52:32,480 --> 00:52:37,230 Right. So as you as you heard in the previous talk by Dr. Ruhr, 516 00:52:37,760 --> 00:52:43,700 essentially one one very interesting thing to do with quantum field theory is, is to study collisions between particles. 517 00:52:44,060 --> 00:52:48,500 Right. So basically. Okay, So this is I want to repeat the story. 518 00:52:48,500 --> 00:52:53,090 So here essentially is a very important problem in particle physics. 519 00:52:53,510 --> 00:53:02,240 And essentially, because it's a very difficult problem, it's it's kind of an outstanding goal for for quantum simulation. 520 00:53:02,360 --> 00:53:05,540 Like, I don't see any long term goal for quantum simulation. 521 00:53:06,840 --> 00:53:14,110 So this is this is what you get. You can essentially wonder if some some cartoon version of this problem. 522 00:53:14,140 --> 00:53:19,920 Of course, this is what we can do in the with the in the setting that they previously illustrated 523 00:53:19,920 --> 00:53:24,960 is very far from what our colleagues in particle physics would like to do presently. 524 00:53:24,990 --> 00:53:32,130 Right. So this is kind of there is a huge gap cover for there before we can actually 525 00:53:32,520 --> 00:53:37,139 simulate something that solves some actual problem in in particle physics. 526 00:53:37,140 --> 00:53:42,990 But it's a legitimate question whether at least the principal ingredients can be realised. 527 00:53:43,180 --> 00:53:49,650 We present we present day machines, right? So what we were curious essentially is to study images on collisions. 528 00:53:49,680 --> 00:53:54,990 So those are like bound states, confined bound states of electrons and positrons. 529 00:53:55,260 --> 00:53:58,950 So I told you that in this one dimensional version of punching at the dynamics, 530 00:53:59,190 --> 00:54:06,600 electrons and positrons are confined pretty much like quarks in in higher in theories of strong interactions. 531 00:54:07,050 --> 00:54:10,880 Right. So you can imagine to prepare to wave packets of this mesons. 532 00:54:10,890 --> 00:54:14,430 Right. So to to most it's prepared with a given momentum. 533 00:54:14,880 --> 00:54:21,810 Right. And so this is the initial stage you want to prepare and then you want to run the real time evolution. 534 00:54:22,110 --> 00:54:29,849 Right. So you want to encode this in your. But Gotham's run the real time evolution and measure for things that you would be interested in, 535 00:54:29,850 --> 00:54:33,720 in particle physics, for example, the scattering matrix of this collision process. 536 00:54:34,140 --> 00:54:38,560 Or you can even do more as I as I'm going to argue. Right. 537 00:54:38,620 --> 00:54:42,370 So this is kind of the the protocols that you want to realise. 538 00:54:42,760 --> 00:54:46,900 Right. And in this paper, we the collaboration with Federica Saraceno, 539 00:54:47,200 --> 00:54:55,570 we have shown essentially how to perform, perform this mappings and this building block steps, right. 540 00:54:55,580 --> 00:55:05,200 So how to prepare in particular the initial states. So which is the, this chart is on with buckets, with a with an arbitrarily well-defined momentum. 541 00:55:05,530 --> 00:55:10,359 Right. And then to run the evolution and to measure the relevant observables. 542 00:55:10,360 --> 00:55:14,589 So remember the list of requirements that are needed for a quantum simulation, right? 543 00:55:14,590 --> 00:55:19,150 And there is initial stage, there is the how many Estonian and there is the observable right. 544 00:55:19,420 --> 00:55:23,400 So a possible observable of interest is the scattering matrix. 545 00:55:23,410 --> 00:55:30,100 Right. And we have shown how to essentially how to use the capabilities of the quantum simulator to access this one thing. 546 00:55:30,550 --> 00:55:34,840 Right now I want to just close with a remark that, of course, this is, as I said, 547 00:55:35,980 --> 00:55:44,559 there is a huge gap to bridge for the to do something that is of interest for for current particle physics, 548 00:55:44,560 --> 00:55:48,160 for example, to simulate a relativistic heavy collision. Right. 549 00:55:48,490 --> 00:55:53,170 But on the other hand, the the reason why we think this is interesting is, 550 00:55:53,200 --> 00:55:58,360 is that there are things that you can do using a quantum simulator, which you just cannot do in nature. 551 00:55:58,600 --> 00:56:07,780 Right. So one of the things that once the simulator naturally gives you access to, for example, is that it allows you to watch inside the collision. 552 00:56:07,900 --> 00:56:13,780 Right. So this is something that is completely unthinkable in a actual in nature. 553 00:56:13,810 --> 00:56:19,760 So natural particle physics experiment right here, we have full control and we can even stop that evolution and look, 554 00:56:20,020 --> 00:56:23,890 look what's happening and understand the processes that are involved, 555 00:56:24,250 --> 00:56:29,350 the complicated processes that are involved in the complicated collision, for example. 556 00:56:29,560 --> 00:56:37,690 And second, we can play with the parameters. So in nature, the the the value of the forces, the coupling constants are just given, right? 557 00:56:37,900 --> 00:56:42,090 We can play with it. So here instead we can change, right? 558 00:56:42,100 --> 00:56:43,179 This is our simulator, right? 559 00:56:43,180 --> 00:56:49,960 So we can do whatever we want, or maybe not exactly whatever we want, but we have a large degree of tuned ability, right? 560 00:56:50,290 --> 00:56:58,239 So we can play with the parameters and explore the the predictions of the theory beyond beyond what would be accessible in actual nature. 561 00:56:58,240 --> 00:57:02,649 And this perhaps would allow us to discover some other effects or some other physics. 562 00:57:02,650 --> 00:57:11,920 Right? So there are reasons to believe that this this kind of approach someday will will be very extremely valuable in for study. 563 00:57:11,920 --> 00:57:17,770 And even in this visit, that is probably the most difficult goal for quantum simulators. 564 00:57:18,760 --> 00:57:23,620 Okay, I think I'm done. So let me skip this drop dance and just jump to the final slide.