 So, thank you again for the invitation to come here and present some of our recent work. And yeah, so during the workshop some of you were here during the workshop, I gave an introduction to quantum information science with trapped ions and today I'll present some very recent research results. Okay, so just to remind you trapped ions, they are extremely useful in quantum information science, actually full-fledged quantum algorithms have been implemented, very high gate fidelities have been implemented, read-out state preparation can be done with fidelities of typically 99.99 and possibly some more nines, so they work excellently. Quantum simulations have been demonstrated recently with 53 ions even, so they work very well. Now the question is, when you want to scale them up to have a real large device, maybe a scalable quantum computer, the way to go is to have integrated microstructured traps. It means these trapped chips not only contain electrodes that confine the ions but also to apply additional fields, for instance to drive the ions by microwaves or even detectors, photodetectors and light sources. So everything you need on a chip basically, so there are concepts exist to do this and then a scalable quantum computer based on trapped ions is not science fiction, it's science, I would say, science that has, of course they are still quite a way to go. Okay, let me point out a few proposals for scaling up quantum computers with trapped ions. So the canonical proposal basically is indicated here where you have a, let's say, an iron trap chip with different, the yellow things are electrodes and then you can move around your ions between these so-called processor zones where you do quantum logic and then you have memory zones where you store your quantum information. So you have to move around your ions in such a trap chip from interaction zones to memory zones and back and so on. So most of the time actually you spend moving around your ions, so about 99% in concrete proposals you spend moving your ions around. Then there are other proposals, a recent one where you do have small sub-processors basically and then you can interconnect them via photons, photonic links, so that's an approach that is being pursued in Maryland and then there's a recent proposal that completely relies only on microwave-driven ions, so there are no more lasers needed for any coherent operation and so this is a small part of a larger trap chip that is proposed for implementing a scalable quantum computer using microwave-driven ions. So that also involves shuttling around ions. So you see these segmented electrodes which is a sign that you apply time-dependent voltages and then you move your ions around. Okay, so and now what I want to show you today is a few recent experimental results from our group where we looked at for instance this shuttling of ions and also a very important aspect which goes under the name of so-called anomalous heating, so I will talk about shuttling of ions, I will talk about this curious phenomenon of anomalous heating and I will show you some recent results with microwave-driven trapped ions. Okay, so this anomalous heating, what is it all about? So ever since people have trapped ions they observed that the motion of the ions gets heated up very quickly and this heating is far beyond anything you expect from let's say Johnson noise in your electrodes or something. So this has been a phenomenon that has been observed for decades now and there are models that can explain it but there is so far no real experimental evidence, no conclusive experimental evidence for explaining this so that's why the name anomalous heating was coined at some point. Let me present just two formulas, the rest is formula 3 physics. Okay so let's look at the heating of an ion, so you have a charge and you have fluctuating electric fields and these fluctuating electric fields they move around your charge and heat it up eventually and you can show that the heating rate is well approximated by this expression where you have the charge, the mass of your ion and the harmonic oscillator the frequency of your trap and this S E is the spectral density of your noise of your electric field noise. Okay so that's the important, so that's the heating rate, that's the spectral density of your noise and I should point out an excellent review article about this topic here is this one. So they compiled all the knowledge that was known up to this point here about this anomalous heating and it's a rather large article. Okay and now what is the connection with what I said before? Basically when we want to have these microstructure traps we want to, yeah microstructuring means small structures that we want to get close to the surfaces which means the heating rate increases dramatically that's an experimental observation and it's important to know how it scales exactly and that's what has been done in this work that I'll present now. Okay so what are the sources of fluctuating electric fields? There are many sources actually so there's black body radiation, if you work at room temperature that's in many experiments not negligible but in this case it is actually so this is not, this is a theoretical source but it's orders of magnitude below what you observe typically then you have direct electromagnetic interference so you have all kinds of electromagnetic fields floating around in your lab from natural sources from elementary particles hitting the ionous field that make fields from power lines so man-made and natural sources that can interfere with your charge, excite your charge then you can have electromagnetic pickup so these fields are induced voltages in some current loop in some loops of wires or something that you have in your lab then you have this truncin noise so just your electrons and your electrodes have a certain temperature and they move around erratically and so they produce this truncin noise then you have all kinds of technical noise sources from the apparatus that you use to apply voltages to your trap and you have space charge because electrons are emitted from your electrodes and they produce charges that fluctuate also and then you have so-called patch potentials so on your electrodes if you have an electrode it's not a completely homogeneous surface typically but it's you find patches so little islands of where you have a certain voltage and then you have another island that might have a slightly different voltage due to crystalline structures or absorbances on the surface so there are many possible reasons and if you look at how they scale so theoretical models exist and it's a reasonable assumption first to assume that this electric noise density is proportional to the frequency of your trap with some exponent to the distance between charge and trap with some exponent and to the temperature and what I want to concentrate on here is this beta thing here so how does the electric noise density scale with the distance to the trap electrodes and you see that you have all these different exponents here in a certain regime it doesn't have to be a power law necessarily but yeah we'll see and you can distinguish them by their exponents and also by this alpha exponent you can distinguish these different types of noise and now this is a very impressive blood done by these people here so it compiles the knowledge about anomalous heating from experiments over quite a few decades so what you see is you see the spectral noise density as a function of the distance between ions and trap electrodes and do you see any law here it's difficult so the shaded area actually this is a power law one over D to the fourth power and these dashed lines that's one over D to the second power and looking at this anything goes basically so this is not really useful evidence for any of these scaling laws so and the reason for that is simply that you have so many parameters that are relevant in determining this heating rate so first of all of course this distance then the geometry of your trap very different traps exist the material of your trap your driving electronics and so this all varies in these experiments and so a real conclusion is not really possible with the exception of two experiments so this one 16 if you look for 16 on this plot you find 16 a 16 B C D E so here you actually see a dependence that was done in a single trap but the thing is this was a so-called needle trap so it it's just two needles that form the electrodes and then you change the distance between these needles and this is so they are geometrical factors involved in interpreting these results which are not completely obvious how to deal with them so that's yeah and then there's a recent experiment also where this was systematically investigated this distance scaling but again the geometry of factors play a very dominant role in these experiments so typical trap sizes electron electrode sizes are in this region here okay so so this anomalous heating is not well understood from the experimental point of view and also from the theoretical point of view so and the experiment I'm I'm going to present now is so we use a very simple structure basically a plain surface and we have one iron sitting above this plain surface and then the only thing we vary is the distance between the iron and the surface and all other parameters are kept constant so that should give you some conclusive statements hopefully yes and it did as you will see in a minute okay and so our trap is a generic five electrode surface trap so this is a picture of the of the trap chip and this is a zoom in of these five electrodes so you have one electrode two three four five basically there are some special features here but I'm not going to talk about them the central electrode is about a hundred and fifty micrometers wide and this determines usually the distance also between iron and surface so the width of your electrodes is typically equal to the distance of the iron from the surf in a typical operating regime of a trap and our guinea pig is uterbium ions so this trap works very well so this is this is a timescale actually so here you see one iron in the trap two three four and so on and you keep them can keep them for many hours so it's a trap that works well and now the important thing is we want to change the distance between the iron and the trap and there's an experimental trick that is applied here which is not completely trivial so you have these five electrodes of your trap that make your trapping potential and see a happy iron here so it's trapped and so this is the typical configuration and here you see the the vertical potential above the surface as a function of the distance so you have this minimum here that's where the iron sits and so that's the typical the usual trap operation but what you can do you can apply an additional radio frequency voltage to your central electrode instead of this ground voltage and this has to be in phase with the rest and yeah and then you can actually change the distance the trapping height distance so here you see this has been changed from about 150 micrometers to about 60 micrometers and by implementing this in the experiment we can change the trapping height in this region here and then observe how the heating changes okay and so this is this is our guinea pig we drive an electric dipole transition where we cool and detect fluorescence and then we have this re-pump laser that keeps the iron in this closed cycle okay and now how do we measure the heating rate we let we turn the heating the cooling laser we turn it off which means the iron starts to heat up and then at some point we open the cooling laser again and we observe the spatial extension of the iron in its harmonic trapping potential and this would be in principle be sufficient to do a heating rate measurement so and then we vary the time during which we let the iron heat up and then we get and from from the extension of this of this image here we can deduce the temperature so we have so we get a rate a heating rate temperature per time but actually what we do here is we measure this in a time resolved way so we have a certain heat up time then we start to cool down again and then we observe this cooling down process how does the spatial extension of the iron in its harmonic oscillator potential shrinks down again so this is a highly excited iron and then the temperature is reduced okay and to analyze this we plot the width of this Gaussian function so it's harmonic oscillator is a Gaussian distribution in space so we plot the width at a certain time and at a second time and a third time and so we do this for many times and then we can fit this data and find the time at zero so that's where we turn on the cooling laser and that's where we want to know how hot is the iron at this point and then we can extract the average vibrational energy simply from the width of these Gaussian so that's the width of the Gaussian and that's the energy okay and now I'll jump right to the results so we measure the heating rate as a function of the trap frequency and we find this exponent here and then we measure the heating rate as a function of the trapping height and this is a unique thing that has never done before even though this has been around this anomalous heating for decades now so and here we measure this exponent minus 3.79 and now if you look at all the models that are around oops sorry this is this is h sorry thank you very much for pointing this out see that's why I did it to wait for your input okay yeah so d actually that's called h here yeah so h to the to this power yeah that's important of course omega was in this slide okay okay so now this thing here is yeah we did basically this experiment and the conclusion now is it's clearly a power law that we observe and we observe this exponent and you saw before in the introduction this alpha minus 4 that comes out of some of the models and this is close to these models not yeah it's compatible with these models here and if you now so all these models have a different combination of scaling of with distance and with frequency and if you now look what matches the scaling that we observed here then you see that the model of these patch potentials that fits nicely and also the model of a thin dielectric layer covering the electrodes so in a typical real experiment you have you don't have the your gold or whatever electrode but you typically have it covered with some dirt or some other stuff that you don't want and so so this these models they are consistent with this okay so that's I think an important contribution to a long-standing question in iron trap physics and possibly beyond iron traps physics okay and now the second part I'd like to show you about what I mentioned in the beginning shuttling of ions so move ions around and if we want to have a scalable quantum computer the ions have to maintain that their coherence their quantum information and that's also yeah okay so I showed you we can do all these high fidelity operations with many nines but for some reason the shuttling the fidelity of the internal states when shuttling the ions has not been so far not been investigated to this precision to have these many nines people just stopped at two or three nines so which is not compatible with these other high fidelity things so if you do a high fidelity gate with five nines and then you shuttle and you mess everything up during shuttling because you only have two nines or three nines then that's not satisfactory of course so as all the other operations you need high fidelity in moving your ions around especially if you spend most of your time moving ions around so that then that becomes very important okay you saw the slide and here and here we definitely need lots of moving around this probably also will involve some moving around okay so that's we saw this and now this has been done with a different trap this is a three-dimensional Paul trap a microstructure trap so you see all these electrodes here and now we can move around the ion here and we move them typically by 280 micrometers so that's a rather large distance for an ion if you think an ion has a diameter let's say of an angstrom and you move it by 280 micrometers that's like moving a human of average size from pier to Rome across lots of bumpy roads and we do this many many times at about 4,000 times and then we measure the coherence of the ion using a ramsey type interferometer measurement so here you see the ramsey interference fringes which tell you something about the coherence of the ion after two shuttling events and then you see it after 4,000 shuttling events and you see a slight reduction of the contrast and then if you extract in a rather intricate procedure you can extract the fidelity per shuttling and you find these 5 9's here and you see that you looking at the arrows this is compatible with one so this is also works with extremely high fidelity and can certainly be an element of a future scalable quantum computer yes yes so you have you move the iron from one place in the trap to another place in the trap yeah if the you shouldn't have ions in the way typically but recently there have been experiments where ions move around each other also yeah and they do not exactly overlap that's what I wanted to point out here because so you have a slight reduction of the contrast here here you see this between the red and the black curve and the reduction is due exactly to 4,000 times moving it back and forth and then you look at the loss of fidelity per move and then that's what you get okay and another thing that's worth mentioning is so these taking this data involved about 20 million shuttling events and the iron was always there so we did not lose the iron so this is a reliable way of transporting quantum information okay now how much time is left for minutes okay so some of you already have heard about magic so magnetic gradient induced coupling which is an approach that is being pursued in our lab and in other labs now to get rid of all the laser light and also have some interesting physical new features in the iron trap and I just want to point out so we have a string of ions typically a magnetic gradient applied and I showed you last week how you can individually address ions and that you get the spin-spin coupling between ions and then this allows you to get rid of all the lasers so typically hyperfine transitions are driven by Raman lasers and they use lots of optical elements and these lasers are typically controlled by radiofrequency sources and then you drive your iron so this is a large detour so this magic scheme allows you to get rid of all the laser stuff and drive directly the ions by using radiofrequency sources so that's a big reduction in complexity of your experiments and it leads partially to new physics okay so our qubit is a hyperfine qubit in a terbium so this has the simplest possible hyperfine structure total angular momentum zero and one and so the one state has three states actually and then we can put this in a magnetic gradient so we have our trapped ions they have all now a difference hyperfine splitting and we can address them in frequency space instead of position space and this is an example so we talk to this ion we do thousands of quantum gates with this ion and then we observe the crosstalk on all other ions and we do this for every possible combination of this quantum byte and then we get this crosstalk matrix here of interacting ions and the crosstalk is very small and so it's below a typical error correction threshold that is typically seen at 10 to the minus 4 but that's a matter of debate of course okay so that's individual addressing that we can do then we can since we have these three hyperfine states here with different dependencies on the magnetic field no dependency positive and negative scaling with the magnetic field of the energy we can also have so-called processor qubits so we need magnetic field dependence to have an interaction and we want no magnetic field dependence for for storage of quantum information so by having a stationary string of ions we can simply recode our qubit and go from a storage qubit to a processor qubit and vice versa and this I want to demonstrate using three ions so that's now three qubits and I symbolize them by these spins here and just to make it more clear the picture we put them not in a straight line but like this and then you have these couplings these mutual spin spin couplings and yeah so now to show you that we can have in a string of three ions simultaneously a memory qubit and the processor qubit I'll show you this data here so we look at i and i i and 1 and we look at the phase shift as a function of time the phase shift of this spin here as a function of time depending on the states of the other qubits so we flip the state of qubit 3 and we don't see any phase shift on i and 1 and here we flip the state of qubit 3 and observe the phase shift on i and 2 so there's a clear dependence so we can do conditional quantum dynamics and memories at the same time having a stationary string of ions so we do not even have to move this here but we can also couple them all simultaneously so all couplings are on at the same time and now we look at qubit 2 how its its phase is shifted as a function of the state of qubit 1 and 3 so you see both qubits 1 and 3 and state 0 you get this phase shift of qubit 2 then you look at this combination of 1 and 3 and you get this phase shift and then you have these two other combinations you get no phase shift so here you can see that the phase of this qubits depend the phase of this qubit depends simultaneously on the state of the other qubit so you have a simultaneous interaction okay and we you can even change the sign of the coupling by changing your basis so so if I use this basis for instance I get and then I measure the coupling matrix I get such a matrix here and now I change this qubit to this basis and then I get these minus signs here all of a sudden so by simply recoding my qubit I can change also the coupling constants okay and this has been yeah an important thing is all these operations are done by simple microwave pulses so in this case you do not move anything you do you don't have any lasers all you do is microwave pulses stationary string of ions and yeah and this has been used to implement coherent quantum Fourier transform with all these couplings on so you have single qubit gates you have conditional dynamics that's the important thing here and then what you can show in the end we look since it's a coherent UFT we have to look at the coherence of each qubit at the output so we do Ramsey experiments for different input states and compare them to theory and since we have no time I don't leave you time to look at these curves but theory and experiment agree well and then we can also measure the periods of a certain function so that's the use of the QFT and for instance in Charles algorithm this also works fine so and just to conclude this part so this is a complete QFT quantum algorithm and this is a single C0 gate and since we use the simultaneous coupling we can actually do the whole QFT in a time that we otherwise need would need for a single 2 qubit gate okay so this works very well and now the outlook yeah we want to go towards quantum simulations using spins and phonons using this and the scalable quantum computers on the agenda and this is vigorously pursued by the group of Vinny Hensinger in Sussex actually okay so thank you very much