WEBVTT 00:01:47.000 --> 00:01:53.000 Thank you. This reflects a broader shift in modern theoretical physics. 00:01:53.000 --> 00:02:05.000 Using controllable quantum systems as laboratories. For IDRs that were once thought to belong exclusively to energy fillets or scale of linear experts. 00:02:05.000 --> 00:02:20.000 It is my pleasure to introduce our speaker, Professor Janis Pajos. He's a professor of political physics at University of Leeds. His research focuses on topological phases of matter and quantum information. 00:02:20.000 --> 00:02:25.000 With particular emphasis on topological quantum computation and the role of. 00:02:25.000 --> 00:02:35.000 And you only considerations in global sporting post. He has made significant contributions to our understanding of how concepts. 00:02:35.000 --> 00:02:41.000 From quantum field theory, condensed matter and quantum information. 00:02:41.000 --> 00:02:50.000 Interact. And in the… and he is the author of the widely used monograph. 00:02:50.000 --> 00:03:06.000 Introduction to topological quantum computation. Today, he will present a perspective that brings these threads together in a particularly striking way, linking spin systems to black hole physics and quantum information flow. 00:03:06.000 --> 00:03:14.000 Please join us. Please join me in welcoming Professor Park. 00:03:14.000 --> 00:03:31.000 Thank you so much for the kind introduction generously. Thank you. I'm really excited to be here and give a talk to you. I started as a high energy physicist, so that's my first love. And you know how the story goes. 00:03:31.000 --> 00:03:38.000 Um, uh… I would like to tell you about quantum simulation of. 00:03:38.000 --> 00:03:51.000 And let me justify why simulation. It's a simulated. You have the fundamental. 00:03:51.000 --> 00:04:07.000 theory of model, and then you have the simulation of it. What can you gain by doing the simulation? For me, an analogy of it explains it better. 00:04:07.000 --> 00:04:22.000 If you want to… if you have emotions, this is an important thing, and you have language that describes it. Now, if you… you can use language to articulate emotions, and that helps you to understand them, and helps you to control them, and. 00:04:22.000 --> 00:04:35.000 It helps your partner also to to explain how things should be. So I believe simulations can help a lot. 00:04:35.000 --> 00:04:39.000 Um, and what they're trying to present to you today. 00:04:39.000 --> 00:05:00.000 is a single model, rather simple. that this content is a spin model, a spin chain, and its fundamental properties give rise to different aspects of black holes, quantum aspects of black holes that were interested and that one. 00:05:00.000 --> 00:05:09.000 the topic of intense research. Tracy. 00:05:09.000 --> 00:05:24.000 Um, let me give you a little bit of picture, but there's a big group working on it. There are a few more people who are not there. Ryan is a big driving force to what I'll talk about today. 00:05:24.000 --> 00:05:34.000 Andrew, and also is making sure PhD students are happy and don't. 00:05:34.000 --> 00:05:42.000 Goes against me. Yeah, so Matthew and Tanne and there's Ian as well. 00:05:42.000 --> 00:05:52.000 Number of people working on this particular topic, actually. And there's a. 00:05:52.000 --> 00:06:06.000 Uh, number, large number of papers that we produce, but I don't want to go into technicalities today. I want to present you the model, and I want to to explain to you. 00:06:06.000 --> 00:06:15.000 Uh, how to get there to use this model to get a glimpse to the fundamental theory that we would like to understand. 00:06:15.000 --> 00:06:30.000 And if I fail to do that, my top also has some entertainment value, so he won't be wasted. A bit of an outline. 00:06:30.000 --> 00:06:46.000 So, the properties of black holes that fascinate people is the Hawking radiation is purely quantum phenomenon. We know black holes, classical particles cannot escape when they fall inside the horizon. 00:06:46.000 --> 00:06:58.000 But fundamentally predicted and actually escape. And give rise to this button effect, absolutely escaping a very particular way that they look at thermal. 00:06:58.000 --> 00:07:14.000 side. And also another topic that attracted interest last 20 years fixed a lot is the chaotic behavior inside the black holes. So the gas of the black hole. 00:07:14.000 --> 00:07:21.000 are really bubbling in terms of quality properties, strong correlations that create. 00:07:21.000 --> 00:07:31.000 optimal scrambling of work and information, let's say. And apparently, these properties do emerge. 00:07:31.000 --> 00:07:37.000 should be there by the description of the blogger. 00:07:37.000 --> 00:07:42.000 Um, what I'll present to you instead is a single toy model. 00:07:42.000 --> 00:07:58.000 Okay? It's a spring chain that has some chiral interactions. I'll define them. And what we see is that, similar to graphene that gives rise to the relativistic Dirac fermions in the low energy limit. 00:07:58.000 --> 00:08:03.000 Similarly here, we'll get the quantum field theory description of this. 00:08:03.000 --> 00:08:10.000 A speed chain, and… We see how curved geometry emerges. 00:08:10.000 --> 00:08:16.000 And that, if you have curved geometry that can indicate a black hole in it. 00:08:16.000 --> 00:08:35.000 Horizon, and you can observe. Hope radiation, we can extract it. And also from the same model, you can observe the chaotic behavior and actually something I'll try to convince you is that we do get the optimal scrambling. 00:08:35.000 --> 00:08:58.000 Of course, that's merit. Um, as we have a single model that can do both, we can look… properties or phenomena of black holes that need both of these effects come together and the. 00:08:58.000 --> 00:09:06.000 It's a number of apply model is this quantum teleportation. 00:09:06.000 --> 00:09:26.000 black holes, and this Hayden and Prescile introduced this protocol to explain how quantum information can be teleported from inside the black hole to the outside in order to to do that is divided in order to explain. 00:09:26.000 --> 00:09:40.000 that information paralyzed black holes. And how they do it is by allowing talking radiation. So quantum matter to escape from inside the black hole to the outside, and also the use. 00:09:40.000 --> 00:09:57.000 the scrambling properties of a black hole, and that's what catapults, if you like, the quantum states from inside to the outside. So it's an ideal, let's say, phenomenon to be described with our model, and I'd like to. 00:09:57.000 --> 00:10:01.000 to present that to you. At the same time. 00:10:01.000 --> 00:10:19.000 As our model is a spin model. a speaker is being had. And these are like qubits can encode the whole thing on a quantum computer and simulate it and see this properties in an actual experiment. 00:10:19.000 --> 00:10:29.000 Um… Physics similar to Ising or XY model of Heisenberg model physicists say hi. 00:10:29.000 --> 00:10:53.000 What you do is actually achieving our way of cheating, because you're… you go high energy, you go… you have your theory, and then you introduce cutoffs and so on, so you… And then you can get some black bone theses. 00:10:53.000 --> 00:11:11.000 Um, let me… Very careful you put the comma between these two. I'll never talk about the combination of the two. And disclaimer, I'm going to give my friends. So the black hole is an opposite. 00:11:11.000 --> 00:11:27.000 Okay? And surprisingly, it's an object that we can extract information out of it, its fun properties without actually having a quantum gravity. 00:11:27.000 --> 00:11:42.000 more than a viable button for the restriction. And that's because it's so extreme object with this curvature and its properties and its singularities and so on, that you can say something about it. 00:11:42.000 --> 00:11:52.000 For example, we know that in the same classical living, which of quantum gravity to get Hofmann radiation. 00:11:52.000 --> 00:12:02.000 And in the fully interactive unit. have the optimal scrambling. So, from the strong correlation and the physics. 00:12:02.000 --> 00:12:15.000 This property has been recently probed by the S5K model. And this is a holographic view of the black hole. So it's like a view, it's not a black hole. 00:12:15.000 --> 00:12:28.000 system, it's a holographic view, and we know that the sprambling properties of this model, the scrambling properties of this model will be equivalent, will be the same, but this is not a geometric model that just. 00:12:28.000 --> 00:12:41.000 It's you up. Yeah. And people demonstrated analytically, and also recently numerically, that this is YK model has optimal scrambling behavior. 00:12:41.000 --> 00:12:45.000 Uh, so that you're using that way, that the blackboard. 00:12:45.000 --> 00:12:54.000 We want this one dimension. 00:12:54.000 --> 00:13:00.000 So, okay, this is my favorite slide. These are the results. 00:13:00.000 --> 00:13:13.000 They give you the nature version of the talk versus the results, and then the methods. I'll present again this same slide at the end, maybe impacts you differently. And what I described here. 00:13:13.000 --> 00:13:21.000 Uh, we have a spring chain. And it's subject to a Hamiltonian measure of polymatrices. 00:13:21.000 --> 00:13:27.000 Here's an XY hepatic interaction. And here is the chiral term sigma. Sigma cross sigma. 00:13:27.000 --> 00:13:39.000 It tries to keep the screen size disoriented for the three successes between orientation. 00:13:39.000 --> 00:13:54.000 I have published UOB. Um, a wicked view of this. This is a free kind of log in and keep that constant. So you can remove it if you like. It's a little bit constant throughout the chain. 00:13:54.000 --> 00:14:06.000 And what they'll do is they'll change the tackling field, the tailoring interactions to be large on one side, and then we'll go small across this carbon, and they will become zero at some point. 00:14:06.000 --> 00:14:21.000 So, we're changing that each space. It won't be a constant, it should be in here, actually. So this V is position dependent, and we'll be changing the space. And what would we see is that the point where V is larger than u. 00:14:21.000 --> 00:14:30.000 It's the inside of the black hole. The region where we is smaller than you is the outside of the black hole. 00:14:30.000 --> 00:14:40.000 you will have, um… The expectation value of this operator actually is non-zero here, and it's 0 here of the title of the term. 00:14:40.000 --> 00:14:57.000 So if you like have, my chain has a chiral face here and a non-chiral face here. So there's two materials, let's say that combine with the Tachit Chandler and the interface between these two materials. 00:14:57.000 --> 00:15:05.000 It's what we would call the horizon. Okay. Uh, I will demonstrate all these things, of course, analytically. 00:15:05.000 --> 00:15:20.000 But there is an interesting aspect is that if you go into the continued this model, similar to graphing, you'll see that you get the dispersion relation on the line comes outside here. So this XY term. 00:15:20.000 --> 00:15:24.000 We give you the normal type of light cone. 00:15:24.000 --> 00:15:32.000 And as you increase B. In position, as you move this direction, this light pane will be tilting. 00:15:32.000 --> 00:15:45.000 This is one particular description of the black hole geometry utilities, and when it over tilts in both future directions point towards the center of the black hole, classically no partial squad state. 00:15:45.000 --> 00:15:50.000 At the same time as this causes the tilting. 00:15:50.000 --> 00:16:02.000 Also introduces interactions. This is a free part. This is interacting as you increase it. The interactions here are strong, and that's where the chaos comes in. 00:16:02.000 --> 00:16:14.000 So that's two things. It tilts. Creates a horizon when you become strong, it introduces strong correlations in the air quality. 00:16:14.000 --> 00:16:30.000 Also, when this V is small, here you are in the semiclassical regime, mean field theory is well defined and it's exactly you get a geometric properties to expect. 00:16:30.000 --> 00:16:53.000 All right, let me now take it easy, and I will get back to this slide. It's just a wonderful class in front of you. Let me take this and take you through a few condensed matter steps, let's say. Um… This is the XY model is XX between neighboring plus y. This s is the Pauli matrices, freely. 00:16:53.000 --> 00:17:10.000 And I have a chain, I have the size, I have a spin, uh, living there. And what we do is this joint Wigner transformation that we translate the spin half particles into fermions. This is C of lattice fermions, if you like. So you can think that I have. 00:17:10.000 --> 00:17:22.000 see furnace on every site. And I'm just tunneling from one side to the other and back, goes here and there. That's the physics is described. 00:17:22.000 --> 00:17:49.000 Um, you can diagonalize this Hamiltonian by Fourier transformation. It's very similar to graphing. And if you… Introduce a unit cell that has two sides. Then the dispersion relation, the energy over momentum has these 2 branches, if like, and this is a negative energy. 00:17:49.000 --> 00:18:00.000 positive, because it's a firmament will fill it out all the way to zero in order to get ground state. And the low energy physics is given by this cone here. 00:18:00.000 --> 00:18:13.000 And indeed, for small energies near the ground state, you get this linear dispersion relation. So the rate will have a direct capacity, a one-dimensional Dirac property. 00:18:13.000 --> 00:18:26.000 Um… I'll be changing the confidence, or, like, for example, the V and so on, or the hue, and that would be, uh… uh, massaging this Iraq. 00:18:26.000 --> 00:18:39.000 code, and that will be interpreted as a geometry background geometry. Similarly, I could be massaging this happening in a slightly different way, and I'll be encoding a gauge field. 00:18:39.000 --> 00:18:54.000 A big classical diagram here is real, and then you can… you know, and they're making fun of them, and so on, but today I'll be speaking only restrict myself only to the geometric. 00:18:54.000 --> 00:19:13.000 Um, next… I'll be adding this type of interaction. And this involves quick space. This involves 2 spins. This has 3 spins. That's why now make my chain into a triangular, let's say, ladder. 00:19:13.000 --> 00:19:28.000 It's this field here. Then I have another 3 and another 3, and so on. So the chirality is a polyn the chirality term I two, and so on. 00:19:28.000 --> 00:19:49.000 Um… I can… Jordan Wiedner transformed the full Hamiltonian. And while this then gives me only the standard infermions. This one gives me several things, gives me paneling fermions between next to nearest neighbor. 00:19:49.000 --> 00:19:59.000 So I'm jumping between the two, either on the blue ones or on the red ones, the two strands of the lander. 00:19:59.000 --> 00:20:11.000 And also, it gives you this… interaction term, actually. This tells you that I can tunnel from here to there, control to the population on the third site. 00:20:11.000 --> 00:20:25.000 You see now, let's like a gate theory, right? Theories are gauge field line kind of effects here. But now this is graphic. 00:20:25.000 --> 00:20:38.000 Yes. Module constraints involves those and so on. This is kind of interaction. 00:20:38.000 --> 00:20:49.000 And interestingly, these two terms. This is caused by that. This term is what tilts your cones. 00:20:49.000 --> 00:21:05.000 changes the direct cones into… symmetric tilting one step encodes a geometry. Well, this term poses the interactions, the strangle. It's amazing that this actually serves both. 00:21:05.000 --> 00:21:14.000 I guess it was an effect. No problem. 00:21:14.000 --> 00:21:21.000 Yes, that's right. 00:21:21.000 --> 00:21:28.000 Let's move to the same classical. Is there a glove somewhere? 00:21:28.000 --> 00:21:43.000 It's okay, I'm keeping the… stop mute. So first of all, we move to the same Glasgow regime because it's an interactive Newtonian. We can't exactly solve it, so we can't. 00:21:43.000 --> 00:21:56.000 Listen, classically, this is equivalent to a real field theory is a consistent way how to get a free model, let's say, out of the interacting. And indeed, it keeps the first two terms that we have. 00:21:56.000 --> 00:22:02.000 And then we can diagonalize it to see what's the dispersion relation. 00:22:02.000 --> 00:22:13.000 Um, it's very similarly chromosome. So you can think of it as light cones. And what you see is that for V0, you have the use of, uh. 00:22:13.000 --> 00:22:23.000 And as you increase the the tilts, and then at some point it over, sorry, it tilts, and at some point it over tilts both. 00:22:23.000 --> 00:22:33.000 Group velocities now point inwards. Hey, Matt tells you that particles cannot escape, but antibiotic growth. 00:22:33.000 --> 00:22:52.000 Let's see. So this is, um… A very positive sign. Of course, we need to do the analysis a bit more carefully. This is the ladder. We introduce a spin or. 00:22:52.000 --> 00:23:08.000 that includes the amplitude of this side and the amplitude of this side. So this is my unit cell. This is the spinner I'll be using. You can Fourier transforming, expand it near the low energy limit. 00:23:08.000 --> 00:23:17.000 And what you get is a linear dispersion relation, but also you can get a spi by and either. 00:23:17.000 --> 00:23:31.000 Which is related to the metric du mu. This is really the group velocity of your particle along here. And if you change it, it means you change the. 00:23:31.000 --> 00:23:38.000 It's five bars, which means that you create curvature. 00:23:38.000 --> 00:23:50.000 Uh, this particular, if you do the steps carefully, you see that you have this metric. This has off the terms as well, and if you increase… if V is 0. 00:23:50.000 --> 00:24:00.000 And then you increase it to something larger than 2V loading everywhere around here that have been careful. 00:24:00.000 --> 00:24:06.000 Allow me that. Um, the fee is larger than you or to you. 00:24:06.000 --> 00:24:12.000 that case. This changes sound, but seeking else you cross the Verizon. 00:24:12.000 --> 00:24:24.000 Uh, which is about… Okay, so you can encode a direct. So this is a Dirac Hamiltonian single particle field theory, Dirac Hamiltonian. 00:24:24.000 --> 00:24:39.000 In the metric, this bootstrap metric. If I keep fixed constant throughout my chain. 00:24:39.000 --> 00:24:48.000 I don't have geometry, I just have one coordinate system and another coordinate system. But if the changes, then this metric. 00:24:48.000 --> 00:25:02.000 Uh, it can be differentiated as non-zero differentiations, and then curvature arises. And indeed, what we do is along the chain, the chain speed from 0 to something non-zero. 00:25:02.000 --> 00:25:08.000 Uh, here's where curvature, of course, emerges when it's constant is no curvature. 00:25:08.000 --> 00:25:22.000 We choose what provided. If we can give, uh… sidechain profile. Then you have any anything we like really doesn't satisfy the Einstein integration so far, but we can. 00:25:22.000 --> 00:25:37.000 encode it to any profile we like. And indeed, by having from 0 to something high, large and non-zero, we have this chiral phase, non-chiral phase, and the interface between the 2. So indeed. 00:25:37.000 --> 00:25:57.000 This describes simulates a black hole physics. So this is a nano basically of the black hole because you've got that metric there which is different to the black hole metric, because you've got that DT by Dx term. 00:25:57.000 --> 00:26:02.000 Which would not be there in the normal, say, Schwarzweil metric. 00:26:02.000 --> 00:26:22.000 Darwin's here. So that's the GM over RC square factor. That gives you the radius of the black hole. All right. Yes. That's right. I could put here, depending on the profile as it shows here, I would have a structure. Yes. 00:26:22.000 --> 00:26:39.000 Yeah, that's right. In this coordinates, you can have recurve coordinates. You can have this Gp coordinates. This is equivalent. Yes. Now the curvature has to be the same, and indeed, because it depends on the derivatives of P, and this external, yeah, and this I can. 00:26:39.000 --> 00:26:56.000 choose to be fine, that's right, yes. So you're free to do that. It's just that for this particular screen model, you get the Gp3. I'll show you later on how to get the Riddler. 00:26:56.000 --> 00:27:04.000 metric, and how this actually does it describe the platform. 00:27:04.000 --> 00:27:11.000 Okay, um, let me now describe you the protein radiation. Again, we have a black hole. 00:27:11.000 --> 00:27:26.000 2-dimensional generalization, 2 plus 1. We prepare a state inside the blackboard forming state, and then we let it evolve. It will move outside the horizon, and then we project it outside state to the outside Hamiltonian. 00:27:26.000 --> 00:27:34.000 And look, what is the dispersion? The populations of. 00:27:34.000 --> 00:27:41.000 of the state on different eigenstates of the outstanding Hamiltonian, and we see that we get this exponential. 00:27:41.000 --> 00:27:48.000 Which means that we have a thermal state, so that it fits well to this thermal. 00:27:48.000 --> 00:27:58.000 distribution. Sorry, what is the meaning of the color scale on this plot here in the middle? That's it. Okay, yes, let's do it. Yes. 00:27:58.000 --> 00:28:08.000 And the important thing is that you get a thermal state. If you look at it only on the outside, Hamiltonian energy, you trace out the inside. 00:28:08.000 --> 00:28:24.000 exactly a different horizon. You have this thermal distribution, and the temperature that appears here is the hotel temperature, depending on the profile of V. So you use a certain profile. The curvature of B. 00:28:24.000 --> 00:28:41.000 And you see that the leads for various. Agreed in Sabid and for various radiuses the the Hawking temperature. What you measure. 00:28:41.000 --> 00:28:53.000 primarily out of this tiny revolution agrees with the curvature at the horizon, which is an unbelievable thing that the things that are here. 00:28:53.000 --> 00:28:59.000 depend only on the curvature there. So the universal effect. 00:28:59.000 --> 00:29:11.000 Okay, so that's the picture. of things that we did afterwards, but let me describe it now in the one-dimensional setting. So we have our. 00:29:11.000 --> 00:29:18.000 Our chain, we have the profile that is large, B, small B here and then. 00:29:18.000 --> 00:29:25.000 We prepare a pulse inside the platform. And then we let it evolve. 00:29:25.000 --> 00:29:36.000 Um, it will go left and right, but the time that goes to the right, it will be… reflected on the horizon part of it, and part of it will be transmitted. 00:29:36.000 --> 00:29:43.000 And the transmitted part actually has a thermal distribution when. 00:29:43.000 --> 00:29:54.000 projected on the eigenstates of the outside Hamiltonian. So what happens? Here is space, and here is time. We prepare a pulse here, we put the pulse already. 00:29:54.000 --> 00:30:11.000 And then we added Evolve. Some of you will go left, some will be right. When it reaches the horizon, it will be reflected in some small part, this is very weak, this is a logarithmic scale, some of it will go outside. It's a very, very small part that does manage to escape. 00:30:11.000 --> 00:30:17.000 But the unbelievable thing is that. It looks terrible. 00:30:17.000 --> 00:30:25.000 It's not truly thermal. This is a free Hamiltonian, right? But if you project it on the full part is thermal. 00:30:25.000 --> 00:30:34.000 Not only that, the temperature is fixed. It depends on the derivative exactly at the horizon. 00:30:34.000 --> 00:30:45.000 And we repeated that thing, uh… for different positions of the initial here. 00:30:45.000 --> 00:30:51.000 It's pretty flat, and you can change the position of the horizon. It's pretty flat and insert. 00:30:51.000 --> 00:31:10.000 The, uh… This time evolution gives you always a halting temperature. It's a universal effect doesn't depend on many details of your model. And of course, if you come from the black hole communities, they get sure that's called radiation. But if you come from a condensed matter community. 00:31:10.000 --> 00:31:20.000 You could two materials, one parallel into context. And then what you tell them is that if you. 00:31:20.000 --> 00:31:34.000 With the population and moves outside. It would be thermal is the temperature above that. So you can predict the thermal properties of this system as universal properties, and which is pretty amazing. 00:31:34.000 --> 00:31:53.000 If you think about it. Now, numerically, um, we can probe the thermal properties, we can find eigenstates and so on. But experimentally, it's hard to see if a system is thermal or not. So we devised another way how to measure the temperature. 00:31:53.000 --> 00:32:03.000 of the system. We monitor the populations at the single site over here. And at the beginning, this population says zero. 00:32:03.000 --> 00:32:11.000 And as, um… of the way Tamsen transmits, this population will increase, and then we'll go back to zero. 00:32:11.000 --> 00:32:17.000 So we're monitoring one side here, we see that we get this type of behavior. 00:32:17.000 --> 00:32:36.000 If we change the slope. Yeah. The temperature changes. And what we've noticed is that this curve, this population will pick at different time. So by monitoring the times for the peak happens. 00:32:36.000 --> 00:32:48.000 Um, we… We draw this line. This is the time where this curve peaks. It goes on the line as inverse Hawking temperature. 00:32:48.000 --> 00:33:09.000 So if we set two points, let's say, and we calibrate this line, then we can… measure when it peaks and will decide what temperature this black hole corresponds to. This is a way how to monitor the temperature without having to throw the thermal properties of a system. 00:33:09.000 --> 00:33:28.000 We've experimented, it's very hard. to your V prime here is the acceleration generated as a result of the surface. But it's the curvature of the space-time that's causing that. Yes, exactly. Yes. 00:33:28.000 --> 00:33:54.000 Yes, sir. This is the universality, I mean, this is at the point, the derivative at the horizon determines the properties of the system far away, which is… anything else, if I had some inhomogeneities, random noise interactions, this result will stay the same. It's pretty cool, actually, if I were this is like — So if we go back to the. 00:33:54.000 --> 00:33:59.000 articles that are inside, they're coming up to the boundary, the event horizon. 00:33:59.000 --> 00:34:22.000 Isn't it just tunneling? Collaborators explain the fact that it's happening and the idea is that the… transmission and reflection, racing and handling depends on the energy of the mold that can zips, and that causes the makes it. 00:34:22.000 --> 00:34:36.000 It makes the distribution to be like that, because energy dependent. That's right, indeed. 00:34:36.000 --> 00:35:03.000 Okay, so I described the Hawking radiation. It's 7 minutes past. Yeah, it's still 10 minutes. I have 10 minutes only. 20 minutes. Chaos. Chaos. We can see that misinteracting term actually causes disease. It's completely chaotic. 00:35:03.000 --> 00:35:12.000 Now, the question is optimally. Are these people use these photos of the time, water correlators, which basically tells you that. 00:35:12.000 --> 00:35:18.000 I want to probe the problems with Hamiltonian. So I put the thermal state. 00:35:18.000 --> 00:35:43.000 And then I evolve… I have two operators here, one in time, and the other I keep back, and I create this for… operators at zero time, time t zero and t, while a distributed row in this particular way, okay? I do that because I want to have some, uh… 00:35:43.000 --> 00:35:59.000 with properties of my relator here. I scaled it so that this is equal to 1 and 0. And I look at it at time t. So basically, if you want something in time with a certain Hamiltonian, what its relation with the. 00:35:59.000 --> 00:36:15.000 Uh, original state you have, and once this goes to 0 5, so exponentially fast, then it means that we have interactions in chaos, and and the fastest possible way that we lose information between the initial. 00:36:15.000 --> 00:36:24.000 state and the final state, because of the evolution of the Hamiltonian, is the optimal sprangler. Classically. 00:36:24.000 --> 00:36:46.000 Yes. Classically, these two can be completely disentangled. Go as crazy as you like. There is not any upper bounds, but quantum mechanically, because of humbitarity, you can't move too fast away from an initial state, so there is a bump. And exponentially decay, but there is a bound. 00:36:46.000 --> 00:36:59.000 And people found that this is it depends on the temperature. T of the thermal state and the optimal bound is to ip. And there is a j happening, another coupling of your systems. 00:36:59.000 --> 00:37:06.000 It has been found also that black holes actually saturate this bone. This is Yakunovich bone. 00:37:06.000 --> 00:37:22.000 So this is the opponent spawn that tells you that these correlators die off exponentially fast, and this exponent is what quantifies how fast the stratum happens. And indeed this lambda. 00:37:22.000 --> 00:37:32.000 is bounded, and the optimal is a black hole. What I'm trying to show you now with the next few slides is that our model actually. 00:37:32.000 --> 00:37:54.000 optimal experience. So what we want to show is that this Japunov exponent that we calculate out of the auto satisfy this equation. First, what we do is we… We fit parameters, because we find different values of lambda for different temperatures, and we put fitting parameters A, B, and C. 00:37:54.000 --> 00:38:07.000 B6. And first we fit this exponent B. If P is small, we find this exponents two outside the horizon. 00:38:07.000 --> 00:38:22.000 And when we start inside the horizon, we find B is equal to 1, which is what we want. And also the 2 is just — so basically we find outside the horizons of functions temperature, the independence formula has this for traffic behavior for small. 00:38:22.000 --> 00:38:30.000 Everybody shares, and this also goes down for that, and is actually even once. 00:38:30.000 --> 00:38:44.000 Um, that the paralysis. And inside the black hole, we get this linear behaviors quite distinctive from the and the linear is what we want. Then. 00:38:44.000 --> 00:38:49.000 We don't want it to be only linear, we want it to be sympi j. 00:38:49.000 --> 00:39:09.000 Uh, so then we plot. The coefficient A divided by B, which is the system size increases this way, this is system size, the dotted lines are exactly the normalization we did. 00:39:09.000 --> 00:39:17.000 And I've presented them a year or so ago in a conference that other people would. 00:39:17.000 --> 00:39:32.000 Welcome to the SYK model with that, and it became… I said, one day, we can't really get furious, they're here, there's there. And he says, no, you can't do it. Your model is not to always optimal is probably have. 00:39:32.000 --> 00:39:50.000 So on, it shouldn't work. So, you know, that's… I agree, but that's what we find. And he finally comes up a coffee break, and then he should be able to chase me and properly done. Well, that's what we did. I'm not claiming anything. 00:39:50.000 --> 00:40:08.000 And then the person's been working on that with the SYK model, if you have the experience, it knows how hard it is. So he said, pass me the email of his postdoc and merge for that model, and he ran away. So I contacted him, and they had this very sophisticated. 00:40:08.000 --> 00:40:29.000 numerical method based on three of methods, and we minus together to verify the exact and then probe its much larger system sizes, which you see that indeed saturates the value we want, so… Yes, if you're angry with what they present, please come and see. So… 00:40:29.000 --> 00:40:37.000 This… concludes that numerically in my mind. But the system is, um, this is the theory in numerics. 00:40:37.000 --> 00:40:54.000 The system is at speed, so we can record it on a quantum computer. And also the properties we like to see, like this function relations, energy momentum, Hawking radiation or chaotic evolutions are time evolutions. That's things that you can do on a quantum. 00:40:54.000 --> 00:41:11.000 computer was called migrants. And I'll present indeed two versions of these black holes. One is based on the XY model that is in the Riddler coordinates, and we have implemented, but also exist in the literature recently. 00:41:11.000 --> 00:41:19.000 And we want to… but this is non-interrupting, doesn't have behavior. And then we implemented our model. 00:41:19.000 --> 00:41:34.000 And I'll show you. what the revolutions are. Now, the time evolution, if you have the XY Hamiltonian, the Chirox Hamiltonian, and then you talk to Verizon, you interchange them. This is a basic block, and then you repeat it many times for some unit T. 00:41:34.000 --> 00:41:56.000 The XY is only a two qubit. a gate, and it's actually native. We did this… the NQCC. They have some time. We run it there and and we're very excited. This is a native to the IBM sleep hardware that we use. 00:41:56.000 --> 00:42:11.000 And this is, let's say, the circuit, and the current term is the three spin interaction term or three qubit gates that you can decompose in terms of given gates, givens. And. 00:42:11.000 --> 00:42:30.000 Yeah. So, it has a… a different setup, so it's easy to do the XY model, because you have this depth. If you want to do the current and the X y, you have to combine these two sorts of depth of your surface creases. So technically it's harder because Qx comes in. 00:42:30.000 --> 00:42:39.000 And here, these are experimental results, all of those. Here's your walker, how it goes for the XY model. 00:42:39.000 --> 00:42:47.000 Read the letter Wardens. Yeah. Okay, very similar facing. Your combs go like this. 00:42:47.000 --> 00:42:58.000 when you cross the horizon. You change space and time, and these are the dispersion relations for different kinds of velocities. And this is exactly what we monitor. 00:42:58.000 --> 00:43:25.000 one side here at the horizon. These are the populations go up and down for different curvatures that we encode in our system. And you see the fault all in one line, you can extract the whole temperature out of that. So we are very… Sorry, but this is the same thing for the chiral model. These are experimental results. These are just numerics, but with the gates that we use. 00:43:25.000 --> 00:43:30.000 We are carrying out the experience here, but because the depth. 00:43:30.000 --> 00:43:44.000 for is a bit bigger. errors degrade the result. So we managed to get the dispersing relation, uh, that we have the tilting of the homes. Now we're working hard to extract the. 00:43:44.000 --> 00:43:50.000 hooking temperature and the scrambling. These are the optics with the gate set. 00:43:50.000 --> 00:44:04.000 So… wait for that. We're still working on this path. So that's my that's where I want to get to. That's what numerically or an editing is hard to probe. I hope that the fund can give us. 00:44:04.000 --> 00:44:14.000 this optimal patient. So here it is. Let me flash again the slide. We have a model where the character. 00:44:14.000 --> 00:44:30.000 huge horizon and needs optimal terms. The same type of interacting term. And you see, it happens, you see, it's not the geometry increasing that causes the chaos. 00:44:30.000 --> 00:44:42.000 Is that by encoding the… The geometry of a black hole necessarily increase the capability. And when coupling V is strong. 00:44:42.000 --> 00:44:49.000 then the geometry loses. Meaning, because of the strong fluctuations. 00:44:49.000 --> 00:45:06.000 Okay? It gives rise to the optimal scrum. Okay? So… I hope that gives you a glimpse of… How did Black Hole Simulator that has both geometry and optimal structure? 00:45:06.000 --> 00:45:13.000 works. Okay, so we have this chiral model. 00:45:13.000 --> 00:45:43.000 That we've seen that it can give you hope radiation. And as a final thing, I'll go very, very quickly the platform teleportation. 00:45:54.000 --> 00:46:24.000 Excuse me. 00:46:27.000 --> 00:46:44.000 Alright, so that's very good. Thank you. That's the best way I could do to present you the why we're interested on teleportation from inside to outside the black hole with a straight face. 00:46:44.000 --> 00:46:57.000 So what happens is that huge black hole is a quantum modern inside the black hole, and as time passes, this quantum matter looks outside some parts of it. 00:46:57.000 --> 00:47:02.000 Now, what we have is, Alice throws a part inside the Black Hawk. 00:47:02.000 --> 00:47:11.000 The motivations are unclear, but as described here is wrong. And then Bob's is on the outside. 00:47:11.000 --> 00:47:41.000 And, uh, Bob is quite powerful. And they can be skilled EPR paths between the inside. From this quantum matter, they can distill it and make some… EPR pairs to find correlations from inside to the outside. The inside is involved with this optimal scrambling Hamiltonian, and Bob does exactly the same, but star evolution. 00:47:41.000 --> 00:47:53.000 And the… There's some more… Both measures. 00:47:53.000 --> 00:47:59.000 boots tooth, and effectively what what happens is that the quantum sleep side. 00:47:59.000 --> 00:48:06.000 Yes, the reporter on the outside, the fidelity is low, but as more. 00:48:06.000 --> 00:48:22.000 consequences are… radiated a panel, you measure more and more, and the fidelity goes to 1. The probability of success is a quarter, and that reflects the quarter of success of the rotation. 00:48:22.000 --> 00:48:34.000 And indeed, we did that with a spin system, and we found that indeed, the more measurements. This is the fidelity of the out state that that increases. 00:48:34.000 --> 00:48:43.000 As you do more and more measurements, and it saturates the bound of one or asymptotically, but pretty fast, actually. 00:48:43.000 --> 00:49:03.000 In our model, in order to encode these two evolutions, we actually put another black hole on the outside. So it's a geo-binary system inside and outside. So this is the equivalent black hole systems. This really done is the same. 00:49:03.000 --> 00:49:14.000 there. And that's that really, that's the quantum interpretation from inside to the outside that Aidan Prescott actually did in order to. 00:49:14.000 --> 00:49:26.000 typically hoping that Hooking says information pilot is real. And then they're poking at me oh yeah like to. 00:49:26.000 --> 00:49:42.000 To provoke, not to provoke. What do we have? We have a model that is a simple, simple, relatively simple model that can do the Hawking radiation and the scrambling. 00:49:42.000 --> 00:49:51.000 Um, we used it in order to, uh… use a highly pressing product, but within the same model. 00:49:51.000 --> 00:49:59.000 Um, so has the fundamental properties of and also the semi-classical. 00:49:59.000 --> 00:50:11.000 So, am I happy with that? Because we would like to probe with it more physics that has to do with this disparity of. 00:50:11.000 --> 00:50:32.000 description, and fully. one description. The ideas were the, uh, the islands of inside black holes have to do with the station and how it cannot be described in classical picture. We want to see evaporation of the black hole where the horizon. 00:50:32.000 --> 00:50:42.000 changes depending on the mass that is inside the black hole, so you can encode that and simulate and then derive. 00:50:42.000 --> 00:50:49.000 What's the evaporation time? What's the page time, and so on. 00:50:49.000 --> 00:51:07.000 And there are possible quantum information obligations. If you have a way, a deterministic way how to do optimal scrambling, you can use it in order to hide information quite fast. It won't recognize where it came from, and then you can apply them. 00:51:07.000 --> 00:51:19.000 reverse abolition to retrieve it. So there might be a possible way how to hide the material information, and of course, we're working on 2 plus 1 and 2 plus 1 generalizations of the model. 00:51:19.000 --> 00:51:28.000 Just presented to you. 00:51:28.000 --> 00:51:42.000 Thank you. Questions? classroom. Very interesting talk, actually. I'll have to spend more time talking to you about it, but a couple of things that, uh. 00:51:42.000 --> 00:51:57.000 I'm thinking about is entropy. You didn't mention entropy. Now, chaos and entropy are quite similar, actually, because you've got maximum chaotics and maximum chaotic system is maximum entropy as well. Is that correct? Correct, yes. 00:51:57.000 --> 00:52:12.000 Um, so, yes, this is a fundamental point. What we analyzed in one paper with a student Yassen is how. 00:52:12.000 --> 00:52:27.000 In the semi-classical limit, if you have only the geometric description of a black hole, not the interactions, you get thermal behavior, but only if you trace at the horizon. If you trace away from the horizon, it's not thermal anymore. 00:52:27.000 --> 00:52:44.000 And indeed, you expect that because evolutionists with free Hamiltonians do not cause thermalization. It's pretty amazing that when you twist at the horizon, you get something that looks thermal. So basically, if you want to see something thermalizing. 00:52:44.000 --> 00:53:00.000 any partition of your state should look thermal is relatively small compared to the full size. And indeed, we verify that inside the black hole where the Harold interactions take place, the optimal scrumming takes place. 00:53:00.000 --> 00:53:09.000 the temperature actually appears to be infinite. So, quite fast, the system becomes fully mixed. 00:53:09.000 --> 00:53:31.000 Uh, inside the black hole. So there's no halting temperature there. But if you see Hawking there is a different physics. Scumbling is different physics, and and that's… I hope that this simple model helps us to understand these concepts. So, but Hawking radiation is dissipation. 00:53:31.000 --> 00:53:40.000 So dissipation would tell you that you wouldn't be able to get maximum entropy because you're losing information all the time. 00:53:40.000 --> 00:53:47.000 And so you… what you're doing is you're actually creating a coherent structure. 00:53:47.000 --> 00:54:01.000 And you can actually generate, and you're in the strong field region inside the black hole, you could get coherent structures being generated rather than chaotic, but you get coherency from chaos. 00:54:01.000 --> 00:54:05.000 Have you looked at that? I'm 100% agree with what you say. 00:54:05.000 --> 00:54:16.000 Having said it so clearly before, but I've been trying to demonstrate that exactly. Okay. Yes, I need to talk to you more about it. 00:54:16.000 --> 00:54:31.000 We calculated the entropies analytically of the black hole 3 Hamiltonian with different motions. And indeed, we find what you say. And numerically, we're dealing with the. 00:54:31.000 --> 00:54:46.000 I haven't interacted with, it's very hard analytic you to probe, and we find this infinite temperature that's different from the bottom temperature thermality. 00:54:46.000 --> 00:54:56.000 Thanks. Any more questions? Hi. You've been able to put the black hole onto? 00:54:56.000 --> 00:55:12.000 to quantum computer simulator, and you've done that for the XY coordinate system, and you're working on it for the chiral. We did also for the chiral. Just the because… and we've got the distraction relation, which is fantastic. For monitoring for the clocking temperature. That's the next thing. 00:55:12.000 --> 00:55:39.000 We are… we have the results, but… Because our separates are rather long to encode the chiral thermal, the coherence hits us quite fast. Unfortunately, we picked up — is anybody working for IBM here? And we didn't anticipate this problem. We thought the connectivity was exactly what we wanted to have life changed. 00:55:39.000 --> 00:55:58.000 Uh, if we chose an iron thrust, would we need very few qubits of data, not the systems are rather moderate. We don't need coherent results and verify it. So that was, yeah, so you quite answered the question that I had, which is, what are your limiting factors? 00:55:58.000 --> 00:56:15.000 You can hear it's obviously… That's right, yes, yes. You yourself have written about error correction and so on. What are the limiting factors and which are the major ones? What needs to happen to make this work? You've done it, so what's the most, yes. 00:56:15.000 --> 00:56:25.000 But onto the factors that are limiting you at the moment? Yes. Very good. So first of all, we're doing patents mutations of a physical phenomena. 00:56:25.000 --> 00:56:40.000 Our, um… requirements are not as triggering as spring one implementation, where you want to define an answer. So we want to have qualitative. 00:56:40.000 --> 00:56:50.000 effect. Okay, put some error box. So this you can verify, and it's not too hard. 00:56:50.000 --> 00:56:59.000 Now, if you want… and you can find also some qualitative values there, like the ocean temperature and so on, but it's an effect you're after. 00:56:59.000 --> 00:57:15.000 One of the cultivation is an artifactorize numbers, an extremely demanding thing, and of course they care about linear correction and so on. In our case, yes, we want to keep it coherent, but the systems. 00:57:15.000 --> 00:57:22.000 are valuable, and you actually wonder what we are interested in. 00:57:22.000 --> 00:57:37.000 And in your case is the is the IO an issue? So certainly when you look at particle physics problems and that's what you're trying to push a whole event, or even just a set of, you know, hits or something in tracking a track trajectory finding algorithm, and even that is. 00:57:37.000 --> 00:58:03.000 It's too much information to try and push on and off. I can only imagine you have lots of information here that you're pushing on and off as well, but maybe you can… why… why is that not limiting you, or is it limiting you? Information pushing on and off. Yeah, so, because you have a certain amount of data you need to pass to the processors and to read out from that processors. That's right, yes. So, um, what we have is a… chain, which is… then we apply our… 00:58:03.000 --> 00:58:09.000 our gates, which is the Hamiltonian at the time of all sin. And then we measure. 00:58:09.000 --> 00:58:22.000 And the measurement is the distribution of your wave functions. So if you use all of those information, you repeat it several times to build this distribution. Now. 00:58:22.000 --> 00:58:37.000 If your circuit is too long, then temperature, all you get might be more probabilistic than quantum physics. So if you try to extract from it the quantum properties. Now, there are different techniques. One is mitigation. 00:58:37.000 --> 00:58:52.000 So, uh, you can guess… Um, or you can manage your data to remove the thermal part and keep the quantum by extrapolating and so on. 00:58:52.000 --> 00:58:57.000 Or do polymer correction. But it doesn't test, but corrects the thermal part and makes it pure again. 00:58:57.000 --> 00:59:09.000 Uh, so these are different techniques. We are more on the mitigation side of things at the moment, rather than requirement, but we have ideas for the quantum error correction as well to apply. 00:59:09.000 --> 00:59:24.000 Thank you. Thank you. I'm sorry if I didn't answer your question. It's a very different type of problem. Probably your problem is more akin to the big game of putting a QF quantum field theory foot onto quantum computing. 00:59:24.000 --> 00:59:34.000 Yes, that's right, yeah. And then, seat time evolution, that's what products can do. 00:59:34.000 --> 00:59:49.000 Thank you for the wonderful response. So I really enjoyed it. But unfortunately I'm not as good as math as I want to be. So 1st question was about the the Hamiltonian that you showed. 00:59:49.000 --> 01:00:03.000 So, you said that the coupling fee is something that varies according to position, right? So it's the way that that chiral system. 01:00:03.000 --> 01:00:09.000 shows a black hole. Is it by like varying that d value? 01:00:09.000 --> 01:00:27.000 Uh, according to that event horizon. That's right. So ignore so V encodes changing the encodes the curvature, and by changing from small bodies to large values is what gives you the horizon at some point. 01:00:27.000 --> 01:00:37.000 Indeed. So you need this watering V, because a black hole is an inhomogeneous system, if you like. So we need this varying parameter to encode it. 01:00:37.000 --> 01:00:49.000 And it's interesting that smaller bars, we correspond to two different materials. One is hard, one is non-ciral. But of course they're connected. 01:00:49.000 --> 01:00:57.000 Also, when you showed that simulation of Hawking radiation 2D. 01:00:57.000 --> 01:01:20.000 Uh, I got… I got the impression that it… It wasn't like a circular… Yeah, yeah, yeah, you're right. Yeah, absolutely, yes, yes, yes. It seemed like a 90 degree rotation. Because it's a square lattice. So the square lattice will have the… this is Manhattan distance, and there's many things that spoiled the… 01:01:20.000 --> 01:01:26.000 Uh, the… the perfect rotational asymmetric. 01:01:26.000 --> 01:01:46.000 And also, we prepared in principle, we wanted the mass wave kind of encoding as regular, but we put populations in this kind of symmetric way. So this C4 symmetry that also the radiations at the of the initial state that also satisfying. 01:01:46.000 --> 01:01:55.000 In the final state. Yes, it's dirty name of the car. 01:01:55.000 --> 01:01:59.000 Any more questions from the room or from Zoom? 01:01:59.000 --> 01:02:11.000 Oh, that's what we're equipped with. So you kind of compare it to a quantum limit and a semi-classical limit. If you look somewhere between those two limits, Jupiter's meaningful information to extract. 01:02:11.000 --> 01:02:22.000 From the muddy details in between those two places. Yes. This is what we want to do, to see how physics. 01:02:22.000 --> 01:02:30.000 achieve this when you move from one to the other. Same class with two. So there's this idea of, uh. 01:02:30.000 --> 01:02:54.000 One of my collaborators is an expert where. It's what if you don't perform private teleportation, but the system due to the scrambling effectively teleports. Now, this happens only if you have interactions. If you don't have interactions, this doesn't take place. So… 01:02:54.000 --> 01:03:03.000 The column highlights are… In this semi-classical limits, what you would need to remove in order to imitate the. 01:03:03.000 --> 01:03:10.000 fully interacting. So it's another way of quantifying interactions. 01:03:10.000 --> 01:03:20.000 The rate of generation of these events. Um… comparing them to a free Hamiltonian. But in time evolution. 01:03:20.000 --> 01:03:35.000 So there are different ways to quantify strong correlations interacting Hamiltonians of a ground state. But now we are looking at the quantum evolution quantifying their effect on the quantum evolution. It's very exciting. That's what we want to. 01:03:35.000 --> 01:03:46.000 to move. For example, you can monitor the entropy of the outside and the representation that will happen naturally will change the entropy. 01:03:46.000 --> 01:03:53.000 If it wasn't? And that would be fantastic to see it in one system. 01:03:53.000 --> 01:04:14.000 So we had a very interesting discussion right before about the quantum gravity, but by should I have all the fun? If you'd like to chat with the speaker after the session, please join him for lunch, and let's thank our speaker for being the person. 01:04:14.000 --> 01:04:20.000 Good thing. 01:04:20.000 --> 01:04:26.000 Okay. 01:04:26.000 --> 01:04:42.000 A very good story.