 Hi, everyone. Good afternoon. First of all, thank you so much to the ICTP. Today, I will give a talk about fast-forward adiabatic quantum dynamics and application to XY-spin model on Kagome lattice. Me, you, and so on, from the physics education department in the Bengkulu, Indonesia, is the outline, introduction, adiabatic quantum dynamics, and fast-forward, FF is fast-forward, fast-forward adiabatic quantum dynamics on spin system, some application to spin and tree spin system, and some way. So this is the motivation, need of speed. So this is the way to accelerate the speed from the transportation, from micro-particle, from classical computer to quantum computer, and then this is one of the dream how to speed, how to accelerate the growing of the plan, one year becoming a half year, and so on. So this idea is started from adiabatic quantum dynamics theory. If you want to move, for example, this glass of water from one position to another position and keep the volume of the water, it can be done but in a very long time. So in this research, we consider how to accelerate the time to move this glass of water from one position to another position, or to keep the eigenvalue of the electron from one position to another position in a very, in a shorter time. So we are considering about how to find a driving energy or additional Hamiltonian to accelerate the system in adiabatic approximation. So this is the story about this method. Previous research is so-called transless and less quantum driving, proposed by these two guys from Imir Blak and Rice and Michael Berry, published in 2005 and 2009. They are pioneer of transless quantum driving theory. The main problem here is how to accelerate adiabatic quantum dynamics by finding the driving Hamiltonian. Some previous research have been done this research. For example, here we have a fast forward scheme. This is, I collaborated with these two guys, Masuda and Nakamura. And also there is another method to accelerate adiabatic quantum dynamics, so-called shortcut to adiabaticity, or HTA, proposed by these guys, Professor Muga, Kampo, and then Professor Sen. They propose another method, so-called shortcut to adiabaticity. In this research, we try to consider how to accelerate the adiabatic dynamics on a spin system. So if we have a spin system like this kind of spin, we can do it and we can accelerate the dynamics of the spin from spin up to the down direction with the driving magnetic field, for example. This is some of the results. So this is the theory, this is the concept, this is the method. If we have, suppose we have adiabatic wave function, it's given here, indicated by the parameter RT. So here we define an adiabatic wave function. We have already half adiabatic wave function, indicated by RT. RT is time parameters including epsilon, epsilon tends to zero. So this wave function is a very slow dynamics and then there is also adiabatic phase here. This is the definition of adiabatic phase. So here we already have adiabatic wave function and to obtain this kind of adiabatic wave function, we also should modify our Hamiltonian. So this is the method. We need a new Hamiltonian to obtain this adiabatic wave function. So here we define an additional Hamiltonian till the H as a so-called regularization term. By using this Hamiltonian, we can obtain this adiabatic wave function. By substituting this Hamiltonian and then the adiabatic wave function to the screwing equation, we can obtain the formula to obtain the additional Hamiltonian or we called a regularization term here in equation two. And then this regularization term is only to keep the motion to be adiabatic. Nothing to do with fast forward. So this is only how to make the dynamics of the spin system keep the eigenvalue from one position or for example initial position to the final position. So for example, ground state for initial position and we will find the same ground state at the final position. So how to fast forward, how to accelerate this kind of dynamics. We try to modify our parameter R here by using a time function. So R here is characterized by this alpha function. Alpha function is a cosine function. So here we see that if t equal to zero and t equal to tff, we have the same condition of alpha. So in the initial condition and at the final condition we will get the same wave function. So this is the standard wave function. This is the standard wave function without fast forward. By using the time function alpha, we can see that to obtain the target state, the time to obtain the target state is shorter than the standard wave function. And then by taking the derivative of fast forward wave function, we can obtain that driving Hamiltonian is original Hamiltonian plus regularization term or additional Hamiltonian. So to accelerate the adiabatic dynamics of spin system, we have to obtain this regularization term or additional Hamiltonian. Here we try to consider an example an XY spin model. This is a two spin system. This is a two spin system. This is the j1 and j2 is interaction parameters. And also there is a magnetic field. From this kind of Hamiltonian, we can obtain the metric representation as given here for two spin system. And this is the time dependent again value for this Hamiltonian. And then we consider the ground state of this eigenvalue. For example, this in line. From the ground state of the eigenvalue by using our formula to obtain the regularization term, we can see that to accelerate the dynamics of this Hamiltonian, we have to add another interaction parameter W, which is W is interaction parameter of for sigma x and sigma y. So originally it is only x, x, y, y in the original Hamiltonian, but to accelerate this kind of dynamics, we have to add this another interaction parameter to the W as an exchange parameter of x, y, y, x like this. So the exact solution of W till the W is given here. And then next, we try to consider the three spin system. We just look to get geometry here as a Kagome lattice geometry. With interaction between nearest neck boards and between next nearest neck boards is j1. Here is the nearest neck boards. And the next nearest neck board is g2, sewn by the single and double bonds. The Hamiltonian of the spin systems is given here. We have j1 and j2 as the interaction parameter. And then j1 is interaction parameter of 1, 2, and 2, 3. 1, 2, and 2, 3, the nearest neck board and j2 is the next nearest neck board. And then also there is a magnetic field. This is the original Hamiltonian for this system. And then the metric representation of the system is 8 by 8 matrix. And then we see that time-dependent eigenvalue of this Hamiltonian is giving here this is the ground state. So here we consider how to accelerate the ground state, the dynamics of the ground state of this Hamiltonian. We obtain that instead of the original Hamiltonian, this Hamiltonian is, instead of this original Hamiltonian, we have also at another interaction parameter w1 tilde and also w2 tilde as interaction parameter of x, y, y, x, 1, 2, and 2, 3. So this is the original one. Accelerate this, we have to add this two interaction parameters. So the dynamics of the wave function initially is a linear combination of this state. And by increasing j2 and decreasing j1 and bx, the system changes rapidly to the non-entangled state up, up, up like this. So we can accelerate the dynamics by including the another two terms interaction parameters. So this is the figure of time-dependence of regulation term. So the efforts to accelerate adiabatic quantum spin dynamics are using candidate regulation terms. In two spin system, the xy model and annealing quantum model, the regression term in driving Hamilton have been obtained. So we have also considered annealing quantum model. Application to co-comulate this with three spin system, option to use regression term and another challenge. Thank you so much. Okay. Questions from the chat? Okay. I have one question. I wonder whether fast forward scaling can be generalized to many systems. And then there is a second one. There are several. How to develop the modeling? Okay. Thank you, Professor Chan. Yeah, we are now considering about how to use the model of fast forward, the method of fast forward to many spin systems. Yeah, the complexity is how to find the, how to diagonalize and what find the eigenvalue of the systems. That's one of the difficulties of that problem. So I think the complex, the problems to co-complex because we have to obtain the eigenvalue firstly and then we can choose with eigenvalue that we can accelerate. So for sure we believe that this kind of method can be done in many spin systems. Other questions? Many functions. Okay. Thank you for the talk. So before you mentioned that there was like these two approaches, the one with the shortcuts to the opacity and this fast forward approach, right? So out of curiosity, I would like to know if, are they the same way to express, I mean, it's just a different language and then because the, the equations you showed are the one for the two-speed, for example, were identical to the one you would get with the counter-adiabatic with the other shortcut approach. So is it just different one language and maybe a different procedure to get the same thing or is conceptually different? Yeah, the main goal is the same and we believe that the method is a little bit different because here we use a time scaling R and also another time scaling lambda to fast forward our adiabatic wave function. So as we know that HTA method only consider about how to find the counter-adiabatic term and they do not consider about the fast, the time scaling. So here we also consider how to accelerate the adiabatic wave function by using time scaling. But the method is a little bit different but the main goal is the same. You can say that a fast forward is one of the methods of HTA, I don't know. Other questions? Okay, if not, we thank you.