 everybody. So it's a great pleasure for me to have Professor Peter Zoller from the University of Innsbruck and the IQOQI which I suppose stands for Institute for Quantum Optics and Quantum Information. He will be talking about programming quantum simulators with atomic atoms and ions and it's a really pleasure for me to have Professor Zoller here. He is one of the pioneers in this field. He received the 2006 Dirac Medal for this work for his pioneering work in this field and also the prestigious Wolf Prize in physics in 2013 and his career has spanned you know the whole continuum going from quantum optics to quantum information theory in quantum computing and in fact some of his work for example in the 90s with trapped ions was really what launched the idea of programmable quantum computer and making quantum gates so I think it's a real pleasure for us to have him tell us about the state of the art in this field, a very exciting field. So I think I will give the floor to Peter. Okay so I managed the first task which is switching on the microphone. Thank you very much for the kind introduction here and I have to say that I'm spending a great time here at ICDP. I mean I've been visiting here several times but you know Sao Fazio and Marcello Dalmonte are my hosts that I'm allowed now to talk to every day so there's a lot of exciting science going on here and my talk today I will speak about you can see the title here Programmable you know quantum simulators with atoms and ions so I would like to talk about programming quantum devices and that's of course something which is a hot topic you might say right now and I will do this from a very special perspective but before I talk about that let me sort of just switch one slide back and mention that all of us are super excited at Anton Seiling I got this year the Nobel Prize you know it was just given last Saturday in Stockholm and he got it for entangling photons together with ASPE and Clouser and he did his work during this time that it was in Innsbruck over here and we have this joint institute together with Vienna because the Kwokwi Institute for Quantum Optics and Quantum Information so at one point I guess it was end of the 90s he teleported himself to Vienna where he is since then you know the work that Anton Seiling did was about photons and I will talk today about entanglement between atoms and and also ions and so to some extent our work has been a little bit complimentary not only because he's an experimentalist and I'm a theorist I will actually tell you in the following about work that has to do with you know building engineered quantum devices in particular in view of possibilities of studying quantum many-body physics and if I go in time now maybe 25 years back or so you know it was people like me and my collaborators like Ignatius Joachim so on that came up with ideas like well we can use trapped ions about develop for spectroscopy to build a trapped ion quantum computer we can take what we call optical lattices where we take counter propagating light waves and then we put cold atoms from the Bose Einstein condensate in here and this becomes an a quantum simulator of a havert model for example we worked on Rydberg excitation with laser and corresponding interactions what we today call a tweezer race polar molecules and then sort of the real quantum optics that has to do with photons and today we look at these devices now 25 years later you know is what we call now a noisy intermediate scale quantum devices the word noisy refers to the fact that we don't have any error correction these devices and they sort of operate the realized basic Hamiltonians and we are going to play with now in the following but for me at the moment there's a very exciting time you know 25 years ago we had some of these ideas on the theory side and then really credit should be given to the experimentalist you know to develop many of these ideas into some things that happen in the lab and the exciting thing at the moment is the fact that these devices are now coming back to us and we had the motivation what we wanted to achieve we wanted to program them play with quantum computers or simulators and this is happening right now and I'm particularly lucky because my colleague Reiner Platten is book works and is trapped I am quantum computing and also simulation and I thought that I would like to focus my talk here today on this sort of you know joint theory experimental work I don't only want to tell you about theory per se but about sort of theoretical ideas and dreams and hopes to build certain protocols for example in these quantum devices but instead of what we did earlier where we simply said well let's slide your theory paper and put this out on the market and hopefully somebody will do it at one point the great opportunity right now is that we're able to right away talk to the experimental and say hey can you do that in the form that I would like to describe to you so things have really changed and I think that this is sort of you know a game changer you know if ideas experimental developments but at the end the devices that you dreamed of you know are coming back to you as somebody that you can play with and this is what I mean by this word programmable up here in the title of my talk so if I go back I don't know 15 years or something like this my talks always had a very you know clear-cut you know way of introducing the topic there was on one side you know quantum computing a sort of a digital quantum processes in quantum processing or then quantum simulation like what you call analog and on this digital side of course you know we would have these ideas mentioned early on that like you know let's take trapped ions and these are simply ions charged particles that we can put into an iron trap and we can store them like a like a Wigner crystal you know it's a one dimensional spring here for example this the iron trap over here and you know this represents a qubit to the extent that these electrons that we have for these ions can be sort of like spin up and spin down or maybe be in one of the metastable excited states representing a qubit and then we came up with ideas how we can build quantum gates that are single qubit gates that's quite obvious it only have to shine laser and then rotate your spin between the two levels or then quantum gates that are entangling and our idea was to use actually the phonon bus between them so I don't want to elaborate on these things I just want to say there's these ideas out and in the meantime we have now small quantum computers like this in the lab that are functioning and you can even program them up to a certain level but the spirit behind all of it was always sort of demonstrating some in probably elementary form quantum algorithms the quantum simulation part in flavors actually rather different what you have there which is to give the example of these atoms in an optical lattice you know where you put cold atoms inside for example these atoms could be fermions hopping around in an optical lattice realizing a Fermi Havert model like the famous case of the 2D Havert model which is this paradigmatic model of high DC and the goal here may be that well let's find sort of phase diagram so the whole problem where we have to first prepare atoms hopefully close to the ground state and then exploring the phase diagram in a certain way so you can see that the flavor behind these studies of this quantum analog simulation was much more to study many body physics very much along the lines of what is in the spirit of what people do in the context of say conance metaphysics but things have changed now and just again give you the example of the quantum gas microscope where one is able in these experiments to get with single side resolution the single shot patterns out so these are photographs of spin patterns you know that you have in these optical lattices and these sort of points to the fact that what the experimental is have obtained recently is the ability not only to measure single sides with a shot but also to the possibility of controlling you know the single constituents like in this case over here the spin full fermions with external fields with lasers or whatever these things are so this amounts to some sort of gaining in a quantum simulator some sort of a programmability so if I want to summarize all of that I will simply say that yeah we can build universal quantum computers and you might pursue the stream as a fully programmable universal quantum device at the moment these exist for small number of qubits at the end we have to do error correction but they're sort of on the complete the other side of the spectrum over here but these analog quantum simulator that are scalable to a very large number of particles this can be easily done for you know thousands or maybe even ten thousands and so on restricted to a class of Hamiltonian well what you realize here is a very specific Hamiltonian like here for the Hubbard model but this Hamiltonian is realized with a very high fidelity so they're sort of at the end of the spectrum that we have over here but you also might wonder you know there's something in between and this is the programmable quantum simulators that I want to talk about and they want to give you two example the trapped irons this is the system that I will talk about afterwards in our theory experimental collaboration or the nose of the Rydberg trees erase here again you take a string of trapped irons over here the main feature being of course that you can you know use a focused laser beam to address also single irons but on a fundamental level the string of iron realizes one particular Hamiltonian and this is an easing Hamiltonian that has actually long-range interactions you know with some power law usually that you can tune plus a transfer field this is a very paradigmatic model and this Hamiltonian is realized with a very high fidelity in these experiments of course by adding over here this single side addressing lasers you might also then come with the laser in and rotate certain spins maybe for example before you measure and we have a very similar system that I don't want to discuss here today which is Rydberg trees erase where we have here lasers that we focus down and we can stochastically load atoms but by seeing if you got an atom or not you can rearrange it and there's some really exciting developments not only by realizing 1d spin arrays but also do these multi-dimensional 2d and then in Paris even 3d again they realize a certain spin model with a very high fidelity okay so to what extent can we use now this thing here as a playground now to do sort of interesting stuff and these nisq devices as we call it and I'm always saying that the novena atomic physics right and that stands for noisy with lower case because we have very little noise okay slight hint you know here you know devices few tens of atoms or scaling out to a few hundred like you know the group of Michelou can output the 256 array in 2d or via Amazon on the web where people can actually program also these devices but let me tell you what we're doing in his in spoke by having our experimental friends downstairs this is the lab of my not sure Josie here who is sort of the key postdoc in the lab owned by Reiner blood and run by Christian Rose here this is the iron trap that you can see over here and the exciting thing is that this is one of these root but these trapped iron simulators such as mentioned the exciting thing is that the latest upgrade now since a little bit more than a year has been that they cannot store 51 irs so we have 51 qubits and we 51 is actually a large number you can try to do non-privileged things it's not that you take your laptop out and you can immediately diagonalize the corresponding matrix at that point classical computers have to work very hard and you sort of trying to approach them of course the regime there you know classical computations become more and more difficult of course if you go to 2d that's will be happening much faster but the other part of the story is that you know we are very lucky in his book because you know we can even access some of these machines from our desks and here this shows a collaboration between Christian Cockail who is a serious student you know my group Rick van Beynand Christina Meyer she's an she's an experimentalist and how they are sort of running this experiment together but in principle we can even write sort of quantum code and then execute these things directly in the quantum machine so we can write classical code that we emulate or simulate the non-classical computations or then we can just send it directly also to the quantum machine and let me now tell you a little bit about this playground of you know playing with this machine in particular in light of these new possibilities of having 50 qubits and this is also already a preview that know I will talk first of all about the example of a variational preparation of quantum mechanical ground state which then form the playground to do some interesting and and exciting hopefully you know fundamental physics but at the end we also talk about certain applications that we have in mind I will come back to that okay yeah good question okay so you know in the early days when these simulators were built you know the obvious experiment that you can do at that point is this that you simply say well I got my string of ions over here and you know and I prepared them in a certain way for example why don't we do quench dynamics you know we got a beautiful isolated many body system over here you can apply your Hamiltonian then you can start to ask questions when do these things thermalize you know for subsystems but it's really playing around with an isolated system and sort of doing this this ideal quench of course in doing so you know you go maybe for example from a product state so some entangled states so these points already that by talking about entanglement this will be one of the core features that I will talk about now here in the following and the way how these experiments are done is at the end over here you make the measurements by asking in a certain measurement basis you know our view qubits been one half spin up or spin down and these are single shunt measurements and by recording then strings know of these measurements over here you can build up probabilities of your wave function as being the string that you have over here and then if you want you know calculate corresponding expectation values and so on but now what we can do and this is now sort of switching over to this programmability we cannot only study now quench dynamics but we can also study things like you know we might actually build up simple quantum circuits and if I ask you what kind of resources we have but I already told you we have this beautiful icing easing Hamiltonian with long range interaction which makes it non-trivial and so we might to sort of gates like the one here I have an entangling gate you know which is generated by this long-range sigma x sigma x is one example that I can switch on for a certain amount of time therefore implementing a unitary like that one that I've over here there's an entangling you know for of all of these ions over here but also then you know the single qubit rotations by a simply shine a laser you know that just rotates his spins here so this gives me a programmability of having then local rotations here and based on that it might simply say well hello for whatever reason we can of course build up now a family of excited of these entangled states over here but just applying these use again and again and experimentally what can be realized will be some low depth circuits which has built up you know some of these layers depending on these parameters that we call your theta up here depending how long you switch it on you might ask you know what are these things useful for well this is something that was actually quite a discussion in particular in the context of quantum chemistry over the last three years if here quantum device that where we can collect measurements over here and that produces now certain wave functions and we can optimize for example these parameters in the following way that we're running here quantum feedback loop it was called variational classical quantum algorithm and what's been done in this particular chemistry community is this that you can write down on a piece of paper a certain Hamiltonian let me call it the HT over here T standing for target and I give you one example now in terms of spins so this target Hamiltonian maybe well you decide in the morning this could be a Heisenberg model or maybe some other one and you write down your Hamiltonian here this will have one body terms two body terms maybe also three body terms that nature normally doesn't give you so easily and so on and then you can ask you know can within my variational ansatz over here can I then minimize my energy landscape here as a function of all of these variational parameters very similar to what all of you learned of course in your quantum mechanics course the first one then you calculate the ground state of an helium atom you know approximately by making an ansatz in terms of some maybe product wave functions then finding out what an approximation to the ground state in energy you get but here we are sort of systematically doing this thing on a very high level of entanglement and the quantum machine provides it naturally so how would this work well what would happen over here will be that we have to measure on our quantum device then over here expectation values for a given theta this was how long we switch on these interactions to measure all of these expectation values set for building up the landscape over here of the energy and what's really great that this is the reason why this works so well in the experiment is that you know you might say to the experimentalist know exactly what their couplings are so that when they switch on that time they stop at the right moment it turns out that these variational procedures are very robust to experimental calibration errors and this is one of the reasons why they turn out to be very successful and let me show you now examples what we achieved a few years ago and where we are right now which is in the playground for the following discussion so you can do energy optimization you know now for certain models and you know a few years ago this was a paper mentioned down here and these are the key player that I mentioned here before what we did was the so-called lattice Schwinger model this is the most trivial case of a lattice gauge theory you might say you got in one dimension you know lattice model the Schwinger model which is one dimension quantum electrodynamics where you got fermions and you cover them to an quantized electromagnetic field and below pictorially you might represent this here but I don't want to spend much time on that of electrons positrons that you have over here and for mass equal to zero in the continuum that's of course exactly solvable but for us that's an ideal benchmark of course and what we do there is that we got fermionic and quantized electric field but in 1d sort of it's a trivial lattice gauge theory because you can always eliminate your gauge field over here and you can map these to a very very ugly you know spin model that I'm not going to explain or write down but a quantum computer doesn't care if it's ugly or not you know we can just present it to the quantum computer and say can you calculate the ground state so I don't want to talk about the underlying physics this would draw me now to let this gauge theory discussions over here but just to see how these well these things work we can do that for 20 ions typically that we have here energy where we are playing around with these parameters and the classical algorithm that we have to develop and sort of you know at the end finds then the optimal parameters and just to tell you what the results are this is the DMRG ground state you know this is the result that we get over here you know with the variational and this would be the first excited state and what underlies many of these things is that Rick van Beinen in particular here has developed you know classical code for this optimization and the challenge in doing that I'm really talk about technicalities over here but the DMT tell you if something works or not you know what you can do in that case is that you have to do in an optimization where you got a noisy landscape because every time that you make a measurement you can only make a finite number you got shot noise and then your machine or your program has to decide your classical computer to want to take more measurement to get one particular point in the energy landscape more accurate or to a rather want to use the same kind of shots that you do in the experiment to explore a landscape you know maybe on a finer structure and this takes a lot of playing around and these things were developed at the end improving this whole thing here by I think it was a fact of 50 in terms of efficiency of us explaining the wrong side so about the question of self verification you know that was done mentioned here earlier we have here we cannot only measure for example age and minimize it but we can also look at the variance you know of the Hamiltonian what we wrote on and a piece of paper and measure it and indeed you know when you did these measurements you know doing while you converge to the sort of best ground set within your answers you can see that we go down here with our variance below the value which would be there again experimentally computed energy for the first excited state so this quantum simulator gives you the energy but it also tells you what the error bar is it's kind of great I mean this is self verification in the sense yeah but this was a few years ago and what are we doing now well I told you that we can take longer strings this is 31 and you might then say make up one morning and simply say okay what are we going to do today well today we're going to choose now the Heisenberg model is one example and it's kind of interesting because it has here this critical regime over here we might even go to this critical point that we have over here which we'll do at the end and again then you can do that kind of thing and of course it is clear to all of you that while you're sort of cooling down you know in this quantum variational algorithm the larger the the ion string that you have is the heart it is to go to the real ground set for the small systems you can for the larger one of course we eventually will not be able to do that and but you can see over here this is sort of this cooling down and when you say what is his cat of data well this is this classical algorithm that's trying to figure out what's going on and you can then you know write down a certain quantum circuit that I'm not going to explain over here you want to write down some short circuits and sort of get an approximate ground state you know within a finite amount of time on your quantum machine and you can see that well in the plot over here with 31 ions we are not we're reaching a final energy which is pretty close to the ground state but if I do the same thing now for 51 ions you know the whole string that you can see down here we're not really going to the ground state but to give you some numbers you know we have here in terms of energy when you plot here you know the lowest Heisenberg model energy at the highest one you know we are sort of in the regime how we prepare this ground state which is in a few percent you know close to the ground state and which is a superposition and if you really do tmrg you can find that out of maybe 300 of the lowest lying states where the total number of states you know as symmetries and I'm ignoring that at the moment will be 10 to the 14 you know it's 2 to the power 51 so we're not doing so bad you know so you might say well we're not going to the ground state but you know be achieving something over here and then you will ask me that point now what do we do okay with that okay so let's now find some playground then there's some obvious things that we can do we can think about applications in basic science where we start to ask things like for example entanglement and I learned about entanglement and I will tell you now some show you some results along these lines but we can also talk about applications and I will give you an application in optimal quantum metrology where we are trying to optimize Ramsey interferometers by putting in controlled way entanglement to increase their sensitivity hopefully going to the limit which is the ultimate you know optimal sensor that quantum mechanics allows for n particles and we can use them and our ideas over here to play these kind of games so let me start with the first part and talk about you know what can you learn about entanglement in these quantum many-body systems over here okay so let me remind you briefly what entanglement in a many-body system is and of course I'm here speaking mainly to theorists and so I apologize for if this is below your level well imagine that we have prepared now say the ground state and they call it psi and I'm drawing here two-dimensional systems sort of indicating that what we are doing talking about in the following well with the ions we have a 1d experiment but in principle the protocols that I'm going to explain in the following will work in any dimension actually you know and with Rydberg's you know if you had the Rydberg lab in Innsbruck we can do that immediately you know in the for example two-dimensional but at the moment we just talk about one and of course if I have here a wave function that's a pure state and I take a certain sub region A out I can define a reduced density operator of course if there's a product state then the reduced density operator by itself would just be the project on the pure state which is the psi A itself and as one measure of entanglement we could use for example you know the for Neumann entanglement entropy that will simply say well if psi is in a highly entangled state then rho A this density matrix the reduced one will be mixed and the mixedness will be tested by the for Neumann entropy that we have over here so this could be taken as one example of quantifying entanglement if you have for example here a pure state but the question is of course how to measure and then some of you might say well you know you've seen papers that talk about measuring the rho A via tomography but if you have tomography then you know the subsystem size enters and it's exponentially expensive and if you ever try to do tomography beyond a few particles then you will realize that this is very very hard so this is not a very good idea what we are going to do in the following is now that we will talk about the so-called entanglement Hamiltonian which is just a reprametrization of the density matrix but it will turn out that in the particular context that we have over here this many body system these entanglement Hamiltonians have a much more simpler structure you know than the density matrix by itself so we actually have a chance that it will show you afterwards to avoid the quantum state tomography in the simple sense where you're completely agnostic when you go in about a quantum state but it will be able to measure this HA in a way that will then demonstrate things like bisuniano Wichmann you know something that we first heard from Marcello Dalmonte while he was still in his book and we were writing some papers but now we see that these things are actually happening in the lab here and once you have this entanglement Hamiltonian of course then computing this entropy or measuring the entropy in the lab will be actually very simple okay but let me now so the goal now will be to learn the operator structure of these entanglement so we want to do an entanglement Hamiltonian tomography and not the state tomography because I will argue at the end that this is something that you can do in the lab and it will be much simpler but let me now go back to to physics and sort of tell you what the problem is that we want to study so imagine that I have here a Hamiltonian for a many-body system and of course all of us know that well let's take again the Heisenberg model over here it has you know these interaction like nearest neighbor interaction we can take this as a target model as a matter of fact if some of you remember that's exactly the model I showed you for that we tried out the variational quantum eigensorb before in the slide previously and then we are able to prepare for example say the ground state over here or you know by an appropriate change of the protocol maybe also an excited state of course when you see ground state excited states in an experiment we never can achieve that but we get something which is pretty close and we make a superposition know this is maybe percent level you know on the scale that we have over here so what is the interesting question now to be asked well again some of you might remember that in a many-body system you know with these finite range interactions we have what's called these this area law that if LA is the dimension that we have over here and today then it scales like LA to the power D minus 1 so this basically means that you know low lying states like the ground state they're actually typically in for these Hamiltonians that we have the material science of condensed matter problems they have sort of less entanglement this is of course the reason why ideas like MPS no matrix product states CMHG and so on work and all of you also know that if I take a typically excited state you know we will have here a volume law entanglement namely that the entropy that is like the thermal entropy scales like the volume you can see D is the power that dimension D minus 1 that we have over here and you know volume law entanglement is most of the states that we have in Hilbert space and area law these are these ground states so the close to the ground state they sort of fill out only a very small part of the Hilbert space and the classical simulators you know built on that that you can simulate this thing more easily because you have less entanglement but quantum simulators on the other hand can easily represent not only these states but also these states over here so this leads then us to the question of asking you know can we see this area law versus volume law in an experiment maybe even using the state that I just showed you before that we can prepare so that's the playground that we are now setting up here and again so let me start out maybe with the excited state over here and sort of appeal for the moment and this is just to I mean use the use the argument I'm not going to talk about it deeper let's sort of appeal to the eigenstate thermalization hypothesis this would tell you that if I supposedly prepared an excited state you know and I take the trace over the second part of the system and I have my reduced density operator over here then basically this will be like a thermal give state that has a certain temperature related to the energy that we have over here and HA will be well normally be the Hamiltonian which is the system Hamiltonian reduced to the you know sub region that we are discussing over here modulo some boundary effects of course you know there will be some boundary effects going on over here and so let me graphically represent this state over here because I will use that afterwards and I want to graphically represent it by you know suppose that I've here a reduced density operator and I'm rewriting this thing here with the local temperature beta I this is a local temperature so that at every point in space of a different temperature and you will tell me well the Gibbs state a road a road up there is one that has constant temperature in space so let's represent it like that and so this would be a graphical repetition of this state over here there's a constant temperature local temperature over here as a thermal Gibbs state and if I make this thing larger and larger and larger you know and I study now the dependence of the system size of course I can calculate the volume law entanglement in this case which for one the system is just the linear dependence this is volume law okay and the other hand they might ask you know what will happen if I cool this thing into the ground state for example you know and it just talked about ground state preparation IE before and this is of course the story that we actually first learned from Marcello that let's assume now that the critical point that this dependence of this inverse temperature here turn should be actually the one of a parabola and if you work out what the corresponding area law is well this is like an a conformal field theory for the vacuum for the ground state here or the critical point in one plus one dimension it should be like a logarithmic dependent you know and if I move away from the critical point it should be something that goes up and then it's flat okay it's really flat independent of system size this is what the prediction so you might ask me now I showed you now volume law you know versus ground state and so let me tell you a little bit more about this you know ideas what the entanglement entropy is you know for the entanglement what they reduce density matrix and the entanglement have been done in this for ground states and let me point out that Marcello et al has written a very nice review recently so I just point to that you know that goes from very theoretical and even mathematical things field theory lattice to experiments and so on that came out recently so he will tell you if you ask him all of the details behind that so what what we are trying to do is this I would like to argue now why we expect for the ground state something like a thermal example that has a local temperature like in the form of a parabola and it really is the quantum field theory you know based on Lorentz invariance if you have a Hamiltonian that has a local Hamiltonian density over here this is famous between Yana Wichmann theorem you know that if I pipe partition my system into two infinite parts over here A and B then the ground state you know has a reduced density matrix as a vacuum state and I'm tracing over the second part over here basically as an exponent so this becomes a Gibbs state but you can see it has here the Hamiltonian again but it has a temperature which is local okay local temperature beta of X and it actually turns out that his local temperature has the form where if I brought the inverse temperature like the beat over here if you go very close to the cut you know it becomes very very hot it's kind of intuitive for it because if I come close to the cut I'm intangling the cross the cut so my mixedness is very large on the other hand you know if I'm moving away from the cut the temperature kind of goes down so there's a prediction here you know that the entanglement Hamiltonian should have a structure it's just the original Hamiltonian but then sort of deformed over here you know with this local inverse temperature that has that has this particular form so this suggests that the entanglement Hamiltonian is essentially you know a deformed system Hamiltonian and you can do very similar things by adding more symmetry to the problem like in conformal field theory and many body physics if you had a critical point where similar things hold over here and you would get the same result but now the inverse temperature has the form of the parabola what I indicated here before at that point of course well this is sort of you know mathematical physics and the context of quantum field theory but you know it was really Marcello pointed out the reason that we should apply these ideas also to the case of many body systems and you know suppose that up that we do some numerics Christian Cocker has produced his plots where we now do the two cases thermal you know and then ground state and what is now this inverse temperature for the ground state you see this very beautiful parabolas that come out here this is theory the MRG calculations exact calculation for a particular system size you can see this very beautiful you know log dependence over here where they coefficient in front and would give you the central charge of your theory and for the excited state this is basically a flat temperature modulus some corrections here at the boundary again giving here the volume law so at that point when I ask you know I just produced for you a ground state can be see all of that in an experiment and the answer is of course yes otherwise I would not be here talking about that you know and so if you take for the ground state now you know going up to subsystem sizes we can go extra to 22 over here can see this very beautiful parabolic dependence which I guess is the first measurement ever at the critical point here of a Heisenberg model you know of this of this entanglement Hamiltonian showing this parabolic dependence and therefore showing this particular case so that is between Yano Wichmann type of ideas in an in a many body system if I go to the excited state you can see that this is sort of flat over here I just want to mention that these are fits over here to experimental data that I will explain later how we actually do this tomography where theory is the dashed line you know and the experiment is this is the red line that we have over here and depending on how we do that these are now technical details this is for this approximate ground state this is for this excited state this is sort of the two cases that we have so it's very excited that we are able to see that we have to work a little bit and we actually have some newer plots in the mean time as on the weekend you know for area law dependence this is supposed to be a logarithm we had some decoherence you know this experimental device that we know now how to pull out so this is a logarithm and this is very clearly a volume law and yeah that's basically sort of confirmation of our expectations so we can see the experiment you see we prepared the ground state approximately we can heat it up making approximate excited state for now we can obviously measure the entanglement entropy in all of these things seeing area law versus volume law on the experimental devices that we have in the regime of 51 particles so it's not so bad after all you know here a little bit more on you know theory dmrg ground state this is the vqe circuit you can see that this is an approximation this is sort of like effectively it's not really in the ground state like a finite temperature and this is the experimental tomography that we get well we are missing sort of formulas here and of course this is a conformal field theory territory here let me tell you what we want from theories that no cft would be nice to have a formula for this entanglement entropy for a finite system a finite subsystem and finite temperature if you have something like this please tell me because then we know how to do a better fits to get our central charges out which at the moment is only 1.1 i guess it should be one but okay so we are working on that okay so but at that point you might also say well we can measure things like entanglement spectrum you know when you see all of these things in the context of condensed metaphysics where people in the context of numerics produce entanglement spectrum so on the message over here simply that we know now how to measure some of these things in experiments okay and this is the you know comparison between theory and experiment of experiment approximate variational theoretically and then the really exact results in TMRG and you know for this entanglement spectrum which is the eigenvalue of the entanglement Hamiltonian you can see there's perfect agreement down here and these are very small contributions to the density matrix and this leads me to the question how do we measure all of that and i just want to show you a few slides and not go too much into detail over here i told you before we talk about programmable quantum simulators and we have used our programmability to produce approximate ground states and if we use this as a playground to speak about entanglement and see what's going on there and we looked at Bissignana-Wichtmann and we saw that you know you know can we also use this programmability and this is the secret behind actually making these plots by not only creating interesting quantum states at the lab but by also program new kind of measurement paradigms a new measurement program so that you prepare first of all the state but then you use the programmability you know in order to get an interesting results out like for example this entanglement Hamiltonian tomography that that i talked about which analyzed all of that so i want to make this very brief you know some years ago we developed what's called the randomized measurement toolbox and on the more quantum information side classical shadows were discussed here by Breskill so we did this independent of these developments over here and Breskill i mean when we presented these results at a conference he was very surprised that we had some of that both work is a little bit complimentary here because we right away applied this to experiment over here there's Breskill over here and his collaborator you know came much more from the quantum information side than predicting you know real rigorous mathematical bounds for some of these things but we were sort of coming together and then wrote a review that came out just i guess a week ago and in nature reviews that you can actually read how all of these things work it's exploiting the programmability that we have to measure interesting stuff and what's the interesting stuff well how do we learn the entanglement Hamiltonian in this particular case i just have really one slide on this thing here so i told you before that what we want to do is to make a tomography you know of the reduced density matrix and i also told you that this is very very hard because it scales exponentially with a subsystem size and okay it's really hard and if you ever had the idea of making a tomography and afterwards taking the logarithm to extract the entanglement Hamiltonian i can tell you it's not a very good idea okay you can try it out but even if you take exact you know density matrices this is a very ill-defined problem but in our case you know i told you before that you have this bisuniana bichmann or conformal field theory parameterization that tells us that the ground state in an approximate form we are on the lattice of course over here has the form of well it's a distorted system Hamiltonian with this inverse temperature and we can of course add over here additional terms and we expect these additional terms that we can add to try out if they are there or not we can add them as maybe three body terms four body terms or whatever these things are the central point being that we have here a parameterization you know of the reduced density matrix in terms of a number of parameters beta you know that scale polynomial with a subsystem size and so we have an efficient parameterization this allows us to make the tomography that normally if you go there in a completely unbiased way which is very inefficient exponential inefficient can make much more efficient and this is a secret you know behind sort of you know being able to to extract you know these inverse temperatures that i talked about you earlier and so the way how these things work and this is very schematic is that you take data you design a certain answers for the Hamiltonian and you do your fitting to all of that over here we do this theoretically of course to write out but also experimentally and the important point is that you take more data and you can verify what you have over here and we can actually write down fidelities and measure fidelities in the lab to what extent you know the fit the answers that you made to sort of really accurate or not okay so this underlies that and if you want to see some more stuff well maybe i should not go through this discussion over here that is sort of based on these randomized measurements so just take it as a message that you know there's two things that physics tells us you know we have an expectation for what the structure of the entanglement Hamiltonian is but at the same time you know the same message is also this provides us with something that we should try as an ansatz and test you know and we can verify if this answers is correct that this makes you know provides our ability to study systems or entanglement the systems much larger than what you can do tomography for okay that's kind of the basic message over here and this was behind the these plots that i showed you here so i could not of course being now here Trieste systems adding something here about quantum gravity in the lab you know special slides for you of course you know what you can see that what we do with a quantum simulator is this that we can for example talk about the entanglement Hamiltonian we can measure entropies entanglement entropies yeah at that point of course you know maybe the proper language being talk about critical ground sets here would be this Merer multi-scale entanglement renormalization ansatz by Giffrey Vidal you know that this is basically renormalization group written out for lattice systems but you know i see some exciting possibilities and take this more you know with a smiling face over here think about ADS CFT correspondence where we have a conformal field theory out here in the sense of this holographic gauge or gravity duality where we have you know you can represent this in this in this Merer ansatz that we have like an RG flow you know in this coordinates i mean there's papers by Swingle for example and talked about these things first where we have on one hand here you know and highly entangled state is a ground state of our conformal field theory that maybe also excited state and this is related or according to these formulas by this paper down here you know to the to the entanglement entropy relating it to the geometry so we have here this entanglement geometry frontier where our quantum simulator sort of sits out here and i think that we have tools available in the lab you know with our simulators where we can study some of these things maybe in cases where we do not know what these you know dictionaries are that translate between these two cases and so on okay i'm start to talk here about things that are a little bit above my own pay grade i have to say but you can see what the possibilities are you know we have possibilities to measure entanglement entropies and entanglement in general and so these kind of studies here could be very interesting frontier to relate these things to quantum gravity and i could not insist of just adding one thing over here these are experimental data actually if you make the ground state of Heisenberg model and you look at what's the entanglement Hamiltonian of systems that are bipartisan this is one partition over here but you want to find then the relation you know again parameterize it as a Hamiltonian here Heisenberg you get here cross terms of the of the of these Hamiltonians people in conformal field theory have written down for special cases some of these formulas we can test them now in the lab okay so we cannot only do entanglement Hamiltonian tomography for the fixed subsystem size we can take this size apart and look at it as a function of distance and there's all of these papers in the context of quantum gravity written about it's called entropic forces you know we know how to measure that in the lab for certain model systems i think it gets kind of interesting here you know but as i said this goes beyond my pay grade here you should talk to me about that let me now talk about something very practical sort of towards the end of my talk here so i told you fundamental science you know we prepare a ground set of Hamiltonian we are able to measure entanglement in the way that we discussed but can we also do something useful you know instead of like for example building a better quantum sensor so i want to show you that that we can you know and we have here a paper that we published theoretically on the theory side you know last year with these people here up at Kalbrojka in East Vasiliev and the collaborators from Hanover and so on then there was afterwards an experimental paper together with the experimentalist using this time not the the simulator I showed you before but it was actually a trap i and quantum computer produced by my experimental friends Reiner Blatt and Thomas Montz and so because the quantum simulator was not available this is sort of from the from the company and this is a device that you can even buy right now if you can give it to your grandmother for for Christmas if you want to you know it's a little hint yeah okay so let me show you what we can do here and now i'm really saying that you know we talked about variation before we use variation algorithms to prepare interesting ground states can we do something where we can build better quantum sensors not only better one but the best possible sensor that quantum mechanics allows okay can we do that and maybe even with a finite circuit depth that we have over here okay so this is now really a change of topics you know we talk about quantum interferometry and i guess all of you in some form know how an interferometer works an n particle interferometer i got an atom and think here about trapped ions you know that have two states the ground state the excited state and we might initially prepare all of them in the ground state and then interferometer always works by having a first beam splitter that makes a superposition of ground and excited state and then an interferometer works by in one arm this maybe the excited state you're putting on a certain phase you know jc's and collective angular momentum operator for all of them we are writing a phase on this and then we are playing this game of quantum parameter estimation where based on measurements that you do at the end after closing the interferometer over here you're making some measurements like you say you know what's the number of atoms up and down and you plot this as interference fringes and from the interference fringes you can infer what the phi is the question is now you know this is of course has shot noise this interferometer you know for the mental quantum noise and the game to be played now is this that when we take uncorrelated particles in a product state like over here this defines the standard quantum limit but if you replace this beam splitter over here which is independent particles operations you know by an entangler we just talked about entanglement and variational circles you know the question is you know can we add entanglement to the story and gain you know and this leads to this question of finding the optimal ramps interferometer something that has been discussed theoretically sometimes ago on a very little bit more abstract level where we have here entangler at the very beginning and entangler and the decoder at the end this is making a collective measurement in Hilbert space it's not a single particle basis you know and but this is the entangler over here and then you might say that well let's represent these unitaries in Hilbert space by approximate unitaries like the one that we can easily do in the lab like for example this I don't know I showed you this is isic model type of things you can use this for our ansatz so simply use the resources entangling resources play around with them and then find you know how close we can get to optimal interferometry principle very simple so what's the idea there well you know imagine now the following discussion that you have with your experimental friend where you say that oh you would like to build an optimal interferometer but can you explain to me what optimality means for you because this is a very subjective thing you know one person might say well for my purpose this is the relevant quantity or this is the relevant quantity think about it like this that you would formulate and the answer that the experimentalist gives to you is something that we call a metrological cost function for example one thing that would be on the list that the experimentalist gives you right away would be that well I would like to have the best signal to noise ratio that I can get okay this would be one example this would be a cost function that would write down can I find the best entanglement you know that gives me the best signal to noise ratio for what I want to do a second example maybe that you also would like to have for example a finite dynamic range that my interferometer should not only work for one particular value of the angle phi but actually maybe for a whole range of angles so if you do atomic clocks I will argue about that this is something that you want to have in this context if you are a LIGO person of course maybe you don't care because your gravitational wave is such small that you only want to focus on one point if you want to build an atomic clock you want a finite range over here for the interferometer so at the end then the game to be played is this that you write down a metrological cost function and then you want to optimize these entangler and decoders over the classes of you know experimentally realizable entanglement operations and single particle rotations to find the the best interferometer that's what we're going to do now the following and the feedback loop over here so how does it work okay so we have here entanglement that we're putting in and we have here decoder but let me now discuss several examples so we're doing our measurements over here measuring the number of atoms up and down you know in every shot of the interferometer and this gives me then a certain distribution p called over here where m is now the number of up and down atoms and this will be a certain histogram over here this is the histogram that you would measure counting the number up and down and from this you would like to infer what the face was and you are the parameter let me now look at several examples you know if i take a product state you know this is the one that everybody uses today in the lab you know we're just pi over two parses and then closing it pi over two parses and writing the face and in the center over here what you would get over here is of course just the usual sign function that determines the interferometer but you can see that if you had here shot noise i mean measurement noise in quantum mechanics that gave you a finite distribution from one measurement to the other one and this leads to a certain error bar over here and if i use a product state you know this defines a sundial quantum limit where the width is uncertainty that you have in inferring this this face over here would square like would scale like one of a squared of n here and if you want to visualize that you can visualize this interferometer on a block sphere where initially all of the atoms are prepared in the ground state and it's like a vector in a block state that the first pi over two parses takes it down and then you're writing the face over here but you can see that the quantum uncertainty of n atoms gives this thing a certain finite width so when you rotate it it is a ball over here that gives you here the finite resolution of the interferometer this is sort of the one of a square and being the number of atoms or uncorrelated particles if you do squeezing what you would do is that you want to squeeze this round thing that you had over here to something very elongated because then you can see if I rotated it around then my resolution will be better that's the reason why squeezing helps an interferometry squeezing is already entangled over here and you can see that this distribution is narrow so you go below the sundial quantum limit and you might even say at that point well you know that what the optimal interferometer is it will be a ghc state you know because in this case you have an interferometer with all atoms down plus all atoms up it's not the answer that we are seeking for as you will see now because if I plot the ghc state over here you can see that the fact that we have n atoms here will lead to interference fringes that oscillate n times as fast as the ones that we had up here realizing of course the optimal thing which is the Heisenberg limit like going one over n here but you know if I add and ask you know what's the dynamic range of my interferometer you know the dynamic range of the interferometer where I can uniquely determine what the phase is over here will be broad and down here you can see it's very narrow so the ghc interferometer tells you that I'm putting in entanglement yes you get the Heisenberg limit but you have to pay a price and the price is that this interferometer is optimal over an range that scales like one over one over n the number of particles and at that time we might also then ask you know it's graphically represented over here you know this is the standard quantum limit over here squeezing goes lower ghc and this is the noise plotted over here and you can see how narrow this thing is what we want is an interferometer which is as deep as possible and as broad as possible and why do we want that because atomic clocks actually demand that and let me briefly argue where this comes from and then show you why the way some experimental results that realize these ideas so an atomic clock normally works like this here's a cavity and light comes out you know and the oscillations or the ticks or the frequency that you have over here they are the one defining the atomic clock and you want to stabilize this thing because your cavity has thermal fluctuations by locking this laser light to an atomic ensemble and how do you do that well you make an interferometric measurement the ramps interferometer where as a function of time over here you can see that this phase in the laser this sort of slowly drifts away you know sort of bronze and bronze and then you want to measure and find out what it is because then you want to reset it to the original value and sort of in this sense keep the o'clock which is ticking always in lock you know with the atomic ensemble that you have that's the idea and you can see that we want to do this thing here for a finite range that we have and so this is sort of you know you want an interferometer which is below shot noise but you also want to give it a finite dynamic range suppose that you go now to an experiment you do all of that so we as theorists can calculate that and we give our experimental friends for a particular circuit that i'm not going to explain to you now in all detail parameters and they type it into their machine and then they're doing measurement as a reference point let me take here the case that we have uncorrelated particles and this is standard ramps interferometry this is my interference french and this down here is the noise okay suppose now that i'm adding now squeezing you know which is entanglement at the very beginning to improve the signal to noise of my interferometer and indeed you can see down the interference doesn't change but the noise goes down and if you see a dashed line and some dots on it this is the theory versus experimental comparison so this machine really works well okay really works well and at that point you might say well let me now add the other part of the story which is that i add an entangling decoder at the end taking out the squeezer for the moment over here what does this thing over here do what this thing does is you can see that it decreases the dynamic range of the interferometer because this is no longer a sine function over here but something which is much more like you know it's it's like a ramp that goes down the ramp and you make it broader in this way but maybe more important you can see that the noise over here it's now the noise window is much much broader so if i combine now a squeezer at the very beginning with a decoder at the end we get this red curve over here where you are very deep and you're very broad but this is exactly what we asked the machine to do and which is sort of useful you know because our experimental friends told us this is what we want to optimize and if you have your own private cost function well we can put it in over here you might ask what the underlying state is i think i'm sort of running out of time with this thing over here so just one two last slides here on these on these ideas in an experimental device very often you have for a large number of particles if we want to do it for a large number of particles the problem that we cannot calibrate our machines very accurately you know the experimentalists are really having trouble so we took here 26 ions for example and the experimentalists were not able to calibrate the machines calibrate in the sense that we as theorists tell them you know the angle that you should put in is like this with these number of digits okay and they simply say well we don't know exactly where we are because for 26 we are having problems this optimization that i talked about cannot only be done on the on the theory side and handing the you know numbers to the experimentalists but you can also ask the machine that you put you know to find the optimal operating point itself you know and then you're robust against any calibration errors and this is what happened over here we take your circuit and again we run our variational algorithm now you can see coherent states standard quantum limits spin squeezing and this is sort of the optimal interferometer allowed by quantum mechanics we're getting actually pretty close with all of that so you can see that on an experimental device the way that you cannot calibrate we nonetheless are able with the low depth circuit to go to something which is almost the optimal interferometer allowed by quantum mechanics and that's sort of an interesting practical application one should use this in atomic clock something that we have was not done yet but to close the story i started out by talking about quantum simulation and many body physics and you know we talked about entanglement so let me sort of close by saying that what we do over here if you do this not on the quantum computer but you do it on the quantum simulator and one example would be that you have a rittberg tweezer wave with a finite range interaction in this case you know you can ask the quantum simulator to search among all of the states that you have all of the entangled states and find the optimal within the given resources to find the minimum and at that point the quantum sensor that you boot and runs this optimization program is now a sensor that finds its own best entanglement in the regime where i is a theorist because this is a 2d problem for a large number of n i cannot calculate anymore so the sensor solves a many body problem who's result when i know that for these dynamical processes you know for this encoder and the decoder that we have here which is the entangler so it solves a many body problem that we can recycle then as the best interferometer and it does something useful at the end you know so this sort of closes the story over here this experiment has not been done yet in this particular form over here but i guess it should and so let me close here by simply saying that my talk here spoke about programmable quantum simulators and giving you a little bit of tour from what's experimentally done but also the fact that we as theorists can use this as a playground and i talked about hybrid classical quantum variation algorithms randomized measurements i didn't really tell you the details behind it this was one of these results these you know predictions of conformal field theory i've not talked about something that i sort of liked there was a perspective that we wrote recently on practical quantum advantage in quantum simulations so andrew daily was sort of the main person what we contributed there this is a topic would be very interesting to talk here but we don't have time is this how you can verify quantum simulators for example in the regime where you can no longer simulate classical and what we are proposing over here sort of studying this is done by you know whole groups of people at the moment but the written series of papers on that is that you give us a quantum device an experimentalist gives us a quantum device and we want to find out the Hamiltonian that was actually implemented as a many-body system and we want to do Hamiltonian learning this would be sort of a very precursor to verifying you do here characterization of a quantum device and if you want to read about that you can read in this nature perspective recently about some of these ideas and this is a plot out here and now at the end of my story the main people you know in and my group here by christian and rick you know contributing to that and for the metrology rafael calpric and also denise here are some x-group members and you know marcello has a very you know a prominent role in all of that i have to say that be oh him pointing out to us this bisuniano wichmann kind of ideas that we now can see in the lab you know and marcello took a very leading role in all of that and adres elmes now at caltech and benoit vermelle steve randomized measurement people which is now sort of a standard over here and here marco diliberto you know this is the experimental group here of course reinerblatt probably everybody knows him and thomas months as a senior scientist christian rose and these are the experimentalists but i particularly want to point out here my knowledge josey who is the experimentalist on the quantum simulator and was responsible for many of these data and christian marsiniak and being responsible as the experimentalist on the on the on the clock on this optimal ramsay stuff over here of course should also mention our you know special friend in the whole thing which is the quantum simulator the quantum computer with trapped eyes which we have available thank you thank you very much questions okay so i start with uh with a question so in this uh effective and dangle and miltonia is that a meaning or can you also say anything to the fact that since you have an effective temperature which is space dependent you will have an energy carpet ah okay the uh or you talk about the entanglement character in energy well if i take that as a beta with a beta of x in principle there should be this is an entanglement hematonium of course right i understand that but i just call it energy current and the scent is associated to this uh what would be an energy i mean i know the case that you know in conformity here of course we have learned from basquale calabresi if you do quench dynamics that we have for example an entanglement hematonium which is not only a deformation of the system hematonium but there's additional terms like momenta term that correspond to entanglement flow sort of in the system something that we can see very clearly in our theoretical simulations but uh in the corresponding experiment has not been done but the energy flow at the moment uh marcello you know what uh what the answer would be for that it's an entanglement card no but he talks about energy current no no but say energy in this effective amiltonian yeah it's an entanglement card okay yeah that's what i okay so yes thanks uh yes so very naive question but uh is there something special about this number 51 because there's another experiment uh right at mit or harvard and that was also doing exactly 51 qubit yes i think you see some sociological and all synchronization here okay so i think maybe they want to take prime numbers and i don't know uh no i think that uh to be honest i mean in the case over here they can very easily load maybe 80 ions in the whole device and also try that but the main difficulty that they have is this that want they want to address the individual ions if the chain gets longer and longer they have more and more difficulty pointing to the right ion near the edge and so this was a very good compromise sort of optimizing some of these problems and this is sort of related also to the fact that didn't really talk about that in detail that you might ask i showed you a variational wave function that gave you the impression well we can produce an approximate ground state for 51 ions you know if you look at it a little bit closer you'll find that you know you have problems with all of these things when you go close to the edge so you have to make a compromise you know in terms of the errors that you have that 51 was a very good number for that so it's really it has some experimental reasons that are not deep at all if the addressing unit is improved then this can immediately done for larger systems i guess if i may ask another question about the challenge you had for conformal field theory people so you want the so what we love let me so we have here we are able to extract you know the dependence you know of the entanglement entropy at the critical point it's a function of the subsystem size which is the logarithmic dependent and has the central charge in front but we are not really in the ground state let's call it an approximate temperature it's not entirely true but let's call it like that but we want a finite strip and we want the subsystem which is again finite and we want a finite temperature and are there some formulas around you know that you can use it because we know all of the cases but there's always one in infinity and so yes but my question is what is the conformal field theory that you want is it the easing yeah easing not the c equal one theory it's a well it's a one having c equal to one here you know and so so is it c equals one or one half no one one okay and maybe i think i know okay good so i made the right remark here okay thank you for a very nice talk i just have this question about this temperature that is showed in the previous slide okay why does it turn is it because of some fine shouldn't it be just linear with x the temperature no no no this is okay so i showed you the result when we take a system because something out from the bulk okay and there's predictions you know in this case from casino herdham mayer's and so on you know what the entanglement hemidonia is in terms of this which is the form of a parabola and the reason why i'm showing it these results is that if you want to show bisuniano wichmann which is sort of a pipe partition for an infinite system and trying to see the linear dependence we have a problem you know that it is a very beautiful ramp which is linear but at the edge you know our variational wave function goes really really wrong and we have an answer at the moment how to fix that but i don't have a slide yet ready we can take the variational wave function i can learn the effective hemidonia back where this thing is the ground set and then plot bisuniano wichmann on top and then it actually is a beautiful ramp but this is a too complicated story to to show here okay thank you for the talk i had three questions one is when you talk about energy scale which energy scale you are considering this quantum computer scales and also the accuracy of the quantum clocks when you say that you are using it as a clocks what is the accuracy of the clocks so and how you can measure this accuracy regarding the instruments that you have and regarding the photons if you replace ions with photons what's the difference main difference okay so that's maybe side so the first one was about energy scale but you talk about the energy scale that they wrote down in the heisenberg model or you talk about the energy scale for the experimentally realized easing hemidonia that we have in the lab for the experiment for the experiment ah okay so this was the coupling there was 720 seconds minus one after converting to kilohertz this was the chick coupling for this you know anti-ferromagnetic coupling that we added is easy model there so a typical time evolution would happen there you know sort of the typical couplings that you might have is maybe 10 kilohertz 20 kilohertz sort of tens of kilohertz type of things okay and regarding the accuracy of the quantum clocks that you are using the clock so we have not built a clock well i'm certainly not because i'm a theorist anyway so uh so uh this was not building a clock this was building an interferometer that could be integrated into an atomic clock operation okay and what we have shown over here simply that when you do and when you take uncorrelated particles versus squeezing but a lot of people are trying to do at the moment with clocks that if you do add these variational sort of you know optimized entangler decoder you can get very close to the optimal ramps interferometer allowed by quantum mechanics and our point at the moment is simply that there's some in the future development of atomic clocks if you are are able to apply like with trapped irons that are that were originally designed to be clocks if you apply these kind of protocols where you combine the ability to run them as a quantum computer and therefore get entanglement but at the same time you can run the same device also as an atomic clock if you combine these capabilities it will allow you at the end to build via getting the best entanglement for encoding and decoding you know build the better clock but this is sort of a longer range vision right now where we will provide one particular no building block for doing all of that and regarding the photons if you replace with the ions and atoms what's the main difference if you replace photons with ions and atoms what's the main difference of the results okay well uh no i have to say that in our case as we know atoms can be trapped you know if you look at the ions you know we can hold them but not me again you know my experimental friends can hold them over weeks even or month or so you know and don't lose a single ion and they are extremely well isolated from the environment we can cool them down so and photons of course are also fantastic qubits but photons like to travel i think it's the speed of light you know and so they are much harder to entangle than to manipulate and so the reason why we do all of that is that we really think that atoms provide a unique opportunity in terms of engineering entanglement interesting many-body Hamiltonians and this is therefore a fantastic playground that's definitely a step closer than what one is able to do with the photons at the moment okay so but photons are very interesting also for other reasons so i see this a little bit as complementary you know photons if you want to build a quantum network like talk about networking of quantum computers you build that quantum computer like over here then you build an interface where you write the atomic qubit which is a superposition of up and down onto a photon and you ask it to travel over you have to absorb it of course you know if you catch it in the right way um b and others have thought about how to do that and it also works in the experiment and then you want to catch it and then sort of you have now networking of quantum computer where you're using photons you know to to entangle the different modules of your architecture and for that of course you need traveling you know qubits and atoms are great stationary qubits and photons are great you know flying qubits that allow you to connect these processors so they all have their own role and of course if you want to do long distance quantum communication i mean you better not take atoms because then you have to you know carry them there and this might take a long time more questions no so let's thank professor solar thank you very much as uh in any colloquium i asked the diploma student to stay in the room so they will have