Come to the fourth day of the conference. We will have the talk by Vedran Dinkyo. And after that, coffee break to discuss everything we learned. Take it, please. Thank you very much for the introduction. Can anybody not hear me well? If I start speaking too quickly, please shout out. Or if I start mumbling, please shout out. I tend to do these things. And I can be understood when I try. So first I would like to thank Marcus and Christof and other organizers, Tiago and those that I forget to apologize. I'm really honored to have a chance to speak to you today. This is not exactly the kind of conference that I attend, but it's exactly what I want to be doing when I grow up. So I'm very happy to be here. Has anybody played PowerPoint karaoke? Does anybody know what that is? Very few. You get enubriated and then somebody puts up a set of slides which are not yours and you're forced to make a presentation on that. Why am I saying this? Because I tried to remember what I promised to talk about here, and then I went on the web page. And I found the title of my talk. And then I was like, really? I mean, it's an appealing conversation to be had, how to have quantum earning advantages. But I don't really know that much about it. But I guess I promised. Then later I realized that, of course, I made a mistake, or somebody made a mistake, it's learning advantages, which is maybe much less provocative, very interesting. But I realized I'd be very emiss if I didn't tell you how to make money with quantum computers. So let's talk about that, at least for a little while. Jokes aside, I do want to talk about quantum machine learning. This is something I'm really, really excited about. But interestingly, I can't tell you something about earning with quantum computers at the very introduction, then forget about money altogether forever. Why? Because I'm excited about quantum machine learning. But if you go online and you scan what people are writing about it, and if you look at Google Engrams, so this is tracking the Syntem quantum machine learning and its popularity, or actually occurrences in literature over time, I realize that there are people who are even more excited about quantum machine learning than I. And I've been in it pretty much from the beginnings. So I get confused. What do they know that I don't? That this is really so cool. And by the way, this is going to be the end of my advice. It is the next big thing. So if you want to get rich, I guess you need to buy stock of all these companies now while the going is good. So this is my end of talk on quantum earning power. And I will not get back to that.  This was a joke. I'm not really advocating buying stock for anybody. And I will not joke anymore too much. What I will say, however, that it's a very good question with the quantum machine learning is really such a big deal. And the answer is we don't know. And this is what I want to discuss. But there are things that we know quantum computers are certainly good for. And if you put your careful skeptical hat on, you will realize that there are many things, but not that many. And ultimately, two things which seem to be uncontroversial is that quantum computers are good for factoring numbers, which may be relevant in very particular applications. And they seem to be very good at simulating very complicated natural systems. And I suspect that everybody here has at least once heard this one of the more popular quotes by Feynman that if you want to simulate nature, you need to use a quantum mechanical simulation. So there's a reason why I have these two gentlemen here. We'll come back to both of them at a later point. The organizers pointed out that everything gets recorded so that I should be careful with licenses of images that I used. And I had a different picture of shore. And I found this one on Wikipedia, which is then free. And I noticed something funny that the picture from Wikipedia is actually from this room. He was here when he was receiving the 2018 Iraq Medal in 2017. So this is exactly the podium that he was standing, which I think is quite cool. And I definitely don't deserve to be here. But anyway, a small, interesting coincidence. So yeah, so I said, we know that quantum computers can factor a number that's an ambiguous advantage. They can also similarly quantum systems. The truth is a little bit more complicated. We know a little bit more. In fact, there's an entire field called complexity theory, which analyzes hardness of problems in the sense of what kinds of resources are needed to solve them. And you may have seen dying numbers of this type, where we have this thing here, which is the class of BQP, which is the problems that quantum computers can solve in polynomial time, and our believed relationship to other complexity classes that we studied over the years, which have nothing to do with quantum. And there are many things here in various intersections. And I will say for the remainder of this talk, I will assume that the diagram is correct. I mean, we don't have a proof that BQP is not really in BPP, but I'm going to assume it is. I'm going to assume that it's even outside of the entire polynomial hierarchy, which some people believe. But we don't really know. But let's assume this is true. I still want to raise the question, what does this say about quantum machine learning? Because it's machine learning. It's a little bit of a different animal than computational problems. So in the community, there had been this common understanding, something we didn't really say very much explicitly, but we all thought it, that quantum machine learning, if it will have advantages anywhere, is going to be when the data comes from a genuinely quantum system. Makes sense. You use quantum to learn quantum. Why would you're not going to classify cats with dogs better with the quantum neural network? Why would you? But maybe find exotic particles in these massive sets of data from CERN. Maybe that's the thing quantum computers should be doing. So this is something I think most of us believed. And I like to think whether maybe Feynman was more interested in sci-fi and knew more about AI, whether he would conjecture that learning about properties of nature requires quantum learners, rather than just talk about simulation. I have no clue. I don't know if he would agree or not. It's not even particularly relevant. What is relevant up until very recently, science we're pointing to know, it seems to be very little evidence that quantum machine learning is going to have advantages for learning data from quantum mechanical systems. And I just want to highlight here something that I'm not talking about machine learning with the data itself is a quantum state. So the experiment is done. The measurements are there. You have your data sets on your hard drive. You're going to analyze it, and you're going to say something about it later. That's the setting I want to consider. These other settings allow for more different types of advantages, but they're also more restrictive because you somehow have to get your hands on quantum data unperturbed. So here everything is measured out. And this is what I want to kind of figure out. So why am I saying that the science we're pointing to know, because data-driven methods are just so spectacularly successful? Like whatever slightly conservative computer scientists and AI people would say, well, this is not going to happen soon. Many of these things actually happened. And one prime example is this conference here, which is talking about the power of machine learning in quantum simulation. You have good ideas of what machine learning could do for many talks on this topic. Recently, I was at a conference for designing molecules. One of the bigger names in classical machine learning, Maxwelling, was talking about how he simulated Schrodinger equations. So yeah, it's a little bit worrisome. And it's interesting to see how this actually meshes with the results from complexity theory, which I just said I believe. And I'm claiming even though I believe this, it is not in contradiction with the possibility that we don't need quantum computers for machine learning from quantum data. Why? Well, because complexity theory separations might not imply learning separations. And the question is, when do they? If we know something about complexity theory, does it ever and when does it tell something about possibility of learning? I think by now you're getting the feeling that this is going to be a rather formal talk. And it will be. I will be introducing a lot of mathematical machinery. I don't expect you to be in love with all of it, but maybe at least hear certain terms for the first time. Maybe you find it interesting, and you can always look me up, and I'll be happy to talk about this to whatever extent you wish. So let's talk about learnability as opposed to computational complexity and how we can have quantum advantages. So I want to talk about things formally. I want to prove stuff, so I have to tell you what I mean by learnability. So let's start with an intuition. Suppose I'm on the following prediction problem. I describe to you a molecule, and I ask, can you please tell me what the ground energy of this molecule is? This is a hard problem for molecules that are complicated enough. But now I ask it, but suppose that I first gave you a data set of molecules from which we've solved the problem. There could be hundreds of thousands of molecules from which we know the ground energies. Does this help you solve the problem for a new molecule we have not studied before? Or do we actually need a quantum computer for a problem of this type? So I need to say how to formalize this learning problem in such a way that I can actually talk about proofs. And what I will be using is the terminology of pack learning. So just out of curiosity, has anybody encountered pack learning before? OK, so it's really still rather obscure. But let me tell you what it does. It's a formalism to capture supervised learning. And you know what supervised learning is. We talk about learning concepts. Concepts are functions which we can, for the moment, pretend go from n dimensional bit strings into a single bit. And what is a concept? It's a labeling function. You can think of a concept being, is this the letter a, where the input is a bitmap, like a black and white image of pixels. And some of them correspond to an image of the letter a, and some of them don't. And a concept for the letter a would say, one if it is, the letter a, and zero if it's not. And a concept class, like this wider set here, would be, for instance, collection of concepts one for each letter, right? So they're capturing what it means to be letter a, letter b, letter c, and so on. Now, what is machine learning? What is supervised learning? Well, I give you, I give to a learning algorithm a, a data set of bitmaps, and labels of the corresponding bitmap, for a concept that I don't know. It's a letter, but I don't know which one. And now my learning algorithm, no, no, no, no, turns, turns, turns, turns, and then spits out a function, which if I put in a new bitmap, new image, it will correctly tell me whether this is the image corresponding to this letter or not. I don't know what the letter is, but it's going to be correctly labeling. Yes, Marcus, please. For now, we're going to, we're going to generalize it. In the end, it could, it could be real value, then we talk about regression problems. It could be categorical, more complicated things will happen. But to understand the basic definition, let's take with binary, right? It's complicated enough, it turns out. So one thing which is kind of, so I think you follow this, what is important to know that, I mean, it is kind of important where these data points come from to define what it means to be a good classifier at the end, doing the right job. So data actually comes from some fixed distribution, like people have handwritings. There's some distribution of more likely and less likely bitmaps that are going to be the letter A or not. It's not flat, it's not uniform. The nature is not uniform. So the only thing I will demand is that whatever this distribution that generated the data said, that's the one relative to which I want my labeling to be correct. That's like, if you're studying for an exam from textbook A, you expect to be quizzed on textbook A. I'm not going to ask you from some other textbook which is covering completely different part of whatever it is you were studying. So this is the definition that I want. This learning algorithm A learns the concept class C. If for every concept, if you give me a data set labeled by that concept, with high probability, it outputs a labeling function such that the probability that it disagrees with the actual labeling function, sorry, when averaged over the data distribution, the one that generated the data, is below epsilon. And this has to hold for a data set whose size is polynomial in the size of the concept, size of the image if you wish, and these two error probabilities. And it's called PAC learning because it's probably approximately correct. This is probably, this is approximately correct. Now, note this thing here only talks about the size of the data set. Some things are not learnable even if you give me a data set of any size. But to really have classical quantum separations, we need something a little bit more. We're going to talk about efficient learners. And this additionally demands that this algorithm here runs in polynomial time. So I'm limiting how much time you're allowed to analyze your data. That's the definition, OK? So when I say a learning problem, what I really mean is a concept class that is defined. Does there exist a learning problem? Means does there exist a concept class where I cannot achieve this with a classical computer, but I can with a quantum? Any questions here? If you remember anything out of this, there's a thing called PAC learning. I'm personally not in love with it. It has many shortcomings, but it's an extremely good starting point to start understanding what learning means in a formal way. Good. So learning separations, can I find a concept class that I can efficiently learn using a quantum computer, but I cannot do so with a classical computer? So one thing that you might want to ask is, wait a minute, you told us that you believe that there are functions that you can evaluate on a quantum computer, but not on a classical one. Let's say a function of this type. This is a good example. I prepare some quantum state, which depends on the input in some convoluted complicated way. I apply some unitary, which depends on some parameters theta that you don't know. And then there's some measurement. And I define my concept thusly. In this case, it will be regression because it's an expectation value. I could put a sign around it if you wish it's not going to change anything. And I'm telling you, I believe that classical computers cannot evaluate this function. Then why is it not immediately obvious that a classical computer cannot learn this? It cannot evaluate the function. How could it possibly learn it? Well, here the difference is emerge. So the difference is between computational complexity and learning problems are threefold. The first one is by far the most interesting for me. The second one is very relevant. The third one is not that relevant for us for the moment. And it is, number one, what I call the data gap that is in machine learning. You have examples of the function you're asked to evaluate what it does. Somebody showed you examples of this. And this turns out to significantly empower what classical computers can do. The second one is I also need my quantum thing to be able to learn it. It's not enough to prove that a classical thing cannot learn something. I also need to prove that a quantum can if I want a separation. And that can be tricky because very simple things are sometimes not learnable at all with any kind of a learner. Like, for instance, learning logarithmically deep Boolean functions, you cannot learn that problem. It doesn't matter. It's not a computational issue. It's like information theoretic issue that you cannot learn it. The last thing is that in complexity theory, we typically ask about the worst cases. Like, you want your algorithm to be correct always. Whereas in PAC learning, I will remind you, I will call this the PAC criterion, I just need to be correct with high probability with respect to some distribution. So this is more of an average case type of complexity that we worry about. And with these distinctions, this diagram might look very, very different, as far as we know. Yes, please. Yeah, the classical computer can do much more. It's much more powerful. I'll show you in a second. Very nice. Well, what I find very illustrative examples. So here's the first one. Imagine, note, all of these statements are asymptotic. I'm talking about scaling. So when I say a function, what I really mean is a function family 1 for each input size. OK, like Hamiltonians come from a family. It's not a single Hamiltonian. It's not a single matrix. So imagine a family of circuits. And they have some gates. You could think of them as randomly selected, except for one. One of them is, let's say, a poly-Z rotation about the angle theta. And there's an observable data measure. And this quantum circuit encodes this function here. And I ask you, can you come up with an algorithm which is going to evaluate this function for every theta? Can you do it? And the answer is, we don't actually know how to do that. I mean, these gates are fixed. It doesn't really help me, because this could be somehow universal gates. It could be a programmable thing inside. We don't know how to evaluate this thing here. It is not BQP complete, as you'll learn in a second. But we still don't know how to do it. However, you can prove that regardless of what these other gates are, this function has to attain this very simple form. It is simply a trigonometric function with a certain number of free parameters, 3 in this case, gamma, beta, and alpha. And the only thing that I don't know about it is what these alpha, beta, and gamma are. But now if I give you a data set corresponding to this, like three valuations of this circuit at three random points, with very high probability you can fit the data, find it with alpha, beta, and gamma are. And voila, you know exactly what the function is. And from that point on, you can evaluate it. You just have to evaluate a trigonometric function. This, by the way, generalizes if you start adding parameters, it still generalizes. And in very many cases, it turns out that here you're going to get something called the general trigonometric polynomial, which in fact is still going to be polynomial sized itself. It's a polynomial of polynomial description size, in which case you give me a polynomial amount of data, I can still learn it. It's a very highly quantum function, but I can still learn it. It has to do with the concept of function obfuscation, which simply means that I'm expressing a very simple function in a very complicated way. It's not the function that is hard. It's my description of the function. So the data changes the computational game. And in a complex theoretic jargon, we want to talk about this new class invented just relatively recently, which I'm going to call BPP slash SAM. So these are things that randomized classical computers can do, having access to samples from what the function does under some distribution. This here implies that I'm going to be interested only up to PAH criterion. It doesn't have to be always correct, just up to some distribution with high probability.  Even if I believe that BPP is not in BQP, well, I mean, for all I know, all of BQP can be in BPP slash SAM. And then we don't need quantum computers for anything except to generate data. That's what we learned at that point. So that's what we didn't know. And it gets very painful, because in very seemingly quintessential quantum tasks, like estimating ground states of a physical system, based on examples, under very, very mild conditions. I believe you may know this paper. It's quite famous. Very mild conditions, you can do that. You can even regress the whole shadows of the system and do whatever you want with the underlying system. So it seems like estimating ground properties, and note, estimating ground properties is not something quantum computers can do. Like if your gap is decreasing, in principle, you cannot do it. If you don't have a good initial state, it's the quintessential QMA hard problem, which is too hard for quantum computers in polynomial time. But then you give me data, and suddenly I can do it on a classical computer. That's how powerful data can be. So it's very surprising. Do we even need quantum computers? Asks Drake. But we do know we need quantum computers. And that's something that people tend to forget. It was actually proven in year 2000 by a Servadian-Gottler, and then revived again in 2020 by Leo Aranachalaman-Theme. And I'll show you the example, because it's also easy to explain and quite neat. So here's a problem. I take integers from 1 to p, where p is some large prime. And I'm going to label them blue and red. And how will I do it? I will put them on a circle. And I will draw a straight line through the middle. And one of the half planes is going to be red. The other one is going to be blue. And the half plane is fully specified by the integer that it goes through first. Is this clear? So I promise you this is an easy to learn problem. I don't know where the hyperplane goes, where the plane goes through. But if you give me a couple of examples, and I kind of take the best guess of where it should be, that's going to be a good answer. You can prove that. This is generalized as well. And I'm going to do a sneaky thing. I'm going to take these integers. And I'm going to apply modular exponentiation to them. So I'll take a generator of the multiple group relative to p. I will power the generator with x whatever x was. And now everything looks like a mess. I've effectively encrypted data. This function here is also related to how we generate random numbers. So now if I try to understand what does the labeling look like, it looks like a total mess. It's not separable by a hyperplane anymore. The points seem to be labeled randomly. So now can I learn this right inside problem? Well, if I could invert this function, it would be easy. I just take your data point, invert it back, and then apply the simple learning algorithm. I'm done. Quantum computer can do that. So the inverse of this function is the so-called discrete logarithm problem, which is in the second part of the source paper and factoring. It proves two things. One is factoring. The other one is a quantum algorithm for discrete log. The same quantum algorithm solves both problems. They turn out to be hidden Sago problems for the Abelian group. So a quantum computer can definitely solve this problem. Classical computer, well, you might be tempted to say, well, if it has to invert discrete log and we know discrete log is not classically easy, then it cannot. But that's not sound reasoning, because there might be another way to learn this function. Maybe there's a way of doing it without learning the problem. And that's the catch. Here, you can actually prove that if it could learn it, then it could also compute it. So learning is not easier than computing for this particular problem. And it heavily uses properties of the discrete logarithm. And the most important property for me right now is the following. For the discrete logarithm, so where data is x, comma, discrete logarithm of x, maybe the most significant bit thereof, I cannot compute f of x given x. But I can generate pairs efficiently. That's a tricky thing. So let me show you how this works. I can first pick a y into the core domain of the discrete log. And the discrete log is bijective. So I pick a y, then I compute the corresponding x by doing modular exponentiation. I'm sorry, this thing is a little bit iffy. And then I just relabel things. I choose y, then I compute a to the y. This is easy. And then this is equal to x, comma, the discrete log of x. Moreover, since the function is bijective, if I chose y uniform at random, this x is also chosen uniformly at random. If you apply a bijection to uniform random distribution, you get a uniform random distribution. So now I have a valid pair. I don't get to choose what my x is that's random for me, but I know it's a valid pair. So now imagine there was a learning algorithm. Well, then I can just put a preamble, generate data, learn the data, compute the function. And this entire box now has no data. The data is internally generating the algorithm. And that's a whole trick. There's a bunch of other properties that you use that show that even if you can solve it for a fraction, it's also hard that even a single bit is hard. And you end up with sort of resolution of all three problems. The data gap disappears because I can generate data at random. Quantum, I can do it because short can factor. So we can solve the discrete logarithm in this case. And heuristic is also hard because DLP has random self-reducibility, attractive mathematical properties, which make it a very good cryptographic function as well. That's the key, right? With proven, data cannot help because I can make it. If I can make it, it cannot help me compute. And that was a big thing. It's a learning separation, assuming the discrete logarithm is not in P. And there was a bunch of works that did the same thing for generative modeling, for reinforcement learning, for whatever you wish. And it's a good technique. You apply the same trick all over and over again. Data does not help because we can generate. And I'm not happy. I'm very, I'm a sad bunny and I'm not happy and this is not what I wanted. And there are two reasons why this is not what I wanted. They're here. I will briefly tell you about why this is unsatisfactory from the perspective of what is a learning separation. But I will focus more on the other problem that quantum data is not generatable. There's no reason to believe that I can randomly generate pairs x, some quantum function of x. In fact, I don't want to promise, but I think next week we're gonna have a proof that this is hard, that you cannot do that. Which sadly means that none of these proof techniques can apply. They're just a non-starter to try to prove a learning separation this way. But let me first tell you about this learning separation business. The catch is there are many, many learning types. Learning is a much more fidgety, subtle thing that I led you to believe. And the subtlety here that I want to highlight is that in our proof, I assume that learning will imply that I can label a new point efficiently. I could have asked a slightly different question. What if you simply told me which concept labeled the data? So I'm not asking you to label a new point, just tell me which one generated it. It's a slightly different question, but for the second one, we have no proof because I do not require you to be able to evaluate it. You might say, well, who cares? I guess people who thought about back learning define it thusly for a given good reason. I would say that's not a good answer because this learning meaning identifying the labeling function rather than evaluating has important applications. That's exactly what learning order parameters is because nobody expects you to be able to find ground states and complete expectation values. If you do Hamiltonian learning, learning parameters of Hamiltonian, I'm not expecting the model to be able to prepare whatever data you use to learn it, which is often properties of the ground state because ground states are QMA hard. But I still know the generator of the physics, right? So that's a very useful thing and there's nothing I can say about that or so it seems. Plus there's a conceptual unsatisfying consequence of this evaluate is that you can construct learning separations where the concept class has only one function inside. So you know exactly the function you're learning. There's only one, yet you cannot learn it according to the definition because you cannot label a new point. A quantum learner can learn it without access to data because there's only one function. You know exactly which one it is. So you might be unhappy with this. I mean, is this even learning? I don't know. I agree, this is not very cool. So we analyze this pretty much ad nauseam in a paper. I will not bore you with that, but just to point out that there are examples where we can prove that identifying the concept is a hard thing. The concepts are all easy, but you cannot figure out which one it is except if you use a quantum computer. So you can have learning separations of all sorts and types. But I wanna focus on this thing here over the remaining 15 minutes or so. Data is not generalatable, so I'm very, very sad because I cannot use these proofs. But I still want to claim this. I want to claim, nah, I'm not giving up. I'm still certain that at least in some cases no classical algorithm can evaluate the function even given access to data. And I will remind you what was the catch. In the proofs we use so far, we were using functions which are both quantum evaluatable, so in BQP, and also random-generatable. That is, I could generate pairs, random pairs of data points, and I needed this property to be able to prove that having data doesn't help, right? So this is the space we were considering before. For those who like history, the correct term for these functions was introduced in the context of cryptography that were called random verifiable. But I think for our purposes, random-generatable is more informative. So this is what we had. And our problem was that we don't know where BVP-slash-Samp is. If it swallows whole of BQP, we're in trouble, right? But then came a way to handle this thing. And I will have to introduce very briefly a new class called P-slash-Poly. So this is a class of so-called non-uniform circuits. It's also known as a class of things that classical computer can solve in polynomial time given an advice string, which depends only on the size of the instance. So let me explain. Suppose you're looking for, I don't know, this is not in P-slash-Poly, what I'm gonna say, but suppose you're asked to solve factoring, and I give you an N-bit number, and you're given additionally a string, which is the advice string, giving you the best possible advice how to factor N-bit numbers. It doesn't tell you how to factor the particular N-bit number you're given, but it's supposed to help you factor all N-bit numbers. Okay, I mean, otherwise it would be trivial, but still the advice is only allowed to depend on the size of the problem. This class is kind of a funky class. It's non-uniform. It can solve certain uncomputable problems because advice doesn't have to be computable. But the catch is, we know two things. Juan Getal proved that BPP-slash-SAMP is in that class. One, two, we know stuff about it. We know by Adelman's theorem, for instance, that it contains BPP. Even though there's no BPP here, by the way, I know that it's just P, not BPP. Second, we know that it's unlikely that it contains NP. There's something called Carpliptin theorem, which tells you that if P-slash-Poly contained NP, then the polynomial hierarchy would collapse to the third level and people say that's not gonna happen. And I said I believe in the diagrams, right? So P-slash-Poly does not contain NP. So I know things about it, right? We then later generalized and proved that also certain inclusions hold for the heuristic classes, which are the ones which are actually relevant for learning. So this brings us to our first lemma. If BQP-complete problems, so these are the ones which are the hardest that quantum computers can solve, if they don't have polynomial-sized circuits, in other words, if they're not in P-slash-Poly, then BQP-complete problems cannot be learned according to the standard definitions, regardless of data. And it's not about data being generated, it's about classical polynomial-sized Boolean circuits which represent neural networks, for instance, are not expressive enough to capture what quantum functions can explore. So it's simply not in your set. You cannot output a function, you cannot output a polynomial description or a classically-evaluatable function because it doesn't exist. Hence, data cannot help you. So this is quite important.  I'm not boring on this, I want to skip to something else. What I want to skip to is sort of the corollary of everything that all BQP-hard problems, including QMA problems, define at least one learning task where a quantum computer, where a classic computer cannot learn it. Okay? You can ask me whether a quantum computer can learn it, I will show you that we know how to do that as well. But before going there, I think I want to tell you something about this Wang et al paper. One of the consequences of this thing that we kind of worked out in detail is if you look at these seemingly mild conditions, they mean something like constant gap and smoothness, we've shown that if you relax any of these, then you get a contradiction with complexity theory. So these mild conditions are tight. You will not be able to learn it classically without causing an uproar in complexity theory. Can a quantum computer learn it? Can a quantum computer learn it? Yeah, we can construct concept classes that it can. For instance, any concept collapse, which is polynomial size. If it's polynomial size, it can brute force check every single one of them, and you might not like it, but it ticks the box of there exists a thing, right? We can do a little bit better than that. In another paper, we've actually looked into more physically relevant cases, and we've proven learning separations for learning quantum observables. So this is the model that I want to study. Let me describe what I said. So this is how the data is gonna be generated, by the way. So there's a fixed input state, and then happens a complicated physical process that I don't control. It's not controllable. I don't get to choose what X is, but I get to find out. So it's heralded. I don't have good examples from the lab. Maybe you can help me with that. I can imagine that things like this, for instance, happen in high-energy physics, right? Where you don't know what the initial state was. You get measurements at the end, but then some side measurements tell you something about what the initial state was. So you know the initial state after the fact, but you could not have controlled it, and you find out something about the end. So there's this process that I don't fully control. I find out which one happened after the fact. There's some quantum state, and then I have a measurement. And this measurement, you can think of it as an expectation value of a K local Hamiltonian. That's a good starting point. So this M is some kind of a parameterization of a K local Hamiltonian. And the problem that I'm asked to solve, the concept class is exactly this. So each concept is labeled by a measurement. So that's the thing that I'm gonna be learning. I don't know which measurement happened, but I'm supposed to determine this based on data where it tells me which complicated quantum process happened, which state was generated implicitly, and what the measurement quantity was at the end. So that's my data. And you wanna show that it's not classically learnable, but it is quantum learnable. And you can make it such. So if this process is hard enough, then it can also be BQP complete. And if it's B, so these are things like time evolutions of certain Hamiltonians. So you can imagine this U of X simply tells you what X is the parameters of the Hamiltonian that actually got time evolved, and you later find out which one it was. It could be a ground state problem. It could be the coupling coefficients of a Hamiltonian, but you don't know which one, but you find out later somehow. So this is a good thing. So if it's a hard enough Hamiltonian, that's what I need. Then you can prove that this function here for very simple measurements here already cannot be classically learnable because it's not in herpes slash poly. There exists no classical polynomial size circuits that can evaluate it. Okay, that's the entire complicated, well, complicated tedious theory that we worked on before. What is more interesting here is how do you learn these coefficients of the Hamiltonian? Well, what a quantum computer can do is for every data point that it gets, like so everything is known in the setup, so it gets a data point. Oopsie, this is the wrong button. For every data point that it gets, it also has a label, but it can also compute the label for that data point for any other parameter setting, for any, sorry, not parameter setting, for any K local poly string. Because U is known, I know what U is, so if I know what X is, I can, on a quantum computer, prepare the quantum state psi of X, and I can measure expectation values of poly strings, all of them. There's only polynomially many of them, only. I can measure all of them, and if I do that, I end up with a system of linear equations, the solution of which tells me which linear combination actually happened in the actual measurement. So I get a linear system. It's a little bit more complicated than that because I'm assuming that the measurements are noisy, they have at least short noise, the system can be over determined, and it can even be unsolvable, but it can still prove that if you use a particular reading of the Lasso regression algorithm, it will actually converge to provably good solution. Provably good in a sense, I will not tell you maybe necessarily what theta is, but the theta that I find is gonna perform well. It's gonna label the thing the same way theta, the correct theta would have. Which is the definition of learning, right? I don't need to find which theta it was, I just need to get something which is gonna do the job, right? That's what the evaluate definition is. So this is a learning problem, so what am I learning? Which measurement happened to complicated quantum state? Measurement being, okay, local, only observable. We can generalize this actually quite a bit, and this is, you can think of it as a meta theorem if you wish. So I'm certain many of you have seen these recent results again by Huang, Kung, and Presk, Lidal, where they're learning unitaries. Like there's an unknown unitary, you get to choose your initial states and they end up being sometimes very simple, like single qubit stabilizes states, plus minus zero one and plus I minus I, you shove it into the unitary. You measure essentially shadows, like in shadow tomography at the end of it, and there's a learning algorithm which reconstructs what you has to be. And it is universal, it always works, and it's quite a shocking thing to realize that those things they can learn in the quantum case, the analogs classically are completely unlearnable. Like I can learn arbitrary shallow unitaries, but if I just want to consider classical Boolean circuits, these are not learnable when the data is classical, when the input is classical, bit strings to bit strings. So there's an interesting mismatch that I don't fully understand, but there are many of these algorithms which learn unitaries, right? So for a particular set of unitaries, there's a setting where you prepare some initial states, you measure something at the end and you figure out what the unitary was. So give me any such algorithm, and I will construct for you a learning problem where the data is classical, the label is classical, and there's a provable learning separation. So it's a meta statement. For every coherent learning algorithm of unitaries, there exists a learning problem with classical data and classical outputs. And the construction is not super complicated. I mean, essentially what it does is it has a part which is going to do something which is computationally hard. Then there's going to be a part which is going to be simulating the preparation of arbitrary, ridiculously slow, arbitrary probe states. There's a part here that's going to effectively learn the unitary from classical outcomes, because ultimately, yes, it's an algorithm that they have where you put in quantum states read all the classical things, but I know which quantum states, I have the classical description thereof, and the outcomes are quantum measurements, but they're classical outcomes, so I have classical information. Ultimately, this is the only thing we work with, right? We don't really deal with quantum states, we deal with their descriptions. So this I can embed in here and get a learning separation. So now, just to summarize, at this point, where we were and where we are now, and this is like a two-year research program that was happening, we were in a situation we had zero evidence that there's a learning separation for any quantum mechanical problem. The only separations we had were for factoring things like this, critically using mathematical properties that we know don't hold for quantum systems, for quantum functions. So this we overcame by realizing that stronger assumptions of complexity theory can actually be used, like this idea of using p slash poly, as the thing we believe quantum computing is not in. Then we looked at the types of separations we get and we asked, okay, but when can a quantum computer actually learn something interesting which satisfies these conditions? And we had the abstract statement, now we had these examples, which end up being examples about learning of observables in very general settings. They're very general settings where learning observables is classically intractable, you can do it quantumly. And I think I have a table here, which this is a paper that is not yet out, where we kind of grouped everything that we know so far. So for time evolution problems, there is a learning separation, ground separation, yes. If I flip around with the label of the concept and input is, it turns out that's classically easy. You can learn it, so you don't need a quantum computer. If observables are parameterized by unitaries, then there are learning separations for learning observable. No learning separations for Hamiltonian learning because we have an algorithm for Hamiltonian learning. And for the problem of identifying the unitary which did it, we don't know. This is open, whether identification is hard or not. Yeah, so that's pretty much all we know. And now I have maybe one or two more minutes just for the, perhaps the most important slide in the case you don't already know these things, is I never told you which Hamiltonians, right? So which are these Hamiltonians that you have learning separations for? And it turns out there is many of them. So specifically, to just give you some examples, for the Bose-Harburn model, it was proven that the time evolution is BQP complete. That's a result of child's and his collaborators from 2007 or so. XY Hamiltonian on graphs, ground state problems are BQP hard. They can be QMA complete. Fermi-Harburn model and to the left is the same thing. The electronic structure problem, this is quantum chemistry business, for fixed basis also turns out to be QMA hard. In high energy physics, anything to do with top, well, many things to do with topological quantum field theories. So that's thanks to, you know, Witten and Kitayev who invented topological quantum computing model. And who thought about how hard it is to compute invariance of knots like the Jones polynomial. Then one plus one massive five four theories, that's Preskelin and Jordan and others, turns out to be BQP complete. This is computing scattering amplitudes of that model. Certain quaggot's asking theories, I'm not sure, but I think they're hard as well. And it turns out certain supersymmetric theories, certainly supersymmetric quantum mechanical theories turn out to be QMA one hard. So there as well you can find learning problems that you cannot learn with a classic computer, but you can with a quantum. They're not all of them, not everything you might want to learn is necessarily hard. But what I'm claiming is that you gave me a favorite Hamiltonian family, I'll devise for you a family of learning problems where you need a quantum computer. Yeah, the key catch was we changed the complexity theoretic assumption that we believe into something slightly stronger, but still reasonable. I will skip this consequence on NISC. You can ask me about this if you care. So I think at the end of the day, I'm now more than ever convinced that quantum machine learning should be working with quantum data and that's the main thing we should be focusing on. I want to thank Kasperi Kader-Machtab that we derived these results with. And we have openings, specifically on this topic at Pozo and PhD level. So thank you. Thank you for this amazing talk. Very interesting. I have a question about your measurements, which you were also mentioning as classical data, or saying like classical data. Does this, would this also include more generalized measurements, like say in a large tidbit space like POVMs, or could they somewhat change the game? I don't see how they would change the game. In none of these things, none of the separations rely on a quantum computer having access to measurements that a classic computer could not simulate. It relies on classic computers not being able to evaluate time evolution of quantum systems.  Okay, okay, so it's like not about say, this like quantum data for you is like, maybe it's also a question like, what would be an actual quantum data for you? So like, it would be more the state itself? Yes, there's a lot of work in there where the input is a labeled quantum data, right? There's a quantum, there's a psi or rho, whatever you wish, comma, some label, and now you can ask, okay, can a quantum algorithm learn some property whatever generated the quantum state, or rather the correlation between the quantum state and data, you could be learning observables again, for instance, but the catch is I mean, it is ill-defined for a classical algorithm, right? I mean, what does it mean to fit a quantum state into a classical, I need to invent an interface at which point, at that point, I've limited the classical computer, right? So if you do that, you can do much more.  Any more questions? Yeah, thank you for the very nice talk. I've got just one question regarding the Hamiltonian learning, because when you say regarding quantum chemistry, that's something that I have a hard time imagining, what do you mean by learning that Hamiltonian? I didn't say, it's okay, so this was not about Hamiltonian learning problem per se, this was referring to the fact that here, I said things like the experiment involves something to do with a hard Hamiltonian, I'm not doing the learning of the Hamiltonian, it could be specifying the experiment itself, and I didn't tell you what it means to be a hard Hamiltonian, right? And there are various flavors to this, but some of them are for certain Hamiltonian families, you can show that computing certain things they can do is hard, like computing time evolution of a complicated enough Hamiltonian, again, what do I mean by computing time? I tell you the Hamiltonian, tell you the input state is all zero, and tell you compute for me the expectation value of the poly observable in the first qubit. That thing is hard if your Hamiltonian is the Bose-Habbert Hamiltonian, generically. Similarly, for these other fermionic Hamiltonians, computing properties of ground states is gonna be hard for a classical computer. I tell you the Hamiltonian, I ask, okay, what is the ground state energy, for instance? The ground state energy in particular is gonna be QMA hard. So this is what I mean by hard Hamiltonian, it's something about it is hard to compute. Yeah, not about learning, learning it is always easy. We always know how to do that. Yeah, thanks for the inspiring talk. So about this quantum data, and so you're looking at classical algorithms, and do you have an intuition kind of what would change if I have now a quantum data, quantum, say, prepare Bose-Habbert in cold atoms, and either I take my measurements and put them into a classical algorithm, or I do kind of controlled rotations on my state, manipulate them as a quantum algorithm? Do you think that would be potentially more powerful, or can you say how this compares? We have a paper called Limitations of Measure First Protocols, which gives us a proof that there are things you cannot do without fully quantum machine learning. So there cannot exist a universal measurement protocol, which is independent from the concept, but specific to the concept class, which is such that you do this measurement on your data, and then classically post-process it, even without computational assumptions. Even if this classical processing was exponential time, you still lose too much information with the active measurement. So we have a paper out on it proving the separation. It goes back to a certain communication complexity lower bounds. You cannot communicate quantum state in a polynomial amount of information. We can talk about it. It's a very interesting question. In that case, let's thank the speaker again.


Hi everybody and welcome to today's Barn's Takeout. My name's Amy Gillette. I'm a collections researcher. Today we're going into room number three, a corner room on the first floor. To look at this little painting, originally a piece of a larger altarpiece entitled The Meeting of St. Joachim and Anna at the Golden Gate in Jerusalem. It was painted in the early 1500s by a German artist, an important German artist named Hans von Kulmach, who was a prominent student of the super famous Albrecht Dürer along with actually the artist of this Madonna and child over here, a person called Hans Baldum Green. And before launching into a deeper discussion of an individual painting, I do like to think about how it fits visually and conceptually into its ensemble. Albert Barn's is named for the way that he arranged the paintings and other objects within any given room or wall. And formally, I think for me the first thing that kind of jumps out to my mind is the series of arches that we can see from the desk down here, up to the arch in the Golden Gate in our own picture. Perhaps we even see it in the sort of bouffant of this lady, the fabulous lady right up here. And then repeated in this wonderful lock made in France by Gustave Marot. And I want to dwell for just a second on this, because the lock features salamanders that are breathing flames surrounded by flames crowned by flames up here. And that's because people used to believe that salamanders were fireproof and therefore impervious to like the burn of temptation. And this sort of narrative of virtue of right being in the world is something that I think emerges in many of these paintings, whether or not it connects to the supernatural as in ours, or certain perhaps ideals of femininity that we might see in this Renoir picture of embroiderers here or in this lady up here. So I'd like to think about this theme of, I suppose, virtue and redemption. So let's go a little bit closer at our picture. So again, saints to Amna Joisin and Anna meeting at the Golden Gate in Jerusalem. So who are they? These are actually the parents of the Virgin Mary and in the Christian tradition. And the scene itself is based on a book called The Proto-Vingelian of James. It's not a canonical gospel now. It was actually written in Greek in probably the middle of the second century CE as a way of filling out the story of the Virgin Mary that the canonical gospels touched on only pretty quickly and loosely, I suppose, because theologically to flesh out who Mary was was another way of, I think, quite literally fleshing out who Christ was and how his divine and human natures may have related to each other. And so in the story of the Proto-Vingelian of James, it opens with a joy team trying to make an offering to the temple. He's rejected because he doesn't have any children yet. And so he strikes out into the desert for 40 days of prayer and fasting. Meanwhile, his wife, Anna, and I think we should know that at this point, the two of them are beyond natural childbearing age, is in her garden awaiting the return of her husband praying by a laurel tree, which is a conventional symbol of a victory and ended up in the Christian belief symbolizing the ultimate triumph over death that Christ introduced. So she's praying beneath this tree for a child and says that whatever it is, a girl or a boy, if I do have a child, then I'll consecrate her or him to the temple. And so an angel comes, makes the announcement that she will have a baby and her husband gets the same news. And so the moment that we see is when he is rushing in from the desert, she goes to the edge of the city walls, they meet and embrace in this, I think, lovely and a very human moment of excitement, of tenderness about this miraculous expectation of a child called the Immaculate Conception. And I'm going to move now to another picture. Looking at this right hand panel, you probably are actually able to tell why that this is the same artist. And it was, as a matter of fact, very common for artists to replicate certain scenes by the use of drawings, for example. So here's another image of the visitation. And we get to see over here in the left hand valve of this triptych, now we've got St. St. St. Washington and Anna having consecrated the Virgin Mary to the Temple of Jerusalem when she's a little girl. And so it's filling out more of the narrative for us and perhaps the piece that we have at the barns would have originally belonged to some sort of ensemble like this. And I should note too that this whole thing is most likely a 19th century confection. Normally, the earlier scene would be to the left and later one to the right, so we could read it like a book. But I like this because we do get to see the Immaculate Conception, its Consequence of Consecrating the Child. And this is where the Virgin Mary stayed until she was 12 years old and got married to Joseph. And many of us know what the Gospel say happened after that where she gave birth to Christ. And we can see the Virgin Mary now crowned Queen of Heaven up here for his ultimate sacrifice on the cross as a way of making human salvation and participation in Heaven possible, again, according to belief. And so here's Christ on the cross with the other members of the trinity. We get to see his human incarnation down here. And here he is amidst the company of a whole bunch of other saints, many of them with martyrs with the emblems by which they were put to death as witnesses to him. And then one more thing that I think I'd like to look at is this piece that we have also at the Barnes Foundation. This one you're going to find in the next room on the meeting at the Golden Gate. And it's the presentation now of Christ in the temple. So there he is as a little baby being presented here to the priest. Here's a prophetess that had recognized him as being divine. We have his mother now, the Virgin Mary, echoing the composition of her own parents in the past one accompanied by his adoptive father, Joseph, who's bringing an offering of turtle dubs in a basket. This is something from the Gospel of Luke where if you were relatively poor and they were as a family of carpenters, you'd bring turtle dubs. And then I think this marvelous detail of this angel, probably great Gabriel, embracing the Virgin Mary as I think a kind of witness to the miraculous nature of her pregnancy, plus the doctrine that when the bread and wine of mass Christ's body is sacrificed on the altar, the angels are actually present. And we're supposed to make that liturgical connection because of not just because of the altar, but because the prophetess here is holding this big candle taper. And this is the presentation of Christ is an event, a liturgical event known as candle mess. And so with these images that we've been looking at, they offer us kind of the best of late medieval art to my mind where they're incredibly instructive in terms of theology. But in order for a belief to be effective, people believed that you had to feel right feelings too. And I think that's where the humanity of these images comes in. So that's it for today's takeout. And thank you so much for listening.


One way to do vegetables is to roast them, and it's so easy. You just basically preheat your oven. You cut up some vegetables and toss them with a little bit of olive oil and salt and pepper, and then you bake them. It's almost better than steaming them sometimes because all the sugar in the vegetables kind of condenses, so they get a more intense flavor. You can add some asparagus, and these guys don't need to be cut too small because they kind of cook a little bit faster than the carrots. Potatoes I'm going to do separately because they're the slowest ones, and you can even roast cauliflower. Cauliflower can get a little bit watery if you over steam it, so sometimes roasting it is a nice way of doing it. And then I'm just going to separate them into small little trees like this that the children can pick up with their hands. And now we're going to just take some olive oil and drizzle it all over these veggies. Some salt, pepper, and you can even put a squeeze of lemon. We're going to toss this up just to make sure that all the vegetables get coated in the olive oil. It's ready to go in the oven at about 350 degrees until it's cooked. So with potatoes, they cook a lot slower than vegetables like carrots or cauliflower, so you have to put them in a separate bowl. And basically, if you want them to cook faster, cut them into smaller cubes. If you have a bit of time, then you can cut them into wedges or bigger chunks. And I like to add a little bit of rosemary, which smells so nice and just makes me feel like I'm somewhere in Greece or the Mediterranean. And then I'm just going to basically take some of these little green leaves and pull them off and drop them in here. And they'll basically kind of infuse the whole dish of potatoes with a nice rosemary flavor. You could use dried rosemary if you don't have fresh rosemary. You could leave the rosemary out and it would be good or you could just use black pepper. I've lined this pan with foil just so that it's easier to clean afterwards. Give them a shake and that's going to go in the oven.


Good evening, judges. Do you know how hard it is to get a phone in Ghana? I've decided we'll pledge $2,000. This is just the beginning for every single company. The time that it takes us to complete this five-minute pitch, three children will have died due to water-related disease. I'm pretty blown away by that.  I'm in for five grand or whatever it is. My name is Carly Byer and this is Shannon Faye and a lot of low-cast, and we are Soccer Girl Problems. I would like to ask $26,000 for a 15% stake in my company. I have to tell you the support team over here was loud and... Thank you, guys. Yeah, I'd kick in $1,000 for that. I'll put $5,000 towards that. Yeah, I'll kick in $1,000. I'm not going to be the only guy. I'm not going to be the only one not doing it. It's been a great experience to be part of the start-up competition. I want to thank everyone that came out today. I want to clap right away if you all be impressed. I agree. It's a social media and scheduling platform for millennials. If you make those numbers, I will take you public. We see great potential in this team as well as all the other teams tonight. Good evening. My name is Kyle King. I'm the co-founder and CEO of Blink. Beautiful banking built for families. The winner of $1,000 is D-Tempest 1. This now concludes our sixth annual start-up competition. Thank you very much for coming.


Hello everyone welcome to another NARC survivor live video and in this one we're gonna be talking about What happens when you ignore the narcissist and of course I should say it's not like You're being mean and you want to ignore them to get back at them For all of the things they did to you all of the abuse that you endured I mean of course as empaths we're not like that For us it's more We end up wanting to ignore them Because of all of the abuse And we just don't want to be harmed anymore It's not that You're trying to punish them or get revenge Although saying that that's exactly what they do to you Because as we know One of the behaviors that narcissists like to do is the silent treatment Which is where they're sulking Because they couldn't get that supply of you So then they become passive aggressive And yes the silent treatment is a form of passive aggression as well But really you're lucky if you even get that Because most of the time they're always on you they're always on your case They don't even have to Love bomb you for you to feel better again Once you've endured so much abuse And then you just have some time away from them when they're giving you the silent treatment It's like for the first time in a long time. You can suddenly Start to breathe Because just their presence around you is keeping you down. It's keeping you miserable Because they're miserable And that's where they come around you in the first place because misery loves company But yeah, just that moment you get when they give you the silent treatment I'm sure many of you can relate It's an incredible feeling But some of you may mistake it as though them or If they do return to the love bombing you can quite easily fooled Into thinking that they've changed into thinking that they're good people Into thinking that maybe they're not an asser says that to roll When in actuality you're just having that break from the abuse So of course you're gonna feel better in that moment. It doesn't mean that it's real Just give it a time and they will switch back before you even know it Because that's who they really are. That's their true character It's just they watch you and how you interact with other people And they pick up on that they reflect your qualities back to you because of course They know you're gonna be receptive to that if that's what you're putting out It doesn't mean that they're about that So, yeah, they will give you the silent treatment as well But when they do that that's COVID passive aggression They're trying to punish you they're trying to get revenge I mean everything they do is an act of punishment or manipulation and control That is really all that they can do as I said before the best you'll ever get for me and our cyst is an illusion They cannot be real. They cannot be vulnerable They can't do like I'm doing right now giving you this information Expressing my emotions. They can't do that All they can ever give to you is manipulation and illusion of a sad a false character They cannot be real Of course at some point you begin to figure that out You begin to realize that yes, it is all fake. It's all of a sad So of course you assume the only thing you can do is ignore them I mean, that's the healthiest option The best decision that you can make in that type of environment The problem is that when you do that You are starving the narcissist of their supply and of course that can cause a big problem There are some narcissists player narcissists If they have a lot of options Especially options where they deem to be more attractive or more wealthier or whatever it is But they think in their minds it doesn't mean that it's actually reality They think that it's better for whatever reason They're not going to be too concerned about you ignoring them Because they're going to look at it like Who cares about you? I can find some analysis like you just around the corner Just around the corner Because they probably had so many experiences in the past So it's nothing for them to just forget about you and find someone else They're not going to lose any sleep over that Because they've already had so many experiences in the past So you're not going to be that significant to them If anything it will be more significant for you in doing that Than it having any significant impact on them Regardless Ignoring them is still the best option But that's how it is for the play a type of narcissist the ones who do have a lot of options As for the ones who do not have many options and this will probably be the one that most of you are dealing with Because let's be real most people they don't have tons of options today I mean they might But not many options who are all attractive and all Having everything that they want as it may be the case for the one percent of narcissists who do So for the one that most of you will be dealing with That type of narcissists of course if you're like their only source of supply They've got no other Source outside of you Like that's it.  Of course They're gonna feel rejected They're gonna see it as an attack They're gonna see it You are taking Something away from them You're taking that supply Even though yes, you may be the source of it. They don't look at it like that They view people as mirrors or they're concerned about it's a reflection. They're getting back from you Of how they see and feel about themselves It has nothing to do with you at all. They're all they're not concerned about the actual mirror Which is you all they're concerned about is the reflection they're getting back So they're not concerned about you at all. They're just noticing that they're no longer get this reflection that they would like Whether it's reflection of Beauty Desire and attractiveness Well, it may be a reflection of power Importance Whatever it is You're giving that to the narcissist and they're eating that up they're participating in it.  They'll discard you first In the hopes that it will leave you chasing after them So then they can achieve this position of significance and relevance This is what you have to understand with narcissists It's never about you. It's always about them. It doesn't matter what they do And even just not only narcissists This is the case for the majority of people in this world Most people do not care about you and I'm sure many of you will have already realized that By this point in life Most people are only concerned about themselves their own emotions their own needs And even when they come out around you And it looks like they care about you They don't Even then they're trying to meet their needs and regulate their emotions through you That is just the reality of it for many of us. It takes us a long time to figure that out Because it's like as soon as you pull away Here they come back again because They sense that your energy is slipping away and that is what they want Most people just want your energy. They don't really care about you And I'm sorry to say that but it's true And you've only got to look at it Why does my channel have over one hundred and seventy thousand subscribers? And over 40 million views and it's far from one one of the biggest channels on this topic This channels on this topic with millions of subscribers and if you put them all together combined We may be talking hundreds of millions of views around the world people care about you They really have an interest in your feelings and situation these videos wouldn't be so popular People would have friends families that they can talk to that would understand that would listen to them But quite clearly they don't and this is how you should know with most people in this world and From statistics it says only one to two percent of the world Our empaths who actually have the ability to share your feelings and experience and feel what you feel And have the ability to connect to you on a deep emotional level With that in mind most people they're not going to care about you in that way They're not going to be concerned about you at all They're not going to feel what you feel They're not going to care about what you're going through And that's just how it is So this will especially be the case with narcissists people with narcissistic personality disorder makeup up to 15% of the world's population Of course aside from that There is also Covert narcissism which isn't included in NPD And then there's people with narcissistic traits this borderline There's sociopathy psychopathy this histrionic bipolar These are just some of the cluster B's of course. There's the cluster A's cluster C's And there's many other personality disorders mental illnesses as well And you've got to think with all of these people with all of these problems all of these emotional issues all of this trauma You really think they've got the capacity to understand or care about you The reality is that they have to accept But luckily for us because of technology we Do have access To the very few of the empaths around the world And as you may know, yes, I do identify as an empath myself And I guess that is my motivation for making these videos every day And I've also Seen other channels on YouTube But most definitely There are other empaths on YouTube as well. I'm sure many of you you may be subscribed to Some empaths who speak about this on YouTube as well One of my favorites has to be Dr. Ramanee. I Do love her videos But I also watch many others as well at empaths typically they will be smeared, gangstalked, bullied, harassed Pushed the suicides Until they're locked up in a mental institution or in jail And that's just how it is. That's what happens to us the people who actually care We're always alone. We don't really have any friends We don't really have anyone who we can talk to And that is why there's hundreds of millions of views on Content with this topic That's the reason for that And of course when you realize that it makes perfect sense Helps you to understand why You feel like no one understands you no one cares no one listens And especially with narcissists They're self-absorbed and they lack empathy All they're ever going to do is exploit you for their own benefit and gain They're never going to do anything out there. Goodness of the heart for you.  They're not even thinking about that They don't focus on the abuse they focus on your reaction to the abuse and how they can Get you to change So that you keep giving them supply tell yourself this Every time they're trying to elicit a reaction out of you Ask yourself, what are they trying to do? What do they want from me? Of course, the only possible answer is that they want you to react Because they're not concerned about your feelings or needs all they care about is your emotional reactions And you will notice that straight away as soon as you stop reacting as soon as you ignore them As soon as you do that they will come down on you like a ton of bricks But really what's worse them doing that? What if they return to the love bombing because if you if they do that it may feel good for a moment?  They became kind. It's almost like they were empathetic Because they've observed you or someone else They know how to fake empathy Yes, believe it or not Narcissists are actually masters at faking empathy And why? Because they know that that is the one thing that they are missing To secure someone as their source of supply So of course, yes, they're going to focus heavily on that Just because they're able to mimic empathy that Don't mean that they care you've got to stop falling for that Yes, they will bring back the false character. Yes, they will try to love bomb you again Just give it time time reveals all they cannot sustain it They will refer back to their true character And their true character is miserable traumatized abusive manipulative Deceptive exploitative all of these things And you've got to look at it like how many times you have to go through this until you finally understand Sometimes have you been abused exploited by this narcissist? It's a clear pattern of exploitative behavior. So of course, yes, when you ignore them and they come back No doubt it's going to be the same thing again. They are never going to change It's never going to be any different Even when it looks like it is it is not It doesn't matter what they do. It doesn't matter if they cry beg scream. It doesn't matter if they get down on their knees It is still fake It's still fake And many of you if you have family members when our cystic You should be aware of that by now. I Mean those of you who are watching you may be in your 20s 30s 40s 50s You've lived an entire lifetime With these narcissistic family members, you've seen how they go back and forth the love bomb devalue discards Hoover Love bomb again How many more times you have to go through the cycle until you finally understand They are never going to change. They're never gonna be any different The only ones who can change be greater are us empaths Most narcissists are not going to change And if you want to know if they are changing In the process of changing just look back At least up the last few months, but preferably at the last few years of their behavior their decisions and You will see Clear progress If that is the case if they are actually changing for real if all you're seeing is Concert ups and downs That is a clear sign that it is fake because otherwise You would notice steady progress Yes, you would see that But they just go up and down they just appear to change and then they change straight back Because they constantly revert back to who they actually are their true character Yes, that's what they really like and of course, that's why When you're finally fed up When you finally have enough you can't take it anymore.  They're not gonna care. They're not gonna understand you They're not gonna be there for you. They're not gonna try to make it better Know what happens?  I mean someone who's empathetic If you ignore them They're going to want to know what is wrong They're going to listen to you. They're going to want to know what happens Why are you hurt? Why are you upset? What are you going through? But when you ignore that arses, do they care about what you're going through? No They do not care and that's how you know what you're dealing with Because an empathetic person they are going to care. They're gonna want to know Yeah, sometimes they'll just manipulate you again. They'll come back with a loved one.  All you do every day is attend to other people Most of all you attend to the narcissist And that is the last person you should be attending to Because they will never care about you But yeah, this is just the world we live in today We live in a narcissistic society And then you start to doubt that Take a look on TikTok, Instagram YouTube Take a look at that Let that remind you That you're not alone But also remind yourself that Although yes, these days we are very rare As empaths we do still exist And we are targeted every day We are abused, we are harassed People want to destroy us They want to ruin our lives Because most people are not like us If they were like us everything would be fine There would be no problem But the reality is that they do envy our empathy They hate our empathy And even Dr. Ramanee The clinical psychologist And professor at UCLA Who's done interviews with Kendall Jenner She's got over 2 million subscribers on YouTube Yes, even Dr. Ramanee she said that in one of her videos She's done a video with that title I'm a narcissist, hate and envy our empathy That's why we're so rare But we do exist And I'm fighting every day To hold on To this beautiful gift, this ability That God has given me Because I know that I have the power to heal I know that just through this video, this message I'm sending you love Cause the vibes Light Yes, I do know that And that is what I intend to do in all of my videos Because I want to improve people's lives I want to heal people And although yes This video, other videos as well It may sound negative Even pessimistic But that is actually high vibe as well Because that's acceptance Or accepting the truth, reality And in actuality Positivity Can be toxic sometimes We need to accept the truth Of what we are actually dealing with But I can tell you that when you do meet an empath That Is an incredible experience When someone looks into your eyes And it's like for the first moment in your life Yeah Someone actually sees you Someone actually knows that you're there Someone actually cares about you Someone actually has your best interest in mind Someone is able to reciprocate what you're giving to them Someone is actually there Someone hears you, they listen to you They understand you They see you And when you're around someone like that It's powerful And powerful It's highly addictive And I guess that's why so many people watch my videos So many people return to them So many people, my day ones I've been watching my videos for For five and a half years now And I myself, I watch YouTubers that I like That I've been watching for many years Because it's so rare to feel like someone actually Is there And they understand Even if it is Through your phone or your computer I mean you go out throughout the day And you interact with people You get back home But maybe you're watching these videos at work On your phone, on your computer Wherever it may be And it's like, shit This is actually more real than anything in real life And I know many of you can relate to that It's like this is a deeper connection Than any real interaction That you have out in the world It's like you can't talk to anyone like this in real life No one cares or no one wants to hear it No one wants to be real No one wants to be vulnerable No one wants to be intimate But this is what we do on here This is what I've been doing now For five and a half years Being vulnerable, being intimate On the internet Through my videos And it's quite clearly attracted a lot of people Around the world Who do not feel heard, who do not feel seen And may never have felt heard or seen in their entire lives I know There were very few times Where I felt heard or seen Luckily I have come across Some empaths throughout my life And I'm very grateful for those experiences And that's what you've got to hold on to You've got to have that contrast Even if it's just me in my videos Like if you just imagine what it would be like If you met me in real life If we conversed, if we talked about life If we talked about relationships If we talked about things I mean we were talking at a very deep level We were talking for hours We were talking for hours About deep stuff, meaningful things Not just official nonsense Have that contrast Because when the narcissist is not like that They don't care to talk about anything They're not even listening to you Because they lack empathy They have an inability to feel what you feel I mean for me if I know that there's something on someone's mind There's just something inside of me where it's like I've got to attend to this It needs to be resolved And that's just how it is As an empath, a chosen one An alpha male Everything that I am It's just the way that I'm built And I'm sure that's the way that you're built as well That's where you relate You resonate with my videos You need to accept, you need to understand You are never Never going to get that From the narcissist And sadly, yes, you do have to accept You're not going to get that from most people in this world Statistics do show Only 1-2% of the world's population are empaths And only empaths Who can feel what you feel I mean that's the basic definition of an empath Only they Truly have that ability to connect to you I know it sounds quite depressing And honestly, I wish it was not that way I wish we were all empaths I wish we could all just Hold hands and love and care about each other I am actually a hippie at heart And I've always been that way Ever since I was a child I could just live out in nature For the rest of my life so easily Just be around the trees The animals, living on a farm There's nothing for me to do that So yes, although it may sound depressing, pessimistic You have to accept the reality I've lived in denial myself For such a long time And where did that get me? It got me fooled, it got me tricked Manipulated, abused, exploited So many times And I'm sure it did for you At some point we just have to accept it You've just got to accept how things are And I'll make it that much easier for you If you ignore that assist And they go on, they punish you They start a smear campaign They turn all of these people against you And they make you believe it's All of them against you You're the problem, you're bad But they're off of the new supply They're living their best life You're down, you're alone, you're miserable I've been through that as well And at some point I came to the realisation The reality is It's actually the victim The target of that smear campaign Of gang stalking They are the chosen ones They're the ones who are real Your experience is the only one Real environment Everyone else is fake Because everyone else doesn't care about you Everyone else lacks empathy Which means they have the inability to connect And reality The subjective reality especially Is based on our ability to connect They're disconnected If they were connected even to each other Why would they all Be exactly the same And develop this group-think mentality This hide-mind If they had empathy for each other That would never be able to take place Because certain people would have their own individual needs Their own feelings So that could never become a reality It does Because they lack empathy Because they have the inability to connect With each other as well So with that in mind It's actually the victim, the target They are the ones who are real They're the ones who are authentic And you've only got to look back Through the thousands of years of human history I mean in pretty much every case It's always the victim, the target I mean There's so many Different targets that you can research On YouTube, on Google So many people throughout time Who were targeted They were the ones who were real Just look at Jesus Martin Luther King Maybe John Lennon as well Pretty much all of the prophets of God They were all targeted They were all singled out They were all attacked They were the realest of all But it seems like it's only after they died That people really began to understand that Because while they're actually in existence Then they're shining the spotlight On everyone around them Which is why it's only once they've gone Then it's so much easier For people to accept But hold on a minute Maybe they were right Maybe it is us Maybe we do need to change But then If they were still around They were targeted And kept down I mean they were while they were alive Because the last thing anyone wants Really Is to be told that they're fake But you've got to think Just look at your relationship With an narcissist Maybe your family as well Anytime they came to you And said that something was wrong with you The first thing you want to do is change You change everything about yourself In order to please them With your identity Because you want to be good You want to be right You want to be real It's just more proof More validation for you That we are not alike Because a lot of people I'm sure Most people in this world are not like that It's not like you're disappointed in them You're hurt, you're upset And then for them It's like I've got to prove to you That I'm good, I'm right No that's just you Only you do that And in all honesty I could give a million other examples I could give a million other examples I really could And I think I have already In so many of my videos I've got 3,500 videos on here Many more to come That narcissist They're never going to be like that for you Remember how you were for them I mean You would run to the ends of the earth You would climb a mountain Run endlessly in a hamster wheel Until the end of time Just to show them that you can be good enough When it's like You can't You can't be good enough for a narcissist For someone who's self-absorbed Because they have a void And that void can never be felt So you're always going to fail In trying to do that And all they're ever going to do Is make you think that something's wrong with you But no matter what you do No matter how you change Or how much you change It's not going to make a difference Because it's not you, it's them They're the ones who are miserable They're the ones who can't be happy I mean you're the type of person You can be happy with nothing With no one And you've got to move mountains And it's like they're still not happy With you That's another sign That's another sign How are you so easily satisfied And that's how they feel with you It's like all they've got to do Is put up the false character Love bomb you again Doesn't have to be anywhere Anywhere as good as it was The first time And it's like Oh, I got you again Because yeah, they know that you're real They know that you're connected To source You're connected to yourself So it's very easy for you to regulate It's very easy for you to be happy And that's how it's supposed to be Love is meant to be easy It's not meant to be hard But it's not like that for them And it is never Going to be like that For them Which is why, of course Yeah, you're better off again You're better off again Yeah, you're better off ignoring them But be very careful when you do that And I would advise Speaking to a licensed therapist Or coach Before you do that Because remember They cannot be happy on their own They cannot sustain themselves They've got to have a target To sustain their false reality And this is just the world that we live in People in general They need to have this contrast This person that they can hate To sustain their false identity Their false reality Just look on YouTube You can click on any video Or on TikTok Any social media Have a look through the comments Look at all of the hate Just look at all of the hate All of the trolls Because most people have a false character They live in a false reality And they need to have someone who they can target To elevate themselves So once you cut that off You take away that source of supply Of course, it triggers them to reflect On who they actually are It triggers them to reflect On the true reality And that is like death to a narcissist It makes them feel like they're dying For us it's bliss I mean anytime when I go out into nature Like I remember when I stayed on a farm in Vietnam Or I'd go hiking in waterfalls on my own That's It's the most incredible feeling In my life It's the most incredible feeling In the world And it's something that I experienced by myself Because that is the true reality The true reality is not in the external world Reality is inside of ourselves And people have known this for a very long time Just look at Buddhist monks Just look at Christians Who close their eyes when they pray Why do they do that? Because they all understand That the true reality is within ourselves It's not in the external world And that is how narcissists are Constantly detached from reality Because they have a void inside of themselves But that is why mindfulness and meditation are so powerful Just close your eyes for a few minutes And notice how you feel afterwards You will feel much better Because you've just connected to the true reality The true reality is in your mind The problem is that narcissists are not connected to the true reality That's why they can't regulate their emotions And that is why they're dependent on you Because you are connected to the true reality You're connected to yourself You're connected to your own emotions And when you realise that You identify that you're dealing with a leech and parasites Of course you will once you ignore them You don't want to leave that alone But some people they can't find fulfilment in themselves So they're constantly seeking escapism They're constantly seeking a distraction from within themselves That's your true reality is within yourself Because that's you That's you Most people these days they drink alcohol They do drugs They smoke tobacco They go to bars, night clubs, have one-eyed stands All to distract themselves from what really matters in life And that doesn't mean that you've just got to shut yourself off from the world Of course no that's not what I'm saying But we should be spending A certain amount of time each day by ourselves Because yes that is the true reality That is how we establish our own identity And what you'll find is that by doing that When you do go out into the world In the future You can experience that much more You have that much more to give You don't gain anything from other people Unless they are doing the same Unless they are spending time by themselves as well Again that's why when you get around an empath A chosen one That's why it has such a powerful effect Because they may be smeared, bullied Targeted They spend a lot of time alone So they're connected to that true reality within They're connected to self They're connected to their own emotions So they can connect to yours That's why it has such a powerful effect Being around someone who is connected to themselves Connected to their own emotions They spend most of their time alone But then they get around you And they connect to you There is nothing more powerful than that That is as powerful as it gets So yeah I can't advise for you to ignore the narcissist I also can't advise for you to continue to engage with them Because of course this is dependent on your individual situation You may be dealing with someone who is very dangerous They may lash out at you if you do ignore them And that's why what I do advise Is for you to speak to a licensed therapist or coach Before you ignore them or go no contact You can book a session with a licensed therapist Like go into betterhelp.com slash Narc Survivor Or you can also book a one on one with me By going to my website Which is NarcSurvivor.co.uk And I'd just like to thank you all, my family For joining me on this live video And please show your support down below By giving this video a thumbs up It will take you just two seconds And it will help the YouTube algorithm To get this message out there to other survivors Who may need to see it And hit that subscribe button and click all notifications So that you will be notified when I upload a new video And let me know your thoughts down in the comment section I'd love to hear from you And read your comments every day And also you can follow me on Instagram It's NarcSurvivor YouTube and Instagram I'm just in my room now We're going to sit in the beds Do a bit of work And then I'm going to Get Again here In the Philippines I've just been doing some exploring And I saw this amazing volcano It's actually the first volcano I've ever seen in my life So I was very excited to see that And I will be posting that up on my Instagram Very soon in my stories I can't wait to share that with you My Instagram is NarcSurvivor YouTube If you would like to follow me on there And you can DM me as well I will respond Alright I'd just like to thank you all For joining me on another NarcSurvivor Live video I do appreciate you all And as always I look forward to talking with you in another one Very soon