 So first of all, thanks to the organizers for giving me the opportunity to present the work here. Yes. The work is about capacitive couplings. I'm coming from the University of Salamanca. Salamanca, this is a very old institution. 800 years old. I think that it's competing with one of the oldest here, as Bologna. And it is in a nice city. So if you are around the center of Spain, come and visit. And if you do, come and visit also the lab. Hi. Hi. Maybe because you cannot hear me. Hi. I'm talk very... Not English one, even. Hi. Hi. I will try to speak louder. I think that is my problem also, that I speak very softly. Yes. Before coming to University of Salamanca, I was in Madrid in the group of quantum information and foundation, led by Juan José García Ripol. And actually, this work has been done in collaboration with him and with all the PhD students in the project, especially María Ita... almost all the work. And all of this is part of a wider project, that is the abacus project that wants to build a coherent quantum arena in Barcelona. And this project is coordinated by Paul Fordia. Okay. So once we have said that, I want to give a bit of motivation why I'm going to go through all these troubles. And the motivation is that we want to improve the quantum technologies using superconducting circuits. I think that everyone would like to do this. The quantum technologies that we are going to... that we would like to improve is quantum computer because as I said, this work is part of the abacus project. So the quantum computer is this gate model. You have this gate model here. And it's based on applying gates to the qubit, to two qubit gates. And you have another model that is this adiabatic quantum computing. But usually with my mobile, when I shake it, it works. But this, it doesn't work. It doesn't matter. And this is based on a slow evolution of the Hamiltonian of your system that you have a high control of A. So you go from a ground state that it is easy to prepare to a one that is more difficult to prepare but still it has the computation... it solves the computational problem that you want to get. So this means there are also quantum simulations and the word that I'm going to say also applies to this quantum simulation. And this is made by many groups. So in principle, these two models are equivalent. This is something that probably you all know. This is from a theoretical point of view. Maybe from a practical point of view it's not so much equivalent. But anyway, all of them require to engineer good qubit couplings and to have good qubit coherence. At some point, you have to sacrifice one of the probes of this requirement to get another one from time to time. For example, I think that here in this computer that is the big wave last quantum processor, this is an annealer. It is not universal but still it falls in the other quantum computer. So what they do is they put a lot of qubit. Those qubits are very connected. This green stuff is one qubit that is coupled to 12 or more qubits. But at some point I think that you sacrifice a bit the qubit coherence. Here the lattice, this is from the IBM quantum processor. The Washington, you have a lattice that is less connected. There are less qubits but you have, I think, a better coherence for individual qubits. So in the talk, what I'm going to focus is in these qubit couplings. We want to improve it. And what we want to do is to get a waste of finding more qubit couplings so we can wider the families of models that we can implement in a quantum adiabatic computing. But at some point I would talk about qubit coherence because from time to time we would have to sacrifice a bit the qubit coherence or the qubit coupling, as I said. As an example of what we want to do. For example, for adiabatic quantum computer, I said that it is equivalent to the gate model of quantum computer and this equivalence can be taken at least theoretically to this model. If you are able, for example, to get this model in a quantum adiabatic computer, you would be able, at least theoretically, to solve any problem that a universal quantum computer can solve. But the matter is that this model is very difficult to implement in a quantum annealer or in a quantum adiabatic computer in a superconductive circuit because you have to get full to nobility of all the parameters, like the gap of the qubit, the coupling of all the qubit, not just two. And you have to have two directions of coupling and this is difficult. So from time to time you may be likely to get something simpler and for this reason, they were looking for non-stochastic model that maybe what you want to do is to implement something that is not so complicated as this, but still you can quarantine some way that you are going to gain something with respect to a classical computer. And what is this? This is non-stochastic model, quantum model. So those quantum models exhibit a sign problem and then you cannot do the computation with Monte Carlo. Then you delete Monte Carlo as a direct competitor of your quantum annealer or your quantum adiabatic computer. So these non-stochastic models were realized by the people of D-Wave a couple of years ago and here are these other regions, the region of parameters. Well, this is the coupling GYY that is there. Well, GYY is not there. Anyway, GYY, GXX, GZZ. And this is the strength of the coupling in gigahertz. The gap is larger and this is an important point. And in these regions, you get non-stochastic model and here non-stochastic model. However, this came to be a bit strange because in these two papers, they showed that even if you are here and you are non-stochastic what could happen is that you can cure the non-stochasticity by doing a quantum Monte Carlo on the full superconducting circuit. At least in this paper, they showed that they can do it very explicitly in a perturbating regime, a non-stochastic model. So, where we are going to, for example, our direction of work is to try to show that we can break these results. Well, not break, but see how you can go together with these results in superconducting Trigio-Sephson-Janxson qubits. And for this, we are going to try to implement a model like this. We are not going to make it, but we are going to make something similar to this and also try to explore the different regions of the perturbating one. So, this is the outline of the talk. We are going to study, in the first part, Trigio-Sephson-Janxson qubits coupled to other qubits and to LC resonators, yes. And for this, well, we are going to show for this that there are two directions that we can couple them strongly. And for this, for two qubits-qubits, we are going to show that we are able to couple them strongly, not in two directions, this is not completely true, but almost in two directions. And for this, and then in the second part, we are going to couple a fluxon encrypted to a waveguide and also see that it gives an interesting model, which gives you quite protected state from decay. Okay, let's go with the first part. So, we have this persistent current qubits. This is a, you all know, this is a loop with a Josephson-Janxon, and here we can, we put two Josephson-Janxons for the three Josephson-Janxon qubits, but in general for a persistent current qubits what you are going to have is a potential like this, so you have the left and right. They are persistent, correct with different directions. You have the qubit gap there. And what we do, what? And let me see a very simple sample of how to induce magnetic interaction, the simple one. So, you write this model, this is the tunneling, going from here to here, and then you can couple with the intensity to an external flux. What you do is you project this operator in the qubit base, and you get these sigma x, and now if you want to couple another qubit, you see that this external field can be induced by a mutual inducer by the other qubit, and then you have here another current operator that you also projected in the qubit base, and you have these two, okay? So, for this, in fact, if you want to get, you have this model, and now can we go to ultra-strong coupling system? Yes, what you have to do is, for example, to get the interaction strong, so the mutual interaction is strong, and also large persistent current, fine, and this was done in these two papers that even they put the qubit together with the resonator, galvanically coupled, and in this one, it was also the case. Fine. Now, going for the capacity coupling, we have, for the capacity in coupling, we are going to have like this one for two qubits, we join it with a capacitor, and we have charge charge, fine. We do the same trick. We project the charge in the qubit base, and we have a sigma y operator. If we put a resonator, we are going to have the standard form with the impedance here, and yeah, fine, then it is straightforward to find the coupling. The coupling, it is in the y-y direction, and it is going to be, you are going to have two, if you do the qubit, if they are similar, you are going to have two gaps here. And then what you find is that the coupling divided by the gap depends on the gap, also, fine. For the qubit resonator, it is different. The coupling divided by the gap, it doesn't depend on the gap, which is much better. Why is it much better? Because if you have something like this, it was discussed for a similar system, not for this one in this paper of Kerman a couple of years ago also, that this is, you cannot use for example, this limits a lot the coupling that you can get, and for instance, you cannot get something to do, to do something like quantum annealing, why? Quantum annealing, at the beginning you have a large gap, and then you decrease the gap up to zero, theoretically, and then you have a large interaction. Okay, but this is very difficult, because you decrease the gap, and then you have two coupling, divided by the gap that goes to zero. So this is not good. For the qubit resonator, it's not that bad, because well, at least this restriction is not there, because you don't have here nothing like the gap. And this is going to be easier to deal with. But anyway, so, but this projected, is there something that we are missing here? Is this projected on the qubit base fine? Well, it is not so much. Why? Because this projection, if you look, it's just the first thing, when you have the effect, you have the full superconducting qubit, you have to somehow project it to the qubit base. But the first thing in this projection, the effective Hamiltonian has a first thing, that is the direct projection on to the qubit base, but then you have a lot of terms, and these terms are a series that take into account that your qubit can interact these two states, go up, and then they can go back again. So when you take into account this interaction, you find that these terms, roughly speaking, some of them, at least, they would go as the amplitude to go up for qubit, qubit, go up to the excited state and come back, and this amplitude, if you take this as a rough approximation of a harmonic potential, it is going to be, typically, h bar omega cubed, which is the distance, and then this is going to be one, so we have to sum the full series. For the qubit resonator, it's not that bad, because indeed, you have the square root of one qubit, and the resonator, but this is much smaller than the difference between the qubit sub-space and the excited state. Here, I am thinking that you have a large anharmonicity, so this separation is large. That could be the case for three Josephson junction qubits. Now, we go back. So, summing up the full series, we did something similar. We improved the, this doesn't work, the word of Consani and word Barton. Well, we based it on their method. We did another method that I think that it is a bit better. All of this is based on the work of this other reference. What we did numerically is to sum up the full series, and we have that in this region, we have the qubit cap that is this one. We have the coupling here and the coupling here that are similar. We have something like this model, sigma yy and sigma sets are similar, that's 0.1, something like this. We have this type of model, which is not a full sigma xy, but still is something that is not in one direction. We have the qubit cap that is of the same order, the amplitude. This model was explained roughly in this reference where you are going to have this one, but we are able to compute from zero that you are going to have a yy in the first order to this model, and also we are able to show that there is quite a strong coupling for this, yes. And also with our theory, you can get an intuitive explanation of why they start to be more, more coupling. So the first order, as I was talking, is that you have a qubit, qubit, they interact, but they stay in the qubit. The second order is qubit, qubit, they go up and they go down, and this gives you a sigma set that is indeed the second order here. And then you have these two processes that you can join it, and you have a sigma xy. So you have always jx that is non-zero. And last for this, if we join it also with a Josephson Jackson that can be made tangible, this is more or less straight forward, and we show it in this paper until this type of model with sigma xx with the Josephson Jackson and also the sigma plus, sigma plus, sigma minus, sigma minus. And this is non-stochastic in principle. At least the spin model is non-stochastic. And it is also, we are able to show that it is non-stochastic and very strong coupling. Okay, this is the case that it was more simple. Here this is the qubit and the resonator. Join it, qubit and resonator. The difference here is that as I said, the first order works and things are much simple. And what you can show is in this plot you have the coupling of the qubit versus the gap of the qubit. This is this line. And the coupling of the, the coupling respect the energy of the resonator. And what happens is that at some point there is this point that omega r, the energy of the resonator one of the gap is the same. And at this point you can explore a model that has the same energy for qubit, for resonator and also the coupling is ultra strong because we reach point of 0.15. So again adding the magnetic coupling we can show something that is I think that has not been studied in superconducting circuit that is the qubit, the resonator and an ultra strong coupling in two directions. And this open, I think that this open new regime of quantum optics. Okay, now, with this I finish with the three Josephson Jacksonal Rice, all of these was for three Josephson Jacksonal Rice, although I think that it can be made for all the type of persistent qubits. Can you say again what are the parameters? Sorry, Denis. Can you say again what are the parameters you have to tune to switch on off the couplings to the resonators and between qubits? Well, for this one you can make it like an square. And for the resonator? For the resonator I think, well, for the resonator in principle it is fixed by construction. But this is also fixed by construction. So, yes. We should, at some point we were trying to get this coupling also because it is not nice that it is fixed by construction. So, you have in mind a simulator not an annealer because with it you cannot make annealing? Yes. Yes, yes. You have to get the tunable capacitor. But the point here is that we want before doing this, we have to see if this works for something or not. So, we have these two papers saying that non-stochastic is cured going to be a superconducting circuit. And then we have to see, first of developing more these ideas and do everything like tunable, we have to see if this is going to work or not. Because if you spend a lot of time and then they come with the quantum Monte Carlo and they say, okay, I can do it in the full superconducting circuit this is not going to be, well, it is worth that it is going to be for nothing. How much time do I have? Okay, perfect. Yes, now. And now I'm going to change a bit. Well, it is more or less the same. We have, we want to study also new models that is how to implement a peak a bound state in the continuum in a fluxon in Q-treat. Now it's a Q-treat. The QBT is 2 level, Q-treat is 3 level. Okay. Couple to a microwave. Okay, so let me say two words about what is a bound state in the continuum. About the state in the continuum can be with this picture that I took it from this reference. So they were first predicted a very long time ago by von Neumann and Wigner. And what happens is that in principle, if you think in a quantum system you can have, you have the spectrum of the quantum system and you can have different type of spectrum. You have the discrete spectrum typically and then what happens is that this is a confined state. You put the particle here and it is confined in the space. Now you go to the continuum. Typically if you are in the continuum the state are not going to be localized. They are going to be extended. You can have with resonance that it means that the particle can stay more time here or it is concentrated here but still it can leak and go to the infinite. And then you have a peak. A peak is a mode that lives in the continuum part of the spectrum but it is completely localized like a discrete state. And this is from the point of view of theory and also from technological application this is an interesting state. So this state has been extensively analyzed in the framework of photonic I would say, but also there has been a couple of some works in superconducting circuits. The one that I am aware, in this one. And those work, what they did is to construct a peak from the field in the, localize it in the waveguide. So the part of this, and they used the qubit they used a qubit in some way to put the correct boundary condition. But then the peak is localized in this part of the waveguide but it is not so compact because it can be localized in a big part of the waveguide. So what I am going to try is to do a more compact to localize it in the fluxonium loop that is much smaller region of the system and also with the hope that it is scalable to do applications. The system that I am going to analyze now for which we have been working is something like this. You have a coplanar waveguide you couple to here capacitively again to something that is a fluxonium that we introduced this morning a couple of times. So you have the large inductant that you have to set here as Juan was saying and this is the original paper where they propose the fluxonium and they analyze it just this system and where are we having in this system we have a dark state in principle we have a dark state. What happens if you write the potential of the fluxonium at zero bias at zero external magnetic flux treating the loop you find this type of potential energy. Now you can put the zero state here the minus one state here we are interested in the Q-trip we are interested to keep these three states. So what happens is that if you are at zero bias you are going to have the superposition the first state is this one more or less and the second state is the superposition because these and these are they generate the superposition an anti-symmetric superposition and then you do those two states that is plus minus. Now in this case we have a flux inversion symmetry so this means that the states have a well-defined parity and the operator have well-defined parity this is very basic so you cannot join with the chart that is given by this operator this coupling you cannot join the ground state to another one that has the same parity because the chart has odd parity that this is that and this you get a wave here you try to aside from the zero to this plus superposition and you cannot do it this is that and this has been experimentally seen in the original work here as a deep in the transmission I think in the spectroscopy so this is the first level the cubic level and this is the second level and they don't see it at the signal a zero flux bias ok so is this a big well it doesn't need to be a big why not because you have a dark state but if you put the state here in the big in the second it can go away well it can decay from plus to minus so we need to suppress this transition so if we suppress this transition this is a thing that can be done going to this regime we are going to have some sort of a big this is going to be more localized and then here we have the transition rate from plus to minus in the scale of milliseconds of seconds the frequency and we see that the tendency is that when you increase cj over ec this is the normal AC but it's a detail that we don't care now when you start to increase this ratio you see that there is an exponential decrease of this transition rate which means that the decay tie roughly also increases potentially with this quantity and then well this decrease is up to a point and this point is where there is a voided level crossing between the plus state and the first cited state so we want to avoid to have this voided level crossing soon what we do to do to make this is to set a large cj over ec which is anyway the regime of the fluxonium and with this we can see that there are huge decaying time or transition rate is very very small so in principle this seems that we have a big in the fluxonium Q3 in the fluxonium Q3 at least so but those huge decaying time are realistic probably but many of you are experimental you are going to say as the previous speaker was in DS in theory you can do whatever you want but in the practice probably not so there is going to be a noise what happened with the noise in principle there is going to be a dangerous sort of noise that you can bias the system with noise and then the sensitivity of this type of transition from zero to plus is very large and if you bias the system and for a long time you are going to allow this transition to Q and you are not going to have a peak anymore however we have in some way we have to put here numbers and estimate what is the noise level and we have done this by computing the typical deviation of the flux for very long time so at the cutoff of smaller frequencies and we can set for the 1 over f noise at very large, at very small frequencies that is in this level so if it is in this level the peak could be realized experimentally at least taking into account this 1 over f flux noise if it is 10 to the minus 5 we are going to have a transition rate in seconds in the inverse of second to 10 to the 4 which is quite huge quite a lot I think well I mean the inverse is going to be quite a lot compared with the typical frequencies of the system at least and we have here flux noise level here we are going to have decaying time up to milliseconds and this is consistent with the decaying time coming from the plus to minus transition that I was saying before so for this for example for this realization for this parameter if the noise is in this level we are going to have this order of time for the decaying that seems to be very large also you can always say well you have to take into account other sources of noise at least we think that for the electric losses it is also fine this we have taken into account and now a couple of remarks about this peak this peak is we expect that you can construct it in a way that is very well protected from decay but then it is very well protected from being created which is very unpleasant and then you have to think in ways how to create it and well we can think in some procedures like here to decide with non-linearities but we are also thinking something very simple which is to put a small bias, populate the peak and then go to the zero bias this is probably not ideal from the point of view of quantum information because in this regime of a small bias you are not protected from the point of view of quantum information so the phasing and all this stuff can come but at least for the point of view of creating the peak I think that it would work and also we have to take into account that the heavier the more heavy the fluxion is this cube that I was showing before the sensitivity is much larger so we can do this in a fast way by setting an Ej over easy large however this always would come to a larger sensitivity to the noise which may be also dangerous and these are the conclusions I think that we have expanded the family of models that you can set that you can implement with current qubits specifically for a three years of injection we have seen that we can do ultra-strong and non-stochastic model with the qubit-qubit interaction and for the qubit resonator we have shown that there is ultra-strong coupling in two directions which is something that has been up to date at least in superconducting circuits for the fluxion in Q-treat we have seen that it may be realizable to construct a very long-lived state a big state, a state in the continuum and now we are also thinking in what to do next which can be see if we can get universal quantum computing, the model that I was talking at the beginning with two orthogonal couplings or also think in the application of the big for quantum information and also for sensing the external fields well, one thing that I didn't say is that these, the results from this fluxion in Q-treat we will put it today or tomorrow in the archive so it is not available yet these two the references are in the main body of the work you can check it if you like and that's all, thank you thank you very much, the talk is now open for question you mentioned the effect of 1 over F noise I suppose it's flux noise and how did you estimate this I didn't get or are you just supposing it's there? no, we estimate it well we get from the experimental work of Manucharian in 2019 at PRX that they say that the model is a flux noise they take it as a constant A over omega with A 10 to the minus 5 10 to the minus 6 this is the spectrum roughly speaking and it's supposing that this is consistent this power spectrum is consistent with the experimental result you have also to set a cutoff and I think that the cutoff in the frequency we put it, the plus cutoff we put that 10 to the 2 second 1 over second and minus 2 the high energy cutoff 10 to the 3 or something like this this was this was consistent with previous work and then we compute long time fluctuations what are you calculating now? yes well, we do these computations up to with typical times that are near the this cutoff this cutoff very slow noise and this gives you an idea that the amplitude of these computations because this is first yes well you take the real part of this we have time for one more question I would have a question actually so it's we're getting the first part of your talk that you could have ultrasonic coupling in two directions and that it could maybe give rise to new physics, could you elaborate maybe? yes, well, actually we didn't get two directions sigma y, sigma y for qubit-qubit coupling but you were referring to the qubit-qubit yeah, I didn't mind like multi-channels spin boson or stuff like that I think that you may be able to do a James Cammie model but usually if I'm not mistaken this James Cammie model came from the rotating wave approximation and then you are always constrained to small values so you cannot go to James Cammie model with an ultrasonic coupling but with this you can do it you can go to very strong coupling because we are showing that we have a strong coupling so it's in some way it's curious I think let's do it again