>> Announcer: From around the globe, it's theCUBE. Covering the UPGRADE 2020, the NTT Research Summit. Presented by NTT research. >> Hey, welcome back everybody. Jeff Frick here with theCUBE. Welcome back to our ongoing coverage of UPGRADE 2020. It's the NTT Research Labs Summit, and it's all about upgrading reality. Heavy duty basic research around a bunch of very smart topics. And we're really excited to have our next guest to kind of dive in. I promise you, it'll be the deepest conversation you have today, unless you watch a few more of these segments. So our first guest we're welcoming back Kazuhiro Gomi He's the president and CEO of NTT research, Kaza great to see you. >> Good to see you. And joining him is Yoshi Yamamoto. He is a fellow for NTT Research and also the director of the Physics and Informatics Lab. Yoshi, great to meet you as well. >> Nice to meet you. >> So I was teasing the crew earlier, Yoshi, when I was doing some background work on you and I pulled up your Wikipedia page and I was like, okay guys, read this thing and tell me what a, what Yoshi does. You that have been knee deep in quantum computing and all of the supporting things around quantum heavy duty kind of next gen computing. I wonder if you can kind of share a little bit, you know, your mission running this labs and really thinking so far in advance of what we, you know, kind of experience and what we work with today and this new kind of basic research. >> NTT started the research on quantum computing back in 1986 87. So it is already more than 30 years. So, the company invested in this field. We have accumulated a lot of sort of our ideas, knowledge, technology in this field. And probably, it is the right time to establish the connection, close connection to US academia. And in this way, we will jointly sort of advance our research capabilities towards the future. The goal is still, I think, a long way to go. But by collaborating with American universities, and students we can accelerate NTT effort in this area. >> So, you've been moving, you've been working on quantum for 30 years. I had no idea that that research has been going on for such a very long time. We hear about it in the news and we hear about it a place like IBM and iSensor has a neat little demo that they have in the new sales force period. What, what is, what makes quantum so exciting and the potential to work so hard for so long? And what is it going to eventually open up for us when we get it to commercial availability? >> The honest answer to that question is we don't know yet. Still, I think after 30 years I think of hard working on quantum Physics and Computing. Still we don't know clean applications are even, I think we feel that the current, all the current efforts, are not necessarily, I think, practical from the engineering viewpoint. So, it is still a long way to go. But the reason why NTT has been continuously working on the subject is basically the very, sort of bottom or fundamental side of the present day communication and the computing technology. There is always a quantum principle and it is very important for us to understand the quantum principles and quantum limit for communication and computing first of all. And if we are lucky, maybe we can make a breakthrough for the next generation communication and computing technology based on quantum principles. >> Right. >> But the second, is really I think just a guess, and hope, researcher's hope and nothing very solid yet. >> Right? Well, Kazu I want to go, go to you cause it really highlights the difference between, you know, kind of basic hardcore fundamental research versus building new applications or building new products or building new, you know, things that are going to be, you know, commercially viable and you can build an ROI and you can figure out what the customers are going to buy. It really reflects that this is very different. This is very, very basic with very, very long lead times and very difficult execution. So when, you know, for NTT to spend that money and invest that time and people for long, long periods of time with not necessarily a clean ROI at the end, that really, it's really an interesting statement in terms of this investment and thinking about something big like upgrading reality. >> Yeah, so that's what this, yeah, exactly that you talked about what the basic research is, and from NTT perspective, yeah, we feel like we, as Dr. Yamamoto, he just mentioned that we've been investing into 30 plus years of a time in this field and, you know, and we, well, I can talk about why this is important. And some of them is that, you know, that the current computer that everybody uses, we are certainly, well, there might be some more areas of improvement, but we will someday in, I don't know, four years, five years, 10 years down the road, there might be some big roadblock in terms of more capacity, more powers and stuff. We may run into some issues. So we need to be prepared for those kinds of things. So, yes we are in a way of fortunate that we are, we have a great team to, and a special and an expertise in this field. And, you know, we have, we can spend some resource towards that. So why not? We should just do that in preparation for that big, big wall so to speak. I guess we are expecting to kind of run into, five, 10 years down the road. So let's just looking into it, invest some resources into it. So that's where we are, we're here. And again, I I'm, from my perspective, we are very fortunate that we have all the resources that we can do. >> It's great. Right, as they give it to you. Dr. Yamamoto, I wonder if you can share what it's like in terms of the industry and academic working together. You look at the presentations that are happening here at the event. All the great academic institutions are very well represented, very deep papers. You at NTT, you spend some time at Stanford, talk about how it is working between this joint development with great academic institutions, as well as the great company. >> Traditionally in the United States, there has been always two complementary opportunities for training next generation scientists and engineers. One opportunity is junior faculty position or possible position in academia, where main emphasis is education. The other opportunity is junior researcher position in industrial lab where apparently the focus emphasis is research. And eventually we need two types of intellectual leaders from two different career paths. When they sort of work together, with a strong educational background and a strong research background, maybe we can make wonderful breakthrough I think. So it is very important to sort of connect between two institutions. However, in the recent past, particularly after Better Lab disappeared, basic research activity in industrial lab decreases substantially. And we hope MTT research can contribute to the building of fundamental science in industry side. And for that purpose cross collaboration with research Universities are very important. So the first task we have been working so far, is to build up this industry academia connection. >> Huge compliment NTT to continue to fund the basic research. Cause as you said, there's a lot of companies that were in it before and are not in it any more. And when you often read the history of, of, of computing and a lot of different things, you know, it goes back to a lot of times, some basic, some basic research. And just for everyone to know what we're talking about, I want to read a couple of, of sessions that you could attend and learn within Dr. Yamamoto space. So it's Coherent nonlinear dynamics combinatorial optimization. That's just one session. I love it. Physics successfully implements Lagrange multiplier optimization. I love it. Photonics accelerators for machine learning. I mean, it's so it's so interesting to read basic research titles because, you know, it's like a micro-focus of a subset. It's not quantum computing, it's all these little smaller pieces of the quantum computing stack. And then obviously very deep and rich. Deep dives into those, those topics. And so, again, Kazu, this is the first one that's going to run after the day, the first physics lab. But then you've got the crypto cryptography and information security lab, as well as the medical and health information lab. You started with physics and informatics. Is that the, is that the history? Is that the favorite child you can lead that day off on day two of the event. >> We did throw a straw and Dr. Yamamoto won it Just kidding (all laugh) >> (indistinct), right? It's always fair. >> But certainly this quantum, Well, all the topics certainly are focuses that the basic research, that's definitely a commonality. But I think the quantum physics is in a way kind of very symbolic to kind of show that the, what the basic research is. And many people has a many ideas associated with the term basic research. But I think that the quantum physics is certainly one of the strong candidates that many people may think of. So well, and I think this is definitely a good place to start for this session, from my perspective. >> Right. >> Well, and it almost feels like that's kind of the foundational even for the other sessions, right? So you talk about medical or you talk about cryptography in information, still at the end of the day, there's going to be compute happening to drive those processes. Whether it's looking at, at, at medical slides or trying to do diagnosis, or trying to run a bunch of analysis against huge data sets, which then goes back to, you know, ultimately algorithms and ultimately compute, and this opening up of this entirely different set of, of horsepower. But Dr. Yamamoto, I'm just curious, how did you get started down this path of, of this crazy 30 year journey on quantum computing. >> The first quantum algorithm was invented by David Deutsch back in 1985. These particular algorithm turned out later the complete failure, not useful at all. And he spent seven years, actually, to fix loophole and invented the first successful algorithm that was 1992. Even though the first algorithm was a complete failure, that paper actually created a lot of excitement among the young scientists at NTT Basic Research Lab, immediately after the paper appeared. And 1987 is actually, I think, one year later. So this paper appeared. And we, sort of agreed that maybe one of the interesting future direction is quantum information processing. And that's how it started. It's it's spontaneous sort of activity, I think among young scientists of late twenties and early thirties at the time. >> And what do you think Dr. Yamamoto that people should think about? If, if, if again, if we're at a, at a cocktail party, not with not with a bunch of, of people that, that intimately know the topic, how do you explain it to them? How, how should they think about this great opportunity around quantum that's kept you engaged for decades and decades and decades. >> The quantum is everywhere. Namely, I think this world I think is fundamentally based on and created from quantum substrate. At the very bottom of our, sort of world, consist of electrons and photons and atoms and those fundamental particles sort of behave according to quantum rule. And which is a very different from classical reality, namely the world where we are living every day. The relevant question which is also interesting is how our classical world or classical reality surfaces from the general or universal quantum substrate where our intuition never works. And that sort of a fundamental question actually opens the possibility I think by utilizing quantum principle or quantum classical sort of crossover principle, we can revolutionize the current limitation in communication and computation. That's basically the start point. We start from quantum substrate. Under classical world the surface is on top of quantum substrate exceptional case. And we build the, sort of communication and computing machine in these exceptional sort of world. But equally dig into quantum substrate, new opportunities is open for us. That's somewhat the fundamental question. >> That's great. >> Well, I'm not, yeah, we can't get too deep cause you'll lose me, you'll lose me long before, before you get to the bottom of the, of the story, but, you know, I really appreciate it. And of course back to you this is your guys' first event. It's a really bold statement, right? Upgrade reality. I just wonder if, when you look at the, at the registrant's and you look at the participation and what do you kind of anticipate, how much of the anticipation is, is kind of people in the business, you know, kind of celebrating and, and kind of catching up to the latest research and how much of it is going to be really inspirational for those next, you know, early 20 somethings who are looking to grab, you know, an exciting field to hitch their wagon to, and to come away after this, to say, wow, this is something that really hooked me and I want to get down and really kind of advance this technology a little bit, further advance this research a little bit further. >> So yeah, for, from my point of view for this event, I'm expecting, there are quite wide range of people. I'm, I'm hoping that are interested in to this event. Like you mentioned that those are the, you know, the business people who wants to know what NTT does, and then what, you know, the wider spectrum of NTT does. And then, and also, especially like today's events and onwards, very specific to each topic. And we go into very deep dive. And, and so to, to this session, especially in a lot of participants from the academia's world, for each, each subject, including students, and then some other, basically students and professors and teachers and all those people as well. So, so that's are my expectations. And then from that program arrangement perspective, that's always something in my mind that how do we address those different kind of segments of the people. And we all welcoming, by the way, for those people. So to me to, so yesterday was the general sessions where I'm kind of expecting more that the business, and then perhaps some other more and more general people who're just curious what NTT is doing. And so instead of going too much details, but just to give you the ideas that the what's that our vision is and also, you know, a little bit of fla flavor is a good word or not, but give you some ideas of what we are trying to do. And then the better from here for the next three days, obviously for the academic people, and then those who are the experts in each field, probably day one is not quite deep enough. Not quite addressing what they want to know. So day two, three, four are the days that designed for that kind of requirements and expectations. >> Right? And, and are most of the presentations built on academic research, that's been submitted to journals and other formal, you know, peer review and peer publication types of activities. So this is all very formal, very professional, and very, probably accessible to people that know where to find this information. >> Mmh. >> Yeah, it's great. >> Yeah. >> Well, I, I have learned a ton about NTT and a ton about this crazy basic research that you guys are doing, and a ton about the fact that I need to go back to school if I ever want to learn any of this stuff, because it's, it's a fascinating tale and it's it's great to know as we've seen these other basic research companies, not necessarily academic but companies kind of go away. We mentioned Xerox PARC and Bell Labs that you guys have really picked up that mantle. Not necessarily picked it up, you're already doing it yourselves. but really continuing to carry that mantle so that we can make these fundamental, basic building block breakthroughs to take us to the next generation. And as you say, upgrade the future. So again, congratulations. Thanks for sharing this story and good luck with all those presentations. >> Thank you very much. >> Thank you. >> Thank you. Alright, Yoshi, Kazu I'm Jeff, NTT UPGRADE 2020. We're going to upgrade the feature. Thanks for watching. See you next time. (soft music)

>> My name is Franco Nori. Is a great pleasure to be here and I thank you for attending this meeting and I'll be talking about some of the work we are doing within the NTT-PHI group. I would like to thank the organizers for putting together this very interesting event. The topics studied by NTT-PHI are very exciting and I'm glad to be part of this great team. Let me first start with a brief overview of just a few interactions between our team and other groups within NTT-PHI. After this brief overview or these interactions then I'm going to start talking about machine learning and neural networks applied to computationally difficult problems in quantum physics. The first one I would like to raise is the following. Is it possible to have decoherence free interaction between qubits? And the proposed solution was a postdoc and a visitor and myself some years ago was to study decoherence free interaction between giant atoms made of superconducting qubits in the context of waveguide quantum electrodynamics. The theoretical prediction was confirmed by a very nice experiment performed by Will Oliver's group at MIT was probably so a few months ago in nature and it's called waveguide quantum electrodynamics with superconducting artificial giant atoms. And this is the first joint MIT Michigan nature paper during this NTT-PHI grand period. And we're very pleased with this. And I look forward to having additional collaborations like this one also with other NTT-PHI groups, Another collaboration inside NTT-PHI regards the quantum hall effects in a rapidly rotating polarity and condensates. And this work is mainly driven by two people, a Michael Fraser and Yoshihisa Yamamoto. They are the main driving forces of this project and this has been a great fun. We're also interacting inside the NTT-PHI environment with the groups of marandI Caltech, like McMahon Cornell, Oliver MIT, and as I mentioned before, Fraser Yamamoto NTT and others at NTT-PHI are also very welcome to interact with us. NTT-PHI is interested in various topics including how to use neural networks to solve computationally difficult and important problems. Let us now look at one example of using neural networks to study computationally difficult and hard problems. Everything we'll be talking today is mostly working progress to be extended and improve in the future. So the first example I would like to discuss is topological quantum phase transition retrieved through manifold learning, which is a variety of version of machine learning. This work is done in collaboration with Che, Gneiting and Liu all members of the group. preprint is available in the archive. Some groups are studying a quantum enhanced machine learning where machine learning is supposed to be used in actual quantum computers to use exponential speed-up and using quantum error correction we're not working on these kind of things we're doing something different. We're studying how to apply machine learning applied to quantum problems. For example how to identify quantum phases and phase transitions. We shall be talking about right now. How to achieve, how to perform quantum state tomography in a more efficient manner. That's another work of ours which I'll be showing later on. And how to assist the experimental data analysis which is a separate project which we recently published. But I will not discuss today because the experiments can produce massive amounts of data and machine learning can help to understand these huge tsunami of data provided by these experiments. Machine learning can be either supervised or unsupervised. Supervised is requires human labeled data. So we have here the blue dots have a label. The red dots have a different label. And the question is the new data corresponds to either the blue category or the red category. And many of these problems in machine learning they use the example of identifying cats and dogs but this is typical example. However, there are the cases which are also provides with there are no labels. So you're looking at the cluster structure and you need to define a metric, a distance between the different points to be able to correlate them together to create these clusters. And you can manifold learning is ideally suited to look at problems we just did our non-linearities and unsupervised. Once you're using the principle component analysis along this green axis here which are the principal axis here. You can actually identify a simple structure with linear projection when you increase the axis here, you get the red dots in one area, and the blue dots down here. But in general you could get red green, yellow, blue dots in a complicated manner and the correlations are better seen when you do an nonlinear embedding. And in unsupervised learning the colors represent similarities are not labels because there are no prior labels here. So we are interested on using machine learning to identify topological quantum phases. And this requires looking at the actual phases and their boundaries. And you start from a set of Hamiltonians or wave functions. And recall that this is difficult to do because there is no symmetry breaking, there is no local order parameters and in complicated cases you can not compute the topological properties analytically and numerically is very hard. So therefore machine learning is enriching the toolbox for studying topological quantum phase transitions. And before our work, there were quite a few groups looking at supervised machine learning. The shortcomings that you need to have prior knowledge of the system and the data must be labeled for each phase. This is needed in order to train the neural networks . More recently in the past few years, there has been increased push on looking at all supervised and Nonlinear embeddings. One of the shortcomings we have seen is that they all use the Euclidean distance which is a natural way to construct the similarity matrix. But we have proven that it is suboptimal. It is not the optimal way to look at distance. The Chebyshev distances provides better performance. So therefore the difficulty here is how to detect topological quantifies transition is a challenge because there is no local order parameters. Few years ago we thought well, three or so years ago machine learning may provide effective methods for identifying topological Features needed in the past few years. The past two years several groups are moving this direction. And we have shown that one type of machine learning called manifold learning can successfully retrieve topological quantum phase transitions in momentum and real spaces. We have also Shown that if you use the Chebyshev distance between data points are supposed to Euclidean distance, you sharpen the characteristic features of these topological quantum phases in momentum space and the afterwards we do so-called diffusion map, Isometric map can be applied to implement the dimensionality reduction and to learn about these phases and phase transition in an unsupervised manner. So this is a summary of this work on how to characterize and study topological phases. And the example we used is to look at the canonical famous models like the SSH model, the QWZ model, the quenched SSH model. We look at this momentous space and the real space, and we found that the metal works very well in all of these models. And moreover provides a implications and demonstrations for learning also in real space where the topological invariants could be either or known or hard to compute. So it provides insight on both momentum space and real space and its the capability of manifold learning is very good especially when you have the suitable metric in exploring topological quantum phase transition. So this is one area we would like to keep working on topological faces and how to detect them. Of course there are other problems where neural networks can be useful to solve computationally hard and important problems in quantum physics. And one of them is quantum state tomography which is important to evaluate the quality of state production experiments. The problem is quantum state tomography scales really bad. It is impossible to perform it for six and a half 20 qubits. If you have 2000 or more forget it, it's not going to work. So now we're seeing a very important process which is one here tomography which cannot be done because there is a computationally hard bottleneck. So machine learning is designed to efficiently handle big data. So the question we're asking a few years ago is chemistry learning help us to solve this bottleneck which is quantum state tomography. And this is a project called Eigenstate extraction with neural network tomography with a student Melkani , research scientists of the group Clemens Gneiting and I'll be brief in summarizing this now. The specific machine learning paradigm is the standard artificial neural networks. They have been recently shown in the past couple of years to be successful for tomography of pure States. Our approach will be to carry this over to mixed States. And this is done by successively reconstructing the eigenStates or the mixed states. So it is an iterative procedure where you can slowly slowly get into the desired target state. If you wish to see more details, this has been recently published in phys rev A and has been selected as a editor suggestion. I mean like some of the referees liked it. So tomography is very hard to do but it's important and machine learning can help us to do that using neural networks and these to achieve mixed state tomography using an iterative eigenstate reconstruction. So why it is so challenging? Because you're trying to reconstruct the quantum States from measurements. You have a single qubit, you have a few Pauli matrices there are very few measurements to make when you have N qubits then the N appears in the exponent. So the number of measurements grows exponentially and this exponential scaling makes the computation to be very difficult. It's prohibitively expensive for large system sizes. So this is the bottleneck is these exponential dependence on the number of qubits. So by the time you get to 20 or 24 it is impossible. It gets even worst. Experimental data is noisy and therefore you need to consider maximum-likelihood estimation in order to reconstruct the quantum state that kind of fits the measurements best. And again these are expensive. There was a seminal work sometime ago on ion-traps. The post-processing for eight qubits took them an entire week. There were different ideas proposed regarding compressed sensing to reduce measurements, linear regression, et cetera. But they all have problems and you quickly hit a wall. There's no way to avoid it. Indeed the initial estimate is that to do tomography for 14 qubits state, you will take centuries and you cannot support a graduate student for a century because you need to pay your retirement benefits and it is simply complicated. So therefore a team here sometime ago we're looking at the question of how to do a full reconstruction of 14-qubit States with in four hours. Actually it was three point three hours Though sometime ago and many experimental groups were telling us that was very popular paper to read and study because they wanted to do fast quantum state tomography. They could not support the student for one or two centuries. They wanted to get the results quickly. And then because we need to get these density matrices and then they need to do these measurements here. But we have N qubits the number of expectation values go like four to the N to the Pauli matrices becomes much bigger. A maximum likelihood makes it even more time consuming. And this is the paper by the group in Inns brook, where they go this one week post-processing and they will speed-up done by different groups and hours. Also how to do 14 qubit tomography in four hours, using linear regression. But the next question is can machine learning help with quantum state tomography? Can allow us to give us the tools to do the next step to improve it even further. And then the standard one is this one here. Therefore for neural networks there are some inputs here, X1, X2 X3. There are some weighting factors when you get an output function PHI we just call Nonlinear activation function that could be heavy side Sigmon piecewise, linear logistic hyperbolic. And this creates a decision boundary and input space where you get let's say the red one, the red dots on the left and the blue dots on the right. Some separation between them. And you could have either two layers or three layers or any number layers can do either shallow or deep. This cannot allow you to approximate any continuous function. You can train data via some cost function minimization. And then there are different varieties of neural nets. We're looking at some sequel restricted Boltzmann machine. Restricted means that the input layer speeds are not talking to each other. The output layers means are not talking to each other. And we got reasonably good results with the input layer, output layer, no hidden layer and the probability of finding a spin configuration called the Boltzmann factor. So we try to leverage Pure-state tomography for mixed-state tomography. By doing an iterative process where you start here. So there are the mixed States in the blue area the pure States boundary here. And then the initial state is here with the iterative process you get closer and closer to the actual mixed state. And then eventually once you get here, you do the final jump inside. So you're looking at a dominant eigenstate which is closest pure state and then computer some measurements and then do an iterative algorithm that to make you approach this desire state. And after you do that then you can essentially compare results with some data. We got some data for four to eight trapped-ion qubits approximate W States were produced and they were looking at let's say the dominant eigenstate is reliably recorded for any equal four, five six, seven, eight for the ion-state, for the eigenvalues we're still working because we're getting some results which are not as accurate as we would like to. So this is still work in progress, but for the States is working really well. So there is some cost scaling which is beneficial, goes like NR as opposed to N squared. And then the most relevant information on the quality of the state production is retrieved directly. This works for flexible rank. And so it is possible to extract the ion-state within network tomography. It is cost-effective and scalable and delivers the most relevant information about state generation. And it's an interesting and viable use case for machine learning in quantum physics. We're also now more recently working on how to do quantum state tomography using Conditional Generative Adversarial Networks. Usually the masters student are analyzed in PhD and then two former postdocs. So this CGANs refers to this Conditional Generative Adversarial Networks. In this framework you have two neural networks which are essentially having a dual, they're competing with each other. And one of them is called generator another one is called discriminator. And there they're learning multi-modal models from the data. And then we improved these by adding a cost of neural network layers that enable the conversion of outputs from any standard neural network into physical density matrix. So therefore to reconstruct the density matrix, the generator layer and the discriminator networks So the two networks, they must train each other on data using standard gradient-based methods. So we demonstrate that our quantum state tomography and the adversarial network can reconstruct the optical quantum state with very high fidelity which is orders of magnitude faster and from less data than a standard maximum likelihood metals. So we're excited about this. We also show that this quantum state tomography with these adversarial networks can reconstruct a quantum state in a single evolution of the generator network. If it has been pre-trained on similar quantum States. so requires some additional training. And all of these is still work in progress where some preliminary results written up but we're continuing. And I would like to thank all of you for attending this talk. And thanks again for the invitation.

Hi, I'm Hideo Mabuchi from Stanford University. This is my presentation on coherent nonlinear dynamics, and combinatorial optimization. This is going to be a talk, to introduce an approach, we are taking to the analysis, of the performance of Coherent Ising Machines. So let me start with a brief introduction, to ising optimization. The ising model, represents a set of interacting magnetic moments or spins, with total energy given by the expression, shown at the bottom left of the slide. Here the cigna variables are meant to take binary values. The matrix element jij, represents the interaction, strength and sign, between any pair of spins ij, and hi represents a possible local magnetic field, acting on each thing. The ising ground state problem, is defined in an assignment of binary spin values, that achieves the lowest possible value of total energy. And an instance of the easing problem, is specified by given numerical values, for the matrix j and vector h, although the ising model originates in physics, we understand the ground state problem, to correspond to what would be called, quadratic binary optimization, in the field of operations research. And in fact, in terms of computational complexity theory, it can be established that the, ising ground state problem is NP complete. Qualitatively speaking, this makes the ising problem, a representative sort of hard optimization problem, for which it is expected, that the runtime required by any computational algorithm, to find exact solutions, should asyntonically scale, exponentially with the number of spins, and four worst case instances at each end. Of course, there's no reason to believe that, the problem instances that actually arise, in practical optimization scenarios, are going to be worst case instances. And it's also not generally the case, in practical optimization scenarios, that we demand absolute optimum solutions. Usually we're more interested in, just getting the best solution we can, within an affordable cost, where costs may be measured in terms of time, service fees and or energy required for computation. This focus is great interest on, so-called heuristic algorithms, for the ising problem and other NP complete problems, which generally get very good, but not guaranteed optimum solutions, and run much faster than algorithms, that are designed to find absolute Optima. To get some feeling for present day numbers, we can consider the famous traveling salesman problem, for which extensive compilations, of benchmarking data may be found online. A recent study found that, the best known TSP solver required median runtimes, across a library of problem instances, that scaled as a very steep route exponential, for an up to approximately 4,500. This gives some indication of the change, in runtime scaling for generic, as opposed to worst case problem instances. Some of the instances considered in this study, were taken from a public library of TSPs, derived from real world VLSI design data. This VLSI TSP library, includes instances within ranging from 131 to 744,710, instances from this library within between 6,880 and 13,584, were first solved just a few years ago, in 2017 requiring days of runtime, and a 48 core two gigahertz cluster, all instances with n greater than or equal to 14,233, remain unsolved exactly by any means. Approximate solutions however, have been found by heuristic methods, for all instances in the VLSI TSP library, with, for example, a solution within 0.014% of a known lower bound, having been discovered for an instance, with n equal 19,289, requiring approximately two days of runtime, on a single quarter at 2.4 gigahertz. Now, if we simple-minded the extrapolate, the route exponential scaling, from the study yet to n equal 4,500, we might expect that an exact solver, would require something more like a year of runtime, on the 48 core cluster, used for the n equals 13,580 for instance, which shows how much, a very small concession on the quality of the solution, makes it possible to tackle much larger instances, with much lower costs, at the extreme end, the largest TSP ever solved exactly has n equal 85,900. This is an instance derived from 1980s VLSI design, and this required 136 CPU years of computation, normalized to a single core, 2.4 gigahertz. But the 20 fold larger, so-called world TSP benchmark instance, with n equals 1,904,711, has been solved approximately, with an optimality gap bounded below 0.0474%. Coming back to the general practical concerns, of applied optimization. We may note that a recent meta study, analyze the performance of no fewer than, 37 heuristic algorithms for MaxCut, and quadratic binary optimization problems. And find the performance... Sorry, and found that a different heuristics, work best for different problem instances, selected from a large scale heterogeneous test bed, with some evidence, the cryptic structure, in terms of what types of problem instances, were best solved by any given heuristic. Indeed, there are reasons to believe, that these results for MaxCut, and quadratic binary optimization, reflect to general principle, of a performance complementarity, among heuristic optimization algorithms, and the practice of solving hard optimization problems. There thus arises the critical pre processing issue, of trying to guess, which of a number of available, good heuristic algorithms should be chosen, to tackle a given problem instance. Assuming that any one of them, would incur high cost to run, on a large problem of incidents, making an astute choice of heuristic, is a crucial part of maximizing overall performance. Unfortunately, we still have very little conceptual insight, about what makes a specific problem instance, good or bad for any given heuristic optimization algorithm. This is certainly pinpointed by researchers in the field, as a circumstance and must be addressed. So adding this all up, we see that a critical frontier, for cutting edge academic research involves, both the development of novel heuristic algorithms, that deliver better performance with lower costs, on classes of problem instances, that are underserved by existing approaches, as well as fundamental research, to provide deep conceptual insight, into what makes a given problem instance, easy or hard for such algorithms. In fact, these days, as we talk about the end of Moore's law, and speculate about a so-called second quantum revolution, it's natural to talk not only about novel algorithms, for conventional CPUs, but also about highly customized, special purpose hardware architectures, on which we may run entirely unconventional algorithms, for common tutorial optimizations, such as ising problem. So against that backdrop, I'd like to use my remaining time, to introduce our work on, analysis of coherent using machine architectures, and associated optimization algorithms. Ising machines in general, are a novel class of information processing architectures, for solving combinatorial optimization problems, by embedding them in the dynamics, of analog, physical, or a cyber-physical systems. In contrast to both more traditional engineering approaches, that build ising machines using conventional electronics, and more radical proposals, that would require large scale quantum entanglement the emerging paradigm of coherent ising machines, leverages coherent nominal dynamics, in photonic or optical electronic platforms, to enable near term construction, of large scale prototypes, that leverage posting as information dynamics. The general structure of current of current CIM systems, as shown in the figure on the right, the role of the easing spins, is played by a train of optical pulses, circulating around a fiber optical storage ring, that beam splitter inserted in the ring, is used to periodically sample, the amplitude of every optical pulse. And the measurement results, are continually read into an FPGA, which uses then to compute perturbations, to be applied to each pulse, by a synchronized optical injections. These perturbations are engineered to implement, the spin-spin coupling and local magnetic field terms, of the ising hamiltonian, corresponding to a linear part of the CIM dynamics. Asynchronously pumped parametric amplifier, denoted here as PPL and wave guide, adds a crucial nonlinear component, to the CIM dynamics as well. And the basic CIM algorithm, the pump power starts very low, and is gradually increased, at low pump powers, the amplitudes of the easing spin pulses, behave as continuous complex variables, whose real parts which can be positive or negative, by the role of soft or perhaps mean field spins. Once the pump power crosses the threshold, for perimetric self oscillation in the optical fiber ring, however, the amplitudes of the easing spin pulses, become effectively quantized into binary values, while the pump power is being ramped up, the FPGA subsystem continuously applies, its measurement based feedback implementation, of the using hamiltonian terms. The interplay of the linearized easing dynamics, implemented by the FPGA , and the thresholds quantization dynamics, provided by the sink pumped parametric amplifier, result in a final state, of the optical plus amplitudes, at the end of the pump ramp, that can be read as a binary strain, giving a proposed solution, of the ising ground state problem. This method of solving ising problems, seems quite different from a conventional algorithm, that runs entirely on a digital computer. As a crucial aspect, of the computation is performed physically, by the analog continuous coherent nonlinear dynamics, of the optical degrees of freedom, in our efforts to analyze CA and performance. We have therefore turn to dynamical systems theory. Namely a study of bifurcations, the evolution of critical points, and typologies of heteroclitic orbits, and basins of attraction. We conjecture that such analysis, can provide fundamental insight, into what makes certain optimization instances, hard or easy for coherent ising machines, and hope that our approach, can lead to both improvements of the course CIM algorithm, and the pre processing rubric, for rapidly assessing the CIM insuibility of the instances. To provide a bit of intuition about how this all works. It may help to consider the threshold dynamics, of just one or two optical parametric oscillators, in the CIM architecture just described. We can think of each of the pulse time slots, circulating around the fiber ring, as are presenting an independent OPO. We can think of a single OPO degree of freedom, as a single resonant optical mode, that experiences linear dissipation, due to coupling loss, and gain in a pump near crystal, as shown in the diagram on the upper left of the slide, as the pump power is increased from zero. As in the CIM algorithm, the non-linear gain is initially too low, to overcome linear dissipation. And the OPO field remains in a near vacuum state, at a critical threshold value, gain equals dissipation, and the OPO undergoes a sort of lasing transition. And the steady States of the OPO, above this threshold are essentially coherent States. There are actually two possible values, of the OPO coherent amplitude, and any given above threshold pump power, which are equal in magnitude, but opposite in phase, when the OPO cross this threshold, it basically chooses one of the two possible phases, randomly, resulting in the generation, of a single bit of information. If we consider two uncoupled OPOs, as shown in the upper right diagram, pumped at exactly the same power at all times, then as the pump power is increased through threshold, each OPO will independently choose a phase, and thus two random bits are generated, for any number of uncoupled OPOs, the threshold power per OPOs is unchanged, from the single OPO case. Now, however, consider a scenario, in which the two appeals are coupled to each other, by a mutual injection of their out coupled fields, as shown in the diagram on the lower right. One can imagine that, depending on the sign of the coupling parameter alpha, when one OPO is lasing, it will inject a perturbation into the other, that may interfere either constructively or destructively, with the field that it is trying to generate, via its own lasing process. As a result, when can easily show that for alpha positive, there's an effective ferromagnetic coupling, between the two OPO fields, and their collective oscillation threshold, is lowered from that of the independent OPO case, but only for the two collective oscillation modes, in which the two OPO phases are the same. For alpha negative, the collective oscillation threshold, is lowered only for the configurations, in which the OPO phases are opposite. So then looking at how alpha is related to the jij matrix, of the ising spin coupling hamilitonian, it follows the, we could use this simplistic to OPO CIM, to solve the ground state problem, of the ferromagnetic or antiferromagnetic angles, to ising model, simply by increasing the pump power, from zero and observing what phase relation occurs, as the two appeals first start to lase. Clearly we can imagine generalizing the story to larger, and, however, the story doesn't stay as clean and simple, for all larger problem instances. And to find a more complicated example, we only need to go to n equals four, for some choices of jij for n equals four, the story remains simple, like the n equals two case. The figure on the upper left of this slide, shows the energy of various critical points, for a non frustrated n equals for instance, in which the first bifurcated critical point, that is the one that, by forgets of the lowest pump value a, this first bifurcated critical point, flows asyntonically into the lowest energy using solution, and the figure on the upper right, however, the first bifurcated critical point, flows to a very good, but suboptimal minimum at large pump power. The global minimum is actually given, by a distinct critical point. The first appears at a higher pump power, and is not needed radically connected to the origin. The basic CIM algorithm, is this not able to find this global minimum, such non-ideal behavior, seems to become more common at margin end, for the n equals 20 instance show in the lower plots, where the lower right pod is just a zoom into, a region of the lower left block. It can be seen that the global minimum, corresponds to a critical point, that first appears that of pump parameter a around 0.16, at some distance from the adriatic trajectory of the origin. That's curious to note that, in both of these small and examples, however, the critical point corresponding to the global minimum, appears relatively close, to the adiabatic trajectory of the origin, as compared to the most of the other, local minimum that appear. We're currently working to characterise, the face portrait typology, between the global minimum, and the adiabatic trajectory of the origin, taking clues as to how the basic CIM algorithm, could be generalized, to search for non-adiabatic trajectories, that jumped to the global minimum, during the pump up, of course, n equals 20 is still too small, to be of interest for practical optimization applications. But the advantage of beginning, with the study of small instances, is that we're able to reliably to determine, their global minima, and to see how they relate to the idea, that trajectory of the origin, and the basic CIM algorithm. And the small land limit, We can also analyze, for the quantum mechanical models of CAM dynamics, but that's a topic for future talks. Existing large-scale prototypes, are pushing into the range of, n equals, 10 to the four, 10 to the five, 10 to the six. So our ultimate objective in theoretical analysis, really has to be, to try to say something about CAM dynamics, and regime of much larger in. Our initial approach to characterizing CAM behavior, in the large end regime, relies on the use of random matrix theory. And this connects to prior research on spin classes, SK models, and the tap equations, et cetera, at present we're focusing on, statistical characterization, of the CIM gradient descent landscape, including the evolution of critical points, And their value spectra, as the pump powers gradually increase. We're investigating, for example, whether there could be some way, to explain differences in the relative stability, of the global minimum versus other local minima. We're also working to understand the deleterious, or potentially beneficial effects, of non-ideologies such as asymmetry, in the implemented using couplings, looking one step ahead, we plan to move next into the direction, of considering more realistic classes of problem instances, such as quadratic binary optimization with constraints. So in closing I should acknowledge, people who did the hard work, on these things that I've shown. So my group, including graduate students, Edwin Ng, Daniel Wennberg, Ryatatsu Yanagimoto, and Atsushi Yamamura have been working, in close collaboration with, Surya Ganguli, Marty Fejer and Amir Safavi-Naeini. All of us within the department of applied physics, at Stanford university and also in collaboration with Yoshihisa Yamamoto, over at NTT-PHI research labs. And I should acknowledge funding support, from the NSF by the Coherent Ising Machines, expedition in computing, also from NTT-PHI research labs, army research office, and ExxonMobil. That's it. Thanks very much.