Prof. Immanuel Bloch - Large Scale Quantum Simulations using Ultracold Atoms

okay good so okay i think thanks a lot for the invitation uh tonight and it's a great pleasure for me to be here today with such a great lineup of speakers exciting lineup of speakers in our field and so i'd like to start and explain a little bit what it is all about with this quantum simulation connection to quantum computing put it in perspective and i think maybe hopefully also lay the basis for some of the talks that will that will come afterwards so i want to talk specifically what what is a quantum simulator how is it connected to a quantum computer i then want to specifically turn to the optical lattice quantum simulators and give you just a single example since time is is limited of what kind of calculations we can do and where they stand basically in competition with with other platforms and techniques all right so let's start out and what is a quantum simulator how is it related to a quantum computer well maybe let's start first in trying to see what problems we are we're trying to to solve well i'm a scientist i come more from the science direction so the problems i'm that got me interested in the field were problems connected to material science chemistry strongly correlated materials and trying to understand those systems better and trying to basically get a have tools available which we allow us to study the systems in great detail and of course then with this knowledge turn that to advanced kind of technologies advanced materials drugs maybe that you could design with this knowledge now one one model system that plays a very very important role in the context of material science in this context that has kept physicists busy for the last 30 40 years is the model of interacting electrons on a lattice the so-called hubbard model which is believed to have strong connections to high tc superconductors so there's an immediate very very big goal here to basically understand how we can deliver power without losses in these systems but still this system defies understanding so it's a good test case for all kind of quantum computers uh quantum simulators you know it's like the reference model we want to basically understand in these systems so i think we'll see a lot of systems try to solve this big problem in material science one of the biggest problems in material science as as kind of the guinea pig model to show how good your system is in solving these real world material problems so what are we trying to do well basically in in this kind of problem we know the microscopic rules of the system very well how these electrons behave and interact with each other but still we cannot calculate what kind of material properties emerge from that that's simply because of the complexity of those systems or number two the question could be how should i change those rules to get a specific material property out of that so those are kind of the questions that motivate this and those of course immediately have a lot of applications and technological relevance so i would like to advocate that quantum simulators and quantum computers can with a caveat in some cases help not in all cases but in some cases they can help to solve these problems we'll hear more i think from antoine also how you can likewise look at optimization problems for example some optimization problems again not all kinds of optimization problems that can be more efficiently solved hopefully more efficiently solved the point i want to make here is that the way these are solved is actually by mapping them onto a physics onto a many-body problem onto a condensed matter problem an artificial one maybe but it's very likewise to solving kind of the the problems we know from the material science world all right so so what's the problem well basically the problem with the quantum system as you probably heard many times before is this exponential complexity that basically a quantum system out of n particles here these n spins can be in a simultaneous configuration of all those particles and just even to store the state of that system can require an exponential number of resources exponentially large memory and you quickly outrun any classical computer and trying to exactly solve that problem now when i say that we should of course be very careful because there have been fantastic calculation methods on classical computers to approximate those problems and that is because the typical physical ground state of a physical system only occupies a very small part of the entire configuration space that you have available for a system and if you can find efficient classical numerical methods to approximate this smaller space configuration space then you can find very good solutions for material science it's more when the problem actually addresses you know evolves into exploring this entire configuration space which in physics we call the hilbert space of the problem that's where really this exponentially large configuration space starts to hit you and you have problems solving for that and that's something for example that very often occurs in the quantum dynamics of systems that we encounter these kind of problems where quickly classical computers uh outperform but i just want to really say we have to be a bit careful that because very often we there might be good classical ways to solve this material science or chemistry problem but we of course have to find those approximate techniques that find this corner in this configuration space now of course the idea behind quantum simulation and quantum computing in general is to use artificial quantum systems to help us solve this problem directly in a quantum mechanical way and in the past 10 20 years fantastic number of different systems have been advocated iron trap superconducting devices the atoms and lattices the rib back freezers that we'll hear about today all of them have this idea uh common that you basically try to solve these problems in a quantum simulation perspective so how do you do that well basically you take your your model system which has a certain rule set encoded the rule set basically describes how for example these electrons behave with each other on a lattice you try this rule set we can express in a mathematical form that is written down for example here in a very simple form we can try to encode this rule set on our quantum simulator we can let the quantum simulator run evolve in time for example and then measure the outcome of the quantum simulator to get the result or alternatively what we can do this is the idea of adiabatic quantum computing basically we can start with the initial hamiltonian we can very slowly change the parameters of the system to end in a final hamiltonian and by going over from the initial to the final hamiltonian we start out with a very well controlled initial state our final rule set our final hamiltonian the ground state encodes the solution of our problem and if we do this very slowly then we found the solution to this complex problem which can be of different kinds and the pro the point i want to make here and is that quantum simulation is basically adiabatic quantum computing but with a caveat with a restricted form so in quantum stimulation you typically do not control all degrees of freedom of the entire system and if you cannot do that you cannot have a universal adiabatic quantum computer but you can still the principle the idea basic idea behind it is still the same that you basically adiabatically change between these two two rule sets okay now what's the comparison how does this compare analog quantum simulation versus digital gate-based quantum computing well basically again you're trying to solve the same kind of problem you're trying to find for example the evolution of a quantum system starting from an initial state and then basically you can do this either by encoding the rule set into your model hamiltonian and letting it evolve over time in an analog way or you can basically try to encode this rule set in a set of elementary operations in a set of gates that you concatenate after each other and building up on these kind of concatenation of these digital gates you can basically build up any kind of rule set whereas in the analog case you typically only have a limited rule set available the advantage disadvantage of the digital approach of course is that it you might need a huge huge amount of digital gates that you concatenate and you might need error correction to be able to do that in an efficient way as i'll actually show you in an example case in a second so yeah let me let me let me show you this here this was a numerical simulation numerical study done by matthias troyer at microsoft andrew daley in strathclyde and peter zoller in innsbruck where we try to compare an analog quantum simulator how good you have to be on a digital quantum computer to simulate the same kind of quantum dynamics and the system we took was this how about model of these strongly interacting electrons on a lattice a 2d system moderate size 10 by 10 system size and try to simulate the dynamics for example over 10 hopping times 10 evolution times in the system and if you just put in the typical errors that we have calibration errors the coherence properties of the physical system we have in the lab right now and you compare what you would need to have on a digital gate-based quantum computer you actually find that to produce the same quality of simulation you would need about one million gate operations with a extremely high fidelity uh that that is written down here for these nist type of devices that are available at present i think this just shows that for certain problems while we are living in this nisk area of quantum computing doing the computation in the analog way if you can do it can have significant advantages to solving your problems on these systems all right okay somebody's writing on the screen interesting okay um quantum simulation now let me turn to the optical lattices and show you quite specifically what we do so in our case we basically create by interfering light beams a artificial crystal this is a crystal of light this is an interference pattern of laser waves that show a bright and dark pattern which is our crystal formed out of light in which we can load our our atoms our ultra cold atoms and they are basically trapped in this crystal of light and can move in this crystal of light and basically simulate the behavior of electrons in a strongly correlated material we can do this with a few thousand particles as i'll show you in a second and we can do this with spin systems so qubits zeros and one but i think more importantly we can also do this directly with bosons fermions or mixtures so electrons are fermions in the physical world and typically when you look at material systems you want to study the behavior of the electrons so for fermions and in order to do this calculation on a quantum computer on a spin based quantum computer you first need to map this fermionic problem onto the spin based quantum computer and that requires a huge overhead in the number of gates and uh available qubits that you need to do that whereas here if we directly simulate the dynamics with fermions for example we of course don't run into this overhead computational overhead problem all right let me give you an example now so how this works how we can measure this system so we have these new tools available where we can photograph such a artificial cold atom system we can take some single snapshots of this quantum state psi which is maybe the ground state that we have prepared in the system that we're interested in and when we want to read it out we take a photo of the system and when we take a photo of a quantum system which is in a superposition of these different configurations what happens is that supers this superposition state collapses onto one of those configurations and this is the configuration that you would then see in the experiment then you have to repeat the experiment again recreate psi measure again and it collapses onto another configuration and at the end of the day you basically get a probability distribution of all kinds of configurations that can occur in the system and this is your output of the quantum simulator from which you can calculate almost all of the relevant correlation functions for example that that you're interested in in your system this is actually akin to all quantum simulations so this destructive process in measurement all of them have to recreate psi again and then do another measurement to them so that's not specific to a cold atom system that any any quantum computer any quantum simulator has this property of course um all right so how can we program these devices how can we on top of those lattices that we create by interference shape the potentials additionally well to do that we use these digital mirror devices which allow us to project arbitrary light patterns onto the atom so we can basically shape the confining potential to be a box with a special lattice we can have reservoirs connected by a wire of light we can have a box potential as you can see here so this this light shaping gives us a lot of flexibility in what kind of physics what kind of problems we want to study and what kind of conditions we can program into the system so let me give you an example of of how we do that in our system so here's the dmd pattern this pattern we put on the digital mirror device so each white pixel is the mirror tilted on if it's a black pixel the mirror is tilted off shining now a laser beam onto this mirror device pattern gives us this kind of light field shining this kind of light field onto the the atoms can structure them in this array as you can see here now you can basically have a readout single shot readout where you can see each atom on those different lattice sizes when we average those you can see the average distribution of the atoms in the lattice showing you how how well we can structure those those systems in the lab this allows us to create different kind of systems so so this allows us to look at for example topological physics uh in these in these chains something that was actually also looked at by the beautiful tweezer experiments in in advanced group and we recently were able to realize a haldane spin liquid in this phase so it allows us to structure these kind of systems these lattices and determine the end configurations the couplings between those lattice size in a fully controlled way we're also able to push the system sizes now to really nice system sizes of a few thousand particles this is a 2500 large mod insulator that you see in the system uh by doing a little bit more cooling we can remove most of the defects in the system so we push out the entropy the defects into the outside region and the inside core is now a few thousand particles again with a filling of above 97 98 percent so that's nice in terms of the system sizes we can now reach with those experiments so in terms of interactions that you control in these systems you have many possibilities so you can either have atoms collide with each other that's direct collisional interactions you can have a dipolar magnetic or electric molecules or atoms that can interact with each other through bipolar interactions we'll hear much more about the rydberg dipole-dipole interactions or something that people have also used is to try to put these ladder systems into cavities and have light bounce back and forth between them to engineer kind of all to all interactions in the system i just chose i just want to show to you that this allows you to really realize a huge variety of different kinds of interactions and control these action interactions in a in a highly controllable fashion in these systems all right let me show go a little bit more into how we detect these feminic systems in in a feminic system you can basically have an electron that is either spin up or down which is indicated here by a red or blue particle you can have no electron on a specific lattice side that would be an empty lattice site or you can have two electrons for example on that lattice side and we would like to know when we take a photo of these images we would like to read out the complete state of this system so we don't only want to read out as in a cubit system with its spin up or down we also want to read out if it's zero or two particles or one particle on that lattice side the way how we achieve that is the following way so we take this single two-dimensional plane this is our physical system and we then split this single physical system into two planes where the spin down goes into the lower plane and the spin up goes into the upper plane in the system and then we take two subsequent photographs of this system so this is the single 2d plane you now separate them you have the spin ups moving into the upper plane the spin downs into the lower plane now you focus your objective onto the lower plane and you take an image of the spin downs then you focus the objective onto the upper plane you take an image of the spin-ups and like that you get a full reconstruction of the spin ups and downs of the holes and doubloons in the system so you get a full configuration readout of this um emulator of electrons in a material now so imagine this would be like taking a photograph of a real material where you see each individual electron in this material that's of course impossible in real materials but here in these artificial quantum systems it's possible so as a simple example that i want to finish off on i want to show you this this very intricate problem of understanding in this hubbard model the role of impurities moving in in these 2d electronic materials so this is a seemingly simple problem but we believe we when i say we the physics community believes it lies at the heart of a problem of of high tc superconductivity the phase diagram i've shown you here here's temperature here's the whole doping of for example cube rate compounds which are the most famous high dc superconducting materials and you see when we start to dope these systems all these interesting zoo of phases pop up where we really have uh not a very good understanding what's actually going on and people believe that the essential physics of this system is indeed captured by this hubbard model i was introducing before and it's basically the question of understanding how impurities that you dope the system with interact with the background antiferromagnetic order in the system what changes what are the effects that can occur there so in a simple picture this captures everything you want to know i'm sorry if it makes you a bit dizzy but this is the the anti-ferromagnetic order and you put a single hole in there and you try to understand how this single hole moves in this anti-ferromagnetic background in the system that's basically what you're trying to understand and you might think this is a simple question but even some of the greatest minds and physics have tried to work on this problem here's a paper from charlie kane patrick lee and nick reed who who worked on this precisely this problem which was perceived the ge duncan experiment at that time but now we can really do those experiments so what actually happens if you put these holes into these antiferromagnetic environment that they distort the anti-ferromagnetic environment around them they create so-called polarons where you have distortions of in this case the magnetic environment around that single impurities that you put into this system and those are difficult to calculate uh they are difficult to they have not been imaged before and the quantum artificial quantum simulators allow us to actually take images of these these systems and here i just flash the some of the results that we've been able to get from this direct quantum simulation of this magnetic polaron this is how the magnetic environment around dopants around mobile dopants is distorted resolved at the scale of single lattice sites so we can directly see how surrounding those impurities we have these uh distortions in the system and directly measure this polaron even more uh more more complex problem now starts to arise when you put more and more of those impurities into the system and this has been a big mystery in physics what actually happens when you start out with this polaronic uh cloud here and they put more and more hole into the system dopants and then end up in the end people have found you end up in real materials with a normal metal the so-called fermi liquid and how this actually works how this crossover actually works has been basically a mystery so far but now with the quantum simulator we can directly continuously dope the system and continuously track the evolution of the system from this polaronic metal into this standard metal regime understand how the conduction properties how the microscopic structure of this material changes so if you want to go to details go to this publication we i just want to basically just say we now really have a detailed understanding when this crossover happens when this breakdown between these two very different phases of matter occurs we can pinpoint at what doping values this occurs and more importantly i think now for theory we can now compare our results to different approximate approximative theories that have been put forward and we can now already say which of those theories are good and which of these theories are bad and in that sense come back to my initial point that i wanted to make we can help try to find better approximations to this um fermi hubbub model that can then be used for example on classical computers verified by this quantum simulation approach okay so just the next steps forward to moving forward where are we going and next so of course like everybody we want to scale up the systems i showed you we can now reach a few thousand particles in the systems electrons bosons uh fermions and bosons in the system we are gearing up with new experiments and these monolithic cavities to make these lattices even larger to be able to go to system sizes of few tens of thousands of particles in these systems i just compare this to the other platforms a few hundred as you will see have now been realized in the tweezer arrays ion traps are typically on the scale of 50 particles 50 ions but of course one also has to honestly say that the level of controllability that we have in these systems goes down from iron traps to tweezers to ultra cold atoms in these lattices and that's of course where we are pushing to develop better better controllability and programmability for these large system sizes that we have available finally one other point i want to make that technological advance in programming these kind of quantum simulators relies a lot on on laser technology as i showed you using these digital mirror devices to program the system you typically put laser beams onto these mirrors and they create artifacts that you can see here so called speckle you've all maybe seen the speckled pattern of a laser that are imaging artifacts that degrade the quality of your your imaging pattern and we're really now working very hard to build new laser sources which allow us basically to fight this laser speckle problem but still have this high power that we have available with the coherent laser light and then eventually hopefully when we when we do this right you'll be able to program each individual um basically lattice link here you can tell me what kind of lattice coupling you want to have between those two links what kind of offsets you would like to have and really control on a microscopic scale the full potential in these systems giving you a huge amount of configuration possibilities programmability in these systems all right finally i just want to mention uh antoine and myself we are working together in this consortium pasquence eu consortium programmable quantum simulators where we're trying to push these different technologies forward the tweezer platform you'll see an entrance talk and later in other talks and the quantum simulation approach in the optical lattices and i think actually while these approaches so far seem a little bit distinct i hope and i think actually the future will see exciting directions in merging those two technologies and i think adam has shown very nice results and how this can be done and i think there's actually a lot of potential for for looking at this in the future and merging those two atom technologies all right with that i just just stopped with giving you a few glimpse into the lab how this actually looks in the real app so it's a complex complex setup still this all can be miniaturized if you put good engineers on it we like our lego systems but i have to say all of these is basically programmed all of these systems are programmed and all of our measurements typically run overnight in a fully automatized mode so in principle one can of course hook these systems also up to the external world and have other people play around with them if they get a little bit more reliable and we don't need the students to run them directly anymore all right with that uh i think i'd like to stop here thank you very much i hope i'm still in time with the talk and uh thank you for your attention if you're interested in our research you can go to our web page uh quantum minus munich dot d a we have a also more on larger quantum effort in munich expressed by our munich center for quantum science and technology and if you want to hear more what's going on in this munich center for quantum science and technology you can also go to that webpage you can see here all right thank you very much yeah thank you very much emmanuel for this really exciting talk um i'm clapping uh for everyone uh we have time for very few questions actually most of the questions came from one person so i'll sample them maybe i'll choose a you you talked about the controllability as a challenge that you need to to improve can you maybe quantify it and compare the current state to the other technology like ions and superconductors um well those are mostly gateways gate-based approaches so here we're pursuing not a gate-based approach so far i didn't talk about this but i think actually collisional gates between atoms were proposed a long time as an idea for for gates and they might have some interesting properties in addition to what you will hear from the river ripwork site on those gates so i think one might go back again especially with lithium there could be interesting configurations where actually you have very good coherence time and very high fidelity two qubit operations but that needs to be needs to be shown but i think that can be done i think in terms of if you ask me now this quantum simulation the calculations that have been done here are far beyond anything that can be done on the superconducting platform the simulations i showed you for the 2d systems i know basically of no simulation serious simulation of the hubbard system on let's say the super conducting platform okay there's a technical question asking you to compare the dmd that you described for example the specialized modulator that other people are using for i think both have pros and cons here i would say it's pretty exchangeable so i wouldn't say there's a big difference in choosing either one the dmd is maybe a bit simpler but you could we could have likewise use use the phase module label um adi i will allow you to ask a question as if can you unmute adi it's special treatment yes adi you can unmute yourself great thanks a wonderful talk emmanuel i'd like to ask about about the limitations so you you measure the probability of occupation of each occupation configuration or the probability of each occupational configuration in your lattice but of course you cannot measure the relative phases between the different components of the wave function what limits what kind of correlation functions you can and cannot measure with this limitation with not no not having any access to the relative phases i should say there's one other thing we can measure which is current we can measure the current operator on a bond so how do you measure this how we do it is the following let's say you pick a bond okay then you basically just turn make to turn the particles you now basically partition the system with double wells into bonds so now you just have bond couplings in that bond you make the part in the system non-interacting and then you just have quarter of a joseph's in oscillation between this double well and that turns the particle measurement into a current measurement so if you after this quarter joseph's oscillation you measure the occupation of the double well it actually allows you to read out the current it's a measurement of the current operator so you can do that on it on on the entire yes that is yes in one shot take photographs of the of the kind i feel uh so you can also get at current current correlation functions uh that's also possible i see that that makes it really exciting okay great thanks okay

Channel: Qubit Community

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Keywords: 5-19-20

Id: Jd15JQJlte4

Length: 29min 28sec (1768 seconds)

Published: Fri Jan 22 2021