 Vse ne možemo tudi početit. Ano. Vse ne so tudi početiti. Ok, vse bom izvrčal, kako je tudi. Zelo se pozdajte. Ok, vse je, bo so tudi, da bomo početiti. Vse je video. Ja. Ok, ne zelo. Zdaj je. Zdaj je. Zdaj. Zdaj. Zdaj. Superconducting qubit, quantum computation. OK. So, yesterday we ended up that if we have our Hamiltonian and we go in the dispersive regime, which means qubit and cavity are not on resonance, but detuned from each other, that we now get this effective Hamiltonian here, which allows us to read out the qubit by probing the cavity. So, we just shine in a tone here. If the qubit is in the ground state, the cavity resonance is sort of this blue-lorenzian shape line, and we will get a lot of transmitted signal, whereas if the qubit is in the excited state, my cavity peak will have shifted over due to this dispersive interaction, and now I will find very low transmission. And we have seen that we can use that in experiments to really do a single shot detection of our qubit, so we can really sort of see quantum jumps if we can use these newly developed quantum limited amplifiers. And I've also shown you what happens without those amplifiers in such a single trace, nothing much is left, so you could only measure expectation values. So, you could still do a lot of averages and then still get the value out for the qubit state, but only an expectation value. Now, this dispersive Hamiltonian also has sort of a flip side. In some sense, people like to call this a W, a W-Q-D interaction, so now I've, this is again the same Hamiltonian, but now I've just taken this term here and combined it with the qubit part. So, now all of a sudden what happens is that the qubit transition frequency depends on the number of photons in the cavity. So, again this disguise, this dispersive shift, and we can actually, for example do experiments where we put the coherent state in the cavity, so in this case it was about one photon. And if we would have an empty cavity, we would only see a qubit excitation peak right here, so I just excite the qubit and read it out by the cavity and see when I can excite it, I would only find a single peak if there's no photon in the cavity, but if I put photons in the cavity and they stay there while I do my spectroscopy, I can actually see this multiple peaks here and the distance here in this case is really sort of exactly this chi I've written it there. So, this means I can really sort of use my qubit to, for example, detect the number of photons in my resonator. So, I can ask the question, are there, or is there one photon in the cavity by just, for example, applying a pulse on my qubit exactly at that frequency and if I make this pulse wide enough, then the Fourier transform of this pulse is narrow enough that it only talks to this one resonance peak and flips the qubit if and only if there's one photon in the cavity. So, I can really do sort of a conditional gate operation on my qubit state conditioned on the cavity state. This, unfortunately, wanted to spend some more time talking about applications of this for quantum optics experiments. It turns out if I have this capability, I can quite easily create trading at cat states in a resonator. I can do state tomography of those states. I can do operations on them and so forth. So, but what I sort of, but unfortunately I won't have the time, but you can find sort of at the end of the slides I uploaded, you can find sort of a summary of that, how you can do quantum optics using these techniques. What I actually wanted to talk a little bit about is some experimental techniques. So, what do we use in the lab to really control these type of superconducting circuits? Let's start out first what are the types of superconductors we actually use. So, typically I would say in a community we use these three. We use aluminium whenever we want to make junctions. So, aluminium is a type one superconductor with the transition frequency of about the Kelvin. Aluminium has the advantage it forms a perfect, if I oxidize it forms a perfect insulator very close to sapphire. I mean it's a amorphous aluminium oxide, but it forms a perfect barrier for a Josephson junction. So, this is sort of the best barrier we know how to do this very thin insulating barrier between the two superconducting halves. And so, with that it's very easy to actually create a junction. I'll tell you in a little bit we use this shadow evaporation technique to actually create junctions. So, aluminium is typically used for cubits and junctions. Niobium is actually quite nice because it has a somewhat higher transition temperature. It's typically used for coplanar waveguide resonators. It's not so ideal for junctions because it's much harder to actually do shadow evaporation with it typically one can only etch niobium very well. A new material which has come up in the last couple of years is, well it's not a new material, but a material that hasn't been used so far up until very recently is niobium titanium nitride. It's also type two superconductor with an even higher transition temperature. And it turns out that this seems to be a very good material to make, for example, capacitors for cubits and so on because it seems it has the better surface or interface quality, I should say, than, for example, niobium or aluminium. So, people use this for resonators in cubits and I've seen very, very great success. Now, all of those materials have to be put on something. So, some form of substrate I construct my structure on and typically there people use silicon or sapphire because those are the two materials which have the lowest lost tangent in microwaves. So, they don't have a lot of dissipation in microwave frequencies so that's why people either choose sapphire or silicon. Sapphire is even slightly better than silicon. With silicon it's always a little hard to control the exact doping and so on. So, this makes it a little harder. So, in really sort of these substrates here if they are not perfect they will contribute to losses and so on we have in the cubit. Now, how do we create all of the structures I've shown you? I've shown you a couple pictures of resonators, cubits and so on. What we have to do is essentially do lithography. So, we, I'll explain you that in a little bit more graphically essentially what we can use is we put sort of photo resist or ebium resist on top of that sapphire and we can then write a mask using optical lithography or ebium lithography so we can define those very narrow structures. So, with that mask we can then do the thin film deposition of the materials so there's different ways of doing that. You can use an electron beam to heat up your metal, it evaporates and gets put down. You can have different sputtering techniques and all of that creates the thin films we then use. And then there's two ways of then actually getting the structures. You can then, you can either for example etch away all the stuff you don't want. So, this is if you sort of, the mask you wrote is sort of the negative pattern. You sort of remove everything you don't like and keep the stuff you want and the positive pattern you would do for lift off. So, exactly where you have your holes in the mask and that's where the material would go down and you deposit it only on the substrate where you want it. So, let's maybe see in a little bit more graphically how we actually do that. OK, so, what you see here is sort of the side view of an aluminum, sorry, sapphire wafer. So, something typically like 300 micron thick. So, obviously this picture is not to scale. Then on top of that we put the so-called ebium resist. So, this is a polymer which reacts to electrons. So, of about 600 nanometers here and another layer of a different polymer of about 100 nanometers. And sort of this is the same chip from the top with those two layers. So, all we see is this gray top layer. What we then do is we take an electron beam and we put electrons on places where ever we want to sort of change the chemical structure of this resist. And depending on the dose we can only change for example the lower one or we can change both of them because this guy will change its sort of chemical structure at a much higher dose than the other one. So, what we then get and we can then sort of take for example isopropanol and water to sort of wash away this whole everything we have developed everything we have hit with this electron beam and what we then get is a mask which looks something like this from the top. So, here this part here would be that bridge you can see here and that part I should have maybe drawn in blue really goes sort of down onto the sapphire. So, this is really sort of everything here that's now open and this is the bridge so this would be cut right through here through the center. So, what we can then do is we can evaporate aluminum under an angle and what will happen is that bridge that's standing here and these edges will actually throw a shadow. So, what will be deposited on the chip will be something like a thin film here right in that gap then we get the shadow from this bridge which forms an opening there and then we get another thin film here on the back and so there's also the shadow coming from this backside here. So, what we can then do say we want to build the Josephson Junction what we have to get is this very thin insulating barrier and for aluminum I already said this is very easy to do all I have to actually do in my chamber is I have to put oxygen in and then what I will get is over time almost self-limiting aluminum oxide film grows if I do it right it will be about ananomite thick now everything is actually covered in a very thin layer of all the aluminum is covered in a thin layer of aluminum oxide and now with the second aluminum evaporation step I've actually created my Josephson Junction because now that shadow from this bridge I have here actually goes into the other direction so now my top aluminum film extends all the way sort of over here and up there and right in this area is where I formed the junction because now Cooper pairs have to come in in this green layer go all the way till here and then they have to tunnel through the barrier and continue on in the blue film so with that I've almost done what's left is I want to sort of wash away all the rest of the mask so this remaining PMMA and MMA layer all the bridge and everything I do that using acetone and what I've left then is just these thin films of aluminum with this barrier in between and sort of right here this is where I've created my junction so here's an electron beam image of an actual junction and you can see it's sort of a very similar structure so here down there this is the bottom layer which has been oxidized you can sort of see it here and then on top is the green layer and the junction is right there so with this technique we can create junctions which are a few hundred nanometers in size so here you have a scale bar so this distance here is like 500 nanometers so this is like 100 to 200 nanometers you can make it even slightly smaller if you want to using these tricks or similar tricks so this is called the Dolan Bridge Shadow Technique to create a junction and create much more complex structures so you don't need to do a single junction you can do in this case like a thousand you can put them you can see in arbitrary shapes you can make them in different sizes you can integrate them with a resonator like has been done here so with that you have really a full design flexibility and can really sort of tailor the circuits to your liking so that means we know how to create such circuits at least in principle what else do we need in terms of experimental apparatus to actually control it well, typically an experiment looks something like that from the control side so you have a computer nowadays typically running some python program that controls all the experiment all the instruments in the lab so you have some here some fast analog to digital converters and digital to analog converters that on one hand create signals in the few hundred megahertz range so this guy here is a digital to analog converter or also called arbitrary waveform generator it creates signals somewhere between 50 to 200 megahertz and this is then put into a mixer and up converted into the few gigahertz range so with that device you then have full amplitude and phase control over the pulses you do all of that is then sent down in a fridge maybe combined with additional signals and then signals come out and now we have to somehow measure these few gigahertz signals we want to digitize them so the best way to do that is actually again mix them down from these couple gigahertz to something like 10, 20, 30 megahertz which you can then easily digitize using an analog to digital converter which samples with say for example a nanosecond or something like that and that transfers the data to the PC where you can post process them there's also additional experiment, sorry instruments like this vector network analyzer which allows us to do frequency sweep so for example measure the spectrum the transmission spectrum of a resonator very efficiently now sort of a big part of course which is missing in this picture here is the fridge so the inside of one of our delusion fridges usually typically looks like that so what is not shown here is that normally you have heat and vacuum shields around sort of out sort of here you have typically a cylinder with a vacuum can around and then it's sort of like those Russian Matroshka dolls that sort of nest into each other you have sort of one heat shield one cylinder after another normally attached to all of those plates so up there this first thing here this is really room temperature then you go down to something like 50 Kelvin on that plate and with an attached cylinder then you have 4K with a cylinder and then you're down to 1K 100 mK until you really reach our sample area where we have about 20 mK temperature and so we have this whole bottom plate we can actually bolt our samples to and sort of nowadays fridges this base plate to give you a dimension is about that size so we have actually quite a bit of room to put all of our stuff there so the actual sort of core of this whole cryostat is this delusion unit here so what actually happens is one circulates a mixture of helium 4 and helium 3 in sort of these pipes so you have a couple of heat exchangers where sort of the gas that goes out pre-cools the gas that is coming in and at the end what happens is you have sort of down here you have liquid helium 4 with helium 3 on top and sort of a little bit of the helium 3 is actually inside the helium 4 and what you do is you sort of on one side you sort of re-inject the helium 3 and on the other side you suck on it with a turbo pump and what you effectively do then more or less everybody does when he eats a hot soup or drinks a coffee if it's too hot what do you do? yeah you blow on it you essentially blow the hot particles away and the same trick we use here with the turbo pump we suck on this helium 4 with the little bit helium 3 inside and the helium 3 comes out and sort of takes away the heat and with that we can actually cool this whole thing down and we can make it now this really is a commercial product you can really buy if you oh those are gold plated this is more not because gold has so these are copper plates which are gold plated the gold plating is not there because it has higher heat conductivity it's there because the copper would oxidize over time and this layer is actually insulation layer so whatever I would bolt there wouldn't be thermally connected very well to the plate and if you make that in gold then it doesn't oxidize so you can always make good connections so you should if you wanna know so to properly explain the cryos that would take a little longer but sort of take away it's essentially a little bit like evaporative cooling there is a very very nice and really well explained YouTube video by Andrea Morello you should check it out if you wanna know a little more how this cryos that works so what else is inside so here you can see so this was the cryos that pretty much empty nothing inside and then you see there is sort of a whole bunch of things that came in so you sort of see again now we have a lot of stuff here on the bottom and also here all of that part seems to have gotten busier so what happened is we have put in a bunch of microwave cables so here you can sort of see these gray lines I hope so those are coax cables made out of stainless steel to transfer microwave signals down we make them out of stainless steel because we don't wanna if it would take copper I would short out this top plate because of the high thermal connectivity of the copper if I use stainless steel the heat load on that plate is reduced and I can actually cool down my fridge then for example here we have this is on top of this four carrying plate we have very low noise amplifiers we actually need to amplify our microwave signals up that we can read out our qubits what we also have here in these lines we actually have attenuators which attenuate our incoming signal but they not only attenuate the incoming signal but also the incoming noise because you have to think about my environment is up here at 300 Kelvin and it radiates noise with a 300 Kelvin temperature and it would come down this coax cable and straight away go into my device which sits at 20 millikelvin so that has to be bad noise coming in pretty much at 300 Kelvin and it is effectively attenuated by six orders of magnitude to get the effective noise temperature down to also something like well below 20 millikelvin effectively which means that there is no excess noise coming down these lines which would excite my qubit unintentionally for example then down here that is yes, it is relatively rigid so you can see here so these are actually stainless steel rods that are bolted top and bottom I mean it's not so if you try and push it it gives a little but not a lot so it does second? no, no, no they're not in sort of more recent fridges they actually use some I don't know exactly some carbon fiber organic compounds to make those connections which has some advantages it's more rigid, it has less heat conductivity as stable and so on but in principle it's a rigid structure actually contracts quite a bit if you calculate it and it's a little hard to see that's the reason why our coax cables have these bends they are not straight because they would put too much stress on them and actually make them bad but if you put those bends in those are a little bigger than necessary you can get away with just a small wiggle but if you have that at every stage that sort of can eat up the compression of the fridge and then the cable even works when the whole fridge got I think it's a couple of millimeters actually shorter now down here we have the sample area so in our case we are working with 3D cavities and waveguides so rather big things so this is actually a waveguide cavity where the qubits live inside you can sort of see here the cables coming out then those here are so called mu metal cans which are effectively a magnetic shield so this is the material with a very very high mu R which ensures that we have a very low magnetic field inside that can then sort of all of those cables come out normally there is even another copper can around this whole thing so while here you can sort of see the mu metal shield assembled so there is a second half which slides on top one more thing we actually need are those isolators up top here maybe some of you know optical diets and these isolators are the same thing just for microwaves essentially they are a one way street for microwave signals so our measurement signals sort of go in the fridge via these heavily attenuated lines but then they go out through those isolators through super connecting cables because we don't want to lose any of the measurement signal through those low noise amplifiers but the problem is those low noise amplifiers actually have some noise that actually comes back out and I don't want to have that go back into my qubit so we use those isolators to sort of isolate and sort of the signal that comes back from these amplifiers is not allowed to actually propagate through the isolator as it's just a one way street out here you could for example see a typical wiring diagram where we have now sort of pretty much explained most of the components so you see typically we have like multiple lines actually going in so that would be the input side with attenuators additional microwave filtering and so on and then sort of signals can come out they go through those circulators or isolators additional filtering and so on up into those high electron circulator amplifiers, those very low noise amplifiers I've shown you in principle we can also then in addition have these quantum limited amplifiers so sort of signals would come out go into that amplifier bounce back off and then sort of come out that line so these circulators are actually sort of come in that port, it routes me through here then that second circulator routes me to there and if I come back I don't go back that way I don't go around and then out so they allow me sort of to use these quantum limited amplifiers which sort of only work in reflection so you see sort of there's quite a bit of sort of state of the art experiment you need quite some cables going in and out of the fridge so unless there are some questions to that part how am I doing with time like 20 minutes or something you mean these ones well yeah I can't go in from the side or typically this is not done because then I have to go as I've said there's like multiple shields around here so cylinders attached normally to all of those plates so I would have to go through those and that would be a very short segment of lines so I would have just because it's so short a lot of heat transport across this very short section so now this is deliberately made long that I have a long section of stainless steel that the effective heat transport across is not sort of the heat input on the next stage I should actually say downward is not too high so I need a certain length of cable to ensure that I don't have too much heat transport so ok so let's talk a little bit about quantum information processing with circuit QED and essentially I'll just show you how we can create entangling states using such a device we've already talked about how to do single QED operations essentially I just shine in a microwave signal that allows me to do X and Y rotations what's been missing is how do we do actually two QED operations so let me show you a couple of nice examples of chips that have been used to create entangling states so this is a four QED chip out of Yale where here in the middle this mannering line that's actually a co-planar wave guide resonator and then you have one, two, three, four QEDs just like that so you see sort of this is again a transmon capacitance here sort of one plate of the capacitor here, one plate there that's where the junctions sit again this is a squid so this guy is frequency tunable and that couples to this co-planar wave guide resonator so this lambda half resonator down here so in this case this is sort of quite a while back coherence times weren't as great for there were only three QEDs were used and coherence times were something like a few microseconds or like a microsecond so and while each of those QEDs has this additional line coming in where I can send current in to create a magnetic field which allows me to change the frequency to change the flux through the squid loop and thus the frequency of the QED so this is a little more recent design from Leo de Carlos group in Delft in this case they actually have five QEDs so you can again see sort of the structures here which is the capacitance that you can't really see the junction area and you can see multiple resonators in this case so each QED has actually its individual readout resonator so that guy here reads out that QED that guy here that QED then have to think so that guy this one that guy that one and then in addition we have these long resonators which actually connect multiple QEDs so I have one which connects that guy, that guy and that guy and another one which connects this one, that one and that one and one can actually do with these resonators is actually mediate interactions between the QEDs so very similar to what you've heard for a trapped ion system where I use my phonon bus to mediate interactions between one ion and another one I can here use a photonic bus, the resonator to mediate interactions between that QED and that one or that one all of those QEDs are again flux tunable and I can change their frequency as I want it in both of those cases you've seen that multiple QEDs are actually coupled to the same resonator so if I want to draw some form of circuit what I get is something like that one QED is capacitively coupled to a resonator with some resonance frequency again coupled capacitively to another resonator so if you sort of then work this out it actually turns out what I get is an interaction between those two QEDs which is of the form sigma plus sigma minus so I again get this exchange of interactions but this time it's mediated via the resonator the resonator though is not on resonance with the QED but it sits off resonantly so now how far this guy is detuned and how well this QED and that QED coupled to the resonator all goes into this effective coupling strength but in essence if those two QEDs can exchange excitations without the excitation ever living really inside this resonator because they are so far detuned another slightly different chip is by the martinis group or Google where they for example have one, two, three, four, five QEDs each of those QEDs has its own readout resonator but these guys are not coupled via a bus, via this cavity but they are actually coupled directly to each other so you see these crosses that's the transmon and sort of here there's two crosses coming really close so they have some capacitive coupling, you can also see sort of in the circuit diagram down here so this is one QED with the junctions and this capacitive coupling to the neighbor so here five QEDs sort of each of them is coupled to its nearest neighbor I have five readout resonators to determine the states all of them are frequency controllable and in this case I don't use the resonator to bring in the signals microwave signals for the single QED operations but I actually use additional lines that come in and couple very, very weakly to my QED so this is sort of possible with this cross shaped design because sort of I can use each end of the cross to do something different to the QED in this case I get a very similar interaction between two QEDs we have pretty much seen that already for the QED resonator coupling the only difference now is that it's not an a dagger sigma minus but it's a sigma plus sigma minus because essentially there's these guys I treat really as QED so they can exchange only one interaction ok so now how can we actually use this type of interaction to do gate operations well if we take one of those systems and this is actually data from this very first system I showed you so those four QEDs coupled to one resonator so I sort of try and excite the QED or the many QEDs and I actually then do read out on the resonator I'll find the following so here this is actually changing the flux through one of the QED loops QED1 so actually QED1 changes its frequency so what I do then is I shine microwave signal trying to excite QEDs and then whenever I sort of manage to excite a QED you sort of see this dark gray response of my resonator read out so initially sort of all of those three QEDs are at different frequency so QED1 is at around 6 gigahertz, 2 is about 7, 3 is about 8 and now as I change the flux through QED1 I can sort of bring it up in frequency and then I bring it in resonance with the QED1 and right here because of this interaction I again have some form of avoided crossing just like we saw in the resonator but this time is directly between the two QEDs so right here I have a hybridization between the two QEDs so I can't really speak of QED1 and QED2 anymore but it's sort of a symmetric and antisymmetric combination of the two and then if I scan further I can also bring it in resonance with QED3 and then even further I bring it actually in resonance or close to resonance with the cavity so one remark on that plot here this is actually measured with direct cavity transmission whereas this is really done with spectroscopy first trying to excite the QED and then doing a read out so here this is really this resonator mediated QED interaction in in out we can actually use this to do a two QED gate operation now quick reminder on two QED gates one popular one is for example the phase gate which means if I write down a unitary you can sort of see that there is nothing happening to sort of zero zero zero one and one zero but the one one state gets a minus one so a pi phase flip now this phase gate is a universal gate so I can build a quantum computer with it so this makes it very appealing sort of very similar to a C naught gate actually phase gate and C naught transform into each other now a little more general phase gate is actually of that form so here I have I don't do anything to the zero zero zero one gets a phase change the one zero state gets a phase change but sort of these are trivial just single QED phases what happens to the one one state in this case is that those two phases add up and what I actually want and that's the interesting part I want this additional phase pi one one here which will actually give me minus one so really I have to find something that allows me to achieve such an additional phase those are single QED phases and the red one is the two QED phases well what's the way of doing that let's have a look at the time evolution of our states if I have those four so this is first a very trivial case so zero zero zero one zero zero one one with the respective energies so ground state I just give define a zero one QED excited is the energy of that the other QED excited is another energy but the doubly excited states one QED and the other excited I just add up those energies so that would be sort of the normal case I would expect and if I then sort of look at the time evolution of that what I get is nothing happens here I get some phase there, another phase here and then just a sum there so for a given waiting time the phase evolution will look something like like this so this is already so this is sort of very straightforward and it almost sort of looks like what I've shown you before the most important part is sort of missing so I want to get something where I have some phases here but I get this additional phase so I want something that gives me that phi one one and the easiest way to do that is to somehow manage that the energy of this one one state does not equal the one zero and zero one state so I somehow want to push the energy of one state down or up I want to change it without changing the energy of the one zero and zero one state and it turns out a good way of doing that is make use of such an avoided crossing what do we do here so again this is I change the frequency of one of the qubits so this is again a flux through this qubit here so nothing happens to the red qubit it stays at the same frequency the same energy if I change the flux to another qubit for example it comes down in frequency and at some point will meet here we have an avoided crossing now that turns out wouldn't help us so what I actually want is I want to somehow get an avoided crossing with that guy up here so right and sort of here this distance here from whatever sort of baseline we have this would give us some phase evolution phi one one phi zero one because I just have this detuning and over time I would accumulate some things now our phi one zero in this case would be zero because I keep that guy at the same frequency all the time so nothing much would happen now how do I actually what happens actually to this one one state here is if you remember our qubits are actually not perfect to level systems and this seems like a bug but actually it's a feature I can now use here to really get what I want because if you think about it I not only have this sort of one qubit excited and the other qubit excited very close to that has to be a state where one qubit is not excited at all whereas the qubit I am changing the frequency of is actually doubly excited so if it sits in the second excited state now if I change the frequency if I change the josef energy the slope of that energy level will actually be twice as deep because there is two excitations living up here compared to that one so this will come in at the steeper angle and at some frequency actually at some flux actually meet one state and we get this avoided crossing and now you see that exactly here this one one state sort of starts to bend down it's sort of this energy level is not the sum of those two energies anymore and this is exactly what I wanted to achieve so I can really sort of now this difference here integrated over time will really give me a phase 511 because it just the energies just don't add up anymore as nicely so what I can do is sort of here sort of the three possibilities where my state can start out and what I do is I sort of change the flux of my qubit which sort of will bring those states sort of slowly in and then back out again so then that guy acquired no phase that guy acquired this sort of phase but that guy now got some trivial phase similar to this one but in addition sort of he got this phase here I marked in red so proportion to that area sort of integrated over time so with that trick we got exactly can realize if we do all the tuning right if you pick the speed of that thing in the right way and so on we can exactly pick up a high phase shift such that we exactly do this gate operation now so just changing the flux of one qubit and sort of tuning into this avoided crossing with this doubly excited state allows us to do a phase gate and with that it actually turns out it's quite easy to generate entangled states so for example this is from paper by the martinis group sort of it's a different chip but using the same gate operation principle so there's five qubits so what they started out with is they do a high half pulse on both qubits so you start in zero to zero you do two high half pulses then you go into a coherent superposition then so I can then sort of rewrite this then you can actually do your z gate which flips the phase of only that state here to a plus and then you I can again rewrite this then it's a little easier to see what the pi pulse pi over two pulses to because here I have a plus x state and this is a minus x state so this guy will actually rotate with a pi over two pulse around the y axis to zero where that guy will rotate to a one so I've created an entangled state then they can actually start concatenating that I can add another sigma z operation a phase gate between qubit 2 and 3 you can run through the same sequence so I start out at zero to zero plus one one I do a pi pulse I'll get that state which is rewritten this one only one of them will get a phase flip which is this last one right here and then I rewrite it again to see what my last pi pulse does and it brings again this state to a zero and this to a one and so on I can do the same then for four qubits I can do the same for five qubits and create all of these entangled states so what you can actually see here are the density matrices of those states so on the diagonal you have the population and here you see zero zero is populated and one one is populated I have no population zero one and one zero and here those are actually the coherences in the density matrix telling me this is actually a coherence well it's a coherent superposition of those two states actually an entangled state so it's not just a mixture I can do the same for three you see I only have zero zero coherences again on the outside the same for four qubits and the same for five qubits you see there is some experimental imperfections if you look closely there are some errors some bars in here which are not perfectly zero and you can also see they don't go up all the way to one half as they should but they are a little shy of that so in back then meanwhile this has actually been improved quite a bit back then they could create this two qubit entangled state with something like 99% and then it sort of goes down until this five qubit states is something like 80-82% state fidelity so that's actually almost ideal so with that I'm actually at the end using these very similar gate operations I can actually then think about implementing algorithms doing more complicated things also like quantum simulation but in principle it sort of relies on those tools ok, so with that I hope I could give you some idea on how to quantize a circuit how to build a qubit and combine everything to such a circuit QED system where we can use resonator for readout and controlling the qubit I showed you a little bit our experimental techniques and then how we can really use such a platform to create entangled state and then in the end use it for algorithms thank you very much for your attention