 Just a moment here. Recording in progress. Okay, can you hear me? And, okay, okay, can you see my slide? Yes, it is. Okay, thank you. Okay, thank you, organizers, for giving me this opportunity. I'm talking about the forward interaction in superconducting search. I'm a searcher working for NEC, and this work is done with CIOC also. And, first of all, this work is supported by the NEDO project that develops superconducting device seeds in collaboration with an IST, Tokyo Tech, Yokohama National University, and Washington University. And this is just a mock-up. This picture is not mock-up of the superconducting quantum mining machine, but anyway, we are developing the actual hardware quantum mining machine. But I'm not talking about experiments and devices, but talking about associate topic for theoretical study of associate topic. My main topic is related to the LHC architecture. Some presentations in this conference on this architecture. So, you know, this is a candidate for a good graph of qubit for quantum annealing or some gate-based quantum computation. And a party of multiple logical qubits are encoded in each physical qubit. The good point is, it does not need couplings of distant physical qubits, but forward interaction is needed, like this Hamiltonian with async-sme variables. S, it takes one minus one. And if the product of the force being S is equal to one for any packets, like the square, like the force spins in the square, S is mapped to the product of logical spin sigma. And at low temperature for the C, this condition, the product of force being equal to one is satisfied. So the ground state of LHC Hamiltonian for large C is mapped to that of logical Hamiltonian. So this is a great theoretical idea. But what about physical implementation? How do we realize the forward interaction in qubits? The theoretical idea to implement the LHC architecture has been already proposed in the paper written by Fiori et al. And where qubits, based on Josephson parametric oscillators are used, qubits based on the JPLs are based on the cut states generated in a C charted squid with a parametrically driven field. This is a schematic figure of the circuit for our JPL. And the two states of a qubit are encoded in the two coherent states on the cut state, like this figure that showed the bigger function of the coherent state that has two, sorry, the cut state that has two coherent states corresponding to states of the qubit. And we're both tackled for the forward coupling of JPLs like this J4 JPLs corresponding to qubit. And a coupler is a single Josephson junction. This is a coupler, and each JPL capacitively coples to the coupler where this capacitor. So this is a basic idea to implement the LHC architecture. But as I mentioned, we need a large coupling constant to realize the LHC scheme. So how do we realize a large coupling constant? This is the aim of our study to find four-body couplers with a large coupling constant for the LHC architecture. And our study is theoretically examining four-body couplers. One is previously proposed one, shown in the previous slide. And we also explore other couplers. And the result is we propose a generalized coupler and appropriate parameter settings that coupler has an additional control norms to increase the forward interaction. And the result gives a guideline for setting parameters to increase the forward coupling constant. First, I showed coupler previously proposed. Again, this has a single Josephson junction here and each JPL trust to be coupled to the JJ coupler, like beer such charged stuff like this. And our proposed coupler is like this. This is generalized version of the previous one. This has a C-shanted to parallel branches of JJs like this, the one branch has an identical JJs in series with Josephson energy EJG, energy divided by EJG. And the other branch has a single JJ with smaller Josephson energy than that of the other branch, first branch with coefficient alpha rather smaller than one like this. And the important point is that we threat half of flux a quantum of external magnetic flux here and through the loop of the two branches like this, 5G is equal to pi zero over two half of flux quantum. And the JPL capacitively couples to the JJ beer is capacitance, if capacitance transfers as the previous one. And this coupler includes a previous coupler for as an n equal to one and alpha equal to zero, this setting in this setting this coupler is used to the previous one. And also when alpha is equal to one by n, this fraction of the coupler is called a quantum, that is a special flux qubit. And this structure is used also for nonlinear two body coupler in this work. So we were inspired by this work and we apply this structure to the folding coupling of the JPLs with some little changes about the time parameters and setting. And we set alpha, parameter alpha close to one by n to increase the folding coupling constant. This is our strategy to increase the coupling constant. And next let me explain the potential of our proposed coupler described like this function V of phi and the phi is the phase difference between the edges of the coupler, here and here phase difference. And the phi is a flux equal to a half flux quantum. And the first term is corresponding to the this branch but at the sum of their potential of their each single joules in junction and the phase is divided equally like this in some condition. I did not explain the details of that anyway. This first term correspond to this branch. And the second term of force correspond to the other branch like this. And the important point is phi G is equal to half a flux quantum. So this product is pi equal to pi. So this term becomes like this. A minus is changed to plus and this is important point. We expand this function like this up to the fourth of the time and EJG2 EJG4 for the coefficient of the second and fourth of the time. And they are expressed like this with N and alpha. So we can show the coefficients, these coefficients by setting N and alpha. In particular when N equal to one alpha equal to zero this corresponds to the previous original version of the coupler, a single JG. EJG2 is equal to EJG4. So we can make them to make them difference from each other, different from each other by setting N and alpha like that. Next, let me, I explain briefly explain the outline of derivation of the effective Hamiltonian for the forward interaction. First step is constructing Hamiltonian with charge and flux varies like this. And the second one, second step is we represent this Hamiltonian with Bosnian cooperators. And then we obtain the total Hamiltonian consisting of the sum of JPU Hamiltonian and coupler Hamiltonian. And the second line corresponds to the interaction. AK dagger and AK are creation and annihilation operators Bosnian cooperators for JPUK and AG plus dagger EJ minus EJ minus dagger are degrees of freedom for the coupler. The coupler has two edges. So the coupler has two degrees of freedom but the HG minus, we also cause the HG minus because it effectively plays a role of the interaction. So we don't have to focus on HG plus. Anyway, the coupling of the Hamiltonian coupling of the JPU and the coupler is represented like this. And the third step is the transform to transform to the previous Hamiltonian to the Hamiltonian for forward interaction. Interactions of each JPU and the coupler here such a capacitor transform to the forward interaction of JPUs. I don't explain the details of that. But anyway, we use some approximations like the rotating wave approximations. And we assume that the coupling constant of JPUs and coupler is small for this coupling. And then we obtain the effective total Hamiltonian like this that consists of the Hamiltonian for each JPU, four JPUs and the coupler, the Hamiltonian for the coupler and the interaction that is forward coupling. There are many other coupling but we can vanish them by using rotating wave approximation. These terms has the oscillating terms. So we can ignore them. But I'm sorry, I did not explain that. But anyway, we said some special relation of the frequencies then this forward coupling term does not have the oscillating factor. So we get these forward coupling terms. And then this forward coupling correspond to the forward coupling of spins in the LHC Hamiltonian. So we obtain this Hamiltonian. So the forward coupling constant G4 is important for us. This is expressed like this. G minus prime is effective coupling constant of the JPU and the coupler. Here it is a capacitor. And that depends on the parameters of JPU and coupler. And ECG prime is affecting capacity energy of the coupler for this capacitance. And EJG4 and EJG2 are the coefficients of the second and fourth order term in the potential of the coupler shown before. And let me mention about the factors involved in the coupling constant G4. There are two main factors. Why is there not coupling going? Okay. No, can you try once more? Just change the slides, try to change the slides. Or maybe you can stop sharing and then again share. No, nothing is happening. So you can stop sharing and again share maybe. Does it work? It is still not coming. It is still not showing in the screen. You can try once more or just log out and log in. Oh really? Just try to share once more maybe. Yeah, maybe let me check. Recording stopped. Yeah, maybe you can just log out and log in and check once more. Same meeting. Okay. Yes, can you share again? Yeah, perfect. So... So... Recording in progress. Yeah, you can try to change the slides also just to share. And where should I return? I guess the last slide was when we were showing the different couplings, this AG plus, minus, AG minus, those Hamiltonian. This one? No. No. I just see only one, four-body coupling constant, only one slide. Can you change the slides? I'm changing. You are at 15. 15, okay. May I read them from here? Tillyard, nothing is changing. Maybe you can try with the PDF or... Oh, you mean the slides are not changing in your screen? We are just seeing the slide 19 and that's it. So... 19? Yeah. Okay, right. So maybe there are these different window options in the, when you shared the screen. Recording stopped. Yeah, so maybe... That doesn't work. Maybe you can just present in the window. Right. Maybe you can stop the full screen in case you are trying to do full screen. Just go to slide 15. Okay, it is... Wow. Recording in progress. Excellent. Good. Yeah. Pardon me. Thank you. Yeah, I'm sharing... I'm supposed to share the screen page 15. Is that okay? Right. Okay, so I resume. Okay, anyway, yeah, this is the total Hamiltonian. And I transformed that. Sorry, the next page. I'm sharing the next page. And this shows that transform the Hamiltonian to Hamilton 4 is a probability interaction like that. And it uses such a transformation, uses the sound approximation, like rotating wave approximation, and the assumption that the coupling constant of J-build and coupler beer is faster, it's small. And then we obtain the effect of Hamiltonian, including the probability coupling like that. And yeah, some other coupling, like the two-body coupling balance it with the under the rotating wave approximation. But we can... Sorry, I do not show that, but we set some relation to the frequencies and then we can keep the four-body coupling tar. This has no roll or slaking time. And then this tar corresponds to the four-body coupling of the spins in the LHD Hamiltonian. So yeah, this is our goal. Sorry, and that, but the important point is the effective four-body coupling constant. We try to set two large. So the G4 four-body coupling constant is expressed like that G minus prime is effective coupling constant of J-build and coupler that depend on parameters of J-build and coupler. And ECG prime is effective capacitive energy of the coupler for this capacity. And EJG4 and two are the coefficients of the second and fourth order terms of the potential of the coupler. We mentioned couplers involved in the coupling constant G4. There are two parts. One is coupling of each J-build and coupler is characterized by G minus prime. And but it should be, we want it to large to increase the G4 before but it should be a small transmission not to strongly affect J-build. So we do not make it large. And so the other factor is not only the idea of the coupler. And this part, and this is divided into two parts, one in capacitance of the coupler related to the capacitor energy ECG prime that is proportional to one of our capacitance of the coupler denoted by CG. So, and it should be small to increase G4. And the other part is the other one is a ratio of EJG4 to EJG2, up here here it should be large to increase G4. So, okay, so what should be done to increase G4? We have two struts. One is decreasing capacitance of the coupler. It can increase G4 without increasing G minus prime. So we satisfy two conditions. And this is the, this showed the result for this strategy. This is for the fully coupling constant for specific parameter values. And we only change CG. And so we show the fully coupling constant as a function of CG, the capacitance of the coupler. And so we decrease CG, fully coupling constant is rapidly increasing but the G, this means that G minus prime does not increase much. And the other strut, the last three, the other strut is setting alpha close to one of m. It increases the abstract value of EJG4 over EJG2. It represented like this as a function of many and alpha. This showed the plot of the fully coupling constant as a function of alpha for different m, different corresponds to different m. Let me focus on n equal to case. For larger alpha than some point, it rapidly increases. And this straight line correspond to n equal to one that is the previous, the fully coupling constant for the flabious coupler original version. So by setting the alpha larger than some value or for example 0.4, we can realize the fully coupler with larger coupling constant than the previous one. But in theory, when we set alpha exactly equal to one of m, it diverges. So we do not set it and we do not set it to exactly equal to one of m but it is enough setting alpha close to one of m to obtain the larger coupling constant than the previous one. And this is summary. Anyway, that is it. Thank you. Cool. Questions? Two questions. Thank you for your presentation. First one is, do you use shear force transformation to get the effective spin model Hamiltonian? What about the? Spin model Hamilton. So you mean, so you mean the chrome here to here? Like what the mathematic tools do you use to get the effective Hamiltonian? The like four-body terms. So you use shear force transformation, something like that? So thank you for question. So you mean the, just sort of step, what we did? Yeah, from the... Yeah, yeah. We transformed the, yeah, we used something like a strip of walls transformation. But the nonlinear terms, we are suffering from nonlinear terms. So some terms remains, does not vanish. But we use rotating wave approximations and vanish them and then this one. But sorry, it's a brief explanation. And yeah, anyway, this is the answer so far. Okay. Thank you. Now the question is, how do you measure the JPO's? What is the computational basis? It's not a persistent current state, right? What measure it? How do you measure JPO dispersive measurement or? Ah, sorry. We do not, in this study, in the theoretical study, we do not consider it a measurement. So we only consider the state in the study. So we can worry the measurement. If you define JPO as a qubit, some kind of state qubit, how do you measure it with dispersive measurement or? That is related to the experiment. Yeah, and there is a conventional way to measure the state in the JPO. And so, yeah, it is not our original work anyway. Okay, okay, thank you. Is this coupling also tunable to the negative values or can you turn it off? Well, where is your point? No, it's just a general question. You mean the G4 may become negative, right? And if you can tune it negative or turn it off? Yeah, in general, this is the figure for G4, but this shows the abstract value, but in fact, it decreases like that. And for larger output, this value is negative, but we can turn the, we can turn, we can change such a sign negative to positive with other method. Sorry, I did not mention that. But anyway, so we do not focus on the sign in this presentation. Because you don't need it for the LHSET architecture or why? Yeah, for the, at least for the LHSET architecture, the positive coupling constant is needed. Okay, thanks. Let's do a quick question. Okay, so I understand that you need to rely on some resonance condition of the four JPO's in order to remove residual two-body coupling terms. And, but when you actually do annealing, you'd need to implement like the transverse terms or something and can you keep that resonance condition at all times during when you do annealing? Yeah, it might be related to the experiment, but anyway, in theoretical view point, for annealing, we vary the amplitude of the spring. I showed the first annealing here is a pump field and we change the amplitude of the pump field. This is annealing for this circuit, for this setting. And resonance, so yeah, I said the special relation to the frequencies are considered. That is the frequencies for the pump field. So we believe that we can keep such a relation even in annealing because the annealing when during annealing, we only tune the amplitude. But you also need to set independently the qubit field, right? In order to program arbitrary problems into your hardware. You meant for in the spring terminology that Jij, like that? Sorry, I don't know, I may not understand you. Yeah, yeah, so in the LHC, it would be the single qubit longitudinal field. Oh yeah. Yeah, that needs to be programmed for different, to map to different problems, right? Yes, so in my setting, we do not consider such an additional coherent driving term. But yeah, we just, it is independent of our argument. I mean, if we also use such a coherent driving our argument holds, but sorry, it is not. Oh yeah, I think it kind of answers your question. Okay, thanks. Okay, so let's send the speaker in. Small? Sorry for my problems. So now it is the time for the break. We again meet at 11.20, 11.20. Recording stopped.