 Yes, I share my screen Okay, yes, we can see you start the screen sharing Okay, so dr. Fukada will talk about benchmarking various types of using machines You can start it's 15 plus five minutes question. Okay. Thank you. Okay Okay, thank you. Thank you for coming to my presentation Let me begin my presentation benchmarking bias types of rising machines and case. Okay. This is this agenda First, let me explain introduction In our world, there are many combinatorial optimization problems This is a problem of searching for the optimal combination among the first number of them While satisfying the given constraints In this problem, the number of combinations increases exponentially as the number of values increases It causes a combinatorial explosion For this reason it is difficult to obtain an optimal solution using a conventional Neumann architecture machine But by using the Ising machine, it is possible to obtain a close optimal solution with high speed and high accuracy Ising machine is a Neumann type machine and specialized to solve combinatorial optimization problems Ising machine has two types. The one is the hardware Ising calculator. The other is the Ising calculator software system In this presentation, I take up three problems quadratic assignment work problem, traveling assessment problem, and slot placement problem And solve them by using simulated unneeding hardware Ising calculator and Ising calculator software system And As a summary, in terms of accuracy, ICSS is the best In terms of execution time, ICSS obtains solutions in set time And ICSS obtains solutions with high speed when the number of spins is small In terms of constraint satisfaction, ICSS and SA is better than HSE Next, I introduce Ising model and Kube model Ising model is a fundamental model in statistical mechanics Ising model consists of spin interaction questions and external field constant Using them, the energy function H of the Ising model can be expressed in this way The smaller the value of H, the more stable And the minimum value of H is called the ground state In a combinatorial optimization problem, if the ground state of this energy function is obtained, it means that The optimal solution to the problem has been found In the Kube model, we use the binary variable, which takes 1 or 0 The binary variable XI can be converted from the spin sigma I by this red equation In no-one research, we use Kube model Next, I introduce virus Ising machines As I mentioned, Ising machine has two types The one is the hardware Ising calculator The other is the Ising calculator software system This is implemented by hardware, but this is implemented by hardware and software I introduce several hardware Ising calculator D-Wave 2002 is Ising machine developed by D-Wave using actual quantum effects Coherent Ising machine is developed by NPD, which measures amplitude of light with oscillator Schmelted bifurcation machine is developed by Toshiba, which is applying the Schmelted bifurcation phenomenon This is a nearly second generation developed by Fujitsu, which uses probabilistic search based on mcmc CMOS unneiling machine is developed by Hitachi, which uses momentum unneiling with SA or GPU Amplifier unneiling engine is developed by Fekstas, which uses unneiling with GPU And I introduce Ising calculator software system Now, at present, Ising calculator software system has only one machine It's digital unneilers such generation developed by Fujitsu This machine, which is searching for a cost function for analyzing the violation state of the constraint time. From this slide, I introduce three combinator optimization programs and these experiments Plus is quadratic assignment problem Quadratic assignment problem called QAP is given several factories and several locations The logistic volume is defined between each factories and the distance is defined between each locations The goal of this problem is to find the optimum assignment that minimizes the total sum of the products of logistic volume and distance This problem can be applied to factory assignments and hospitality or hospital room assignments and so on I explain how to map the QAP to the Kubo model Let's borrow the speed like this This is the example of the QAP This is the example of spin matrix This is the example of spin matrix using spin xik when the number of factories f is equal to 4 The energy functions are respectively expressed like this The energy function constraint 1 to constraint 2 takes minimum value 0 when all constraints satisfied Next, I perform experimental evaluations of the QAP using Ising machines I use QAP live as the QAP instance and three Ising machines shown here Plus, as Ising calculator simulator implemented by software SA, I use simulated annealing sampler developed by D-Wave This is one of the Python libraries I set initial temperature to 10,000, final temperature to 10 the number of iterations to 1,750,000 and hyperparameter alpha to 10,000 In this way, I use this energy function and set it to one solution Finally, I take the average of 10 lines Second, as hardware Ising calculator, as you see, I use digital annealer unit 2 called DAU2 In DAU2, I use parallel tempering balls And I set the number of iterations to 1,000,000 and the hyperparameter alpha to 10,000 as the same SA Third, as Ising calculator software system, as it says, I use the digital annealer set generation called DAU3 DAU3 can set various parameters In this experiment, I set the searching time to 10 seconds and GS level to 0 GS level is the parameter of level of the global search The default value is 5, but if the problem has one hot constraint, it is recommended to specify 0 In nitrogen, the DAU3 searches automatically the value of the hyperparameter of the constraint stamp So I set alpha to 1 In HSC, I use this energy function and HSC adds to the 120 edge solutions In NICES says, I use the energy function So in NICES says, I use the energy function of the cost stamp and the constraint stamp respectively And IC says, I use 10 solutions Finally, I calculate the minimum cost of the solution that satisfies the constraints This is the experimental results The red asterisk means optimization cost of QAP live and hyphen Hyphen means in calculator level since the upper limit of the number of spins of DAU2 was exceeded As this table shows, compared to QAP live, the cost is 222% larger for SA and 7% larger for HSC On the other hand, IC says obtain the same solutions as the QAP live in all instances In execution time, SA and HSC tended to increase in execution time as number of spins increased In constraint satisfaction rate, the rate of SA and HSC says was 100% for all instances while the rate of HSC tended to decrease as the number of spins increased Next idea is the traveling salesman problem traveling salesman problem called TSP is given several states and the distance is defined between each states The goal of this problem is to find the shortest cycle visiting all states once each This problem can be applied protein structure analysis and travel route optimization and so on I explain how to map the TSP to the Kluber model Let's borrow a speed like this This is an example of spin matrix using spin XTI when the number of states M is equal to 4 The energy functions are respectively expressed like these Next, I performed experimental operations of TSP using Ising machines I use TSP live as the TSP instance and 3 Ising machines Experimental environment is the same as the QAP's experiment This is the experimental results High home means incalculable as the same QAP's experiment and NA means unable to obtain feasible solutions As this table shows compared to TSP live the cost is 362% larger for SA and 141% larger for HSC and 11% larger for ICCS In the execution time SA and HSC tended to increase in the execution time as the number of spins increased In constraint satisfaction rates, the rate of ICCS was 100% for all instances While the rate of HSC tended to decrease as the number of spins increased Sad eye to take up the strut placement problem The strut placement problem is given several items, several wires connecting two items and several lattice loads The goal of this problem is to find an optimum item assignment to lattice loads It means to minimize the total weighted wiring length called TWWL This problem can be applied to FPGA logic block placements and delivery management and so on I explain how to map this problem to the KUBO model Let the bars be like this This is the example of assignment and spin matrix using spin XAI When the number of items M is equal to 3 and the number of struts T is equal to 4 The energy functions are respectively expressed like these Next, I perform experimental evaluations of strut placement problem using Ising machines As the problem instance, I generate the instance randomly and use three Ising machines Experimental environment is the same as the QAP's experiment This is an experimental result Compared to SA, the cost is 19% smaller for HSC and 26% smaller for SSA In execution time, SA and HSC tended to increase in execution time as the number of spins increased In constraint satisfaction rates, the rate of SA and HSC is the same as the cost of SSA In constraint satisfaction rates, the rate of SA and HSC was 100% for all instances While the rate of HSC tended to decrease as the number of spins increased Plus, I simulated this presentation Today, I introduced combinatorial optimization problems and parasizing machines In our experiment, I solved the QAP, DSP and strut placement problem with SA, HSC and the ICSS In terms of accuracy, ICSS is the best Although good results were obtained with ICSS in this time experiment It cannot be said in general that ICSS is better to SA or HSC And so further evaluation, further experiment with other problems and icing machines is needed In execution time, ICSS obtains solutions in set time and SA obtains solutions with high speed when the number of spins is small In terms of constraint satisfaction, ICSS and SA is better than HSC This is my future work This time, I took up three problems and three icing machines Besides, it is needed, searching the value of the hyperparameter The experiment with different appropriate ST parameter And the experiment with different combinatorial optimization problems and icing machines That's all for my presentation. Thank you Okay, thank you. Thank you, Dr. Foujada So, questions also from the online participants Thank you very much for the talk Please, while comparing your different type of icing machine Are you able to find a Coraline's Time Which gives you the idea of which one can be the best icing machine to use for further research The reason is there are many types of icing machine So I want to research the evaluation of each icing machine So, I want to see the difference between the icing machine Sorry, I want to see the difference between the icing machine Okay, thank you. Any other urgent questions? And then we move forward Sir, I wonder if you point out that on this slide you point out that icing machines are better than classical computers But yet your conclusion is that Fujitsu device and Simulating Canealing are outperforming cut solutions But these like Simulating Canealing is a classical algorithm Fujitsu device also does not exploit the quantum effects So why do you say that they are performing classical computers and aren't they classical? Sorry, are you asking compared to the icing machine? I'm asking why you say that they are better than classical computers while they are classical, no? Yeah, I asked the classical But in this experiment, our experiment is executed on the icing machines Does that make sense? Very brief, we have to move forward Thank you for your talk. Can I ask how do you tune your hyper parameter for SA and HIC? Yes, wait Yes, I have to in this experiment I set the hyper parameter to 10,000 But I think this is not appropriate hyper parameter So as my future work, I have to investigate the appropriate hyper parameter art form So yes Okay, so let's thank Dr. Fukada again for the talk