Quantum AI: Quantum Kernel Advantage

Key Takeaways

Hello community, so great that you're back. Yeah, I think it's time we have to talk about quantum AI system. And today we have a beautiful example, and we will talk here about a high-dimensional complex valued Hilbert space, where we will apply complex quantum artificial intelligence. So, let's start. Now, I understand you might say, "Why now? Why quantum AI now?" And you say, "Don't you know that according to you from von Neumann projection here, measuring here, if you go quantum physics, a state vector, if you measure it, it forces it to irreversible collapse into one of the operator's eigen states?" And you might say, "Do you not understand what complexity we will encounter?" And you might say, "But look, we have the classical AI." Such a beautiful thing here, here we have Stanford University, Stanford AI, Department of Radiology, and they have here Look, unified generative pre-training for vision language model. For medical imaging for an X-ray. And you might say, "Hey, look, we have so many problems in the classical AI system." Published here April 24, 2026. Why do we have to go quantum AI? Well, it is exactly because of this article. Just 3 days later, April 27, 2026, we have this. This is here from MIT. Critical data, this is here from Republic of Singapore. This is here from Politecnico di Milano, this is here from Bordeaux in France, this is here from Johns Hopkins University. And all of they of this beautiful artists, they are now talk telling us, "Hey, we do need a quantum kernel advantage over the classical collapse in the medical foundation model embeddings." And when I saw this, I thought, amazing. So, finally we are starting here in medicine to check out if quantum AI has some additional value for us. And of course, you know me, yes, they do have a GitHub repo just 15 hours ago. You have here everything, and they call here for a quantum SVM for the medical imaging classification using also chest X-rays. So, you see, the topic that we are talking about is just a medical topic, and it is the simplest you can imagine, a chest X-ray, not an MRI machine, a simple X-ray. But you know what we can deduct is just amazing. And if you go down the files and you have everything down, you see, "Okay, now we train here a Q SVM with a quantum kernel." And you might say, "Help, what is happening here in the code?" So, I think, let's take the time, let's have 10 minutes and talk about what is here the idea in quantum AI, and how can it help us? We start here with the simplest theoretical model we can imagine, an SVM. A support vector machine. You know this here from kindergarten. Yeah. A supervised machine learning algorithm used for a classification task, and we did this before even AI was invented. Yeah. Now, in machine learning, the kernel machines are a class of an algorithm for a pattern analysis. So, this is exactly what we have AI for. Just find a particular pattern. Whose best known member is, of course, of a kernel machine, an SVM, a support vector machine. So, you see, this is something that you are familiar with. They just have a little bit of a strange naming, support vector machine, kernel machines, but you are familiar with what is happening here. And if you think about what is the main essence of the kernel methodology, it is a technique used in SVM to transform some non-linear data. You have a bulk of data, and you want somehow to do a classification of those data. Yeah. But they are not really separable. So, what you do, you take this non-linear separable data, and you put it here in higher dimension, and yes, there the miracle of mathematics happens, and with a kernel methodology, you can separate here in higher dimension those non-linear data streams. So, we can see a kernel is basically a mathematical shortcut that measures here the similarity between two data points here on a particular hypersphere by pretending that they are in a much higher dimensional space, where drawing here a line that will separate here the group A from the set B is easy, and it is a linear separation in a high-dimensional um yeah, Hilbert space. So, okay, this is all that we want to do. Now, of course, a quantum kernel does this using here the actual physical state, let's say, of a quantum computer as a high-dimensional space. So, now the quantum computer calculates here the similarity score, and you know the similarity score. Yeah. In our classical vector space, it was a cosine similarity. Yeah. Now, it is also a product, an inner product here, almost the same similarity score. It is just the mathematical space that we are operating in is completely different. So, in a quantum computer, we calculate the similarity score between two data points that have been transformed now into, and hold on to your socks, into quantum states. So, now it is not a vector anymore in a classical vector space here. Now, we go really quantum mechanics, not field theory mechanics. So, therefore, we go from a kernel methodology now to a quantum kernel methodology, and the simplest instrument that we have there is a quantum support vector machine, a Q SVM. So, let's talk about the simplest case. You remember stochastic gradient descent in the classical AI. Guess what? It is a simple yet very efficient approach fitting linear classifier under a convex loss function such as a support vector machine. So, you see, you are absolutely familiar with this. Maybe there are different terms that you never heard before, but it is something that you know how to work with this. Now, let's assume we have here at the bottom here a set of different elements. Let's say here some red little bubbles and some green or blue bubbles. Yeah. And then you have now the task here simply to separate this. Find a pattern in this mash here of red and blue bubbles. And you will try to do it in a classical AI way. And you will find that you encounter here limitations. But if you go to a quantum SVM with a quantum kernel advantage, and I will explain what this is in a minute, you suddenly have with a quantum machine, you have a tool, you have an instrument that you can separate this. So, you see, an SV It is still an SVM. You still thinking about a particular hyperplane that somehow can separate here two areas of a particular Hilbert space, so you can have your separation problem solved. Of course, we are high-dimensional quantum feature space, and I will explain what this is. Just notice now our Hilbert space is not a real valued, but now we are complex valued. We have now phase rotation here in this Hilbert space. So, the mathematics is just jumping here about a 100 years into the future to the 19th century, almost 20th century. Yeah. We going to talk about the quantum kernel matrix, but in the end, we will have a separation that is achieved because the quantum kernel are able to see a linear separating hyperplane in a high-dimensional RKHS. And if you're not familiar, never mind, I will explain this in a moment. So, machine learning, you know this. Yeah. Quantum machine learning, a complete different beast. And you might ask, "But why do we need quantum models here?" Yeah. Now, it turns out because the regular computers that we have and go with whatever Nvidia GPU that you want, they do not have the memory or the power to calculate similarity scores in mathematical spaces that we have to calculate, but those spaces can grow exponentially large. This is where, even if you have 1,000 Nvidia GPU, it will not be able to compute this. So, therefore, we have to quotation mark invent a new mathematics, and we go now to a quantum computer. We have not single zero or one, but we will calculate here with qubits, and we will also go here with quantum theory, with quantum mechanic, with insights that we have from this theoretical physics construct, and we will utilize this. So, a quantum computer exists in these massive spaces, exponentially large spaces, naturally, 2 to the power of n, if n is the number of qubits, for example. And by using our quantum computer strictly to calculate these massive similarity scores in these extreme spaces, we can also, same idea, process highly complex patterns that a traditional AI machine cannot calculate, cannot do. So, quantum machine learning promises some computational advantages through the use of quantum feature map, and you remember the feature space in the classical AI, that embed classical data into an exponentially large Hilbert space. So, suddenly we are here facing here a new kind of mathematical space, Hilbert spaces, and depending on your If you love mathematics or not, where you have been trained in, you understand what I mean, or maybe you have to check it up what exactly is a Hilbert space. Never mind, just get familiar with the terms. Now, quantum kernel methodologies, and in particular, the quantum support machine, we will have a look. Realize that this promise here by computing here the inner products of a quantum state now instead of explicit feature vectors. My goodness, the time when we had to deal with vectors was so nice. Potentially enabling now a richer decision boundaries of our SVM with fewer parameters than any classical alternatives because now we are calculating qubit structures. So, we just change a little bit a methodology how we work. We just go here to quantum mechanics. We work with qubits. We have quantum states here that represent here physical system. And it is so much easier to go with really exponential large Hilbert spaces. Now, this is essential and it is not easy to really understand because quantum models in essence are actually just kernel methodologies in disguise. So, therefore, we don't need to guess and check here the weight of a quantum circuit at all. And in the beginning here of quantum computing, the people were doing like with the weight operator here in the classical AI system, no? Guess and check here and adjust here the weight of a quantum circuit at all. But we don't need to do this. Because if we treat your quantum computer merely as a tool to measure the distances between data points in a Hilbert space, we can use then traditional reliable convex mathematics to train the model perfectly every time. So, it is essential that the quantum models are actually just kernel methodologies in disguise. This will open us up a trick for us. Uh something that we will utilize here to be even faster. So, this means we can use the quantum computer only as a feature extractor to evaluate how similar different pieces of the training data are to one another in our Hilbert space. And once the quantum computer has generated here this grid of similarities scores, we call this here a density matrix or then later on a gram matrix here, we can hand that grid back to, let's say, a regular classical AI computer, no? And then a classical AI computer can easily solve this for the best decision boundary for an SVM methodology. So, what is the core hypothesis? What is the main idea? Any supervised quantum machine learning model optimized via classical data, and this is, for example, the X-ray images here in a hospital, is mathematically equivalent to a classical kernel methodology evaluated on a quantum computer. If you really got a feeling about this sentence here, you have 90% of the complexity. Because discovering here the optimal quantum measurement for a given task can be rephrased as a finite dimensional convex optimization problem over the particular RKHS defined here by the encoding strategy alone. So, it is important how we encode classical data into different quantum state and superposition of quantum states, and this is the most important part, and we don't have then to go and optimize here a weight structure. Mathematically equivalent to a classical kernel evaluated on a quantum computer. You want to see this. This is here published here in version 6, April 15, 2026. This is also algorithms trained on normal chest X-rays can predict the health insurance type. And you have here Taiwan, Canada, Toronto, York University, MIT critical data, MIT Institute of Technology, Journal Mass Journal, Right Cam, USA, and so on. And I thought, wait a minute, what do you mean we can have if we have a look at X-ray images, we can predict the insurance type of those persons. That's What do you mean? We're talking about medicine. We're not talking about the insurance type, no? You have this here in the personal medical record of the patient, no? No, I was wrong. It turns out they have now an inside. They have here hidden patterns in the chest X-rays that will tell any AI machine about the insurance type, if it's without an insurance or private insurance or the top level insurance. And AI can deduct this from your chest X-ray what in- how much insurance you pay, if you're rich, if you're poor, if you are in a marginalized group, if you are living wherever. And I said, this is crazy. This is a This is a hidden pattern, a hidden structure in an X-ray image. This is How should this be possible? And if you have a look at the study, it turns out it is possible. Because deep networks may be internalizing such minimal, hardly noticeable traces here of clinical environments, of equipment differences, or of care pathways, and learning about socioeconomic circumstances of the patient. And if this person belonged to a particular group, a minority, or a group with socioeconomic status not as high as the ultra-rich person in a country, and so on. You understand what I mean. And I was absolutely perplexed that in an X-ray you can see this. If a person is rich, how the nutrition of a person is, if it has a private insurance. I mean, unbelievable. But you see, those are those subtle traces here that are hidden. These patterns are hidden deep deep into the image, but any AI can detect those patterns. Which I found amazing because I just thought it is about medical indicators here. And therefore, now you understand why I'm so amazed about this study when they say we have a classical collapse in the medical foundation model and the embeddings because it shows us that we hit a wall with the classical AI methodology, and now more or less they tell us, "Look, we examine now the quantum kernel advantage, and it out- the quantum methodology outperformed here the classical AI methodology. So, for me this is here and never mind it is medicine or it would be finance. It doesn't care. This is the first time I see really here the the boundary here, the wall of a classical AI methodology. And you want to tell us our objective is to evaluate whether the quantum kernels improve here the separability of our indicator of our dense mass of data points within this representation space without claiming the learned signal is clinically causal. So, this means whatever you see here on a medical X-ray chest image, okay, you have all the medical implications, but you also can deduct from the particular pattern that you see on this image, I don't know what about that the density of the bones or certain indicators, visual indicators, if those person is eats healthy, is doing a lot of movement, is not sitting at home, or just eating some junk food, or whatever. But they really can now separate here your insurance class, which is just just amazing. And they tell us the finding carried direct implications for health equity. And they say, "If the socioeconomic and demographic signals are encoded in medical images, clinically AI system trained on those images risk learning and perpetuating some disparities. A concern supported by evidence that chest X-ray classifiers systematically under-diagnose underserved population." Like, let's say, minorities, whatever the kind of minority is. So, this means the training data set that you give to your AI machine to learn on different chest X-ray classifiers. And if you have If you do this in a region where you have a lot of people that are really rich, perfect nutrition, perfect movement, they train, they are active, healthy life, beautiful, whatever, then those, let's say, visual sign become the dominant indicator, and it might under-diagnose here a complete different region of population living in a city where they are maybe not as wealthy as the first group. And you want to say, "Okay, let's do this. Let's do a Let's extract a high-dimensional embedding from three frozen medical foundation model. Never mind, if you are in medicine, you know them. If not, never mind. Sickle cell 448, a Dino, and a vision transformer patch 32. And compress them into Q dimension via classical PCA, and then compare the quantum SVM against the classical SVM baseline at the identical feature dimensionality. Let's see if the quantum machine is really better in separating here those distinct patterns." Now, I give you the result, and you have a lot of experimental data in the study, but just to give you the result. Quantum kernel clearly have an advantage across all tested configuration, especially about non-quantum system. There is a structural explanation and given the rank of particular matrix here for the classical collapse in the AI system, and the quantum SVM outperforms here all the kernels tuned to the same rank at all four Q4 qubit counts tested here in this experiment and so on. So, quantum is better. Full stop. Now, quantum kernels now if you think about why is this possible? What is happening? Suddenly, looking for this really minor minor little patterns here in those huge data sets, if we have now the possibility to go with exponential large feature spaces, now our quantum kernel methodologies are really able to exploit the ability of quantum circuit to compute here the inner products in a way that it is possible to detect those minor features in those exponentially large feature spaces. Now, I would like to give you here a literature. I found this extremely helpful. This is here you see here the HTTPS link. This is here the author manuscript here. This is if you want to make yourself familiar with kernels. This here is from Max Planck Institute für biologische Kybernetik in Tübingen in Deutschland and the Australian National University in Canberra. And they give you here not on the quantum level, on the classical level, uh beautiful mathematical introduction to the kernel methodology to support vector machine to kernel feature spaces here and everything. And the kernel trick, what does it mean? All the various kernel's representation that you can choose here and the application of the kernel methodologies. So, if you really want to have a deep dive, you really want to understand kernels at the basic concept, I highly recommend this paper and they also published this here several books. So, if you look for those authors, I like them. And as you see, they show here also the architecture of SVM machines here. You have your test vector, you build your support vectors here, then you have your map vectors here, you have the dot product here and if you combine it with weights, you have here the output. And if you look at this, you say, "Hey, wait a minute. This is here a classical neural network, of course, no?" And you see, this is the beauty here. We have a mathematical apparatus that we can apply almost one to one here on our neural network structure and we immediately understand the mathematical methodology that is behind those things, no? Or you go here, Wikipedia. I just noticed this is German. Okay. [laughter] Anyway, you have here a set of dots, no? And you say, "How can we separate here these red dots from the blue dots?" And you just go to a higher dimensional representation here of all the dots and you see then that all the red dots are here really at only at the bottom here of this three-dimensional object and you just can build a plane and separate here those two groups perfectly here with a hyper uh manifold here that you can mathematically calculate. Real simple. If you want another highly It sounds strange, but it is gorgeous. This is here from MIT. This is here a PDF file. An idiot's guide to support vector machines here. If you want to have also a very good introduction with a little bit of mathematics as you see here with the Lagrangian formulation here into the SVF problem and how you build your Lagrangian function at extreme points that you have to train for, I would highly recommend here MIT this particular paper. It's not even a book, it's not even a article. It seems to be an internal MIT document, but have a look at this. It is really funny. It is yeah, easy to understand. So, coming back now, you have now a feeling that we went from the classical kernel methodologies here and we tried to cross over to quantum computing in a very specific way and we use here an inside that there is here a bridging function between those two areas, if you want, no? Because, and this is the next paper I want to show you. This is from 2021, but it is one of the outstanding papers, if you really want, in my opinion, to understand here the connectivity between the kernel methodologies and quantum computing here. So, if you come from artificial intelligence and you understand our probability distribution, no? Our feature space, our data space. And then we have access here via a kernel methodology to compute here this new higher dimensional space. And how this is more or less corresponding here to the quantum computer image, no? Where we have the input space and then we have not a feature space, but a Hilbert space, a quantum Hilbert space and we have access here not via the kernel, but via actual measurement, but in quantum mechanics, if you measure something, you you change it the system, you have a fall back to some eigen states here of the system, no? This here is here a paper I really recommend. You see, it's not any AI, it is about quantum physics, of course, published here, but they talk about computing and kernel methodology are based on similar principles. And they say, "Both have mathematical frameworks in which the information is mapped into and then processed in a high dimensional space to which we only have limited access." They say, "In the kernel methodology, the access to the feature space is facilitated through the kernels or you notice the similarity, the inner product of feature vectors, no?" You want to know the semantic similarities of two terms or if you're searching for your rack construct, you have a particular query vector and then you look here for the cosine similarity. You look for all the semantic similar vectors that are in a within an epsilon environment to your query uh vector and those are of course you calculate this with a cosine similarity and this is the inner product of the feature vectors. Now, you do the same methodology in the quantum computing thing. But of course, your mathematical space is a completely different. Your algebraic fields are completely different, but it is the same idea and this is why I want to show you this. Now, in a quantum computing case, you have access to the Hilbert space of the quantum state and it's given here by measurements, which can also be expressed by the inner product of quantum states. What a beautiful parallel idea. Now, understanding the quantum models now as kernel methodologies means that the expressivity and the optimization and the generalization behavior of the quantum models is largely defined by not by the calculation, but by the data encoding strategy or if you want, by the quantum embedding, which fixes here the kernel. So, this is now interesting. The authors tell us now of this paper, "Listen, it is not about that you have to calculate with, I don't know, 1,000 5,000 10,000 qubits. It is about the data encoding strategy that is the most important thing. How if you get the quantum embedding right, like we have here with a classical rack system where we build a vector space or a vector database, it is more or less the same here in the quantum case. What am I means that while the kernel itself may explore high dimensional state spaces of the quantum system, the quantum model can be trained and operated here in a low dimensional subspace. Now, this is something very nice because then maybe I don't have to go to a quantum machine, to a real quantum computer, but I can do um I don't know specific set of Nvidia GPUs here and have quantum machine simulations that I can run if the number of qubits is well, yeah, around 20, I would say, but depends how much money you want to spend on it, no? So, quantum models usually consist of two parts, no? A and B. The data encoding part where you have here your state and your encoding here, which maps you to data inputs to a quantum state S of X, effectively embedding them into the space of the quantum state and then you have the processing then the measurement, no? So, you interpret the quantum circuit as a machine learning model. Of course, this is exactly what we want to see. Now, careful now because the feature space is not identical to the Hilbert space of the quantum system, no? Because the bridge between the computer the the quantum machine learning and the kernel methodologies formed by the observation that the quantum model map data into high dimensional feature space within which the measurement defines a linear decision boundary. So, we are now in the space of the inner products. This is not absolutely identical to the Hilbert space. The measurement of the quantum model defines the linear decision boundary in the feature space. So, you see, it's always the same idea. Just the mathematical implementations are a little bit different, no? Okay. Great. Let's talk about it. So, we need to define our the data encoding density matrix that is here a feature vector instead of here of the classical quantum mechanical direct vectors, Dirac vectors. Now, the density matrix is a little bit special, no? Our alternative description of a quantum state as her- Hermitian operators, which are handy because they can also express probability distribution of a quantum state. And guess what? Probability distribution is what we know from classical AI, no? So, therefore, we can consider the space of complex matrices enriched with the Hilbert-Schmidt inner product as, guess what? The feature space of a quantum model. And now we have the bridge function finally established. Yeah, we need a tiny little bit of physics. Now, if we go here in this particular publication, you have here Let's define our quantum model. So, we need to need to define the measurement. In quantum computing, a measurement produces the observable result of a quantum circuit and then that will be seen as the final step of a quantum algorithm. A measurement corresponds to a mission operator M acting on the vectors in the Hilbert space of the quantum system H. Just like density matrices, measurement operate can be represented as elements of the space of a 2 * 2 ^ n * 2 ^ n dimensional complex matrix. Hilbert space live in a subspace of the data encoding feature space F. And a mission operator can always be diagonalized and written here. And those are of course the I the eigenvalues of M and therefore we have an orthonormal basis here in the Hilbert space of the quantum system. And this is of course here the outer product and can be sort of the density matrix. So, now immediately have here the reference back to the quantum mechanical analog. Expectation derived from expressing the quantum state and the eigen basis of the measurement operator and everything that you know from quantum physics. Beautiful. But now let's define the quantum model as a measurement performed on a data encoding state. So, let row of X be a quantum state that encodes the classical data X and M a mission operator representing the quantum measurement itself. Quantum model is the expectation of the quantum measurement as a function of the data input and the space of all quantum models contain here the function F. And for a pure embeddings with row here this simplifies here to this beautiful definition of our function F. Okay. So, careful. So far we've been dealing with two different kind of Hilbert spaces, now? We have the classical Hilbert space H of the quantum system itself and then we have the feature space F that contains the embedded data. And now comes finally the moment that I can explain RKHS to you. So, we will now construct another feature space, a third feature space for the quantum kernel, but one derived directly from the kernel itself with no further notion of the quantum model. Now, of course this time the feature space is a Hilbert space here F of the functions and due to its special construction it will be called or it is called the reproducing kernel Hilbert space. So, now we have made again the bridging function explicit. Beautiful. So, our RKHS, the relevance of this feature space is that the function it contains turn out to be exactly the quantum model functions, which is a bit surprising at first. Because this feature space contains the linear models defined in the equivalent feature space. If you bring your head around this, you might say, "Okay." But now we come to the problem. How do we train these quantum models to make them perform their their classification task as I showed you here for the human X-ray chest images. And this is simply not possible to do in this video because I was trying to be as simple as possible. It is not perfect and I know that maybe I have not really met here the point where you immediately say, "Hey, I understand it immediately." But you know, I have no idea where you are with your knowledge in theoretical physics and mathematics. So, it is really not easy to give here a presentation for everybody here. This is the paper would If you want to read one paper, would say go with this paper from 2021, but I think it's a reference paper. This is exactly about what we talked about supervised quantum machine learning. And they are kernel methodologies. This is it. And this paper gives you the complete mathematical the quantum mechanical interpretation here of this supervised quantum machine learning. So, if you read one paper, this should be the paper. So, therefore you see now coming back to the main paper here, our medical quantum kernel advantage over the classical collapse, you might say, "Okay, so what about the collapse?" The collapse is here in the experimental data of those authors. It is a little bit too heavy if you're not familiar with theoretical physics. So, therefore if you want to know the details, have a look at the paper. Otherwise I would say, "Let's just go and say, 'Okay, we do have a classical collapse and we understand that the quantum kernel has a clear advantage here for the medical information.'" If you insist the classical collapse, what is it? It is about a low rank structure here of the classical chronic kernel that clarifies when the quantum advantage window really opens up. Because remember the classical support vector analysis machine here classify the data by finding a maximum margin hyperplane in the classical feature space. Remember, this was this this this road this highway in the middle separating here the blue set to form the red set. And now what we have is a kernel trick enables now a non-linear classification by implicitly mapping here the inputs to a reproducing kernel Hilbert space. So, therefore the effectiveness of any kernel depends critically on the rank structure of the resulting kernel matrix itself. A low rank kernel cannot distinguish the samples whose projection onto the kernel's feature space coincide. It cannot distinguish the dissimilar vector structures. So, this observation from the theoretical basis for understanding the classical collapse this is only valid here as the authors show us here in this publication at a low PCA dimensionality. So, of course the more dimensions you add, the more resolution you give to the mathematical space to encode complexities, then the classical collapse can be postponed maybe, but the authors show here the classical collapse here at low PCA dimensionality. And if you want to see here all the numerical values and the data, have a look at the study. As I told you they were operating here with three medical foundation models, Sickle Dino and Vision Transformer patch CLS. You have 448 dimensional, 768 dimensional CLS token embeddings here. So, you really have here good cross-section of medical models that they had a look for. If you want to see here the quick start, if you want to code this, if you want to run this locally Python, if you want to have here the classical SVM, all the project structure, data set requirements of the quick start code, if you really want to follow here the coding here, you go. Notice that they operate here with a firm Nvidia. This was here the version released April 13, 2026. They have this particular Nvidia Quantum SDK. This is a set of high performance library and tools for accelerating quantum computer simulations on normal and normal quotation mark Nvidia GPUs. Five major components and you have here everything. So, Nvidia's Quantum SDK is a software library for simulating quantum circuits. But of course we are not limited here by the simulation of quantum circuits. They go here to Qiskit's state vector simulation that you know from IBM. You can go there if you are at a university, you have access here to those machines on the cloud IBM provides for I'm not sure all universities or just a certain range of universities uh access to their quantum computer. So, you have access to quantum computer via the cloud network. Yeah. All QSVM experiments here in the paper that we just looked at used here the Qiskit's state vector simulator here. Results on the real quantum hardware may differ due to gate errors, decoherence, limited qubit connectivity, and readout noise, but you can also go here in the cloud and go here to the real quantum computer. If you want to be a little bit more familiar with the IBM quantum platform that provide you for universities as I know it free access here. Here they worked with state vector estimation here. So, you have your class of Qiskit primitive state vector estimator and here you have the complete explanation. So, if you really want to go into quantum simulation or you really want to go here on your first quantum machine. And you want to have here an experiment, this is the way I would go. So, there we have it. Now finally, unbelievable. I took the opportunity here by this new paper here on medical X-ray images. Can you imagine that they find out if they apply no quantum AI system and here the simplest quantum SVM with a quantum kernel advantage that goes beyond the classical AI system, they can really deduct information. They can find patterns in an X-ray. That is just amazing. They can give you your social economic facts, who you are, where you are living here. It is absolutely amazing. Imagine if you can read this out of an X-ray image. Imagine what you can do if you have like say like Facebook or some social media more information about this person. You can do a personal profiling that will be just amazing in the details. So, quantum AI machine and quantum computing, it is coming. It is providing here another step in the performance of artificial intelligence. I find it absolutely fascinating. So, therefore I want to start here coming up here with more and more videos. Maybe I failed today. Maybe I could not communicate here the beauty and your ideas here of this quantum computing process, but please then you have to go. You have to read the paper yourself. You have to see I want to understand this because I think this will be the next topic in artificial intelligence and we do have to prepare for these upcoming technologies. I hope to see you in my next video.