 So, hi everyone. First of all, it's really great to be here, and I mean, I was a bit shocked and also amazed at how many people seem to be interested in quantum computing. For me, this talk is actually kind of special because it closes a circle. The first time I was at the CCC was in 2001, and back then I was still in school and I was coming here from my small town in southwest Germany. And when I arrived here, this was kind of like magic fairyland. So they were people doing all kinds of amazing things, like playing with electronics, picking locks, and there was one presentation as well on a Tesla coil, so to say. So, physics student showing around the Tesla coil that he made himself and like explaining the physics and how it worked. And this is kind of how I got very interested in all these kind of things in physics and finally took the decision to study that as well. So today I hope that with my talk, I will be able to instill in some of you also something similar, like an interest in quantum phenomena and quantum computing in general. Alright, so as I said, my talk will be about quantum computers. And some of the results, I will show you a lot of results from different groups. And some of the results are from my PhD thesis, which I did at the CACLE. So I want to just thank all of my former colleagues and my PhD advisors for their support during that work. Alright, so my motivation. So that's kind of the motivation for me to give this talk, because as you probably all noticed, there's a lot of buzz about quantum computers in the media. So every month there's an article on wired or on venture beat showing the latest results from like groups in quantum computing. And also now there was this big announcement that Google invests money in building superconducting quantum computers. So there's a lot of information floating around and all kinds of ranges between, yeah, quantum computers will like change everything for us or quantum computers are kind of hokum. They will never work probably. And what I want to do with this talk is actually to explain what quantum computing is, why we want it and how it works actually. So the outline first is to, yeah, as I said, show why we want actually to build quantum computers, then how to like solve some interesting problems with them, for example, cracking passwords. And afterwards I will show you how to build a very simple quantum quantum processor using superconductors, resonators and microwave signals. And finally I will show you some of the recent progress in quantum computing. All right, let's get started. So what is the history of quantum computing? Well, the beginning can be probably traced back to the 80s when physicists were already using conventional or classical computers to help them to simulate physical systems. And back then people were asking, they were seeing that it is actually pretty hard to simulate a quantum system with a classical computer. Somehow, as soon as you like add a little bit of complexity to your quantum system, the classical computer is no longer able to kind of simulate it. And in the famous conference, 1981, Richard Feynman, a physics Nobel Prize winner, gave a talk on exactly this subject, where he discussed how to build a computer that would actually be able to simulate quantum mechanics. And this is, so to say, the birth of the quantum computer as a concept. So in the beginning, this was really devised to help physicists to simulate a quantum mechanical system. If you now go one step further, you can of course see that, okay, a quantum computer seems to be more powerful than a classical computer because it can simulate quantum systems. So maybe it can also help us to solve some other problems, which are not of like physical nature, but some abstract mathematical things. And amazingly, the answer to this is also yes. And now I want to show you how this gets done, so to say. So to understand quantum computing, we first need to have a look at the basics of classical computing. And this will be very useful because later on we will use a lot of concepts that I will introduce you here, so it will help you to understand how exactly quantum computers do what they do. All right. So, as you probably all know, computers use bits as the basic unit of information. A bit is an assistant that has two states, zero and one. And it's kind of an abstract mathematical concept, but nowadays if you think of bits, you probably think of a voltage in a wire and a circuit. So you could say, okay, the state zero of your bit can be defined by having a zero voltage, a zero volt in comparison to like some ground state, and a bit one would have, for example, five volt. All right. To do useful things with bits, we need many of them. So we put them in a so-called bit register. Here the bits are enumerated from top to bottom. So there are n bits in this case. And if you want to write the state of the whole bit register, you can just kind of multiply them, the individual values together and write them like this. And you would see that for n input bits, you would have two to the n possible states. So it's a pretty efficient way to store information. Definitely better than using Roman literals. All right. Now you, of course, want to do something with your bits. So you need gates. And a gate is also an abstract concept, which is a function in that sense, which has one or several inputs and one or several outputs on the other side. And now for classical computing, there are some circuits which are so-called universal gates. For example, the NAND gate, which you see here, which has two inputs and returns a one for all the possible input states except if the two input bits are one. And this gate is universal in the sense that you can construct any other logic gate from this by using combinations and concatenations of this single gate. All right. So that's basically all we need to get started solving problems of our computer. Now let's have a look at a fictional problem. Let's say, for example, that our beloved leader wants to launch a missile. And of course, not everybody should have to write to launch missiles. So we need the password. And if you want to check now if the password is correct, we need somehow a function that does this for us. And this function, which is shown here in which I call fj, looks like this. So it has N inputs on the left and one single output. And it returns a zero for all of the inputs except for the one that corresponds to the correct passwords. All right. So this means that we have two to the N possibilities here. And if we make the input register large enough, we can have a pretty secure system. All right. Now imagine that we want to crack this password. And now there's several possibilities. We can of course try to reverse engineer this system and try to find out how the function f works. But now for this talk, let's assume that the function is secure and that we cannot do any kind of reverse engineering. So then the only way to obtain the password is to actually brute force it, which means that we have to try all the possible values of the password and see if the function returns one. And if you want a computer to do this, we have to teach him to do it. And for this, we use a so-called algorithm, which is basically a baking recipe that the computer can follow to obtain the solution. All right. So our algorithm is pretty simple. We would start by setting the register state to the first value, which is 0, 0, 0, 0, etc. Then calculate fi and check if the function returns a one. And actually for a lot of cases, when people choose 0, 0, 0, 0 as their password, it does. So in this case, our algorithm has terminated and we can directly return the password that we found. And for some other cases, for people that use a more secure password, we actually have to check the other values as well. So we increment the value by one and we go back to step two and repeat this until we find the password. All right. So now you can ask yourself how efficient this is actually. Well, it's pretty easy to answer because if we have n input states, we will probably have to check the password at most, the function at most n times. So in the best case, we would check it only once. And in the average case, we would check it probably n over two times. So if we plot now the number of evaluations of the function f versus the size of the search space n would get a linear relationship. So which means that if we double the size of the search space, we also have to double the number of function evaluations. And this is the so-called time complexity of this algorithm. And the idea behind this is that the cost that you have in cracking this password is in calling this function f, which can be really complicated. So you really want to measure how often you have to call this function to obtain the answer you need. All right. So please keep this in mind because we will see the graph again later in the talk. Okay. So that's all I wanted to tell you about classical computing. And now we're going to have a look at quantum computing. So again, I'm going to go through the basics of quantum computing first. So like for a classical system in a quantum system, we have also a fundamental unit of information, which is called a quantum bit or qubit. And as the name suggests, this is a quantum mechanical two-level system. Basically, it is also an abstract concept, but I find it really helps if you imagine it as an atom with two states, which I call here zero, and the second state one. And this atom has, of course, in a quantum mechanical state, which I indicate by putting this strange vector around the one. So whenever you see this symbol later in the talk, you know that I'm talking about a quantum state. All right. So now one of the strange things about quantum systems is that they can not only be in the state zero or one, but kind of in both states at the same time. So in this case, we wouldn't be able to like write the wave function of the state as a simple zero or one, but we would have to write it as a more complex function here, which I call psi, which is kind of a sum of the state zero with some amplitude A plus the state one, which has an amplitude one minus A. And in addition, some phase, which is a complex number here, and which kind of makes that we cannot only add the two states together, but we can also subtract them or do more complex things with them. Now, this is probably pretty hard to get your head around it, so at least for me. And I find it always helps to imagine this as a particle wave. So for example, here would have a particle or a wave that comes from the left. And this wave would encounter like a barrier with two holes in it. And then you would have like circular waves going out from these two holes. And here in this picture, this is also like a single system, but it kind of shows like strange interference effects. And the two waves here overlap, and depending on the phase of between them, they can kind of like subtract or like add themselves up. So I think this is a pretty good way to think about a qubit state as well. All right. The second difference to classical bits is concerning, concerns the measurement of quantum bits. So for classical computers, I didn't even mention how we measure them, because it's really trivial. We can just measure the voltage of our wire, and then we get the information if we're in the zero and the one state. But for quantum system, it's a bit more complicated, because in fact, whenever we measure the system, we also change its state. So let's assume that we have a measurement apparatus here, which is shown on the right, and we want to measure if the quantum system is in the state zero and one or one. So what we do is that we switch on some kind of interaction between the two systems. And what will now happen is that we will have a so-called collapse of the wave function, where the qubit state will get projected either in the state zero with a probability that's proportional to the amplitude of the state zero and the wave function, or into the state one with the complementary amplitude. So this is something that is kind of unique for quantum systems, and which we will encounter later, again, when we try to measure the results that we obtain using our quantum processor. All right, like for classical bits, we also need many qubits to perform useful operations. So we have a quantum register, and as before, we order the individual qubits from top to bottom and write their wave functions like this. And now if you want to write the wave function of the whole qubit register, we just multiply the individual wave functions together like this. And so since there are a lot of parenthesis there and it's kind of tedious to read, I will often just put all the terms in one parenthesis and write it like this. So when you see a state like this, you know that actually you have a multi-qubit state where each individual qubit isn't the state indicated by its letter. All right, a key resource in quantum computing is the fact that we can have so-called multi-qubit superposition states. So let's remember again, the two slides ago, we talked about the fact that a qubit can be in the state zero and one at the same time. So now let's imagine that we prepare a qubit register state where each individual qubit isn't an equal superposition between the zero and one state. So this I'll show you like here, and you can see the factor of 0.5 raised to the power of one over two is just a normalization constant. So now if I want to obtain the wave function of the whole register, I can again just multiply the individual wave functions. But now the difference is that I have kind of like a sum of products here. So if I want to like obtain the wave function, I have to like multiply out these parentheses. And if I do that, so we do the n times, if I do that, I will get a quantum state which looks like this. So you can see that we have here the state 0, 0, 0, 0 etc. Then you have the state 0, 0, 0, 0, 1 up to the state 1, 1, 1, 1, 1. So basically it means that in this register we have all the possible states of the qubits at the same time. And now this is pretty exciting and it's kind of a key resource that we can make use of when using quantum computers to solve problems. All right. And yeah, often since the terms are a bit tedious to read as well, I will just omit the normalization when I write a state. So you will often see them like this. Okay. Last thing we need to learn about for quantum computing is quantum gates. Like classical gates, quantum gates take a number of input qubits and produce a number of output qubits. The difference is though that now since we have a quantum mechanical system, the quantum gate also needs to perform a quantum mechanical operation. And this means that some things which are possible in classical computing are no longer possible in quantum computing, most notably copying qubits for example. But still, like for classical computers, they also exist the concept of a universal gate, which means that we can find a set of gates that will allow us to realize any classical gate operation with a quantum computer. Okay. Now, if you combine what we have learned about multi-cubate superpositions and quantum gates, we can see that if we apply our quantum gates to an input state, which is a superposition of all the possible inputs, then we'll get an output state which contains a product of the input state multiplied by the value of the function that we want to calculate for all these input states at once. So this is kind of magical because it means that we have evaluated this quantum function only once, but we have calculated its value for all the possible input values. So when people tell you that quantum computers harness the power of the multiverse, then this is what they usually mean, so-called quantum parallelism. All right. The last thing that we need to learn about is quantum entanglement. And this is a concept which can be understood like this. So assume that we have a two-cubate state where the first qubit is in the state zero, the second qubit is in the state one, and then we take these two qubits and we apply some function to them, which we call f here again. Now, the effect of this function is for this input state here which we have to return an input state which looks like this. So it's a superposition between the zero one state and the one zero state. And now this state looks pretty inertial, but actually it's kind of weird because as you might notice, we can no longer write the individual qubits separately. So we can no longer factor out the first qubit and the second qubit. So somehow both of them are kind of intertwined. And now if you would imagine that we would make a measurement of the first qubit, as we said before, the probability of obtaining either the value zero or one for the first qubit is 50 percent. So assume we obtain a one. And what is then really bizarre is that we seem also to have changed the state of the second qubit because now it's in the state zero. So this is kind of really weird and means that somehow there is like ghostly interactions between the two qubits, which makes that when I measure the first qubit or do something with it, it also affects the state of the second qubit. And now if you think that's weird, then you're in good company because Albert Einstein wrote a famous paper on this, so-called EPR paradox, where he argued that this must be a reason why quantum mechanics is incomplete. And in fact, this is actually, it's completely valid behavior and we can use this also to speed up computations when we use a quantum computer to solve problems. All right, so this was a lot of stuff to digest. So just let's do a small recap of what we learned. So we saw that qubits are quantum mechanical two level systems that it can be in a superposition between the state zero and one that a measurement of a qubit state will either zero or one and project the qubit in the respective state and that qubits can become entangled with other qubits. All right, so back to business. We still have to find the password for our missile launch system. Now let's imagine that we have a blueprint of the function that calculates the passwords and we are able to implement the quantum version of it. If we can do that, then we can, like before, produce a superposition of input states, calculate the function operator fj and then obtain the values of the password hashing function for all possible input states. And amazingly, of course, there will also be the value of the correct password in there. So now we have kind of almost solved our problem because we have calculated all the possible outcomes of the password hashing function. We have identified the state which contains the right password. Now the only thing that remains to be done is to get this state out of there. And now what we could do for this is just to try to measure the values of the qubit after applying the operator. But since I told you that a measurement will kind of change the qubit state and project it into one of the an arbitrary state of the superposition state that we have, the probability that we'll actually measure the correct state here is only 1 over n, whereas the probability that we will get some other state, which is not the solution to our problem, is 1 minus 1 over 1. So that's pretty bad news actually. And this is kind of the dilemma of quantum mechanics or quantum computing. Because you are able to evaluate a function for all possible input states at once, but you're not able to extract that information from the quantum state. So what can we do? Actually there's a solution for this. It's a so-called Grover algorithm, which was invented or discovered by Love Grover in 1996, and it gives us a way to extract the information from the quantum system. And the algorithm does that by applying a pretty complicated sequence of gates to the output state that we obtain after applying it to the function, and then repeating this square root of n times. So after doing this, we can then perform a measurement. And what the algorithm has done is to transfer all the amplitude to the state, which corresponds to the solution of our search problem. So when we now make a measurement, we will have a probability of almost 100 percent to obtain the correct answer, which of course is great. All right. Now if you have a look at the efficiency of this, we can visualize this for the case, for example, of 10 qubits. So for 10 qubits, the search space of our passwords is 1024. And we can now plot the probability of obtaining the correct solution after applying the Grover operator a number of times. And as you can see, in the beginning, the success probability is quite low. So it's less than 0.1 percent. But as we keep applying this Grover operator, the probability goes up, up, up until it reaches almost 100 percent after 25 iterations. And this is pretty great because it means that we have to evaluate our search function not 1,024 times, but only 24 times to obtain the correct solution. So if we go back to the graph from before, where we have plotted the time complexity of our classical algorithm, we can now compare that to the quantum algorithm. And we can see that the quantum algorithm is actually much faster for this kind of problem, because it only needs a square root of n attempts or evaluations of the function to find the correct solution. And so when people tell you that quantum computers are faster than classical computers, what they actually mean is that for some problems, quantum computer exists algorithms on quantum computers that have a smaller time complexity than the best known algorithms for classical computers. And the difference between the classical algorithm and the quantum algorithm is the so-called quantum speedup. In this case, it would be so it would be a quadratic speedup, as you can see. And now I use this example because it's pretty easy to explain. And it's also something where we can prove that there is no better classical algorithm. But most of you probably know quantum computing more from code breaking or from so-called shore algorithm. Because most classical asymmetric cryptological methods are based today on the fact that it's pretty easy to obtain a number by multiplying two large prime numbers together. But it's pretty difficult, on the other hand, to obtain the individual prime factors of that number from the multiplied one. So the best classical algorithm for this problem is kind of sub-exponential. It looks like this. Whereas for a quantum computer, we have an algorithm, so-called shore algorithm, which can solve the problem in logarithmic and to raise to the power of three times. And this is actually a pretty big difference because it can make, it can change the runtime of such an algorithms from millions of years to a few hours. But contrary to the search problem that I showed you before, there's actually no, or to my knowledge, there's no proof that for a classical computer that doesn't exist a better algorithm. So here we cannot really say that quantum computers will always be faster than classical computers because we really don't know if we can find a better algorithm for a classical computer that could solve this problem faster. Okay, so sorry if this was a bit theoretical. So I promise no more equations in this talk. And now I want to show you how you can actually build a quantum processor. And well, there are actually many different answers to this question. And I talked before about qubits as kind of atoms. And that's a good analogy because there are actually people or research groups that are using atoms that they trap in an electromagnetic trap, which is shown here, and use them as qubits. So this photo here is from a research group in Innsbruck. And what they do is that they trap a number of ions in a so-called pow trap. And they can put these ions inside there like pearls on a string and then manipulate them using laser light. And since the atoms are also coupled to each other by the vibration mode of the whole system, you can perform quantum gates between individual ions. And so this is a pretty successful and pretty nice way to perform quantum computing. And the largest system that I built today with this kind of approach and compass about 50 to even 100 qubits. All right, so what I want to talk about today, though, are superconducting quantum processors. Like the one I show here, which is from the University of Santa Barbara from the research group, which just announced a collaboration with Google to build quantum processors. So as I said, these quantum processes are realized using thin layers of superconductors on microchips. And for those of you who don't know what a superconductor is, it's basically a metal, or in most cases a metal that loses all of its electric resistance at a very low temperature, and which at that temperature also exhibits quantum mechanical behavior. And superconducting quantum bits are quite attractive because the reasoning is here that if you manage to build a few of them and you manage to make them really good, it would be really easy to scale the number of qubits to a very large amount because you can just fabricate them like we fabricate most of the microchips today. And of course, there are many more technologies that allow to build quantum processors. For example, there are nuclear magnetic resonance spins, there are quantum dots, even both Einstein's condensates can be used to realize quantum bits. So I just want you to take away that superconducting quantum processors and iron trap quantum processors are not the only approaches to quantum computing. All right, now I want to briefly talk about a very simple two qubit quantum processor I built during my PhD thesis, and this processor uses so-called transmon qubits, which are an invention of a research group in Yale from 2004. And what I show you here is an electron microscope image of the whole qubit chip. And this is actually a nice system to discuss the basic blocks of quantum processors because it contains all the elements that you would also need for a larger scale quantum processor. So you can see that the chip is about 20 millimeters in size. And it's realized in a material called niobium, which is a metal that also becomes superconducting at about minus 264 degrees. And on the chip, you see a lot of coplanar waveguides, which we can use to send microwaves to the qubits, and some other signal lines which we can use to perform other operations with them. And so if you ask yourself where the qubits are actually on the chip, the answer is here in the center. So you can see two of them. And in the zoom-in, you can actually see, well, you probably can't see it very well here because the contrast is not very high. But it's a large capacitor that is realized in aluminium, which also is a superconductor, and which basically acts as a support for our qubit. And the qubit itself is then on the top of this capacitor, and it's so-called jussison junction, which basically is just an element that consists of two thin layers of superconductor separated by an insulating barrier. And it's what we call a bad contact because under normal conditions, there couldn't be any current flowing to the system. But when the system becomes superconducting, we have a superconducting wave function. And the wave function can somehow tunnel through the barrier, and there can be a supercurrent flowing between the two sides of the structure. And now the qubit itself is realized as different states of this system here, which we call also an artificial atom because it kind of has a ground state and a few excited states that we can control using microwaves, actually. So the difference is here that the frequency of the qubit is compared to an atom much lower and in the range of a few gigahertz. All right, yes, the phase difference. And as I said, we can, sorry for the cheesy animation, we can manipulate the qubits using microwave signals, which we send to them through this snake-like structure, which in fact is a coplanier wave guide resonator. You can think of this probably as a guitar string, which when we like excited would vibrate at its own eigenfrequency. And the function of this resonator here in the qubit chip is actually two-fold. On one hand, it isolates the qubit from the environment and protects it from the noise. That is, for example, coming from the input line. And on the other hand, it also allows us to measure the state of the qubit after we have performed some operations on it. All right, now I talked about two qubit gates earlier. So in order to do them, we need some kind of interaction between the two qubits. And what we do for that is that we put a very small capacitor between them, which kind of couples them always when they are the same frequency. So that means by changing the frequencies of the qubits, which you can do by changing the current in these lines here, we can bring them in and out of resonance and realize two qubit gate operations with them. All right, so that's basically it. Now to operate this chip, we first glue it to a special microwave PCB, which also contains coplanar waveguides that we can hook up to our equipment. Then we take this whole thing and mount it in a sample holder whose main function is to also protect the qubits from any stray electromagnetic fields and also to anchor it to the dilution cryostat. The dilution cryostat is basically shown here. So the sample holder gets attached to the bottom of that. And what this thing is is basically just a very fancy refrigerator, which cools down the qubit to about 20 millikay, which is at minus 274 degrees Celsius, just slightly above absolute zero. And we have to do this because on one hand, the superconductors wouldn't be superconducting if we were at room temperature. And on the other hand, if we would operate our qubits at room temperature, we would find that the thermal noise and the thermal excitations of all the materials that are around the qubits would destroy the quantum state of them really fast. So we really, really need to cool them down to a very low temperature to be able to operate them for a sufficiently long time. All right, so that's the short version of how to build a quantum processor. The long version takes about two years and lots of microwave calibrations and chases for superconducting leaks and stuff. So what I want to show you here are just the results of one of the experiments we ran with this two qubit processor. And what we basically did here is to run the Grover search algorithm, which I showed to you earlier for the case of two qubits. So it's really not a practical problem that you want to solve, but it kind of demonstrates all the abilities that you need to build a large-scale quantum computer, because it contains single qubits gates here, for example, for what you used to create the input superposition state. And it also contains multi-qubit gates. For example, here we have the so-called I SWAP gate and two single qubit rotations, which together implement the function fj that we talked about earlier. And in this case, the function fj marks the state 00 as the password or as the solution of our problem. All right. Now for the two qubit case, the Grover operator has to be applied only once to the state to obtain the solution. So these two gate operations there do this. And afterwards we can just then measure the qubit state and see if the algorithm has worked, so to say. Now you can see the pulse sequence of this gate operation here. What you see there is actually the time on the x-axis, on the y-axis, the amplitudes of the microwave signals that we send to the qubits, which we show in green, as well as the frequency changes of the qubits, which we show in red. So you can see here that in the beginning we have the two microwave pulses that create the superposition. Then we have an interaction between the two qubits where we perform our two-qubit gate. Then we separate them again, perform some more phase manipulations. Then we bring them in resonance again for the Grover operator. And finally we change the frequency and we measure out their state. All right. So now we want to see how successful we are actually at doing this. We can run this gate sequence, which takes about 200 nanoseconds and do that a lot of times and then just average the results to obtain some good statistics. And we have done this for the case of this function f00. And what we see here is the success probability, so to say, or the probability to obtain different output states as a function of the search function that we are looking for. And you can see here that for this case of the functions f00, the success probability is about 67%, which is less than 100% what we would expect. And I will explain to you why later. So to be more scientific, we have to repeat that not only for this case of the function f00, but also for the other possible search functions. So we do that and every time we calculate the success probability afterwards and we see that for all the four cases we are above 52% or 50%, sorry. And this is pretty nice because 50% is the so-called classical benchmark against which we can compare our quantum processor. Because if you would think of an algorithm, a classical one, that gives you a solution to your 4-bit search problem, then you could think of an algorithm that like evaluates this function once, which has a probability of 25% of yielding the right answer. And if it doesn't find the right answer, just takes a lucky guess and returns some of the other remaining tree states. And so this is what I call here the I'm feeling lucky bonus because the success probability of this classical algorithm would then be 50% and this is what we measure our quantum processor against. So you can see that for this simple case, we can actually achieve quantum speedup in an experimental quantum processor. All right. So now you probably ask yourself, why can't we just scale that up and build a quantum processor with like a thousand or 10,000 qubits? And actually, there are several problems which keep us from doing that. And a few of them I listed here. So the biggest one for the quantum processor, which I realized during my PhD, is so-called decoherence. And decoherence means that basically the qubit is not only manipulated and measured by our own signals, but also by other quantum systems, which are in the vicinity of the qubits, for example, on the chip itself or in the dilution cryostat. And these quantum systems manipulate the qubit state and also perform a measurement on it. And as we've learned before, a measurement destroys the quantum state. So what this does is basically it kills the state of our qubit in a pretty short amount of time. For the processor, which I realized this was on the order of a few hundred nanoseconds. Okay. Then the second problem is the gate fidelity and the qubit-qubit coupling. For the case of two qubits, it's actually pretty easy to devise a coupling scheme where you can perform gates between the different qubits. But now if you would scale up the number of qubits, you would see that it's pretty difficult to switch on and off the interaction between two individual qubits with high fidelity. It's kind of like if you have a phone line with a certain frequency bandwidth and you want to have, for example, 100 or 1000 subscribers on it. And if every subscriber takes some amount of the bandwidth of the line, at some point you will have no bandwidth left for new subscribers. And this is kind of what happens with the qubits here. At a certain point we have used all our frequencies that are available for the qubits and we cannot longer add new qubits without kind of interfering with the other ones. So the same goes also for measuring the qubit state, because in our case we can perform a measurement of the qubit and get the correct result with a probability of about 90%. But this means, of course, that in 10% of the cases we cannot reliably measure the state of the qubit, which is also for this kind of a system a big problem. All right. And of course there are some other problems which I want to talk in detail here, which for example concern the reset of the qubit. So for quantum computers it's actually pretty hard to reset the state of your machine to zero. And this is also like a problem which has to be solved and which is not fully solved in practice yet. Okay. So I want to finish this talk with a small outlook on our small summary of the recent trends in superconducting quantum computing. Now there are several groups in the world that are trying to improve the state of quantum processors and help to really build a large-scale quantum computer. And here I show you an image of the research group at the University of Santa Barbara in the Jamar Chines lab, which recently partnered up with Google to build quantum processors. And what they are doing is basically to devise new types of architectures that also use transform qubits like the ones I showed you before and resonators. But that couple these elements in different ways that makes it easier to produce a large number of qubits on the same chip and actually get a real quantum computer out of that. So these approaches are for example called rescue or surface code architecture. Okay, then you can as well think about improving the qubits themselves and the resonators. And some groups, for example in Yale and Delph and in other places around the world, are doing this by replacing these coplanar wavecard resonators that you see here on the left by actual 3D resonators, which are boxes of aluminium that can also resonate at microwave frequencies. So here for example we see a system that has a 3D cavity resonator with two qubits which are placed on a sapphire substrate. And the advantage of this is that you can control the environment and fabrication parameters of the qubit to a much better degree than you would be able to do with normal microchips. So the coherence times and the lifetimes of the resonator or the quality factor of the resonator in this case is much better than for these so-called 2D qubits. Another thing which some groups are working on is called quantum error correction because you cannot only say okay let's build better qubits but you can also say let's work with bad qubits but devise algorithms that can help us to correct errors if they occur. And amazingly this is actually possible even with quantum bits and there are several approaches where groups devise quantum processors that can to some degree correct errors and like keep the quantum state of the qubits alive for an indefinite amount of time although the results which are obtained here for example in the Yale group are not yet at this point. All right the last thing is then to instead of using a normal solid state or superconducting qubits to use different quantum systems to to store or process quantum information. So here for example I show you work from the group in the clay which is a hybrid quantum system that uses a diamond with so-called NV senders which are nitrogen vacancy senders in diamond which actually are responsible for the color of this this diamond and which amazingly can store quantum information. So what we do with the system is that we have a qubit and when you want to manipulate the state of the qubit you keep the state on the chip but if you want to store it you can transfer it to the NV sender in the diamond and keep it there for a long time without having any interference or any decoherence in the qubit state. All right so as you can see there's a lot of research going on in this domain and you could actually plot kind of a Morse law for quantum computers or superconducting quantum computers and if you do that you would see that when we said when the research started on this subject in 1999 the qubits that we had at the time had a coherence time of less than one nanoseconds so they were really really primitive by today's standards and in the recent in the following years in 2002 and 2004 there were new types of qubits devised which had a much longer coherence time and actually is trend of increasing the coherence time of the qubit seems to go on at a similar or like a pretty fast rate until today. So in 2013 we have actually superconducting qubits that have coherence times in the order of a few hundred microseconds which is large enough to envision to actually use these qubits for for real quantum computing. So the takeaway here is probably that quantum computers are coming but there's still of course many many engineering challenges that we have to overcome and maybe to end this talk in a slightly political way the bad news is that probably the quantum computers will come to the hands of all the wrong people because right now it's mostly the research in qubit quantum computing is mostly funded by governments and big corporations so this technology when it will become available will definitely not be available in like a democratic fashion to everybody. So all right that's basically all I wanted to say I just wanted to point out that if you're interested in quantum computing and hybrid quantum systems there's a talk on it tomorrow diamonds are a quantum computer's best friend which is at 1245 in hall six by Nicolas Wuerl. Okay so with that I thank you and I'm open for question. Thank you for your talk we now have 15 luxurious minutes of Q&A so please line up at the mics there's six mics one two three four five and six in the back. We also have the ISC and twitter as I said before if you're physically unable to move as in not just caffeine deprived but actually not able to stand up then please raise your hands we have a backup mic for you. Okay mic one go ahead. Hello thanks for the very interesting talk I've learned a lot into the mic. Oh sorry well first of all thanks for the very interesting talk I've learned a lot and if I understand it correctly quantum computing is at the moment limited by the amount of qubits you can have interact with each other plus the amount you can keep the qubit stable. Do you have any idea at what amount of time and what amount of qubits quantum computing can reach a level where it can actually compete with normal computing in say doing error say calculations etc. That's a very good question and the answer to that is a bit complicated but in fact what you want to achieve with quantum qubits is the so-called error threshold because as I talked about there's a possibility to perform error correction with qubits so if you are below a certain level of errors for each individual operation that you perform on a qubit you can basically correct that away and have a system that works perfectly on the raw conditions so and for classical approaches or like the traditional approaches to quantum gate computing this error threshold was pretty low at the order of like a few fractions of a percent but with new approaches like for example the surface surface coding approach this error threshold has actually moved up quite a bit to a few percent so today it would actually be invisible to to have qubits that are good enough to build real large-scale quantum computers although as I pointed out there are still a lot of other challenges which keep us from doing that okay does that answer your question yeah yeah it does thanks does the internet have a question yes there are two questions the first question is in your example we got the right answer with a probability close to one by applying grover's algorithm is this true for other quantum algorithms also so there's a small probability of getting wrong results for most quantum algorithms yes this is the case because most of them are so called probabilistic algorithms which give you the right answer to a problem with a certain probability that is close to 100 percent but not necessarily 100 percent so in this case it could be the case that we get the wrong answer in which in which case we just have to to like repeat the process and check again of a couple of times so yeah and I mean there are a lot of quantum algorithms and I don't know them also there might be some which are more deterministic in that sense but to my knowledge most of the quantum algorithms are probabilistic by nature number six that's you hi thank you very much for your talk I have a pretty layman question conventional computing units in order to make them better you either increase the density get more bits right or you make them faster or you elder the instruction set in some way which of these are feasible for quantum computing I mean you answered a bit with probably can answer it so I think today the biggest challenge in quantum computing is not like having higher packing densities of qubits on a chip so I think it's really more having the ability to even like produce a large number of qubits regardless of the of the size of the structure so I think in that sense we wouldn't it wouldn't be like a very high priority to optimize the the packing or like the size of the individual qubits on the the chip and I think it's more about if you talk about like the performance you can also of course of course try to decrease the the amount of time you need to for example perform quantum gates and this can be done by increasing the the frequency of the qubits and also increasing the coupling between individual qubits which will though also increase the arrows because there will also be arrows in cured when you like bring the qubits in and out of coupling so it's always like compromise between speed and reliability or fidelity so to say thank you answer your question yeah thank you very much okay we have a question from a camera angel yes thank you what do you think about linear approaches for quantum computing based on linear optics so in principle the photon is a pretty nice unit because it's basically free from decoherence and there are a lot of approaches in 2002 with free space optics and now they are being integrated into one chip and what do you think about these approaches I'm not a not an expert in optical quantum computing so I don't want to comment on that too much but I mean as I said before there are many approaches to quantum computing and as of today the rays is still open on who will build the first working quantum computers and if I would have to bet I would bet either on like iron trap quantum computers we saw before or like superconducting qubits but of course the optical systems and photonic qubits are also very interesting and they could prove to be a viable alternative in case we should meet like a roadblock with either superconducting qubits or another technology so I think it's yeah every technology that can realize qubits is worth checking out and then you have to like measure it against like different criteria for example how far how easy is it to like make a large number of qubits how easy is it to couple qubits with each other and how good is the fidelity when you realize individual qubit operations so these are really the criteria that you want to measure against I think yeah maybe we can chat about this later sure yeah we'd love to yeah number two please hi when you have your interference problem with the with the frequencies isn't this a question of using a more complicated probability space maybe you can get around that okay what problem are you referring to when you have a you have a scaling problem if you add a lot of qubits and you don't have enough frequencies for them yes okay now I see yeah I mean the problem with our qubit processor was that the coupling scheme was really very simple as I said as I showed it was just a capacitor that coupled the qubits to each other whenever they were the same frequencies and these architectures for example the one here at the University of Santa Barbara use more intricate coupling schemes that rely on like different qubits being isolated from each other by multiple resonators so the coupling factor or like the coupling strength in these approaches goes down much faster when you change the frequencies of the qubits than in our case so these approaches are kind of more reliable and yeah better suited to like realize a large number of qubits I would say so they are yeah definitely lots lots and lots of approaches that you can can can try to yeah to do why don't people use better superconductors because we can do much better than 20 mk by now yeah well I mean the the temperature is really not not the the worst problem that we have and yeah so we operate at low temperatures mostly because we want to avoid the thermal excitation of the qubit and like noise and like changing the material of the superconductor would be possible but it would also be very complicated because for those materials I showed you aluminium and niobium they are actually very good fabrication processes in place which have been optimized for like 10 20 years and if you would take a new material it would be probably quite tricky to get like a film of the same quality and yeah all right cool okay okay internet please um how many qubits would be necessary to crack a 2048 bit rsa key oh that's a really good question and I don't want to lie to the uh to you now but uh I mean to my knowledge the number of qubits that you need to solve this problem goes linear with the problem size so you would also need of the order of 2000 something bits there so as as many bits at least as as you have bits in the number that you want to crack but this could of course vary by a factor by a constant factor of two or three depending on how many more bits you need for things like error correction and other stuff so but I would have to really I can look it up in the in the shore algorithm to give you an exact answer on this number five hello hello um I was wondering the the talk seemed like the the direction of the research is how we can use quantum computers how to solve the problems that we have with normal computers today um but the but the the thing that uh white crypto was doing usually is to create problems that are hard to solve is there research in that direction too uh yeah of course I mean the basic thing about quantum computing is that with as I said with the quantum computers we are able to solve some of the hard problems that we use for cryptography today much faster than with the classical computers so this kind of eliminates the security we have in these methods and there is some a lot of research actually and on post quantum cryptography I mean I think there was a talk here on that as well but I'm really not an expert in that subject and I wouldn't like comment on that now so but yeah definitely there's a lot of a lot of going on also when it comes to like quantum cryptography itself okay thank you number four hi um I'm curious to know what your thoughts are on uh in the future in a world where a lot of these hurdles have been removed where we have quantum computers that can work with meaningful numbers of qubits and relatively widespread access to this technology what do you think um you know some of the most promising uh applications of this technology would be so for me personally um I don't think that cracking passwords or reading people's email is like the the thing where we should build quantum computers right for me it's mostly the ability to simulate quantum systems because if you even if you look today at conventional electronics um for example a processor you would see that the the size of individual transistors comes down really fast and approaches the limit where we actually have a transistor that would consist only of a few atoms so such a system would would by definition have quantum mechanical behavior and if you want to understand and simulate these systems we will definitely need quantum computers to do that also there are many other applications for example protein folding and like biology genetics etc which would require a profit from this kind of computer so it's for me it's really not about cracking codes but about like doing science with that yeah thank you number one one one oh thank you uh what I would like to know is um you've you've in the popular press I've always heard that uh scaling to a larger number of bits is uh is hard and I I assumed that this was because when you get too big they they don't uh interfere with each other anymore um today I'm taking away that um the the errors the the the noise is a big problem and that the retention is a big problem um and in the beginning you mentioned that the ion trap has up to a hundred qubits already yes can you can you say more about this ion trap thing and and what its parameters are and and why you're going in this way if the other one is already so far so um yeah as I said I'm not an expert on ion trap quantum computing but the qubits which they have there are really very good quality because the coherence time can be in the range of seconds and the speed of operation can also be comparable to that of superconducting qubits so you can have gates which operate in like nanoseconds or microseconds and you can also have a readout fidelity so um the so to say the success probability when you read out the given qubit state which approaches like 100 percent by uh like several like yeah six digits or so so um these systems definitely seem to be very promising um what kind of uh could be a problem is probably the scaling because um if you go to a very large number of qubits you would have to somehow accommodate them inside a trap inside an electromagnetic trap which which could be tricky but also for this problem there are solutions devised today for example you have like uh atom traps which are on a ship uh so you can really take individual qubits or atoms or ions if you like like and shuffle them around on the chip and transport them to to to other other sides and like that like isolate them from each other so um as I said for me the race is completely open and right now ion trap computing seems to be ahead but this could change of course if we keep improving the superconducting qubits uh like we did in the last 10 years so number six number six hey um as you told at the moment we still use the binary system with two level systems but we are not um we can use higher level systems are any thought experiments to overcome the binary system with higher level systems um yeah you could of course do that and in fact um we did experiments where we used also the the second and the third energy state of the qubit to have like a like a higher order base for our calculations um but this is usually not done because uh the the speed up or like the the gain in information that you that you achieve there is not exponential so you could say that if you have lower for example a quantum system of three states you would have a uh a state space which is three to the power of n for n qubits whereas for the two qubit state it would be two to the power of n so it's still a big difference but it's not going like like it's not the number that that we change is not in the exponent so to say so um that's kind of why that kind of why most people don't do it okay thanks mm-hmm okay we are out of time i'm very sorry but i'm sure you can find andrea's outside later thank you again please oh we have seen you