Satoshi Kako: Today, I’m talking about the Coherent Ising Machine on Chip. And before jumping into that presentation, I’d like to thank all my colleagues, especially Professor Timothee Leleu at the University of Tokyo and Farad Khoyratee, Dr. Khoyratee, at Riken (Japan). So, let’s get started.

As we saw in the video, there are many important Combinatorial Optimization Problems, in our society. Let’s take a look at some. So, this is a drug discovery, life science, probably, it’ll enrich your life. And the wireless communication or logistics, and sparse sensing. It allows us to reconstruct the information from the limited data, by using the sparsity. And this is a machine learning. And then last one is FinTech. For example, the portfolio optimization problem, that might gain your profile.

So, interestingly, these combinatorial optimizations can be converted or transformed using the Ising model. This is a completely different from these guys. And actually this is a, just a toy model of the physics, to understand the model magnitude.

And then to find out the solution for this combinatorial optimization is converted to find the minimum energy state, of the corresponding Ising problem. When I knew this fact, I very much have surprise. Because if once we have the smart way to solve this Ising model, then we can solve every combinatorial optimization problem. That thing is not so simple. Let me introduce some famous examples.

Traveling salesman problem. So, this problem we want find out the route from one city to another city. And we have similar problem, the optimization, in our life. After the five cities, or five stores, or whatever, we can manually try to find out the solution. Just this number. But once the number of cities increases to six, it’s already 60. It might be possible to find out that. How about 30, just five times larger. It’s almost, an astronomical number.

And at 60, the total number of combination of routes, become the total number of atoms in the universe. It’s almost, that’s why the thing is not so simple. So, people want to find out that clever, or smart way. So, we need some trick, that smart people having been fascinated to find out.

Okay, in our life now we are using the conventional computing. Every day, every moment, even now, we are using the conventional computing, digital computing. And our life won’t run without these conventional digital computing platforms. And recently people see some slow down of the performance increase, even though data needs are increasing. And also we have some limitations – communication, bandwidth limitation between the memory and the processor, the so-called a Von-Neumann bottleneck. So, we need some way to overcome this problem, to solve the combinatorial optimization. And actually people have been seeking the unconventional computing, approach.

So, let me show you some examples from the unconventional computing approach. Gate-based quantum computing is very famous, and the quantum annealing. These are inspired by quantum physics, and here is analog/digital neuromorphic chips, and dedicated electronic chip. It’s inspired from the brain science and the classical physics.

And our approach, coherent Ising machine, have been proposed and demonstrated, as a machine with both genes from quantum physics and brain science. And actually this is a physical CIM, one of the implementations of physical CIM. We have a special kind of optical oscillators, optical parametric oscillators, and these oscillators form the network, so, with these electronics.  And the once we input energy, via pulses, pump pulse or injection pulse, then this network finds a solution of the Ising model. Through this process, once we can convert our problem, our combinatorial optimization problem, to the Ising model, we can solve the combinatorial optimization using the CIM.

And now, using the physics and mathematics, we can model these CIM, physical CIM. And this is one of the simplest models of the CIM. And recently, in 2019 from Timothee Leleu at the University of Tokyo, we added some additional equations like this. And actually this is very powerful, and then we have already demonstrated, this algorithm improved CIM performance dramatically. And recently, we implemented this CIM algorithm on this dedicated chip, FPGA or GPU, in an efficient way.

So, we can use these, we call this system the Cyber CIM, and we can use this Cyber CIM system to explore the explore the application in an efficient way. So, these are stable and scalable and ready to go. So, that’s why we want to seek it.

Okay. So, before we jump in to the demonstration, let me take a look at the problem we solve in the demonstration. This is a max-cut problem. This is a common benchmark instance, benchmark problem to evaluate the Ising solver.

And in the, in the case of N equal five, the node equal five, we can solve, manually one by one and test the cut number. And because of just 32 candidates, we can find the optimum solution. If we go up to the sixteen, it’s already 65,000. We can do that but it takes a long time. And if we go up to the 100 already, as an astronomical number, an enormous number, And how about a thousand? We have 10 to the 300 power, quite a huge number. And we are going to today, give the demonstration for this thousand problem.

So, in the demonstration, we solve the Ising model. So, we try to find out the minimum energy state. This corresponds to finding the max-cut problem, because the max-cut problem is actually converted to the corresponding Ising model. So, to find out the max-cut is equal to find out minimum energy of the corresponding Ising model.

So, jump into the demonstration.

First, I will show you the simulated annealing. That is a very famous and powerful heuristic algorithm for this kind of Ising program. And let’s see. So, this is a simulated annealing, running on the Intel i9 16-core processor. And we solve five instances of the size of one thousand. And in each instance we try 100 trials. And in this case, 3000 annealing steps.

Now we have the simulation running. And then, as you can see, that the simulation is slightly slower. So then, we need it to speed up. So, now we have the simulation is going on, and now finished. So, let me show you some results. This is quality of the solution. And see our algorithm does not always find the solution. In this case, just for instance five can the optimal solution. If we look at the computation time, it takes about 10 seconds for each, for the one hundred trial. So, this is demo of the simulated annealing, as a reference.

So, let’s jump into the CIM on chip demo. So, we currently have cyber CIM demonstration, and we switched to the system that’s hosting the FPGA based cyber CIM. And we solve the exact same five instances. And this time we increased to 10 times the trials, so a thousand trial. And this time the simulation itself is very fast. It almost the one second, for those instances. So, then it’s a real time, and a boom, boom, boom. So, then we can almost complete, and now the simulation is complete. And if you look at the solution quality, in this case, the Cyber CIM can find the solution for every instance.

And if you look at the computation time, it 10 times faster, compared with the simulated annealing. Even for the ten times more trials. That means, we have 100 times speed-up, compare with the simulated annealing. So, I hope this a demonstration gave you some insight into how powerful our Cyber CIM is.

Okay, let’s go back to the slide. Now we are here. Mainly, we are benchmarking our Cyber CIM, or the other similar Physical CIM. And in order to explore our application, we need to go up, go beyond from the thousand, to ten thousand, a hundred thousand or more. And actually we are now in development of this direction. And then, this demonstration today, is just a first step towards that future progress.

Okay. So, this is our team, our collaborators. We always collaborate with the smartest collaborator in the world, and we are developing actually the, the Cyber CIM and the Physical CIM, as well.

And also we have been conducting the basic research, with these. And then actually, that, that’s basic research will potentially improve our CIM algorithm or architecture. And then in terms of the application, recently we have some examples.

So let me show you that one example from Tokyo University and in terms of the portfolio optimization. And that’s actually the, we recently have the preliminary results. And then from that result, Cyber CIM outperforms that simulated annealing in the higher gain.

And another example, from the Tokyo Institute of Technology regarding that compress sensing. Cyber CIM actually the outperformed the standard approach based on LASSO. That’s our current status.

So, with these collaborators, we are going to go beyond. And if you interested in our work, we have actually the technical session tomorrow. So, please come and see, for more detail. Thank you very much.