 OK. So, welcome to this joint ICTPC's CMSP colloquium. And before I forget, and when I see you to stay until the end, actually after the talk, there is refreshment on the terrors, so we go there. And today's speaker is Professor Levi Jofi, who is currently a senior researcher at Google. But Professor Jofi is a well-known researcher in the field of these other systems, superconductivity, and the like. He got his PhD from Landau Institute in 1985. And has since covered several positions bot in Europe at Laboratory Physique Theorique in Paris, and Rutgers University and the University of Wisconsin Medicine. And as I said, since a couple of years, he's a researcher at Google, where he's helping the effort of building a quantum computer. He will be telling about us about this today. And so, without further ado, I just leave you the podium. Thank you, Levi. Thank you very much for inviting me here and for the opportunity to give this talk at your wonderful institutions. So I will talk not so much about building the quantum computer today, but about how to use them, how to use what we currently have, which is, of course, not a full-scale quantum computer, but something which is already quite interesting and unusual from the viewpoint of conventional solid-state physics. So I should warn the senior people in this audience that it's really a colloquium-style talk. So beginning will be very introductory, trivial for them. So I suggest that they have a good sleep after lunch and wake up in the interesting content in the second half of the talk, and not the other way around. That is, fight with the sleep right now, and then fall asleep when I talk about something interesting. So that's at least will be my approach. Very good. So I'll start, as I said, with something very basic that was a system that we all have in mind at the moment is array of bits. You can also call it array of spins. And it's typically two-dimensional array. With what we can do, we can do, we have an interaction between nearest spins, in which can be translated into the gates, into the two-qubit gates, between nearest neighbors. And we, of course, can do almost any operations on a single, not almost any operation on the single spin or bits. I will use the words spins and bits interchangeably, because they are really the same. So there are many possible physical realizations of this general thing, which is quantum, such sort of embryonic quantum computer. But I'll talk only about superconducting qubits today, because first of all, I'm more familiar. And second, they look at the moment very most promising, although other systems like cold atoms rapidly catch up. And I think, well, but anyway, I will limit myself only to superconducting qubits. So first, because I'm going to talk what is possible and what is not possible, I need to introduce a little bit the superconducting qubits, because a lot is determined by their strengths and weaknesses. So what are these superconducting qubits? They are all based on Josephson effect. And again, I remind you what is a Josephson effect. If you have two pieces of superconductor, then as Brian Joseph realized more than 50 years ago, 60 years ago, actually, they energy of these two pieces of superconductor is described simply by a cosine of the phase difference between them, and there is a dissipationless current generated by this phase difference. The fact that it's dissipationless is crucial, because what we want in the end of the day is to have a fully unitary dynamics. So any source of dissipation is our enemy, and eventually the death of the quantum computation. So when you start to think about applications of this Josephson effect, you immediately realize that it looks almost impossible. And the reason is that, as the formula above tells you, that Josephson energy is inversely proportional to the resistance. And the resistance, as you, of course, realize, is exponentially, depends on the distance of the thickness of this insulator as exponential. What is in the exponential? The exponential, of course, is the distance divided by interatomic spacing. So you will think that if you change the width of this thickness of this insulator by one atomic distance, it shall change by a factor of 3, roughly speaking. So you need to, in order to control this Josephson energy, you need to control the thickness of the insulator within atomic precision. And it looks like a fantasy. And it's indeed true that Josephson effect cannot be used for anything controllable, for anything like quantum computer, except that nature, or God, depending on your beliefs, give us one miracle. One miracle is called aluminum oxide. It's not a coincidence that all implementations of quantum computers are based on this aluminum oxide. Actually, in the simplest implementations, it's aluminum, aluminum. What is this? Aluminum, aluminum oxide, aluminum with junctions. It can be not aluminum. It could be some other metal for the superconductor. But aluminum oxide is unavoidable, because miracles do not happen twice. So even one miracle is surprising. So how we use this miracle? We use this miracle in the simplest possible way so that we attach a capacitor. And it's literally a capacitor that you learned about in the high school. That is, in fact, the same aluminum. And to the Josephson junction. And then, because the phase of the superconductor is canonically conjugate to the charge, the Hamiltonian of the system is nothing but the Hamiltonian of the physical pendulum. It's cosine of the phi. And the kinetic energy is q squared, which is the charge, which is nothing but the momentum of this physical pendulum. So what is the most important thing about this pendulum? The most important thing is that it is not exactly harmonic. It's almost harmonic, so we have very good prediction of the levels in it. But it's not exactly harmonic term, which contains n squared, that distinguishes this potential from harmonic one, is crucial for all applications, for its application as a quantum bit of information. So the idea is that if we do slow evolution, if we change the parameters of our system slowly compared to this energy, and notice that this energy is relatively small compared to the main term, then we can ignore the fact that this system has more than two levels. We can only limit ourselves to the lowest energy state and the next one and forget about the rest. And that is how we convert this, in principle, relatively complicated system of many levels into what we want, which is a qubit with just two levels. So that's the basic. And then, just a little bit more detail, that we want to be able to control both the Jordanian energy and apply also some driving pulses to our artificial bit. People sometimes say artificial atom. So in order to control the EJ, which is the main parameter of our Hamiltonian, we, in fact, built our qubit out of two Jordanian junctions in parallel and changed the magnetic field, which penetrates this loop. That allows us to change the effective z field, which acts on our bit, and also to drive it in the external electromagnetic field. We apply also sigma x perturbations. So that is these two knobs. One is changing the flux. Another is applying the RF field. Is exactly what we want to have a fully controllable single bit system. So that is the basic physics of the superconducting qubits. So notice a crucial drawback immediately, that although the frequency of our qubit can be quite large of the order practically, it's of the order of a few gigahertz, let's say, five, the fact that we can operate it relatively slowly compared to this frequency. And I repeat that EC is much smaller than the distance between the levels means that our gates are relatively slow. So we lost a lot in the time of which we can do the operations. And that will be crucial in the second when I discuss limitations. Practically, this time of operations is not less than 10 nanoseconds. Whereas the frequency of each qubit is, as I said, is, let's say, five gigahertz, so we lost a factor of 50. And of course, a factor of 50 doesn't come for free. OK, so now, so what I told you that the frequency is, sorry, the gate operations are 10 nanoseconds, but you should ask me what I should compare it with. What is this 10 nanoseconds? Maybe it's very good. So we'll discuss what really controls the time scales in a second, but first let me go through another part of the story, which is the two qubit gates. And two qubit gates are achieved by, essentially, I don't want to go into the practical details, but you can think about it as attaching a variable capacitance between the qubits, which provide exactly capacitive coupling. In reality, it's done in a slightly different way that you attach another elementary block of the same nature between them, and so use it as a virtual state, but it's irrelevant, because at the end of the day this more complicated physical system behaves exactly as variable capacitance. What variable capacitance does is that it provides you some interaction between the charges on these two devices, which are called transmons, and so the effective Hamiltonian is just the charge-charge interaction, which if you rewrite it in the basis, in our basis of computational states, you remember it's a state 0 and 1 of each qubit, then you get sigma plus, sigma minus. And as you know, and then, well, in reality, you also have a little bit of the interaction, but this is not so important at the moment. So what we achieved is that we have all ingredients to perform arbitrary unitary rotations. The scale, again, crucially, is how long it takes us to perform that, and that is how large is this j-interaction. And in reality, this j-interaction is about, can be up to 30 megahertz. Again, it's limited by the fact that we cannot do things too fast, otherwise we start to admit these higher levels, which are always present, but we want to ignore them. And so, roughly speaking, we get the same 10 nanoseconds for these operations. OK. So now, what these nanoseconds, or anything like that, should be compared with? Well, as always, quantum computation relies on the coherence of the states. So what are the enemies of the qubit which destroy the coherence? So, first of all, it is anything in the environment which has the energy, which is equal to the energy difference between zero and one state. And, of course, in our life, because we live in a dirty, solid environment, we have many things. We have photons, we have photons, we have quasi-particles, we have two-level systems, many things. And, of course, all of them are enemies, and all of them we have to be very careful not to allow to limit their number, basically. We cannot prevent the interaction with them in these of these transmons, but the only thing that we can do is to decrease their phase volume by cleverly designing our system. So, that is decay, right? Because if we have, you know very well, that if we have excited level, then, and we have something in resonance with this excited level, this excited level can decay and excite the parasitic excitation in the environment. And so this typically people characterize this process simply by decay time t1 of the qubit. Another enemy, and that is really specific to the design that I was discussing before, but other designs have their own drawbacks, so I don't want to discuss that, is the fact that magnetic flux, which is crucial for our operations of a single qubit, is not set in stone. It's produced by something, right? And also, if you have, it's always the case that if you have a knob, then the fluctuations in this knob can only lead to the coherence of your system defacing. So, in fact, in our, in this case, it's very simple that our Jolson energy depends on the flux in the loop and the flux has some fluctuations. So, now, what are the numbers? So, numbers are that one can decay, so decay of the qubit can be up to milliseconds milliseconds, even actually, there was IBM paper recently that I forgot to put here, which shows a few milliseconds time, but that is sort of record, and you cannot hope for such good decay times in a large system of the qubits. What you can hope is, let's say, 200 microseconds, and then the question is if you can achieve these 200 microseconds consistently in a large array of qubits, and, well, then it becomes really tricky issue that there are some claims that you can, but more typically, let's say, 100 microseconds, and the defacing time is of the same order, again, in the sort of the system that anyone can do is about 20 microsecond, and in the best systems that were more, that are currently being produced by the leading groups, it's around 100 or more microseconds, but in this bullpark. So, you see, now, let's remember these numbers and think what it translates into, in the terms of any realistic computation or simulation or whatever. So, as with, so, typical number of qubits that one can realistically put on the chip currently is about between 100 and 400. So, of course, this number will raise in the future, but we do not expect that it will raise by a factor of 10 in a few years. So, single qubit operations are limited by 10 nanoseconds and two qubit gates, as we said, are limited by 10 or 20 nanoseconds, and the coherence time is optimistically 500 microseconds and pessimistically 50. Okay, so, if you talk about a single qubit, that means a lot, because it means that you can make many thousands of gates before the qubit decays, right? But single qubit is not interesting. Single qubit you can simulate or completely understand on a laptop or actually even on a piece of paper. So, you are interested in coherence dynamics of many qubits, let's say, of the few hundreds of qubits. What does it mean? If you have a coherent state of hundreds of qubits, it means that you have at least 100 excited qubits among them or about that. So, and of course, the most interesting states are such that a decay even of one qubit ruins the system because if it is robust with respect to decay of one qubit, then it means that it's not really a quantum state. If you can think about it as some product state, which is, again, simple to understand. And we really would like to see what other interesting states that our big system of qubits can simulate. Okay, so even a single decay in this system ruins it. That should be the restrict requirement. And therefore, we should decrease this number of T1 which looked so nice that it produces few thousands of qubits by a factor of 100. That immediately makes it much worse that instead of having a few thousands of gates, we have only a few hundreds of gates, more realistically 200, and more realistically even less than 100. However, there is one additional trick that one can do. Namely, if one is clever, one can study the problems in which the number of excitations is fixed. And then at the end of your simulation or process, we can check if one excitation disappeared. And if it disappeared, we simply throw away the results and we repeat the experiment until we find the realization in which not a single qubit decayed. That allows us, of course, if we, let's say if our decay time is one microsecond and we impose it, not as we look for the evolution, such that not a single qubit decay during, let's say, 10 microsecond, 10 times longer, that will happen with probability of exponential of minus 10. So we will have no results for this experiment. But still this error mitigation is a bit useful. It allows us to bump the typical time by a factor of roughly speaking five. So as a result, we can get to the number of gates which are in the range of a few hundreds. So that actually ends my introduction and description of what we have now. We have a system of qubits, which is between 100 and a few, between 100, maybe a few hundred qubits, and we can do the number of gates which are in the range of a few hundreds. So now the main question is what can be, what is useful, useful now meaning interesting, not anything more, we can do with this system. So as you know, some time ago Google group showed that one can do useless quantum evolution that cannot be reproduced classically, which has a big name of quantum supremacy with a blue star here. I will say useless quantum supremacy. So then somewhere I didn't put it correctly, because in this picture, but somewhere in the upper right corner of this phase is the real, really practically important simulations of quantum chemistry which require fermions and many other things. And we are, well actually it's too optimistic as it's shown here, we are not yet there and we will not be there in the next few years. However, here in the middle, there is what I call spin liquid that is interesting physical problems which relate to spin dynamics of these hundreds or a few hundreds of spins which cannot be simulated classically and which are interesting from the viewpoint of physics of fundamental science and you name it. So that is our, that's the most attractive thing that we have on our horizon now. So, what are these? So, before we discuss what could be interesting about these spin liquids and generally the spin systems, so what we are looking for? We are looking for the systems that cannot be simulated classically because otherwise why we do, we have all this trouble of using quantum computer. We, and the one which are interesting and so in this talk I will discuss the first step in this direction in which we studied quantum one dimensional chains and in which we reproduced the results of exact solution and discover something new. I should tell you that to be honest we didn't discover this new doing the quantum simulations. We first found this new things by doing the analysis, the numerical analysis of what we expect by quantum computer and found something that we didn't expect. So, as a result of this numerical analysis and quantum computer perfectly reproduced what we found numerically. So, it was not really a discovery by quantum computer, it was really a discovery by a classical simulation of what quantum computer should give us. So, now before I continue and discuss what was the practical, this existing experiment let me emphasize that there are a few important difference between the simulations that we can run on a quantum computer and what is this quantities that we usually study in the solid state physics. First of all, we know the Hamiltonian parameters exceedingly well, incomparably better than in any solid state system. Second, we can create very unusual states that is in normal solid state physics we are limited to finite temperature or maybe very low temperature or even high temperature but it's very difficult to create a non-trivial state. Here we can create extremely correlated and unusual states and study the revolution. Second, we can study the correlators of non-hermitian operators which you cannot simply measure by a conventional solid state experiment. So, this combination actually shows that we can study some new physics that is not allowed to us normally. Okay, so, now, in this view of what can be possibly interesting I should immediately tell you that standard solid state approach to theoretical approach to interesting states is that one discusses usually the ground state of the system that is, for instance, the ground state of frustrated magnets or which are not conventional anti-ferromagnets or ordered states but display some topological order parameter or some algebraic correlations and whatsoever. However, that problem of studying the non-trivial ground states is not very natural for the existing computer because it requires some sort of adiabatic cooling and that takes too long normally. I won't say, not say, it's never possible but it's not a natural problem for this quantum computer as I described to you. So, and second, we want to compete and we want to get something new, right? And therefore we have to compete with existing numerical methods and there is a number of very powerful methods for numerical study of the ground states and when they do not work, quantum computer also has problems such as solution of NP-complete problems and so on. So, but what quantum computer can do much better than normal classical computer which studies the same quantum system is dynamical evolution. We can create some interesting state on our quantum computer, we can study, we can see how it evolves and if it involves chaotically sort of non-trivially then it is very difficult generally to simulate on a classical machine. So, and again this presents some opportunity because quantum chaos is generally a non-trivial problem. Very good. By the way, what is my time limit, I shouldn't know. No, I know the time. Yeah, 20 minutes. 20 minutes, aha, okay, very good, yes. So, let me make a little destruction that is ask, so you can ask essentially because I'm not studying the ground state, I'm studying the sort of some high energy states and the high energy states probably are very simple and it's not, that's why it's very wrong. So, and a good example that I would like to introduce to you because I'm sure that people in this audience with a possible exception of one or two and do not remember this, is that even the simplest problem of liquid helium, not superfluid helium, but liquid helium is still not understood physically. And the point is that it is known empirically and if it's known to any experimentalist who designed the cross-stud that the entropy of the liquid helium above the superfluid transition point follow the strange law and there is no explanation. So, that was just to emphasize that the study of systems, quantum systems at relatively high temperatures or noniquely away from the ground state can be extremely non-trivial. And always this non-triviality is due to the fact that essentially you study the system which is heavily constrained, like these cars on the parking lot, so that you can move them in the case of helium, you can move the molecules, but you can move them in sort of circles because they are like balls which are closely packed and it's very difficult to move, like these cars again on the parking lot. So, what we can learn from our quantum computer are some new physics about the systems which behave sort of like these highly interacting balls. So, now a few words about chaos before I go to the actual experiments is that classically we very well know that if the system is sufficiently complex it exhibits chaotic motion and such as the weather. And even Newton was worried about it. So, it's true, but not always true, for instance, our very existence is due to the fact that the solar system is not completely unstable, that the planets remain roughly speaking where they are. So, what is the quantum equivalent of that? Quantum equivalent of that that we will study in this work is the following, that we have a chain of bits, which are shown here in gray. This chain of bits is described by this Hamiltonian or actually equivalent of discrete evolution, discrete gates, but you can for simplicity think that it was really due to Hamiltonian, there is not much difference. There is difference, but not crucial. And so, if without these red qubits, which we call hairs for obvious reason, the system, the bolt system will be exactly solvable because it's just one dimensional chain with x, y, z interaction. However, with the hairs it's not solvable. It's not that there are no integrals of motion which govern its dynamics, and therefore the very natural question is how much the dynamics change if we grow the hair. So, now let's discuss for a moment this simple system of one dimensional chain, that with the dynamics which are given by these discrete gates, which we apply alternatively on the even and odd sites. Okay, so this is, if we have just one single excitation in this chain, this single qubit in state one, then this problem is not much more difficult than the problem of a motion of single particle on a chain of sites. The problem that one solves as a first problem in solid state physics when you want to explain what is the band theory that appears in any material. And only here, because we apply alternatively the gates on odd and odd sites, we have two different types of sites. Therefore, we have a brilliant zone which was folded, and the evolution matrix is a matrix of two by two, not by one, by one, and therefore we have the spectrum which is shown here. Again, it's cosine and g sine squared p. So, it again demonstrates my previous statement that not much changes between the evolution which is controlled by the continuous evolution, which is written here between all sites, and this discrete evolution which is the alternative product of unitary on even and odd sites. The difference is very small. And now in the interacting model we can, then we can ask what happens when we have two excitations. So, in the two, so the point is that this, let's discuss for a second the model in which we have no zz term. It's much simpler to understand and the physics is basically the same. So, this model is described by the, again, two by, now it's described by four by four matrix, but for zero phase it can map to the discrete dynamics of referments even though it is discrete. Now, but due to the interaction between this zz term that I showed to you before, there is some interaction between these referments and, of course, as you realize, for finite band, it doesn't matter the sign of the interaction. Depending on the sign of the interaction you form bound states either below or above the band, but you always form them. So, the problem here for just two particles you can solve the problem on a piece of paper and not any much effort in half an hour, but for an arbitrary number of particles you need to have a machinery of better answers which was done by Igor Alejner and who showed that these bound states of a few particles are always produced in this system. So, let me skip these equations. I think that they are not so relevant. So, how do we, first, how do we study this, how do we check that our quantum simulator indeed shows what we expect for the bound states, for the production of bound states. We can do very simple experiments in which we create particle inside one and let's say we just measure the same particle at side later in time and we just study the propagation of its density. However, as I told you before, we can also study the green function of this particle and so how we do, we have the following trick which is impossible to do for normal solid state experiment. So, because we can measure, not just we can measure not only sigma z, but sigma x, sigma x correlators and the following way. We start with a state which is a superposition of zero and one and we evolve it over time and so we ask and then we do the transfer, measure it in x basis and so if you just follow this computation, you see that we measure exactly the green function of these particles, of these particles. So, unlike so we have a way to study not only the density density, but the green function. Okay, very good. And then we can do it in this little chains and we see beautifully that the peaks that we see in this green function exactly reproduce what we expect for the spectrum. Very good. So, now the most important thing is that we can do the same for many particles. We can create a combined object which people sometimes call a cat state which is the coherent superposition of the state in which there are no particles and there are particles in state one on a few sites and measure the correlator which tells us the propagation of this combined object if it exists. And this if is crucial because we see that indeed when we do numerical simulations and you will see that in experiment as well. We see big peaks that correspond to the coherent propagation of this combined, very complicated object and some small peaks which are due to the sea of our particles. Very good. So, now, so let me, now we introduce our friendly hairs that I was talking before and these hairs destroy the integrability and surprisingly they have very little effect on this propagation of the bound states and that was the surprise that I was talking about that integrability although it is destroyed does not completely take away within the formation of the bound states which actually have no reason to exist without integrability. Ok, so we can see that five particle bound state is stable with respect to the destruction of integrability and so on. So, now we come to the real ex, yeah. Yeah, because everywhere there are hairs I don't understand what does mean. About one. There is nothing special. It's not that they avoid the hairs. Yeah, it just goes back and forth, yeah. So, here, so now I want to show you the data it's really the data from the quantum computer which demonstrates exactly what I was telling you. So, the first experiment is that here you create some number of particles, some here close together and you ask how this number of particles propagate together. So, it's if you wish density-density correlator. So, here you clearly see that two particles propagate, sorry, one particle propagates in this way. Then the two particles form this big cone. Three particles move like that. And notice that, of course, when the number of particles becomes larger and larger the object is heavier, so its velocity is smaller. And so that's only to be expected, but in fact we have the exact computation of this velocity and we can compare this width of this cone to the expected velocity and we see beautiful agreement with the predictions. So, yeah, so that is, so the upper row here is sort of raw data and the load is their analysis by separating the center of mass motion. Very good. So, now, we can also, as I explained you, we can also ask, we can also study the correlator of the green function which allows us to extract the full spectrum of these particles and here you see comparison of this spectrum with the theoretical result. There is no adjustable parameter, it's just direct comparison and you see again that this is perfectly in agreement. Finally, we come to the last point which is probably the most interesting one, this unexpected stability of these bound states and you see here, well, probably the most important plot is on the right where you see that we only increase the amplitude to move into these hairs and you will expect that this amplitude, even a small amplitude should be sufficient to completely destroy integrability but you see that the peak is remarkably resilient so the peak is here, of course at zero, it tells us that the energy, there is energy of the bound state corresponding to this value and then when we increase the coupling to the hairs and up to the coupling which is sort of for the order of 1, pi over 3 is exactly 1 in radians so nothing happens basically, it becomes slightly wider but really the peak width if you plot it as a function of this interaction with the hairs is, well, until pi over 6, well, this is probably some experimental fluke, this decrease of the angle, that will be too much, decrease of the peak width will be too much but then it really starts to grow only close to pi over 3 so nothing really happens to them which is very unexpected because, again, as I said, you expect that without integrability there is nothing which prevents the decay process in which the bound state is converted into, let's say, the bound state of 3 particles is converted into 3 particles which move outside in the spectrum, OK? So now, since it's exactly the time, let me conclude that this, of course, was not really what I presented was not really a discovery by quantum computation because we discovered it really doing by simulations what we should see in quantum computer and in fact we expected, we, meaning theorist, expected that the integrability is very sensitive and once we destroy integrability even a little bit we shall see that these bound states disappear, in fact we found, first numerically and then experimentally that they are resilient but it was a miracle experiment first and then quantum computer but I can, I hope that in the next few years hopefully soon, very soon we shall see expected results which come directly from quantum computer and not from the numerical simulations of how it should behave. So and the most interesting questions at least for me personally are the behavior of this non-nergodic but delocalized states and non-nergodic extended states formed in interacting systems like the spin system that we have naturally. So and finally is the last but quite important point that we are welcome, we welcome all realistic proposals for such experiments from the academic groups. Thank you. So we have time for questions. Before other people collect the questions. Lev, I didn't quite understand why was it so unexpected because calm theorem is known and it tells us that not immediately because if you use simply the usual argument based on Fermi golden rule you get a large amplitude for this process and somehow the matrix elements happen to be zero very small. We don't know if they are really zero or very small. So it is basically like a formation of the Fermi golden rule which is which is not immediate and which resilience is that Fermi golden rule is very slow to pick up. Actually before Marcela I wanted to ask and since Volodya almost asked but since you are looking at the propagator you see some width. You don't see. We have finite one and don't forget that we have all these noises in our system. We also have finite number of qubits so we cannot have infinitely sorry sorry So for the time for your transform what we are really limit if you talk about the width of the peak in the frequency space we are really limited by finite time and finite decay time that gives us finite width always. OK, but do you think that the true width is smaller than what you observe or you think you are observing it? Well I know from numerical simulation unfortunately so the system is not so good. So I have a question about the stability with respect to finite size of these bound states and the reason is the following. When you mention this Fermi golden rule thing what comes into my mind is that also in the context of quantum scars there is some sort of finite size and expected stability because if you Yeah, it's some relative of the scars. So you are telling us that somehow there is a very strong finite volume effect but in an infinite volume at finite gamma That's a very good question I didn't want to discuss it because I do not fully understand the answer. There are two competing opposite claims in the literature after our work. One was that in the limit of infinite size this effect disappears and another was that it stays. So I do not have my own opinion on this works Yeah, yeah Yes, and actually things from Matrunjiš there was a paper on this subject that stated that it maybe it was the other way around I forgot, sorry but two papers definitely one from Matrunjiš Question Yeah, hello Thanks for the talk. Two-part question second part What about mid-circuit measurements? So how well do they perform? How fast can you do them? And connected to that question do you think there could be error correction useful for also tasks like this where you want to simulate spin chains? So the first question is easier So currently the read-out is a very is really a serious problem because it takes too long So if you do it naively that is you have evolution then you want to read out so you stop evolution and then you continue you lose enormous amount of time during which qubit decay so it's very costly procedure However what you can do is so you can do the gates so that you read your state into anciller and then slowly it measures anciller while the dynamics continues If your system allows just purely by geometry or design of the Hamiltonian such procedure then it's not a problem because just in numbers gate takes let's say 10 nanosecond and readout takes a few hundreds of nanosecond and the whole lifetime of the system is a few microseconds So you can measure you have time to measure but if you do it all the time during evolution you are dead but if you can copy it into anciller that's also okay because then you have enough time to measure it So in the second I do not know how one can effectively combine this with some error correction because error correction requires enormous overhead And so the whole drive to this discussion is that what can we do while we do not have error correction and some error mitigation is possible and that's what I discussed in the very beginning that you can really error correction in all channels I don't think it's very realistic once we have error correction we can have much more interesting problems Yeah, thank you So I just wanted to ask in order to improve these systems so what is the bottleneck do you have to grope it actually the oxide what can you do in the material science in the material science or so well what so you have to somehow control these parasitic modes in the environment one of the most important modes is associated with quasi-particles so you need to make sure that your system does not generate quasi-particles by itself or if it generates them they are somehow pumped out of the system because a very dangerous process is typically that the qubit, which is an excited state it excites the quasi-particle which goes somewhere and then it meets phonons or whatever so if you don't have quasi-particles close to the qubit this process is not so bad so quasi-particles is one extremely important thing that one needs to control and another is of course omnipresent Taylor's two-level systems but when you talk about very large systems like few hundred qubits you should start to worry about the modes in these big systems some electromagnetic modes but we are far from it to be honest because that's probably at the next stage so a curiosity if possible do you have quasi-particle traps do you need them inside the chip or you don't need them well we don't or it's secret I think that it's known that we don't but my opinion that we need it we have time for another question so if not let's thank Professor Joffke