 Okay, yes, you can start, you can start sharing, okay? Okay, I'll start recording. Good, please. Okay, I will start my presentation. I'm Rihonda, first year master's students from Keio University. I will talk about structural optimization methods of tourists by quantum analytics. First, I explained the topology optimization problem. The topology optimization problem is to find a combination of components or shapes that we provide high performance at the lowest possible cost, as shown in this figure. Topology optimization is sometimes used in bridge design, as shown in this image. When trying to solve a combination optimization problem, such as topology optimization problem, using methods that are widely used today, it is possible to get stuck in a local solution during the competition. Therefore, the competition must be repeated many times to obtain the overall optimal solution, which results in high computational cost. So, new computational methods that do not fall into the trap for local solutions are becoming increasingly important. Next, I will explain quantum annealing. In recent years, the practical application of quantum computers, which are computers using qubits as basic elements, has been attracting attention. Quantum computers are divided into two types, quantum gating and quantum annealing. Among these, quantum annealing specializes in solving combinational optimization problems. Recently, D-Wave has developed a machine that can handle more than 5,000 qubits. Quantum annealing uses the tunneling effect of quantum fluctuation to find the solution. This figure shows an image of quantum annealing. Initially, by increasing the quantum fluctuation, the state can be transitioned while ignoring the potential value due to the tunneling effect. And by gradually decreasing the quantum fluctuation from that state, we can finally reach the optimal solution with minimal potential. An example of previous research of quantum annealing to computational optimization problems includes traffic volume management and mass scheduling. These studies have shown that the computation speed is about 100 million times faster than with computational methods. However, there are a few cases where quantum annealing has been used to analyze S-Rates. The purpose of this research is to develop a new policy optimization method for S-Rates using quantum annealing. As an example, we will use quantum annealing to solve a topology optimization problem for S-Rates structure, such as the one shown in this figure, which is to find structure that has high strengths with limited total volume of members when starting force is upright. The following section describes the actual use of quantum annealing. To use quantum annealing machine, a combinational optimization problem must be converted to an S-Rates model or a cube. The energy function of the optimization problem is expressed in the form of Hamiltonian. And quantum annealing is used to find the combination of variables that minimizes the Hamiltonian. First, the S-Rates model is represented by some of the products of two S-Rates model using variables that take 1 or minus 1. The G-Alpha-Veta, Sigma-Alpha-Sigma-Veta represents the energy of interaction between the two S-Rates variables. For this, the positive or negative of these two S-Rates variables are the same or different. This determines whether the energy of the interaction is positive or negative, and Hamiltonian increases or decreases. The cube form uses a binary variable that takes the value 0 or 1 instead of the S-Rates variable. The equation for the S-Rates model and the cube form equation are essentially equivalent by simply transforming the S-Rates variable, Sigma, and the binary variables into variables such as Sigma equal 1 minus 2 cube. In this study, the energy is expressed using a cube form, and annealing analysis is performed. As mentioned earlier, the only variables that can be handled in cube format are binary variables that can only take values of 0 or 1. On the other hand, the variables used in structure analysis of Atras, such as nodal displacements and member cross-section are real numbers that can take values other than 0 or 1. Therefore, in order to use quantum annealing for structure analysis of Atras, it is necessary to represent real numbers using binary variables. Therefore, I used the method to calculate some representation of a real number. Much of the random numbers between 0 and 1 are prepared, and a real number are represented by the sum of these random numbers. By expressing first a random number, it exists or not using binary variables. The real number are, in the range minus a to a, can be expressed using binary variables as in this equation. Next, we convert the energy of Atras into a cube form. First, the elastic energy of the member between nodes i and j of Atras as shown in this figure can be approximated by this equation, given that the deformation is made. And the difference between the potential energy of nodes i before and after the information is the product of the bidirectional levels and the bidirectional displacements as in this equation. We will convert these equations to cube format. Atras structure is in balance when the sum of elastic and potential energies is at a minimum. To confirm that the atras can be analyzed using quantum annealing. We perform the quantum annealing analysis using the elastic energy convert to cube format as the fermiutomy of the objective function. This figure shows the results of the analysis of the compression of the atras. And the blue line shows the shape before deformation and the red line shows the shape of the information. The result shows the compression and confirming that it is indeed possible to analyze trust information using quantum annealing. Next, a formulation is given that takes the cross sectional area as the variables to optimize the structure. The spring constant is expressed in terms of the cross sectional area of the member as Young's modulus times cross sectional area divided by natural length. Using this equation, the elastic energy can be written as this equation. And by expressing the cross sectional area as binary variables as in this equation. Patimization calculation by quantum annealing is the cross sectional area as variable becomes possible. Under the condition that the atras structure is force balanced, the stiffness structure is the one in which the sum of elastic energy of all members is the greatest. However, elastic energy minimization for balancing and elastic energy maximization for stiffness maximization are simply in balance of each other's objective function. Just in principle, they cannot be performed seamlessly in a single calibration. Therefore, in this study, the displacement and cross sectional area calibration were performed separately for optimization. First, the cross sectional area is assumed to be a constant and the displacement is used as a variable and find a balanced position. The Hamiltonian use, in this case, it's the sum of the elastic and the potential analysis as a previous example. Next, with a displacement value obtained fixed and the cross sectional area as a variable, we look for the structure with the maximum sum of elastic analysis. The Hamiltonian uses, in this case, is the sum of the elastic energy multiplied by minus one. These calculations are repeated to optimize the structure and then constraint functions are added to the cross sectional area change. And first, if the cross sectional area is simply changed so that the elastic analysis increases, the cross sectional area of all the members becomes maximum. To avoid this, constant constraint functions is added to ensure that the sum of the cross sectional area of all members is always constant. Added constant function to the Hamiltonian that presses a limit on the amount of increases, increase or decrease in cross sectional area per member per calculation. And not that in this analysis, the value of this is not the cross sectional area value itself, but the increase or decrease value of the cross sectional area. Similarly, the displacement and the cross sectional area values affect each other, but in this analysis, only one of the two values is changed repeatedly. Therefore, if the values of the displacement and cross sectional area are changed or advance, the structure will be derived from the optimal solution each time the calculation is repeated. Resulting the appearance of such incorrect structure. And therefore, by restricting the length of the cross sectional area that can be taken as viable so that the cross sectional area changes little by little. The calculation can be repeated with some preservation of the relationship between the displacement and the cross sectional area. We should move towards the conclusion, please. The initial cross structure and the analysis results after 30 steps are shown, it can be seen that the upper side of the cross structure is tension and the lower side is in compression as in the beginning. The cross sectional area at each step is also shown. The cross sectional area at each step is shown to increase for members with high strain and to decrease for members with low strain. Optimization calculation using quantum annealing. We varied our structure at the tip of the road, not upright, as seen in conventional optimization methods. And also optimization analysis using quantum annealing was performed for this loaded 3D process. The 3D process also shows the structure that taper at the end. Conclusions in this study, it proposed methods to perform information analysis and towards the optimization analysis of the cross structure using quantum annealing. The results of the variation of the proposed method shows that these things. That's bringing me to the end of my presentation. Thank you for your attention. Okay, thank you very much. A few quick questions, maybe? No, from the online participants. No? Okay, so let's thank Dr. Honda again. And we move to the another online presentation by Dr. Imoto. Quantum annealing with twisted fields. Okay, Dr. Imoto, you're there. Okay, start screen sharing.