It looks like you're having connection troubles. Reconnect now.
01/13/2021 14:14:31
31c3-talk-6261 Latest text of pad 31c3-talk-6261 Saved Jan 13, 2021 |
Hallo Du!
Bevor du loslegst den Talk zu transkribieren, sieh dir bitte noch einmal unseren Style Guide an: https://wiki.c3subtitles.de/de:styleguide. Solltest du Fragen haben, dann kannst du uns gerne direkt fragen oder unter https://webirc.hackint.org/#irc://hackint.org/#subtitles oder https://rocket.events.ccc.de/channel/subtitles erreichen.
Bitte vergiss nicht deinen Fortschritt im Fortschrittsbalken auf der Seite des Talks einzutragen.
Vielen Dank für dein Engagement!
Hey you!
Prior to transcribing, please look at your style guide: https://wiki.c3subtitles.de/en:styleguide. If you have some questions you can either ask us personally or write us at https://webirc.hackint.org/#irc://hackint.org/#subtitles or https://rocket.events.ccc.de/channel/subtitles .
Please don't forget to mark your progress in the progress bar at the talk's website.
Thank you very much for your commitment!
======================================================================
So hi, everyone. Um, 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 seemed to be interested in quantum computing. For me, to stock is actually kind of special because it closes a circle. Um, 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. Um, and when I arrived here, this was kind of like Magic Fairyland. So there 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, I recall 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 and physics and finally took the decision to study that as well. So today, I hope that with my talk, I would be able to to like instill in some of you also something similar, like like an interest in like interest in quantum phenomena and quantum computing in general. All right. So as I talk with you about quantum computers and some of the results will show you a lot of research from different groups. And some of the results are from my PhD thesis, which I did that basically. So I want to just thank all of my former colleagues and my Ph.D. advisors for their support during that work. All right, so much of it. 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 is an article on Wired or on VentureBeat showing the latest results from like groups and 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 it all kinds of ranges between quantum computers were like, change everything for us or quan
tum computers are kind of hokum. They will never work, probably. And what I want to do this talk is actually to to explain what quantum computing is, what we wanted and how it works, actually. So the outline for us is to. Yeah, as I said. Sure. 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 computer 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 it, a little bit of complexity to your quantum system. The classical computer is no longer able to to kind of simulated. And in a famous conference in 1981, Richard Feynman, physics Nobel Prize winner, gave a talk on exactly this subject where we 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. From the beginning, it was really devised to help physicists to simulate quantum mechanical system. And if you now go one step further and you can, of course, see that 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 how this gets done, so to say so, to understand quantum comp
uting, 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 to you a year or so. It will help you to understand how exactly quantum computers do what they do. So, as you probably know, um, computers use bits as the basic unit of information A is a system 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 way a voltage in a wire in a circuit. So you could say, OK, stage zero, if you bid, can be defined by having a zero voltage as zero zero volt in comparison to like some ground state. And bit one would have, for example, Five-fold. All right. To do useful things with bits, we need many of them, so we put them in a so-called register. He had a bizarre, um, enumerated from top to bottom. So there are bits in this case. And if you want to write the state of the whole wheat register, you can just kind of multiply them. The individual is together and write them like this. And you would see that for an input. Bitzer You would have two to the N possible states. So it's pretty efficient way to store information. Definitely better than using Roman literals. All right, now, you, of course, want to do something with your boots, so you need gates and a gate is also a abstract concept, which is a function in that sense, which has one or several inputs and one or several outputs on the other side. Now, for classical computing, there are some circuits which are so-called universal gates, for example, the nannygate, which you see here, which is two inputs and returns, one for all the possible input states, except if the two input Bitzer one and this Gateson universal in the sense that you can construct any other logic from this by using combinations and concatenation of the single gate. All right, so that's basically all we need to get started solving problems of our computer. No
w let's have a look at a fictional problem. Let's say, for example, that our, um, beloved leader wants to launch a missile. And of course, not everybody should have the right to launch missiles. So we need the password. And if you want to check now, if the password is correct, we need somehow function that the justice for us and this function which is shown here and which are called F.J. looks like this. So it has an input 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 to to the end possibilities here, and if you make the input register large enough, we can have a pretty secure system. All right, now imagine that we want to to correct first password and now there are several possibilities. We can, of course, try to reverse engineer the system and find out to try to find out how the function works. But now for this dog, 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 a 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 a solution. All right. So our algorithms, pretty simple, would start by setting the register straight to the first volume, which is zero zero zero zero, etc. Then calculate F.I. and check if we return, if the function returns of one. And actually for a lot of cases, when people choose a zero zero zero zero as their password, it does so. In this case, our algorithm is 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 to check the other values as well. So we go as
incremental value by one and we go back to step two and repeat this until we find a password. All right. So now you can ask yourself how efficient this is actually. Well, it's pretty easy to answer because if you have an input state, we will probably have to check the password at most to function at most end times. So in the best case, we would check it only once and then the average case we would check it probably another two times. So if you plot now the number of evaluations of the function F versus the size of the search space and would get a linear relationship, so which means that if we doubled 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 us is that, um, the 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 for because we will see the graph again later in the talk. OK, so that's all I wanted to tell you about classical computing, and now we are going to have a look at quantum computing. So, again, I want to go through the basics of quantum computing first. So, um, like for a classical system in a quantum system, we have also a fundamental unit of information, which is called the quantum bit cubed. 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 a as an atom with two states, which I call zero and the second third one. And this atom has, of course, a quantum mechanical state, which I indicate by putting this strange vector around the one. So whenever you see this disembodied underdog, 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 understood zero or one, but kind of in both states at the same time. So in this case, we wouldn't be able to, like, ride the wave function of the the state as a as a simple zero or one. But we would have to write as a more complex function here, which I could say and which concert, which is kind of a sum of the state zero with some amplitude, a plus the state one, which is an amplitude one minus eight. And in addition, some phase, which is a complex number here in which kind of makes that we can only add the two states together, but we kind of can also subtract them or do more complex things with them. And 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 wave that comes from the left and this wave would encounter like a barrier of two holes in it. 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 substract or like add themselves up. So I think this is a pretty good way to think about it. Cubit state as well. All right, the second difference to classical bits as concerning some measurement of quantum bits, so, um, 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 of ground zero on the one side. But for quantum system, it's a bit more complicated because in fact, whenever we measure the system, we also change the state. So let's assume that we have a measurement apparatus here which is shown on the right, and we want to measure the state of the quantum system in the state 011 or one. So what we do is that we switch on some kind of interaction between the two systems. And wha
t will now happen is that we will have a so-called collapse of the wave function where the Cuban said we get projected either in the state zero with a probability that's proportional to the amplitude of the state zero and the wavefunction 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 to measure the results that we obtain using our quantum processor. All right, um, like for Classico, but we also need many cubits to perform useful operations, so we have a quantum register and that's before we order the individual cubits from top to bottom and right away functions like this. And now if you want to like, um, right. The function of the whole Cubitt register, we just multiply the individual functions together like this. And so since there are a lot of vertices there and it's kind of tedious to read, I will often like just ah put all the terms in conference and write it like this. So when you see a state like this, you know that actually you have a multi cubitt state where each individual cubit is in the state indicated by its letter. All right, a key resource in quantum computing is the fact that we can have so-called multi superposition states. So let's remember, again, the two slides ago we talked about the fact that a cubit can be in the state 091 at the same time. So now let's imagine that we prefer a Cubitt registered state where each individual cubit is in an equal superposition between zero and one state. So this is show you like here and you can see the factor of zero point five of one or two is just the normalization constant. So now if you want to obtain the wave function of the whole register, I can again just multiply the individual 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 very function, I have to multiply out these four entities. And if I do that. So to t
he end times, if I do that, I will get a quantum state which looks like this, so you can see that we are fuda states, zero zero zero zero, etc. Then you have to state zero zero zero zero one up to the state one one one one one. So basically, it means that in this register we have all the possible states of the cubits at the same time. And now this is pretty, pretty exciting and it is kind of a key resource that we can make use of when making when using quantum computers to solve problems. All right, and you often are, since the terms are a bit tedious to readers. Well, I will just admit to normalization when I write a state. So you will often see them like this. OK, last thing we need to learn about for quantum computing is Quantum Gate, like classical gates, quantum gates take a number of input cubits and produce a number of output. Hubert's. 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. And quantum computing, most notably copying qubits, for example. But still, like for classical computers to also exist, the concept of a universal gait, which means that we can find a set of keys that will allow us to to realize any classical gate operation with a quantum computer. OK, now, if you combine what we have learned about multi keyboard super positions and Quantum Gate, we can see that if we apply our quantum gate 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 inputs state 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 har
ness the power of the multiverse, then this is what they usually mean. So 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 we understand like this so soon that we have to cubitt state where the first cubit is instead zero. The second Cubitt is in the state one. And then we take these two cubits and we apply some function to them, which we call F here again. Now, the effect of this function is to allow for this input state, which we have to return, and an output state which looks like this. So it's a superposition between the zero one state and the one zero state. And now the state looks pretty innocuous. 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, like, factor out to the first Kuban in a second cubed. So somehow both of them are kind of kind of intertwined. And if you would imagine that we can would make a measurement or the first Cubitt, as we said before, the probability of obtaining either the value zero or one for the first Kupets is 50 percent. So assuming we obtain a one and what is then then really bizarre is that we seem also to have changed the state of the second Cubitt because now it's in the state zero. So. This is kind of kind of really weird and means that somehow there is a likely, like ghostly interactions between the two cuboid, which makes that when I measure the first of it or do something with it, it also affects the state of the second cubitt. 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, 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 a lot of stuff to t
o digest, so just to a small let's do a small recap of what we learned. So we saw that Hubert's are quantum mechanical two-level systems, that it can be in a superposition between the state zero and one that a measurement of Cubitt state will either zero one and project a cube within the respective state, and the Cubans can become entangled with other qubits. All right, so back to business, we still have to find the password for for a 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 F.J. and then obtain the values of the password hashing function for all possible input states. And amazingly, of course, they will also be the value of the correct password in there. So now we have kind of almost solve our problem because we have calculated all the possible outcomes of the consultation function. We have identified the state which contains the right password. Now, the only thing that remains to be done is to get the state out of there. And now what we could do for this is just to try to measure the values of the cubitt after applying the operator. But since I told you that a measurement were kind of changed to Cuban state and projected into one of the an arbitrary state of the to superposition state, that we have the probability that we'll actually measure the correct state here is only one over. And where is the probability that we will get some other state, which is not the solution to our problem is one minus one over one. 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 as ones, but you are not able to extract that information from the quantum state. So what can we do? Um, actually, there's a solutio
n for this and the so-called Grover algorithm, which was invented or discovered by 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 end times. So after doing this, we can then. A performance 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 cubits. So for 10 cubits, the search space of our passwords is one thousand twenty four. 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 probability is quite low. So it's less than zero point one percent. But as we keep applying this Grover operation operator, the probability goes up, up, up until it reaches almost 100 percent at after 25 iterations. And that's pretty great because it means that we have to evaluate a search function not one thousand twenty four times, but only 24 times to obtain the correct solution. So if we go back to the graph from before we apply to 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 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 exist algorithms on qu
antum computers that have a smaller time complexity than the best known algorithms for classical computers. And the difference between the classical algorithm and quantum. Isn't this the so-called quantum speed-up? In this case, it would be so it would be a quadratics beat up, 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 the so-called short algorithm, because, um, most classical as a metric krypto cryptologic methods are based today on the fact that it's pretty easy to obtain a number by multiplying two large 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 exponential and looks like this, whereas for a quantum computer we have an algorithm so called your algorithm, which can which can solve the problem and logarithmic and to restore the power of tree time. And this is actually a pretty big difference because it can make, um, it can change the runtime of such an algorithm from millions of years to a few hours. So but contrary to the 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, better algorithm for classical computer that could solve this problem faster. OK, so sorry if this was a bit theoretical, so I promise no more equations in this talk. And now I want to, um, to show you how you can actually build a quantum processor and went to actually many different answers to this question. And I talked before about qubits as kind of atoms. And th
at's a good analogy, because there are actually people or research groups that are using atoms that are trapped in an electromagnetic trap, which is shown here and used in as cubits. So these are two years from the research group in Innsbruck. And what they do is that they trip a number of ions in a so called Paul trap and they can put these ions inside there like string pearls on a string and then manipulate them using laser light. And since the atoms are also coupled to each other, use 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 larger system that they're able to do with this kind of approach and compose about 50 to even 100 cubits. All right, so what I want to talk about today, though, are superconducting quantum processors, like the one I showed 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, um, um, these quantum processors 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 on 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, large amount because you can just fabricate them like we fabricate most of the microchips today. So and of course, there are many more technologies that allow us to build quantum processors, for example, to a nuclear magnetic resonance, spins their quantum dots in both Einstein condensates can be used to realize quantum bits. So I just want you
to take away that superconducting quantum processors and I interrupt. Quantum processors are not the only approaches to quantum computing. All right, now I want to briefly talk about a very simple answer to Qubit quantum processor I built during my PhD thesis and this process of using so-called transman cubits, which are an invention of a research group and year from 2004. And what I show you here is an electron microscope image of the whole Kubitschek. 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 about at about minus two hundred sixty four degrees. And on a chip you see a lot of Coplin a waveguide 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 cupboards are actually on the chip, the answer is here in the center. So you can see two of them. And in the zoomin you can actually see ah, well, you can probably can't see very well here because the contrast is not very high, but it's a large capacitor that is realized in aluminum, which also is a superconductor and which are which basically acts as a support for a cubit and a cubit itself is then are on the top of this capacitor and so-called Justesen Junction, which basically is just an assistant element that consists of two thin layers of superconductor separated by an insulating barrier. And it's what we call a bed contact because under normal conditions, there couldn't be any current flowing to the system. But when a system becomes superconducting, we have a superconducting wave function and the wavefunction can somehow tunnel through the barrier and it can be supercurrent flowing between the two sides
of the structure. And now the the cubit itself is realized as different states of the system here, which we call also an artificial atom, because it kind of has the ground state and a few excited states that we can can control using microwaves, actually. So the difference is here that the frequency of the is compared to an atom much lower and in the range of a few gigahertz. All right, um, yes, the first offense and as I said, we can sorry for the cheesy animation, we can manipulate the cubits using microwave signals, which we sent to them through this, uh, snakelike structure, which, in fact is a of waveguide resonator. And you can think of this probably as a as a guitar string, which one we like excited would vibrate at its own frequency. And the function of this resonator here in the cubit chip is actually twofold. On one hand, it isolates the Cuban 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 cubit after we have performed some operations on it. All right, now, I talked about Tacuba decades earlier, so in order to do that, we need some kind of interaction between the two cubits. And what we do for that is that we put a very small capacitor between them. Which kind of couples then are always when they are at the same frequency. So that means by changing the frequencies of the qubits, which we can do by changing the current. And is these lines here, we can bring them in and out of resonance and realize to cubitt good operations with them. All right, so that's basically it, um, now to operate a chip, we first glued to a special microwave PCB, which also contains Koechlin and safeguards that we can hook up to our equipment. Then we take this whole thing and mounted in a sample holder, whose main function is to also protect the cubits from any stray electromagnetic fields and also to anchor it to the dilution that the delusion cries that is bas
ically 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 to Cuba to about 20 Malicki, which is at minus 274 a degree 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 you would operate our cubits at room temperature, we would find that the noise and thermal exploitations of all the materials that are around cubits would destroy the quantum state of them really fast. So we really, really need to call them down to a very low temperature to be able to to operate them for a sufficiently long time. All right, um, so that's the short version of how to build a quantum processor. The long version takes about two years and lots of, uh, microwave calibrations and, uh, chases for a superconducting leaks and so and stuff. So what I want to show you here, just the results of one of the experiments we ran with this Tsukuba processor. And what we basically did here is to, um, to run the global search algorithm, which I showed to you earlier, for the case of two cubits. 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 Kubicki. It's here, for example, for which we use to create input superposition state, and it also contains a multi cubed gates. For example, here we have the so-called ISO upgrade and to single Cuban rotations, which together implement the function F.J. that we talked about earlier. And in this case, uh, the function of J marks the state 008 as the password or as the solution of our problem. All right. Now for the two Cubitt case to the grower operator has to be applied only once to the state to obtain a solution. So these two gate operations there do this and afterwards we can just m
easure the Cuban state and see if the, uh, the algorithm has worked, so to say. Now you can see the sequence of this gate operation here. Um, what you see there is actually the time on the X axis, on the Y axis, the amplitudes of the microwave signals that we show that we are sent to the cubits which we show in green, as well as the frequency changes of the cubits, which is shown red. So you can see here that in the beginning we have the two microwave pulses that to create a superposition. Then we have like an interaction between the two qubits where we perform all to give it good. Then we separate them again, perform some more face manipulations, then we bring them in resonance again for Grover Operator And finally we change the frequency and we measure out the state. All right. So now we want to see how successful we are actually at doing this. We can run this great sequence, which takes about 200 nanoseconds and ever 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 of zero zero. And what we see here is the success probabilities are to see or the probability to obtain different output states as a function of the the, uh, the search function that we are looking for. And you can see here that for this case of the functions of zero zero, the success probability is about sixty seven percent, which is less than 100 percent. What would you 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 of zero zero, but also for the other possible search functions. So we do that and we every time we calculate to success probability afterwards and we see that for all the four cases, we are above 52 percent or 50 percent. Sorry. And this is pretty nice because 50 percent is the so-called classical benchmark against which we can compare or quantum processor because of you would think of an algorithm, a classical o
ne that gives you a solution to your two bit search problem. Then you could think of an algorithm that like emulates this function once, which has a probability of 25 percent of yielding a right answer. And if it doesn't find the right answer, just takes a lucky guess and returns some of the other remaining three states. And so this is what I call here, that I'm feeling lucky bonus because the success probability of this classical algorithm would then be 50 percent. And this is what we measure our quantum processor against. So we can see that for the simple case, we can actually achieve quantum speed up in an experimental quantum processor. All right, so now you probably ask yourself, why can't we just scale it up and build a quantum processor with like a thousand or ten thousand cubits and actually have several problems which keep you keep us from doing that? And a few of them I listed here. So the biggest one for the quantum processor, which I realized I'm doing my PhD, is so called decoherence and decoherence means that basically the cubitt is not only manipulated and measured by our own signals, but also by other quantum systems which are in the vicinity of decubitus, for example, on the chip itself or in the solution. Krogstad and these quantum sys systems manipulate the Cubitt state and also performance 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 cubitt in a pretty short amount of time for the processor, which I realized this was on the order of a few hundred nanoseconds. OK, then the second problem is to get food allergy and acute cubitt coupling for a case of Tsukuba, but it's actually pretty easy to devise a coupling scheme. We can perform gaits between each between a different cubitt. But now, as you would if you would scale up the number of cubits, you would see that it's pretty difficult to switch on and off the interaction between two individual cubits
with high fidelity. It's kind of like if you have like a phone line of a certain frequency bandwidth and you want to have, for example, 100 or 1000 subscriber 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 Kubicki. Are we? At a certain point, we have used all our frequencies that are available for the Cubans and we can no longer add new Cubans without kind of interfering with the other ones. So the same goes also for measuring the Cuban state, because in our case we can perform a measurement of the cubit and get the correct result with the probability of about 90 percent. But this means, of course, that in 10 percent of the cases, we cannot reliably measure the state of the Cuban, which is also for this kind of a system, a big problem. All right. And of course, there are some other problems which are one talk in detail here, which, for example, concerned the result of the. So for quantum computers, it's actually pretty hard to to reset the state of your machine to zero. And this is also like a problem which which has to be solved and which is not fully solved in practice yet. OK, um, so I want to finish this talk with a small outlook on our small summary of the recent trends and superconducting quantum computing. And now to the several groups in the world are trying to improve the state of quantum processors and help to really build a large scale quantum quantum computer. And here to show you an image of the research group at the University of Santa Barbara and John Martinus 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 transman qubits like the ones I showed you before and resonators. But that couple of these elements and different ways that makes it easier to produce a large number of qubits on the same chip and
actually get get a real quantum computer out of that. So these approaches are, for example, code rescue or service code architecture. OK, then you can as well think about improving the Cubans, Cubans themselves and the resonators and some groups, for example, in Ireland and there and in other places around the world are doing this by replacing these copely. Now, Waveguide got resonators that you see here on the left by actually treaty resonators, which are boxes of aluminum, that that can also resonator microwave frequencies. So here, for example, we see a system that has a 3D cavity resonator with two cubits which are placed on a SSAFA substrate. And the advantage of this is that you can control the environment and fabrication parameters of the Cuba to a much better degree than you would be able to do with microchips. So decoherence times and the lifetime of the resonator, the quality factor of the resonator in this case is much better than fodder for these so-called like to decubitus. All right, another thing which some groups are working on is so-called quantum error correction, because you cannot only say, OK, let's put 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 Cubans 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, um, instead of using non as solid state or superconducting cubits to use different quantum systems to to store or process quantum information. So here, for example, I show you work from the group in Suckley, which is a hybrid quantum system that uses a diamond with so-called envy centers, which are nitrogen
vacancy centers and Diamont, and which actually are responsible for the color of this diamond and which amazingly can store quantum information. So what you have to system is that we have a cubitt. And, uh, when you want to manipulate the state of Tacuba to keep the state on the chip, but if you want to store it, you can transfer it to the to the NBA center in the diamond and keep it there for a long time without having an interference or any decoherence in a Cuban state. All right, so as you can see, there's a lot of research going on in this domain and, um, you could actually plot kind of a Moore's Law for quantum computers or superconducting quantum computers. And if you do that, you would see that when we when the research started on this subject in 1999, decubitus 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, uh, and the reason in the following years, in 2002 and 2004, they were new types of cubits devised, which had a much longer coherence time. And actually, this trend of increasing the concern with the Cubans seems to go on at a similar or like a pretty fast rate until today. So in 2013, we have actually superconducting Hubert's that have coherence times in the order of a few hundred microseconds, which is large enough to envision to actually use these qubits for four real quantum computing. So the take away 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 selected political way. Uh, 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 and 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 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 quantum computers. Best friend, which is at twelve forty five in Hall six by Nicholas. Well OK. So with that I thank you and question. Thank you for your talk. We now have 15 luxurious minutes of Q&A, so please line up at the mikes there, six mikes, one, two, three, four, five and six in the back. And we also have the AC 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 back up mic for you. OK, make one. Go ahead. Hello. Thanks for the very interesting talk. I've learned a lot today, Mike. No, sorry. Well, first of all, thanks for the very interesting talk. I've learned a lot. And if I understand this correctly, quantum computing is at the moment limited, limited by the amount of cubits you can have interact with each other, plus the amount you can keep to keep it stable. Um, do you have any idea at what amount of time and what amount of Cubitt quantum computing can reach a level where it can actually compete with normal computing in, say, doing Aerotek calculations, et cetera? Mm hmm. And it'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, uh, error threshold, because as I talked about, there is a positive possibility to perform error correction of Cubitt. So if you are below a certain level of errors for each individual operation that you perform in a cupboard, you can basically correct that away and have a system that works perfectly under the right conditions. So and for, um, classical approaches, like the traditional approaches to quantum computing to zero 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 to error thresholds has actually moved up quite a bit to a few percent. So today it would actually be invisible to 12 cubits that are good enough to to build real large scale quantum computers. Although, as I pointed out, there are still a lot of other challenges, challenges which keep us from doing that. Okay, so that's a question. 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 Grovers algorithm. Mm hmm. Is this true for other, uh, quantum algorithms also? Um, 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 case we just have to to like repeat the process and check again a couple of times. So, yeah. And I mean, there are a lot of quantum algorithms and I don't know then also there might be some which are more deterministic in that sense. But to my knowledge, most of the quantum algorithms, probabilistic by nature. Number six, that's you. Abbi, thank you very much for your child. I have a pretty lame question, um, 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 eldard, um, uh, instructions said in some way. Which of these are, uh, feasible for quantum computing? I mean, you answered a bit with, uh, probably closer. So, um, I think today, um, 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, um, having the ability to even, like, produce a large number of cubits regardles
s of the of the size of the structure. So I think in that sense, we wouldn't wouldn't be like a very high priority to optimize to the packing or like the size of the individual qubits under the chip. And, uh, I think it's more about if you talk about, like the performance, you can also, of course, try to decrease the amount of time you need to, for example, perform quantum gates. And this can be done by increasing the frequency of the cubits and also increasing the coupling between individual qubits, which will also increase the errors because they will also be errors and cured when you bring decubitus in and out of coupling. So it's always like a compromise between speed and reliability or fidelity. So to say things that answer your question, you think be a question from a camera angle. 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 freespace optical Nohria been integrated into one chip. And what do you think about these approaches? Mm hmm. Um, I'm not, uh, 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 race is still open. And whoever built the first working quantum computers and if I would have to bet, I would bet on like quantum computers before or like superconducting qubits. But of course, to the optical systems and photonic cube, it's also very interesting. And they could prove to be a viable alternative in case we should meet like a roadblock with a superconducting Hubert's or another technology. So I think it's yeah, every technology that can realize cubits 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 make a large number of qubits? How e
asy is it a couple of cubits with each other and how good is the fidelity when you realize individual cubitt operations? So these are really the criteria that you want to measure against. I think maybe we can chat about this later. I'm sure you would love to have. 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. OK, what problem are you referring to when you have you have a scaling problem if you add a lot of cowbirds, the frequencies for them. Yes. OK, now, see, I mean, the problem with our Cubitt processor was that the coupling scheme was really very simple, as as I showed, it was just a capacitor that coupled the cubits to each other whenever they were at 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, um, I like the coupling strings and these approaches goes down much faster when you change the frequencies of the cubits than in our case. So these approaches are kind of more reliable and better suited to, like, realize a large number of cubits, I would say. So there are definitely lots, lots and lots of approaches that you can can, uh, can try to. Yeah. To do. Why don't people use better superconductors? Because we can do much better than 20 amk by now. Hmm. I mean the the temperature is really not uh not uh the worst problem that we have. And yet we operate at low temperatures mostly because we want to avoid excitation of the cubitt 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, aluminum and niobium, they are actually very good fabrication processes in place which have been optimized for like 1
0, 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, uh. All right. OK, OK. Internet, please. Um, how many cubits would be necessary to crack a two thousand forty eight hours? Oh, that's a really good question. And I don't want to lie to the uh to you now that 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 two thousand doesn't something. But there are as many bit at least as as you have Bedzin, the number that you want to create. 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 shower algorithm to give you an exact answer on this. Number five. Um, hello, um, I was wondering the, uh, the talks seemed like the the direction of the search 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 as they are research in that direction to uh. Yeah, of course. I mean, uh, the basic thing about quantum computing is that, 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, uh, there is some a lot of research, actually, on quantum cryptography. I mean, I think there was a talk here on those as well. But I'm really not an expert in that subject and I wouldn't like to comment on that now. So but yeah, definitely there's a lot of, uh, a lot of going on also when it comes to the quantum cryptography itself. OK, thank you. Mm hmm. Number four. Hi, um, I'm curious to know what
your thoughts are on 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 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. Um, for me, it's mostly the ability to simulate quantum systems, because even if you look today at conventional electronics, um, for example, a processor, you would see that 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 the systems, we would definitely need quantum computers to do that. So there are many other applications and 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. What I would like to know is you in the popular press, I've always heard that scaling to a larger number of bits is hard. And I assumed that this was because when you get too big, that they don't interfere with each other anymore. Today, I'm taking away that the the arrows, the noise is a big problem and that the retention is a big problem. And in the beginning, you mentioned that the iron trap has up to 100 cubits already. Can you say more about this iron trap thing and what its parameters are and why you're going in this way if the other one is already so far? So, yeah, as I said, I'm not an expert on 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 gaits which operate in like nanoseconds on microseconds and you can also have a readout fidelities. So to sort of say the success probability when you reload, given Cubitt state, which approaches like 100 percent by like several like six digits or so. So this systems definitely seem to be very promising. Um, what kind of could be a problem is probably the scaling, because if you go to a very large number of qubits, you would have to somehow accommodate them inside a trap, inside a magnetic trap, which would which could be tricky. But also for this problem, there are solutions devised today. For example, you have like R atom traps, which are on a ship. So we can really take individual cubits or atoms or ions, if you like. They can shuffle them around on a chip and transport them to to to other other sides and like that like isolate them from each other. So as I said, for me, the rest is completely open. And right now I am computing seems to be ahead. But this could change, of course, if we keep improving the superconducting qubits like we did in the last 10 years. So. No. Number six. Hey, as it all at the moment, we still use the binary system with two systems, but we are not, um, we can use higher level systems. Are there any thought experiments to overcome the binary system with higher level systems? Um, yeah. You could, of course, do that. And in fact, uh, we did experiments where we used the second and the third, uh, energy state of Tacuba to have like a like a higher order base for our calculations. Um, but this is usually not done because, uh, the speed up or like to to gain information that you that you achieved 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 state space, which is true to the power of four and
cubits, whereas for the cubic state it would be two to the power of. And 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 the kind of way most people don't do it. OK, thanks. OK, we are out of time. I'm very sorry but I'm sure you can find a dress outside of Nater thinking like place.
