Sadia Afrin Purba: Yeah. Share your screen.
Sadia Afrin Purba: Otherwise, I won't be able to see slides.
Sadia Afrin Purba: Okay, so thank you all for joining us today. We are here to…
Sadia Afrin Purba: Towards for Sadia for the next hour and a half, of all of us. Now, this is Sadia's PhD preliminary exam. Sadia's in her third semester here at Temple.
Sadia Afrin Purba: Pursuing a PhD.
Sadia Afrin Purba: Dissertation area is probably going to be…
Sadia Afrin Purba: Quantum entanglement and sheet learning type things, so it's going to be actually fairly close to what she's talking about today.
Sadia Afrin Purba: But to remind everybody, this is a preliminary exam, not a dissertation proposal.
Sadia Afrin Purba: Oh, okay.
Sadia Afrin Purba: Savi's had a pretty productive time in our group. She's got a number of menace publications coming out this year.
Sadia Afrin Purba: And she's so… Most of them evolving, around our work in machine learning.
Sadia Afrin Purba: hopefully what she talks about today will begin her journey towards a dissertation in a not-too-long time, so…
Sadia Afrin Purba: The format is the first hour is public, open to the public.
Sadia Afrin Purba: People are encouraged to ask questions as they go along.
Sadia Afrin Purba: And then we will excuse the public, everyone about the committee, and the committee will spend some time asking her questions on her materials. And then the committee will defer and…
Sadia Afrin Purba: Be informed of the decision shortly thereafter.
Sadia Afrin Purba: So, Sally, you're welcome, and good luck.
Sadia Afrin Purba: Thank you for the introduction.
Sadia Afrin Purba: Hello, my name is Shadyafing Purva. I am here to talk about the quantum correlation enabling quantum advantage in machine learning.
Sadia Afrin Purba: So I hope by… after this presentation, everyone has some idea about quantum computing, and why it is very important for machine learning.
Sadia Afrin Purba: Okay, so my outline is we have many definitions, like quantum advantage, quantum correlation, so I will define those first.
Sadia Afrin Purba: Then, I'll talk about my motivation, why the quantum correlation is very important for machine learning tasks.
Sadia Afrin Purba: Then I'll talk about some fundamental quantum computing and quantum information, related topic.
Sadia Afrin Purba: Then the main issue, the main topic, I'll… I have selected three, papers which actually, prove, quantum advantage in machine learning field, so I'll discuss their contribution.
Sadia Afrin Purba: And based on those papers, I have created… I come up some roadmap that we need to focus on for our future research in quantum machine learning.
Sadia Afrin Purba: Sure.
Sadia Afrin Purba: What is actually… what is quantum, actually? I mean…
Sadia Afrin Purba: Quantum deal with subatomic particles. So, when we are talking about quantum mechanics, we are talking about the physics that are, that are in the subatomic
Sadia Afrin Purba: Particles, for example, electron and photon, and many physicians and computer scientists describe the quantum mechanics as a generalization of classical probability theory.
Sadia Afrin Purba: And in quantum mechanics, we have two important probiotics, and these are very important. One is superposition, and another is entanglement.
Sadia Afrin Purba: And quantum computing is a type of computation that uses these two
Sadia Afrin Purba: Basically, these two, properties to process information in a way that the classical computer cannot do.
Sadia Afrin Purba: And by quantum advantage, I meant that we have a goal that we want to prove that a programmable quantum computer can solve a problem.
Sadia Afrin Purba: That no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem.
Sadia Afrin Purba: This particular term was coined by Dr. Preskill in 2011, but the concept of having a quantum computer for simulating our nature is from early 80s.
Sadia Afrin Purba: So, there are… there are three examples. For example, in 2019, Google, showed the, random shark gate sampling that would take only 200 seconds.
Sadia Afrin Purba: In quantum computer, but it would take 10,000 years for a, supercomputer, so that is a huge speedup.
Sadia Afrin Purba: Another is a very famous algorithm, Google's algorithm.
Sadia Afrin Purba: It provides quadratic speedup, if we run the unstructured search in a quantum computer. And then this is a famous Shores algorithm, which is… which deals with integer factorization.
Sadia Afrin Purba: And if it is… so far, it is, theoretical, but when we have a… when we have a quantum computer that can perform the source algorithm, the internet is broken, the RESA, increasingly is broken, and that particular day is called Q Day.
Sadia Afrin Purba: Now, when we are talking about speedup, a natural question is, why do we need speedup? I mean, we have many cluster high-performance computers, why do we need that?
Sadia Afrin Purba: Now, the concept is, for example, there is one algorithm that solves a problem, and the complexity is O of, O of root… O .
Sadia Afrin Purba: And no matter how much, how many classical computers are we running, the internal complexity does not change.
Sadia Afrin Purba: But.
Sadia Afrin Purba: Quantum computing, and with help of superposition and entanglement, we have the power to reduce the complexity. So it is a…
Sadia Afrin Purba: It is a different kind of computation, so it is not like apple-to-apple comparison.
Sadia Afrin Purba: So, let me ask a question about the second…
Sadia Afrin Purba: There's the first and third, somewhat familiar with the second one.
Sadia Afrin Purba: the program's algorithm. Yeah.
Sadia Afrin Purba: Can you say a little bit more about the speedup, is this a theoretical speedup? Is this…
Sadia Afrin Purba: And speed up the… It's demonstrated in the… Things are… Exactly under what conditions.
Sadia Afrin Purba: what's disproven to get this kind of a speedup? Is it parallelism? Is it what… what's giving it this, rather dramatic speed up in search? It specifically used superposition property very well. So, it simultaneously, starts the…
Sadia Afrin Purba: Search the database with a specific key.
Sadia Afrin Purba: and simultaneously get the result within a… I mean, with a root over n, in time complexity. It is first… first of all, it is a theoretical bound, but, we have, there are experimentation in current hardware that it is true. We can get,
Sadia Afrin Purba: with this ratio, with a limited number of… for example, I think it, the experimentation was shown with 20 qubits.
Sadia Afrin Purba: And this is just an across…
Sadia Afrin Purba: Yeah. Unshorted. No, no, nothing. Just a database search. I mean, unsorted, you have a key, you have an unsorted data set, you are… you want to search the data.
Sadia Afrin Purba: Make reasoning.
Sadia Afrin Purba: I, the superposition.
Sadia Afrin Purba: Because… So it's being able to do…
Sadia Afrin Purba: It's a form of parallelism. Yeah, yeah. We do multiple things.
Sadia Afrin Purba: That's one. Yeah.
Sadia Afrin Purba: Now,
Sadia Afrin Purba: Now, classical correlation, we all know, it is, it describes, how two random variables are linearly, related, but our classical measures obey by classical, probability theory and local realism theory.
Sadia Afrin Purba: What is local realism theory in classical world, before calculating the
Sadia Afrin Purba: probability, we have all the information about the random variable. I mean, we can… we can know the prior information, right?
Sadia Afrin Purba: the nearby events influence each other. For example, we are dealing with a coin. If we are dealing with coin, the nearby coin will influence the probability. It is not like one coin is here, another coin is here.
Sadia Afrin Purba: There is no communication, so how do you measure the, measure the probability? In classical world, there is no way.
Sadia Afrin Purba: But in quantum correlation, it is a general term of quantum mechanics that refers to non-classical statistical relationship between two or more, particles.
Sadia Afrin Purba: For example, we have, like, two quantum dice, and they are very far away. One is here, another one is probably in another planet.
Sadia Afrin Purba: And if I dice, the…
Sadia Afrin Purba: if I roll the dice, it always… the both of the dice always give the… give the same output. So that is the entanglement.
Sadia Afrin Purba: So the non-local pro… non-local feature is very important here in quantum correlation.
Sadia Afrin Purba: And the strongest form is quantum entanglement. There is also a general type of weaker quantum correlation, which is called, quantum disc code. And my presentation is focused on this quantum co-entanglement and quantum disk code.
Sadia Afrin Purba: So, what is the motivation? In machine learning tasks, our main goal is to model a distribution. Given X, we want to model the distribution of Y.
Sadia Afrin Purba: And based on the training data.
Sadia Afrin Purba: And we use some kind of parameter and loss function to learn that.
Sadia Afrin Purba: Now, classical models rely on the joint and conditional probability.
Sadia Afrin Purba: Which is only capture the statistical dependency.
Sadia Afrin Purba: We can, no, not… traditionally, we cannot capture the physical relationship between the variable with, in the classical model.
Sadia Afrin Purba: And correlation are local, meaning information is shared through the explicit data feature or parameter.
Sadia Afrin Purba: And it is also constrained by cars of dimensity. For example, if we have more data, we need to model more
Sadia Afrin Purba: More, hype, more hidden layer.
Sadia Afrin Purba: So, my question… my motivation is, can non-local quantum correlation provide a technological or quantum advantage for machine learning tasks?
Sadia Afrin Purba: So, do you have any questions at this point?
Sadia Afrin Purba: Your definition?
Sadia Afrin Purba: learning. Would you say that's a generative model or a standard model?
Sadia Afrin Purba: For this particular case, I choose a… supervise.
Sadia Afrin Purba: modern, I mean… That wasn't the true.
Sadia Afrin Purba: Generative or disternative? Dominative. Dominative. That equation, you believe, describes a determinative model.
Sadia Afrin Purba: No, I didn't put the, What? Joint probability.
Sadia Afrin Purba: Well, I think it's a narrow… it's a narrow definition of machine learning. Yeah, yeah. Because this is more what you expect of a generic model that you're able to
Sadia Afrin Purba: understand the statistics. We don't really… in classification, you don't really care about the statistics, you just care about your ability to learn the mapping. Yeah, but how do you map that? You need…
Sadia Afrin Purba: you need the similarity or some kind of correlation, the dot product, that is. Right, but you don't really care if it…
Sadia Afrin Purba: If you can directly model… you can accurately model the
Sadia Afrin Purba: The conditional distributions and things, you just care about the ability to do the class assignments.
Sadia Afrin Purba: Bingham.
Sadia Afrin Purba: Okay. Yeah, I should have put a very big, general definition, yeah.
Sadia Afrin Purba: Good.
Sadia Afrin Purba: Now, in quantum ML, the quantum advantage is the ability of quantum systems to perform a learning task. As we are talking about machine learning, we focus on learning tasks faster, with fewer ratios, and with greater or greater accuracy. Any of them.
Sadia Afrin Purba: If we achieve any of them, we can say that, yeah, we achieve quantum advantage.
Sadia Afrin Purba: And…
Sadia Afrin Purba: I am… I am arguing that quantum correlation can, learn information beyond the training distribution, because it has some
Sadia Afrin Purba: capability to learn the global information. It does not only, process, variables locally, it has the idea of… the, idea of the system global… in a global sense. And I think the…
Sadia Afrin Purba: In classical world, we also only deal with the local information.
Sadia Afrin Purba: And also, the phase correlation allow contrastive interface, which,
Sadia Afrin Purba: Which actually boosts your learning and efficiency.
Sadia Afrin Purba: And, cancel out the wrong answer, and boost the right answer.
Sadia Afrin Purba: And also the entanglement-based correlation It is a very, efficient.
Sadia Afrin Purba: information transfer, transfer system. I mean, if two systems are correlated, if I measure one system, I… I don't need to measure the other system.
Sadia Afrin Purba: So, the… The information transformation or the communication bottleneck can be…
Sadia Afrin Purba: Can be reduced by using entanglement correlation.
Sadia Afrin Purba: What do you mean between the difference between global dependencies and global dependencies?
Sadia Afrin Purba: It's a little bit lost.
Sadia Afrin Purba: Okay, for example, Like, global…
Sadia Afrin Purba: For example, we want to,
Sadia Afrin Purba: we want to understand that if it is a… if… we want to understand an image classification task, okay? So, we only understand
Sadia Afrin Purba: We can only model the image classification task in terms of the training data. We are… the model can never inherit knowledge.
Sadia Afrin Purba: From beyond the training distribution.
Sadia Afrin Purba: Okay, so that is a local part.
Sadia Afrin Purba: Now, the quantum is the… Quantum, quantum entanglement deal with, subsystem, okay? Now, it has…
Sadia Afrin Purba: Some, it has to… Not all knowledge, it has the whole perspective, a global perspective from the
Sadia Afrin Purba: each subs, system. So that is the global, global perspective. And from that global perspective.
Sadia Afrin Purba: I mean, it is in a third-party perspective, so it can actually, extract the feature.
Sadia Afrin Purba: Beyond the training dataset, whatever.
Sadia Afrin Purba: Providing it.
Sadia Afrin Purba: I'm getting work today. Okay. Can you go back to your example of the image processing? Yeah.
Sadia Afrin Purba: what a global dependency would be.
Sadia Afrin Purba: Image processing, or whatever, like, Okay. For example, you have, trained your…
Sadia Afrin Purba: train your image classifier with a certain breed of dog, only a certain breed of dog and certain breed of cat, okay?
Sadia Afrin Purba: Nothing else.
Sadia Afrin Purba: Okay. So, do you think if you give him a very odd-looking, but that is also a dog.
Sadia Afrin Purba: to the email… to the model, it will classify.
Sadia Afrin Purba: Depends on how similar that is.
Sadia Afrin Purba: Oh, no, it is not very similar, but it is a dog. Yeah. So, in quantum world, suppose all the dog, the, all the breeds, they are dog, right? They are entangled. So, when I learn, when I, make my model learn one kind of dog.
Sadia Afrin Purba: due to the entanglement property, I know this is a dog. I mean, the property… I have learned that it's a dog. So, due to the correlation, the quantum correlation, not the classical one, the quantum correlation, it is theoretically possible that, yeah, I can…
Sadia Afrin Purba: learn about, or I can understand, I can recognize any kind of dog in the world.
Sadia Afrin Purba: Is that because the pixels within the image are somehow quantitativeled? Yeah,
Sadia Afrin Purba: Not on… Physically, I'm the same, I don't get it physically, how it works. I…
Sadia Afrin Purba: I know a little bit of quantum from many years ago, but I still don't get… So what…
Sadia Afrin Purba: A little more specific. You have a stack of pictures of dogs. Yeah. Right? A stack of pictures of cats. Yeah, and these are quant… entangled data.
Sadia Afrin Purba: How can you say that? What does that mean? I, I have some, I have some classical feature. I run the classical feature to a entangled circuit.
Sadia Afrin Purba: I get some quantum state, right?
Sadia Afrin Purba: So that is a… entangle dataset.
Sadia Afrin Purba: So you have to prepare the entanglement.
Sadia Afrin Purba: Yeah. Which involves adding information.
Sadia Afrin Purba: No, it involves representing information. Yeah, not adding information, representing the information in a different dimension. Okay.
Sadia Afrin Purba: Would that take as much time as the time you saved by being able to do the consultation faster?
Sadia Afrin Purba: Okay, I'm… I mean, the… could you do the same thing in regular…
Sadia Afrin Purba: non-quantum machine learning. I mean, you could say, you could teach it, this is what
Sadia Afrin Purba: breed number one looks like, and this is what breed number… How many data points do you need? Meaning… You're talking about entangling all these data points. Yeah, if I use entanglement, okay, it is possible that I need only one document to classify all the documents.
Sadia Afrin Purba: It is theoretically possible.
Sadia Afrin Purba: Okay, but in classically, if I want to classify all breed of all breed of dog.
Sadia Afrin Purba: I need probably trillions of images.
Sadia Afrin Purba: So they are…
Sadia Afrin Purba: I have to create the entangled… yeah, I have to create the entangled dataset. That is a very big research area, how to do this.
Sadia Afrin Purba: We gotta talk about that.
Sadia Afrin Purba: Let's probably going concrete about this at that time.
Sadia Afrin Purba: The data itself could be a table.
Sadia Afrin Purba: We've talked about data sets that are clearly from entangled data, like
Sadia Afrin Purba: One of the sets I've been trying to get her interested in is traffic flow on the Google Express. Yeah.
Sadia Afrin Purba: Because you wouldn't believe that…
Sadia Afrin Purba: The way people behave is a handled in some way, and it's not a resentment like the raw data.
Sadia Afrin Purba: But now you're talking about actually creating a model of entanglement, like artificial entanglement. Yeah, because we have to… we have to…
Sadia Afrin Purba: You, why do you think it is a limitation? We have to…
Sadia Afrin Purba: Whatever sort of differentiates between what they should really call it something like artificial intelligence.
Sadia Afrin Purba: No, I don't… okay, probably, probably. And also, how do you model the…
Sadia Afrin Purba: I mean, we have all… we have, I think, all, experienced some kind of spooky event, like.
Sadia Afrin Purba: I… out of nowhere.
Sadia Afrin Purba: intuition comes, and yeah, you feel like you should not go there, you didn't go there, and something bad happened. Okay. Similar… similar kind of the mother-child telepathic.
Sadia Afrin Purba: This is real. The mother tell everybody, it happened with me many times, with my mother. How do you model such thing with the classical… any kind of learning mission?
Sadia Afrin Purba: So they are beyond some…
Sadia Afrin Purba: event that cannot model with classical machine learning or classical algorithm. That is not possible.
Sadia Afrin Purba: But that's possible to really support them? Yeah.
Sadia Afrin Purba: Yeah, I mean, I am not saying it's possible, I am saying that there are reviews potential that if we exploit the entanglement or quantum correlation, this property in our modeling, in our mathematical
Sadia Afrin Purba: Modeling, then we can extract more information.
Sadia Afrin Purba: That we cannot by doing classical algorithm.
Sadia Afrin Purba: I mean, physicists in the lab have created particles that entangled things on purpose. Yeah. And then collapsed it by observing it. Yeah.
Sadia Afrin Purba: Yeah, so that… with that concept, we want to simulate that mathematically in our machine learning task.
Sadia Afrin Purba: So what do you mean by coherent influence?
Sadia Afrin Purba: That's… Okay, cool.
Sadia Afrin Purba: For example, the… image classification problem. Quantum image classification problem. I have a quantum… Yeah, I have…
Sadia Afrin Purba: Okay? But I have a quantum in it, okay?
Sadia Afrin Purba: I have a quantum document.
Sadia Afrin Purba: I have prepared the quantum entangle somehow, so I have a quantum document.
Sadia Afrin Purba: And I learned that.
Sadia Afrin Purba: King.
Sadia Afrin Purba: No.
Sadia Afrin Purba: I can, I mean, now I get a, new quantum document with a new breed, okay?
Sadia Afrin Purba: No.
Sadia Afrin Purba: I mean, I can instantly know that that is a dog. This is an instant, information transfer. I don't need a communication channel.
Sadia Afrin Purba: I mean, yeah, in practice, if we want to build a quantum internet, we need a classical channel and all that stuff, but let's just not focus on that.
Sadia Afrin Purba: without any communication, without any measurement, I can know that, yeah, there is another image that is, a dog. So that is the coherent… and that is a right information, not a wrong information.
Sadia Afrin Purba: In classical world, if you want to communicate that, you need some kind of channel, or you need some kind of bit transformation, right? In quantum, there is no bit transformation.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: Okay, then I have selected these, three papers. The first one actually, described the entangled base.
Sadia Afrin Purba: Quantum advantage for them.
Sadia Afrin Purba: learning task, and another one is a quantum freelance theory. It is a theoretical paper, and this paper actually theoretically proved that if we have entangled data, then only one, training sample is enough to learn the whole system.
Sadia Afrin Purba: This is the theoretical proof of this paper.
Sadia Afrin Purba: And another is, discourse is also a quantum correlation, so it is a discourse code-based advantage.
Sadia Afrin Purba: Okay, then it is just timeline. I want to, give an impression that we are very early in a quantum computing, and very early in a quantum computing with machine learning, so we should be very open-minded and
Sadia Afrin Purba: You know… optimistic. At least I am very optimistic. So, these are the…
Sadia Afrin Purba: mainly focused on entanglement. It's actually acquired by Strodinger in 1935. Einstein didn't believe it, but in 1964, a theory came, Bell's theorem, which actually challenged Einstein's view.
Sadia Afrin Purba: And in 1972, it was proven that, yeah, entanglement is a true thing. It is not something theoretical. We can create entanglement, so Einstein was wrong in this particular case.
Sadia Afrin Purba: And in 2009, there is the first algorithm, HHL algorithm. I don't know about very deeply about this algorithm, but this particular algorithm was invented to solve the linear system.
Sadia Afrin Purba: And what did Einstein say about quantum mechanics?
Sadia Afrin Purba: There is two… yeah, there is two famous quotes that God does not play with dice, and another quote is, I would like to believe that the moon is there when I am not looking at it.
Sadia Afrin Purba: Because in quantum, mechanics, there is an interpretation that when I… there is an object, only when I see it, there is no real existence of this object.
Sadia Afrin Purba: But then we also say, if you think you understand what I'm saying?
Sadia Afrin Purba: I don't understand… paramilia.
Sadia Afrin Purba: women.
Sadia Afrin Purba: Yeah, I don't fully understand quantum mechanics, but I understand enough to appreciate it.
Sadia Afrin Purba: Okay, now, the… But we're in this… Nice area.
Sadia Afrin Purba: Like, it does things for you. Yeah. Okay, so even though we're only in a disk, it's good enough to do stuff with them now. Tisha, currently we…
Sadia Afrin Purba: Yeah, currently we have a thousand… mostly thousand qubits, and also those are very noisy, so we have to create error-corrected algorithm and all that stuff.
Sadia Afrin Purba: Okay, so we are here right now, and probably within 10 years, we will have a full fault-tolerant quantum computer.
Sadia Afrin Purba: Okay, now some fundamental. Now, I, really like to,
Sadia Afrin Purba: Now, in the fundamental, I am going to talk about the qubits. Now, the best way to represent qubit is, like, electron and its nucleus.
Sadia Afrin Purba: So, we are… I always think that electrons stay either CAT0 or CAT1, either ground state or excited state. But in… in practice.
Sadia Afrin Purba: it cannot make up its mind. I mean, it is a probability… a cloud of probability. For example, the red portion means that, yeah, here is a high probability that we can find the electron in here.
Sadia Afrin Purba: And the blue one means that, yeah, there are low probability. So it is not discrete. There are some kind of probability and, cloud of probabilities going on. So how can we
Sadia Afrin Purba: represent the… information. We can represent that CAT0 and CAT1. This is the quantum bit.
Sadia Afrin Purba: With alpha and beta. These are probability amplitudes. It, it is telling us that, if we, it is telling us that, this side, the quantum state, in,
Sadia Afrin Purba: Could be in a ground state with alpha probability, alpha square probability, or in a
Sadia Afrin Purba: Excited state in a beta square probability.
Sadia Afrin Purba: This alpha and beta itself, probability amplitude, not probability, because it could be minus 1, it could be a complex number. So, from there, we can get probability, but these are a probability amplitude, so there's a slight difference. Any question?
Sadia Afrin Purba: Do you know the paper that that electron bill paper indicates on that?
Sadia Afrin Purba: Yeah, it is from probably 2003's paper.
Sadia Afrin Purba: Yeah.
Sadia Afrin Purba: I don't remember the name.
Sadia Afrin Purba: Oh, okay.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: Yeah, I got the image from that.
Sadia Afrin Purba: Yeah.
Sadia Afrin Purba: Yeah, that is cool.
Sadia Afrin Purba: Okay, so the difference is classical bit can be 0 or 1, right? We can never get any kind of probability in beating, but in quantum bit, there is a probability that we can get here.
Sadia Afrin Purba: Which is a superposition.
Sadia Afrin Purba: And if we measure that, we will have a, classical probability.
Sadia Afrin Purba: So, I would like to view in a, vector form.
Sadia Afrin Purba: CAT0 means
Sadia Afrin Purba: 1, 0. I like to say is that Cat0 means the probability of finding the qubit in a ground state, or upspring, or any kind of physical property is 100%, because the alpha for this position, the zero position, is 100%.
Sadia Afrin Purba: Similarly, CAT1 means that it is in a 100% probability that I will find the electron in a ground state.
Sadia Afrin Purba: And more generally, we can write in this format, and by doing the square, magnitude square, we will get a classical probability, and the classical probability has to be 1.
Sadia Afrin Purba: Sorry.
Sadia Afrin Purba: Okay, now, we can also represent this in a blot sphere. It is a sphere. This is our zero cat, this is… this is our one cat, and there are…
Sadia Afrin Purba: Many states where the, electron can be.
Sadia Afrin Purba: And this is our quantum circuit, it is also the quantum algorithm or quantum model, whatever it is. Now, this is nothing but linear sequence of
Sadia Afrin Purba: linear transformation of quantum gate. Quantum gate is also, like.
Sadia Afrin Purba: Some metrics, some specific metrics that are helpful to do the linear transformation.
Sadia Afrin Purba: And the quantum gate has to be unitary.
Sadia Afrin Purba: It has to be unitary, and Hadamat is a very famous git to create the create the… superposition.
Sadia Afrin Purba: And Poly XYZ, they also rotate the computational basis in a particular angle and all that stuff. And for, creating the entanglement, we need the CNOT gate.
Sadia Afrin Purba: And why we need to… why the quantum gate has to be unitary? Because we want to reserve the probability. And unitary has some very cool, feature from linear algebra, so we need the gate to be unitary.
Sadia Afrin Purba: And how can we do the measurement? By convention, we always use a jet basis to do the measurement. When we measure.
Sadia Afrin Purba: The electron makeup is mine, and it can be only 0 or 1.
Sadia Afrin Purba: So, it is just, more in detail that how it is happening. I mean, if I apply Hadamatt gate to the zero state.
Sadia Afrin Purba: Then simply metric multiplication, and we will get 1 by root over 2, 1 by root over 2, which is 50%, and that is why it is the… it is very famous to say that a qubit can be in a state of both 0 and 1 at the both… at the same thing.
Sadia Afrin Purba: This is the superposition.
Sadia Afrin Purba: And, this is a very, simple start kit.
Sadia Afrin Purba: And if we calculate the probability, we can see that it is 50-50%. After measurement, the electron makeup, it mines and, collapses through one, one, one basis.
Sadia Afrin Purba: Any question?
Sadia Afrin Purba: cool, but you need it? Because I guess it encapsulates the… For the single qubit, I think the visualization. For the visualization, we need that. Yeah.
Sadia Afrin Purba: Yeah, we can do that.
Sadia Afrin Purba: There's a maintenance.
Sadia Afrin Purba: Yeah, it is 556 chance before the measurement.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: One.
Sadia Afrin Purba: No, when I measure, I measure in a particular basis, J basis, and when I measure it, with… there is a form, measurement, postulate, I mean, we… there involve eigenvalue and all that stuff.
Sadia Afrin Purba: And then it makes up your mind that, yeah, it is 50-50, so randomly choose zero, when it is 50-50. But suppose, suppose in this case, in the zero, there is a high probability. If I run
Sadia Afrin Purba: many times, then it will always, collapse to zero, the highest state. For 50-50, it takes randomly. It shows randomly.
Sadia Afrin Purba: And so what am I supposed to work.
Sadia Afrin Purba: Yeah, yeah, yeah, because, probability has to be 1.
Sadia Afrin Purba: But we could have just received even outcome 1 instead of outcome 0. Yeah.
Sadia Afrin Purba: So, it is also another circuit, where, the zero… Zero probability is higher.
Sadia Afrin Purba: And if I use 2 qubits, then we have equal, equal probability.
Sadia Afrin Purba: But it is not fun, you know? If we use only superposition, we will always get the equal probability. It is not fun.
Sadia Afrin Purba: And… The… for the… that particular thing, we need correlation.
Sadia Afrin Purba: That is why the correlation is important, not only superposition. With superposition, we are not getting anywhere.
Sadia Afrin Purba: So, we can create the correlation by CNOT gate. It is very simple, it is a control gate, and it is a target gate. We will change the target.
Sadia Afrin Purba: We will flip the target if only the control bit is 1. This is a simple logic.
Sadia Afrin Purba: By doing that, okay, previously.
Sadia Afrin Purba: When we use only Hartamatin, rotation gate, even if we don't use the rotation gate, the probability will be equal.
Sadia Afrin Purba: But, when we… When we use the CNOT gate, It is kind of,
Sadia Afrin Purba: extra logic, right. So, this particular 0, 1, and 1, 0, this state can never basis.
Sadia Afrin Purba: Right? So, we get zero probability, and we get 50-50% probability for 0, 0 and 11.
Sadia Afrin Purba: So, correlation is important to filter out the equal probability thing, get some good information, and all that stuff.
Sadia Afrin Purba: Then, I'll just skip this slide.
Sadia Afrin Purba: I want to make the point that the definition of entanglement is
Sadia Afrin Purba: Suppose we have a quantum state, and we cannot vector out that quantum state into an individual state. So, this was an example that proved that if we use C0,
Sadia Afrin Purba: It has to be in Dengal.
Sadia Afrin Purba: And… Then we have some other kind of, correlation, as I mentioned.
Sadia Afrin Purba: that is quantum disc code. From my understanding, I think the quantum discord is a very generalized quantum correlation. For example, in this particular paper.
Sadia Afrin Purba: they showed that up to this G position, mixing parameter J, up to this position, we get, entangled state.
Sadia Afrin Purba: Below that position, we get some separable state, but we can get some correlation there also.
Sadia Afrin Purba: Okay, so if we use 0, we have equal probability for all the BCs.
Sadia Afrin Purba: If we increase the J value, the 0, 1,
Sadia Afrin Purba: And one zero. This correlation, increased, and other decreased.
Sadia Afrin Purba: Which one?
Sadia Afrin Purba: we don't get any correlation here, because these two particulars, 0 and 1, these are correlated to each other. So, if the first qubit is 0, the second has to be 1. If the second is 1, the…
Sadia Afrin Purba: This, this has to be zero, so this kind of correlation.
Sadia Afrin Purba: Now, just moving to the paper.
Sadia Afrin Purba: Okay, now, the main problem is the classical model faces a communication bottleneck.
Sadia Afrin Purba: Where the internal height, latency dimension, or the hidden space, scale linearly with the number of sequence. For example, if we have… we want to, model a
Sadia Afrin Purba: translation task. We have to, we have to have
Sadia Afrin Purba: more hidden layer to capture it properly. So it's linear… linear with the number of samples.
Sadia Afrin Purba: And how did they solve it? They used… they actually, came up with a very specific sequence translation task.
Sadia Afrin Purba: And then they use entanglement to, solve the… Shoulder communication bottleneck.
Sadia Afrin Purba: How did the endanglement shelf?
Sadia Afrin Purba: And that non-correlation, non-local correlation provided by entangle substitute the need for explicit communication required to coordinate remote part of the input sequence. That is what I… giving… I was…
Sadia Afrin Purba: I was giving a example that suppose we have a one entangled pair. I think we have a one entangled image. We know about it.
Sadia Afrin Purba: So, we don't need to measure the other one.
Sadia Afrin Purba: So that we don't need to do the, back and forth, or the information transfer… transformation. That is…
Sadia Afrin Purba: How the entanglement helps that… helps us.
Sadia Afrin Purba: Now, I really have to just quickly go through this game, the Magic Square game.
Sadia Afrin Purba: Suppose we have two players.
Sadia Afrin Purba: And there is no communication between them.
Sadia Afrin Purba: And there is one referee. The referee will provide the two player, either 1, 2, 3, and the player will provide, some bit string of 3LIN.
Sadia Afrin Purba: And the win condition is that
Sadia Afrin Purba: Each row, the LS will provide the row string, so the each row must have auth parity, and even… and the column must be
Sadia Afrin Purba: Event parity, sorry, row would be… row must be what parity, column must be event parity. And the intersecting cell has to… in the intersecting cell, the bit value should be same.
Sadia Afrin Purba: So, it is… for example, the referee gave, X equal to 2 to the L is, so the row is 2, and Y is 1. Column is 1. And…
Sadia Afrin Purba: Alice has to provide a, auth parity.
Sadia Afrin Purba: So, he provides 010, and Bob provides 101. And in the intersecting, cell.
Sadia Afrin Purba: The big string match, so they win.
Sadia Afrin Purba: But, in this case, when the row and column is 2-2,
Sadia Afrin Purba: The big string doesn't match, so they lose.
Sadia Afrin Purba: So, if we play this game, mini-round, and fill up the…
Sadia Afrin Purba: fill up all the shell in the classical way. Whatever base classical strategy you come up with.
Sadia Afrin Purba: There is no chance you can do better than 8x9.
Sadia Afrin Purba: In one case, you will always lose, but if you… if you use any quantum, state, or quantum strategy, then there is guarantee that you will win 100% time.
Sadia Afrin Purba: So here, quantum strategy gives you, accuracy advantage.
Sadia Afrin Purba: Negotion?
Sadia Afrin Purba: And that's just because Alice and Bob communicate with each other using quantum entanglement.
Sadia Afrin Purba: In quantum, in quantum case, they cannot even, they cannot communicate during the game, but before that, they can, come up, come up with a strategy.
Sadia Afrin Purba: But during the game, they cannot, communicate. Okay, now, suppose…
Sadia Afrin Purba: This one, yeah, it's a little mask.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: So, suppose, the… they…
Sadia Afrin Purba: they come up with a quantum strategy, and they prepare a quantum state. This is one… one of the states.
Sadia Afrin Purba: Okay, as the… one of the states.
Sadia Afrin Purba: They plan that, yeah, we will measure our, measure our quantum state based on the row column we get. That is their strategy. They decided before the game. Now.
Sadia Afrin Purba: For example, the referee gives, row 2 and Bob, column 3.
Sadia Afrin Purba: Then… by measuring
Sadia Afrin Purba: It is like we are rotating the quantum state in a X2 and Z3. This is just…
Sadia Afrin Purba: some predefined basis, X3 and, J3.
Sadia Afrin Purba: And we… and when we measure it, it collapsed to one state, one of the states, okay? We have this, superposition, state, and after measurement, we have this state.
Sadia Afrin Purba: Now, the first two bits are for, Alice, and the last two bits are for Bob.
Sadia Afrin Purba: Now, she saw that, she got 01, and the rule is she has to provide odd parity. So the third… so she knows that the third parity… third bit would be 0.
Sadia Afrin Purba: Similarly, the Bob knows that, yeah, the first, first, two must be 1, 0, and the last has to be 1.
Sadia Afrin Purba: And if they do that, if they follow their measurement outcome.
Sadia Afrin Purba: they will always win. It is not only 2 and 3 case. For every row and column case, they will win.
Sadia Afrin Purba: It is proven. So they will get 100% winning probability.
Sadia Afrin Purba: If they use this kind of superposition and, entanglement stuff.
Sadia Afrin Purba: Okay. But this cannot be done.
Sadia Afrin Purba: No, not classical… with classical probability, you'll get…
Sadia Afrin Purba: What makes it not possible to ask a problem? Because in classical wall, how can you… There is,
Sadia Afrin Purba: I mean, there is no way that all the columns are odd probability, or odd parity, and all the rows are, even parity. I mean, in one of the cases, they lose.
Sadia Afrin Purba: In the classical world.
Sadia Afrin Purba: Or if you just design it using classical problems. Yeah.
Sadia Afrin Purba: Yeah.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: So, if the game played, for example, 5 times, And Goldman Emmys…
Sadia Afrin Purba: they have a state of one estate, and one quantum mistake other. So, as I know that one quantum state will collapse, as you do another.
Sadia Afrin Purba: So, they will not get the information after one tax.
Sadia Afrin Purba: How come they will continue this play?
Sadia Afrin Purba: Oh.
Sadia Afrin Purba: For every round, they will collapse them.
Sadia Afrin Purba: quantum state, and get the beat value. Yeah. So they will need, for 5 times, they will need to organize it?
Sadia Afrin Purba: But, the, we know the initial state. This is the initial state. So, we need one, one initial state. Five times, they probably used up, main, the same initial state.
Sadia Afrin Purba: Okay, yeah, I got your point, that, for example.
Sadia Afrin Purba: the… every time it will provide, it will get this way, but the randomness comes from the row and column value. Referee will provide you the, column and,
Sadia Afrin Purba: Row number randomly.
Sadia Afrin Purba: So, when you measure, the value would be different, everything.
Sadia Afrin Purba: Because, the, measurement… Ms. Armin…
Sadia Afrin Purba: operator, X2. X2, if you measure with X2, it will be different.
Sadia Afrin Purba: If you measure with X3, to the same quantum, quantum state. It would be different, right?
Sadia Afrin Purba: So the randomness comes from the row and column value that is given by the referee.
Sadia Afrin Purba: Yeah, yeah, I know.
Sadia Afrin Purba: I know, I know. Okay.
Sadia Afrin Purba: Now, what they did, they take the concept of this magic rule and build a very specific sequence translation task. I really want to skip this part, but we can come back here.
Sadia Afrin Purba: And they come up with a very specific role, not… not any of our traditional machine learning role.
Sadia Afrin Purba: But it is also a, lining test. They are, lining some kind of sequence. Inputs… they are providing input and, predicting the output.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: Now, now the main outcome is…
Sadia Afrin Purba: But by doing that, the main outcome is, if the same task they perform, classically, the…
Sadia Afrin Purba: accuracy, or the score will never be 100%. But with quantum strategy.
Sadia Afrin Purba: They get 100% accuracy, 100% score.
Sadia Afrin Purba: So, and based on their findings, they provide, three
Sadia Afrin Purba: theorem. The first theorem established that,
Sadia Afrin Purba: During inference, we get exponential separation.
Sadia Afrin Purba: in complexity. Because, in inference.
Sadia Afrin Purba: We have to suppose the next token prediction. To predict the next token, we have to iterate all our previous token, right?
Sadia Afrin Purba: In classical world, so it is linear. But in quantum world, it has, it, it will not grow, within a number of, number of, number of sequence. It will, it is constant.
Sadia Afrin Purba: And another one is, they, they…
Sadia Afrin Purba: provide the inference advantage with constant noise. So, they use constant noise and see that, yeah, they are advantageous. The O , the constant, advantage still remains.
Sadia Afrin Purba: And…
Sadia Afrin Purba: Same training identities. For training, algorithm, we need… if we have n-dimensional data, we need n-dimensional hidden layer to capture it… capture the perfect, output.
Sadia Afrin Purba: But, for quantum, we need a constant, requirement. This is a quantum side, circuit.
Sadia Afrin Purba: Now, here is a, little numerical, demonstration that if we used a quantum
Sadia Afrin Purba: Quantum algorithm, we would need only 1.28 parameter.
Sadia Afrin Purba: But if we use any classical algorithm, any, recurrent algorithm or encoder-decoder, there is, like, 3, 3 into 10 to the power 4, or 6 into 10 to the power 4 parameter. And by using quantum algorithm, we are actually, getting 100%
Sadia Afrin Purba: Accuracy. So, parameter-wise, accuracy-wise, it is good.
Sadia Afrin Purba: These are their experimentation results, so the main outcome is the quantum model achieved a perfect score for this particular task.
Sadia Afrin Purba: about 2 to 3 order of magnitude for your trainable parameter than the classical algorithm. That is the main
Sadia Afrin Purba: Dish of this paper.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: Do you have any
Sadia Afrin Purba: But we only got the 5 minutes.
Sadia Afrin Purba: The webinar queue tried to summarize the other two papers quickly.
Sadia Afrin Purba: Okay. And then we'll continue some of this… The private sector.
Sadia Afrin Purba: Thanks.
Sadia Afrin Purba: Okay, the second… the entangled data and quantum intervals. The main idea is
Sadia Afrin Purba: We need only… if we have an entangled dataset, if we have that, and we want to learn anything from that entangled dataset, we only need one
Sadia Afrin Purba: Training, training point.
Sadia Afrin Purba: To learn the system.
Sadia Afrin Purba: That is the main summary.
Sadia Afrin Purba: Okay, and they provide a theory. This is the generational risk theory.
Sadia Afrin Purba: And it is also a numerical thing, for example.
Sadia Afrin Purba: We have one, one training data, and…
Sadia Afrin Purba: the system is maximally entangled. Then the law, then the risk is minus.
Sadia Afrin Purba: But the quantum risk is non-negative by definition. So, when we get a minus value.
Sadia Afrin Purba: It is… means we are getting a zero value.
Sadia Afrin Purba: Okay.
Sadia Afrin Purba: This is a circuit they use.
Sadia Afrin Purba: And, they, simulate their result.
Sadia Afrin Purba: Now, there are many open questions. For example, this particular system actually use, assume that we have
Sadia Afrin Purba: a perfect training condition. It does not happen like that way, right?
Sadia Afrin Purba: And the third paper, In the third paper,
Sadia Afrin Purba: They use quantum disc code, not the quantum, quantum entanglement, because quantum discord can provide some, correlation, and they use that correlation to get, advantage.
Sadia Afrin Purba: Okay, they provide, they say that if there is no covariance.
Sadia Afrin Purba: Then, the, kernel system, the…
Sadia Afrin Purba: carnal machines cannot learn anything. That is their one theory. So, if we have a coherent quantum system, the learning performance of a kernel function, we can learn a kernel function.
Sadia Afrin Purba: And another theory is, if we have a coherent quantum system, we can generate some, this… that is another theory.
Sadia Afrin Purba: So, this is the technical thing.
Sadia Afrin Purba: And this is, they actually show that
Sadia Afrin Purba: Alpha is a purity value. If they improve the purity, the accuracy also improves.
Sadia Afrin Purba: But there are many open questions. For example, there are lack of
Sadia Afrin Purba: comparison between, between the classical algorithm and their algorithm. Also, there are many, quantum algorithms that, classify… that is used to classify the carnal metrics. They didn't compare those algorithms together.
Sadia Afrin Purba: So, there are many open questions about that.
Sadia Afrin Purba: So, in summary, we have this, that if we use entanglement, there is possible that we will get computational speedup and data efficiency.
Sadia Afrin Purba: And… The second one is theoretical and sensitive to noise, but…
Sadia Afrin Purba: It is a very important theorem.
Sadia Afrin Purba: And if we use, this code.
Sadia Afrin Purba: Then we can get some advantages at present time.
Sadia Afrin Purba: So, but the most of the proof assume the script data. For example, in the first paper, they used 01-bit string only, and assume perfect training condition, and constant device noise, but in practice, we deal with,
Sadia Afrin Purba: continuous data training error. So, there is a huge gap in the in their, theorem.
Sadia Afrin Purba: So we need a quantum research roadmap that is theoretically complete, measurable, and deployable.
Sadia Afrin Purba: So, for that, I have some roadmap. For example, we need
Sadia Afrin Purba: At least two theories that actually reformed the quantum freelance theory.
Sadia Afrin Purba: I mean, we have… we need a learning theorem.
Sadia Afrin Purba: That also… that also consider imperfect training.
Sadia Afrin Purba: Condition, and also another, theorem that, consider
Sadia Afrin Purba: All, all machine learning tasks, not only, not only a specific handmade machine learning task.
Sadia Afrin Purba: And we need a proper data encoding, and try to figure out how data encoding, in, data encoding.
Sadia Afrin Purba: Effect the quantum advantage, and evaluation metric.
Sadia Afrin Purba: For classical one, we need, we use p-value or statistical significance. But in quantum world, if we only rely on the p-value, we actually are not going to…
Sadia Afrin Purba: going to get the, proper evaluation. We need to consider the, wall clock value. We also need to consider that quantum device might use less amount of energy, rather than the high-performance computing.
Sadia Afrin Purba: And… We have to consider those, not only the p-value and all the… and all the accuracy thing.
Sadia Afrin Purba: And then we don't have any proper benchmark data set. First of all, we need entangle dataset.
Sadia Afrin Purba: We… we can generate integral datasheet from the lab, but
Sadia Afrin Purba: there is a… there should be a good recess field where we try to find out where is the entangled data, how can we find the entangled data, or how can we convert the classical data to entanglement? And…
Sadia Afrin Purba: As a classical dataset, most of the literature use MNIST
Sadia Afrin Purba: classical data. This is very easy data for
Sadia Afrin Purba: Classical problem. We need some more difficult problem.
Sadia Afrin Purba: To have a proper benchmark result.
Sadia Afrin Purba: And then, we have to build a system, a hybrid system, where a quantum and classical will be, tied together. And here, also, we can,
Sadia Afrin Purba: we can mix up the different kind of correlation. For example, we can use the entanglement for the expressive model, and this code for a noise-resilient system.
Sadia Afrin Purba: And then the pilot domain could be an easy signal segmentation, because it is a very difficult task in a, classical setting.
Sadia Afrin Purba: Or multimodal classification. Multimodal classification, as I mentioned, because if we want to, classify all the breed of the dog, we need trillions of data. We can minimize that if we use the quantum entanglement and quantum property.
Sadia Afrin Purba: So, these are the roadmap.
Sadia Afrin Purba: And I want to close my thought that
Sadia Afrin Purba: We… why do we want to do machine learning?
Sadia Afrin Purba: Many… because we want to solve the intelligence, we want to understand our… how our brain works, and all that stuff.
Sadia Afrin Purba: But, only focusing on that, we forget about that there are other intelligents, other intelligents from the animal. In fact, there are some intelligent in the plant. For example, the leaves move to a certain direction to get the sun and all that stuff.
Sadia Afrin Purba: And if I look into this video, I,
Sadia Afrin Purba: It is using bread as a trap, and didn't catch the big fish, because it cannot carry it.
Sadia Afrin Purba: But, it will carry, it will catch the small fish.
Sadia Afrin Purba: So, I think it is a very intelligent BART, and if we provide… if we create a robot bart with lots of data, still.
Sadia Afrin Purba: That part can… that robot bird cannot give such performance.
Sadia Afrin Purba: And the quantum system, the quantum particle is universal. So, to get a artificial general intellect, we really should focus on this quantum
Sadia Afrin Purba: Machine learning mechanism.
Sadia Afrin Purba: And also, recently, we have figured out that in our brain neuron, we, we can find out quantum properties. So it is a very miracle that in the noisy environment, there are… there can be quantum effect. So…
Sadia Afrin Purba: This is very… This has many more potential, I think. And this is the references.
Sadia Afrin Purba: Thank you.
Sadia Afrin Purba: In the interest of time, I will excuse the… Now, committee members?
Sadia Afrin Purba: Continuous.
Sadia Afrin Purba: Is it coming?
Sadia Afrin Purba: Hammers?
Sadia Afrin Purba: No, actually. I… Yeah, fucking stop, work.