I want to start from what I imagine you all know and go from there and I want to start with today's technology and this is the inside of an FPGA a field programmable gate array in it and it kind of represents the state of the art form from the point of view of an approach to information processing based on silicon and transistors and conventional electronics that the thing which is always plotted in Moore's law over the last 40 years this is kind of reaching its its it's end point and it's reaching its end point for a very obvious reason and that has to do with the size of the wires that are inside if you look at this this scale bar on this diagram that's a hundred and twenty nanometers if that means that these wires are about 20 nanometer wires so at some point not only can you not get smaller but the physics of quantum mechanics starts entering into the problem in a bad way in this case the physics of something like tunneling through energetic lis forbidden barrier is something that happens on these length scales as you as the electrons start to feel like that they're inside of atoms instead of feeling like they're inside of large wires but what's interesting about this whole progression from you know from 1947 and the invention of the transistor all the way through today is that there are a whole bunch of features of physics I would say features that are not controversial physics that are part of even you know undergraduate bachelor's education in which there's essentially no disagreement about that the correctness of the ideas but which is not used and it may be that it's not used simply because everything else was working so well and things were going along in a great mad rush of technological explosion until you get to the point where things aren't you know getting any better or any faster and then you start to go back and you realize that there were all of these things in in the physics catalog that that somehow never got used and maybe we're never needed and they're they're a challenge to use them I mean that's one reason probably why they didn't get used there they're not as easy I should say as the technology that we have today but they may be an extremely promising resource and that's what the talk today is about is about bringing in other aspects of the physical laws that govern the movement of electrons inside of wires that that are not used um this picture should look a little bit familiar it's probably more familiar in more polluted countries than Sweden and Denmark but when a droplet of gasoline or a droplet of oil lands on the surface of water it's it's a rather familiar sight to see the interference pattern of the thin film of oil on the surface of water I I would guess I'm gonna ask the people in the first two rows because it's all I can see familiar phenomenon visually you've seen it before you might have even taken a class in which you solve the problem of which which parts turn red in which parts turn green and you would learned when you were in class I didn't think you probably spent a lot of time thinking about why it happens but you learned at least how to calculate things that would give you the correct answer that metaphor is something which will pervade this talk which is it very often in physical sciences we learn how to calculate things when we get the right answer without ever stopping to ask you know what does it really mean so when we have that when we want to calculate this we say that you know in order to keep the the the waves adding like this so that they so that they double the the amplitude and quotient you know in square for the intensity instead of like this where they cancel out you have to be at a certain angle and that angle tells you which ones are red and which ones are blue and which ones are green and you can set up all kinds of related interference patterns and it's this kind of interference pattern that we learn to understand when we wrote down eventually the the physics of light that light should behave like a wave and that the wave should show the properties of interference in fact we it's kind of a definition of what it means to be a wave the wave is something in which there's an amplitude and the amplitudes can subtract to give you zero or they can add to double etc water is another example of a wave you can you can stick your finger in two places on the surface of water full of water and if you stick your finger here and here where I'm shining light now it'll send radiating waves out toward the edge of the boundary of the pool of water and it's not a surprise to anybody because if you've ever splashed around in water you know that there will be places like like right here oh sorry there will be places like right here where the waves from splash number one in the way from splash number two added up to make a an especially bright wave sort of like when it turned green and the waves were adding up and sink and then there were other places like right here where the minimum of one wave the wave coming from one of the sources added up with the maximum of the other wave and it added up to given nothing it's so far so good I really don't think that this is a puzzlement and it should be rather intuitive for the distance away in general waves behave and you can make this same kind of argument you can figure out where they interfere destructively shown here or whether it interfere constructively and you can do similar things with light you can have two sources of light or two slits in a pattern that lets light go through in two slits and they'll do the same thing they'll add up to places where the light is bright and intensity in other places where the light cancels out now all is fine here's how you solve the problem it doesn't matter um all is fine until you recall what it was that Albert Einstein got the Nobel Prize for and what was one of his great accomplishments in 2005 was the realization that light actually is delivered in small packets called photons and those photons are discrete objects which will impinge upon for instance your retina or anything that absorbs light and that the energy from that light will be delivered in a single package and that without that phenomenon you wouldn't be able to see nothing would work and the whole physics of light wouldn't wouldn't be as we understand it so imagine the same kind of experiment where you readily acknowledge the existence of these particles of light impinging upon the screen as photons and you imagine this is a cartoon but we'll we'll talk about real experiments in a bit here's a light gun that's shining through two slits just as if it would make these two radiating patterns only now I've accentuated the fact that light will land in the form of discrete events on the screen so the the the photon that lands on the screen right there will make a spot and that that's I mean I'm not saying anything brain bending by saying that's where it is that's where it was when it when it hit the screen it had a location its location is clear its location is the position of the green spot but if you continue to let the photons accumulate you'll see a pattern on the screen which resembles the interference pattern of the light that propagated through the two slits in pass through two slits so evidently as the light was passing from where the individual photons were passing from this source through the two slits they were delocalized like the surface of a wave they didn't have a location they must have been a wavefront that passed through the two slits in in a sense not having any particular location like a wavefront doesn't have a location but then when measured in impinging upon the screen suddenly was localized at some point now you could say well there's a lot of photons and a kind of a spray paint of photons but we could let them go through very slowly one at a time what I mean by one at a time is that you can let the the interval between photons be sufficiently long that the the first one has already gotten to the screen and made a blip before the second one has even released so you can really do the experiment one at a time and you'll still see the same pattern and you know you've probably seen it before but you know in the physical sciences and in most sciences we have this process where we're after enough times you begin to confuse familiarity with understanding and I think probably you've heard this you know particle wave duality and all of this say you know it's a hundred years old so but you have to stop for a minute and say you know what is it what does it really mean take a crazy example like the wave front of light that comes out from a distant star and moves through space in some radial pattern moving out from the star then that light you know comes through the millions of years of traveling as light and then suddenly by a process that is seemingly statistical it lands in your eye and that photon is at your eye suddenly the information that says that the photon is not in any of the other places that it could have been in that wavefront must instantaneously be transmitted to the photons that were on the far side of that star billions of light-years away now you think yourself well that just sounds like I mean it's not India obviously nothing nothing is transferred to the other side surely the photon that landed in my eye was on its way all the time to my eye I mean I might not have known where it was until it got into my eye but surely there was one there before it got to my eye no that's not right you know that's not right because the photon must have been in all of those locations or else the pattern wouldn't appear and we don't have any better story to tell now than the story that I just told you that is if it sounds like I'm sorry but there's no other story I mean which doesn't mean it's not it just means there is no there's no less less sounding story than that one so now I want to come back to electronics into the the revolution that that this idea and quantum mechanics set off and bring it to the context of chips so here's a surface of a semiconductor this happens to be gallium arsenide doesn't matter and it has a channel that's cut into it where electrons can pass with this way or that way and it's pretty small and it's measured at low temperatures so that so that the measurement of the position of the electron by all of the vibrations latus doesn't take place and if you apply an external magnetic field that that takes the role of effectively making one path longer than the other it does the same thing as looking at different positions on the on the screen of bright dark bright dark patterns and and what this tells you is that the electron has proceeded from top to bottom via both paths that is it was delocalized during its journey it was in both places at the same time if you want to say it that way and the evidence is this so-called Aronoff Bohm effect of the interference of an electron with itself now the thing that makes electrons even more interesting in a sense than photons is electrons carry charge and charge can be used for instance the charge on a capacitor plate can turn a transistor on or off so imagine now that we've said that this electron is both you know going both ways at the same time so this one's going this way this one's going this way and we use the charge that is on this side when we say it's on this side to turn a switch off and when the charge is on this side we use that charge to turn the switch on now we say within this quantum mechanical picture in which the charges in both places at the same time that the that in that sense the effect of that charge will both flip and not flip the switch at the same time so the switch will then be in a state of left down right on and that would be all you could say now if you measured that it was left then the switch would go to the down position but if you don't measure it then you just have to describe it as left down right up now that's interesting because if that switch is on it can let other electricity flow and that electricity could flow to the other side of the chip and turn on another transistor and then you'd have to say that if the charge was on the left that the switch would be down and the transistor would be uncharged and the switch was up and the charge was sorry I said it wrong on the right to the switch was up and the charge was in the electron was uncharged so you have to keep all of those possibilities coexisting now where we're gonna go is that nobody's ever built one of these things before this is all perfectly good even you know boringly old-fashioned statements about quantum mechanics but it's never been done I want to just say some notation because I'll use it in a little bit um you can think about like computer scientists and call these things zeros and ones and then you can say that the the state can be in a 0 and a 1 at the same time you can use in physics we characterize the state of a two-level system a system that can be in one of two states as looking like a spin vector so we can call it up and down same thing and then the rule of quantum mechanics that we've discussed so far is this idea that things don't have a particular state until they're measured there in both states as possible so we can say that this quantity which we'll call sy the wave function can be in some kind of superposition of being down and up at the same time and that's allowed within the laws of physics and something that is certainly not used in any chips that we build the amount of up and the amount of down doesn't need to be 50/50 and so we can characterize all the possible super positions in the following way let's call down something like a down arrow and oh sorry 0 a down arrow and 1 an up arrow and then all the possible super positions given the constraint that they should add up to some total probability can be written as any position of that vector on the surface of a sphere so that for instance if it's a 50-50 mix of 0 and 1 we'll call it the east direction if it's a negative version that's right the amplitudes can be negative in fact they can even be complex so these a and B variables can be complex numbers and so any arrow on the surface of a sphere represents the generalization to quantum mechanics of what used to be called a binary variable or a bit so this thing will get the name a qubit to represent the two-level system of a binary variable now in its quantum mechanical generalization including the possibility of complex superpositions of those two so you see it's a pretty technical talk now in in computer science this is the subject that you all know and I don't know so you know what I want to learn about computer science I just watched a YouTube called how to add numbers in one lesson and this is about the extent of my knowledge of classical computing however what I know is that there are combinations of of gates like an or gate and a not gate NAND gate that can produce any possible set of gates and so I wanted to talk about this Universal set of gates for a classical computer out of which you can build in principle any possible computer and to say that there is an analog of that in quantum computer science which says that if you have a couple of possible gates namely something called a unitary that unitary that u stands for unitary and what it says is it's sort of the analog of a not instead of saying it to goes from a zero to a one or one to zero it takes you from some state to some other state of that variable and it's more general than a not because it can go to any possible angle but what it does is it rotates you from one to another one other gate which is sort of you know like a like an X or it's the it's the analog of an X or it says if this one is a if this one is up then leave the the one it touches alone if this one is down then flip it and so this thing which which couples to and and and will be the the embodiment of something that we'll learn in a minute it's called entanglement but here we just say that this is a kind of a gate that if this one is up it leaves it alone and if this one is down it and if it's down it flips it are all that you need unit Ares and these X ORS are all you need in order to build a universal machine in which any possible computational function in the full quantum mechanical space can be realized okay so it's a kind of a theorem for quantum computing but what we've really done in thinking about this is written that the state of a computer let's say that these numbers represent the state of every transistor in a so this is should be you know this should be a billion zeros long for representing the state of every transistor and that this will go all the way down to every transistors in the on position to every transistor is in the off position and what we've said is that the wave function of that chip must look like a superposition of all of these possible states with some mixture of ratios of all of them which can be complex numbers and so if I think of this thing as n transistors that means that there's two to the N of these objects and that means that the description of the state of the computer is a point in a 2 to the n dimensional space now if you think for a minute that if I had for instance 300 transistors that the dimension of the space in which the point is located is more than all the you know every proton in the universe okay so very quickly the space in which this system lives as a point in a vector space that's 2 to the n dimensions becomes astronomically big and then you say how could I possibly have a computer in which there's a point that's moving in a space that has more dimensions than there are particles in the universe and I don't have an answer for that except to say you know maybe those are in other universes somewhere and I want you to know I know that sounds like but nothing that I'm saying is disagreed upon within the community okay there's a there's a I mean by the community I mean physicists and you know this is standard stuff it's just you know we use it we write it down and we learn to calculate where the bright spot is and we forget what it all means and I haven't even touched on the weird parts yet because in fact imagine we did the following experiment take a helium balloon and take one atom of helium as you remember a helium atom has two electrons circling circling and nucleus and the two electrons are in the lowest shell that's why it's a noble gas and the two electrons if you did take chemistry class or physics class you'll remember that they fill the first shell one goes in spin up and one goes in spin down and then the first shell is filled and then when you have to make the next element you have to you have to go out to the next shell this shell is full so take the two electrons that make up this condition and in fact we don't write usually ones up and ones down because you don't know which one is want which and which one is the other so you write a superposition of this ones down this ones up and this ones up and that ones down and you put a minus sign in between so that they obey the laws of electrons which is when you switch their place the overall wavefunction has to take on a minus sign that's a bit of a detail although it's gonna come back later so in any case there's a minus sign we choose a minus sign but you don't care just let's call it this with my thumbs ones up in ones down but you'll remember that that means ones up and ones down or the other way and take them and separate them a long distance a very long distance without disturbing their orientation and send one with some distance away and the other one another distance away and then measure one of them because they're oppositely oriented if you measure one of them the other one will be naturally oppositely oriented but what's interesting about that statement is I didn't suggest when you measured this one over here what orientation you would put your detector I mean maybe you would turn it sideways or maybe you would oriented some orientation and no matter how you oriented it this one would be the opposite so somehow the act of measuring one would connect through space instantaneously somehow in effect not just its own outcome but the outcome of its partner this level of unbelievable Nevada Dine Stein in 1935 late in his career this is a picture of Einstein in 1935 so he was a guy by then and and yet the paper this I'm Stein Podolsky and Rosen paper with this grammatically challenged title can quantum mechanical description of physical reality be considered complete is these days his most cited work if you go to Google Scholar you type a Einstein to see how many how many how many hits all the papers have this is number one because of the controversy that this paper created by talking about this separation because you remember Einstein from relativity said nothing travels faster than the speed of light and let you measure the basis of a spin in this direction and it gets set in the other one and the conclusion of this paper was one is thus led to conclude that this description of reality given by the wavefunction is not complete and the paper was careful to not say wrong because you can calculate things with and you get the right answer it's just that it simply must be some kind of provisional understanding that must not be the deep penetrating truth of what's really going on because it you know it's because it sounds so crazy and um it's very interesting what happened during this period 1935 the same year that was from March the same year in July so it didn't take bore very long to write a response paper with this exact same grammatically challenged title can quantum mechanical description of physical reality be considered complete and to summarize Bohr's response he said in fact this new view of natural philosophies he bore understood this wasn't a statement about physics this was a statement about everything this was a statement about the way we think the universe is but it's not that when you do something somewhere it can't have an instantaneous effect somewhere else and and yet what what Bohr it seems correctly these days said was that this requires a radical revision of our attitude as regards physical reality and that was 1935 and between then and now I mean as you can imagine experiment is the arbiter of whether this is true or not who wins the Bohr Einstein debate is not who's a better arguer it's how did the experiments come out and so immediately this is it took a while but this was you know circa 1972 thirty years after the Borenstein episode in 1935 this was reduced to an experimentally testable practice by a guy named John Bell who said if you set up the following experiment you can find out whether or not those states were predetermined before they were measured or whether or not the act of measuring this one determine the outcome of that one and all of those experiments right up to the present day so here's from from a year ago 2015 where now these two are separated by more than a kilometer in the detector sorry Einstein quantum study suggests spooky acts spooky action at a distance is real so every experiment that's been done between then and now has verified this idea that not only does the does a system not have a state until it's measured but if it's a multi particle system with correlations across the system measuring one will instantaneously determine the other and it may be that the difficulty of the intuition of understanding this which frankly doesn't matter I mean if it if we don't have an intuition for something that doesn't mean it's not true that just means that that our evolution didn't require an intuition for it in order to survive so that's right we don't have any intuition for this it seems like it's wrong to us but why should we have an intuition for how things work inside of atoms or how they work in milli Kelvin temperatures or how they work in photons that have been prepared in some way that wasn't that didn't exist until we evolved to do it another way of saying what I just said I quote famous American theoretical physicist Richard Feinman quantum mechanics describes nature as absurd from the point of view of common sense and yet it fully agrees with experiments so I hope you can accept nature as she is absurd but now when we think about information technology we can imagine that we set a transistor here that sets electricity to go over here or doesn't at the same time and sorry and it doesn't at the same time and that flips a switch which turns this on and doesn't turn it on at the same time and and sets the whole chip in some state of this exponential number of possible states because every time you get to an X into an intersection you have to remember that each one could or could not go into the following state and then and then you you know measure this one and it suddenly sets that one which determines what this one is across the chip it's all consistent with the laws of quantum mechanics and it's never been built and that to me is enough of a challenge to dedicate myself to trying to do it because it just seems really cool but there was an added kicker that brought the attention of the world and the added kicker is is this in 1903 in 1996 Peter shor then Bell Laboratories now at MIT wrote a paper that said the following in the abstract a digital computer is generally believed to be an efficient universal computing device that's this Universal classical computer that I talked about this may not be true in quantum mechanics is taken into consideration that is there may be problems that cannot be efficiently simulated on a computer what this paper considers is a problem which is hard factoring integers now factoring integers doesn't seem that hard but it is a hard mathematics problem and what Peter shor showed in this paper was that if you had a machine that could do that thing that I talked about in the previous slide um you could solve that problem very fast so here's the problem I think you know the problem the problem is one it's a big part of RSA algorithms were for secure communication two numbers that multiply together to give you two prime numbers that multiply together to give you a known number so I give you the known number you have to find the two prime numbers I can only see the first two rows does anybody know what those two numbers might be yeah what are they yeah yeah he says but then he does but then he doesn't know okay yeah five and three okay okay mr. yeah yeah yeah two prime numbers that multiply together to give you four thousand six hundred and thirty three twenty three and twenty one is not correct 41 and a hundred and thirteen and each of you can ask yourselves how do you how do what I have done that how would I figure that out I think you're kind of you know it's not like you missed that day in school where they taught you how to find those those numbers there isn't a good efficient algorithm for solving that problem and in fact as the problem gets bigger it gets harder much faster so the RSA algorithm asks the question if I give you this number can you find these two prime numbers that multiply together to give you that number and that is a problem which is in solvable of course if I give you one of the numbers then you know it's instantaneous that you can divide one by the other find the other one but but to find the two is insolvent what what I mean by that is this oh sorry I'm gonna skip I put this one in here twice sorry about that here's what I mean by that as the number of bits in gets to be gets to be large then a computer or a hundred computers more or less however fast they are if you take the clock speeds from 2003 when the paper was written or the clock speeds extrapolated to 2018 it doesn't matter once you have a thousand bit number it takes the age of the universe to solve the problem but depending on the clock speed going from gigahertz megahertz even kilohertz if you have one of these quantum computers that can keep all the parallel States alive at the same time the problem becomes much simpler now I and many others were already interested in this problem because it was a cool problem but this is when the world lit up when the idea that internet security could be compromised if somebody had a quantum computer um got things going but I want to emphasize and I think that this is a really a maybe the key point for the talk that's not the end of the story and and how could it be I mean this is such you know the idea of computing in in a billion dimensional space cannot be just good for factoring numbers and solving internet problems but what's an active area of study now is exactly what problems that we need computational advances in can be addressed by using this kind of superposition and to a large extent it's not known it's not known what class of problems can be accelerated by using a quantum computer current work so here's from you know May of this year addresses some some interesting problems here's one about finding a the the the ground state of a chemical that is used in the production of fertilizer which you know is also big business so there's a there's a there's an iron atom in the middle of some large complex and it's it's it's used to in in the production of the catalysis of fertilizer and so this was how you know how can you find the ground state of that molecule it's relatively simple molecule and how many of these qubits would you need to do it so this is one example of a problem where you can solve it but depending on the details of what kind of errors the qubit haves whether whether the rotation angles for this unitary rotation makes an error of one part in a thousand or one part a million or one part in a billion you may need something like a billion cubits or ten million cubits or a million cubits now that sounds like a lot but actually you know there's a billion there's a billion cubits right here so I mean there's a billion bits right here anyway so we just have to make the version of it which respects the quantum mechanics so I don't think that the that the problem of step-and-repeat to make a billion things is the hard part or maybe it was the hard part but we already solved that problem the problem is to get the quantum coherence into the system in the first place without it getting hard as we scale it up so we're beginning now these are really brand new kinds of results to begin to understand what kind of machine would we need to build and it's very interesting that the hardware builders like myself are in the exact same situation as the the theorists who trying to figure out what to build in parallel I think it's a different it's it's a different kind of field than most where we don't know exactly what it is that we're trying to do we're trying to figure out to build a few qubits while at the same time people trying to figure out what what it is that we'll do with them but it's not surprising that industry has entered into the problem so you know IBM Google Microsoft all the big companies are now beginning to invest and governments also so there was just announced this year a billion euro program in the out of the European Commission to study this and other quantum technologies that take advantage of superposition entanglement and these other attributes so keep in mind the time line this was you know the 1930s when people were understanding that this physics was correct the 1990s when people were realizing that certain problems could be solved with this but it's not until now that people have begun to make hardware and begun to see the first few qubits do what they're supposed to do and now you see this great pouring of interest into the problem I'm going to ask somebody who has a watch on because my my battery's dead what time is it okay so a lot of interest is pouring into this problem but I I mean what I'm gonna report to you is that the progress is is difficult and you know pretty pretty incremental at this point I'll talk about two examples of technologies that are going on in my own lab not because they're better than what's going on in other labs but because I know about them and I'll mention some things that are going on in other people's labs but I but I just I don't know about them as much so one example was how do you make your first qubit oh I discovered something if I stand back here I can see okay it's open for questions now anybody who wants to ask questions I can see you now as long as I stay back here it's okay if I stay back here am I out of the light now you can't see me right if I come back up here you disappear and I appear okay so here's an example first of all it's an example that shows you don't need to spend very much time on graphics in order to have an influential paper but what this paper said in a time when it wasn't technologically possible was if you could make a box and you could put one electron in the box like you could make a transistor like a capacitor plate that could hold one electron then if you could connect those two capacitor plates so that they would make one big capacitor plate for some controlled period of time the during the time that there were two electrons on a capacitor plate they would try to do the thing that helium did which is that they would try to go into some opposite spin orientation and then you could separate them and you could use that as a kind of a control mechanism for how do this thing where if this one stays this one flips and if this one doesn't stay then this one's down then it flips the other guy you could do that by just using the laws that made the helium atom in the first place all you'd need to do would be to make a box that could hold one electron and you could read it out by trying to see the orientation of that electron by putting it in contact with a ferromagnet etc they honestly these theorists went a little farther than then was their own comfort zone about how you do all the rest of it but they worked out the math of how you do this interaction to show that it was the same as that two qubit gate that you needed in order to do universal computing so the the idea was that the desired operations are affected by the gating of the tunnel barrier between two neighboring dots and it would produce Universal we propose an implementation of a universal set of 1 & 2 cubicle quantum gates so you know no idea that it was the best thing to do but it seemed doable and it was one of the ones that I took on about 10 years ago to give this a try the first thing that had to be invented was a box that would hold one electron the way we did it was by taking gallium arsenide and putting metal on the surface of it this is a so-called two dimensional electron gas heterostructure of two different kinds of gallium arsenide with with an electron system that lives at the surface and we put metal on and not surprisingly if we put negative voltages on the metal the electrons don't like to go near the negative voltages so they stay away this is about one micron from side to side so it's not particularly small compared to modern technology it's just that this is a material that is basically free from disorder so we can make a box of electrons here and a box of electrons there and we could measure where the electrons were and we could then go to begin to do the helium experiment that I talked about earlier which is to say that we could put the two electrons here whose ground state would be this up down – down up singlet configuration we could then change the voltages on those gates separate the two electrons and see how long it took to have those two electrons be independent subsequently measure them but all we wanted to do for this experiment was to hold them apart for a while and to ask the question how long can you hold those two electrons apart before they lose their singlet correlation before this idea of separating them and then measuring them later falls apart and the way we did that was by eventually trying to put them back in the name box so this is a little bit more complicated but we would prepare separate in measure P s M by taking the two electrons stayed here the ground state was the singlet configuration we would separate them to what was a mix of the singlet and the triplet the parallel oriented spins then separate them and ask did they go back into the state or not go back into the state and we found something very interesting when we did that when we asked the question do you go back into the state that you came from or not we got an extremely surprising result which I think will surprise you also which is when we separated the two electrons for something like 10 nanoseconds or 20 nanoseconds separate them leaving there and then try to put them back in the same box they all went back in the same box again here they all went back as a singlet again but if we waited something like 50 or 60 nanoseconds none of them went back in the box they had turned into a triplet but then if we waited 120 or so they all went back in and then not and then yes and then no and then yes and then no and even if you look carefully you see even the period is inconstant it's kind of faster down here than it is over here so there was something that was taking these two electrons and screwing with them but in a kind of a periodic way so that they were processing one relative to the other and it took us a long time to figure out what the what the rate of procession wasn't even constant time so something was causing this procession it would have to be something like a magnetic field that would make up a spin process where how could there be a magnetic field difference between the two sides on a few hundred nanometers separation what kind of what kind of magnetic field would have a strong enough gradient over 100 nanometers that it could make this happen well eventually we figured out what it was and it was as surprising to us as it probably will be to you which is that there's an effective magnetic field produce by the gallium and the arsenic nuclei that live inside the crystal that is we make these things out of gallium arsenide but gallium and arsenic have nuclear spins in the nuclei of those of those atoms was causing the electrons to process around the nuclear spins I mean who would have thought that we had to worry about the nuclei of the atom of the semiconductor crystal that we were working with but that was performing the measurement so then life went on things got more tricky and other people this is from it from a different group this happens to be from the group and in Delft started working with other materials they specifically pick materials that didn't have nuclear spin now interestingly a material that everybody here is familiar with silicon is a material that doesn't have any nuclear spin well actually that's not quite true silicon-28 the predominant species of silicon and germanium is a same story is mostly silicon 28 is is nuclear spin 0 great so at least that problem won't exist but there's this residual 4% that silicon 29 in naturally-occurring silicon and those spins were enough to cause the problem so when people moved to a silicon silicon germanium quantum dot to do these experiments later same problem from the residual 4% so then came a whole community of people who were interested in trying to produce 99.9999% pure silicon 28 now you'll notice the nationality of a lot of the of the authors of this paper and and these were the these were the communities that used to be spinning plutonium in their in their centrifuges in the soviet union they're now in the business of purifying silicon to make quantum computers and other applications as well but so the motivation was to get rid of this decoe hearing mechanism once we had discovered it so you know you could say is this technology or is this physics and you know I don't know but in any case each time you discover something that's measuring the spin that you want to be left unmeasured you then have to start a whole technological approach to get rid of it so where are we now well you know we have now rows of quantum dots here's 15 of them in a row and we can move them around and gate them and you know it's far from being a quantum processor but it's a technology in which we can measure a long coherence time for these spins and we can measure where they are by using these sensors at the top and it becomes now a control problem to try to measure them there are other technologies with this is based on a superconductor this is from John Martinez's group this was when John Martinez was a University of California Santa Barbara John Martinez now works for Google and is doing the same thing there but here you know it's pretty similar to the status of what I talked about before this is five quantum dots that are all in a row and here it's announcing something called the threshold for fault tolerance and what that means is if the individual errors of the qubits are sufficiently small this rotation angle for instance is sufficiently small then you can correct the error without doing any measurement that is remember you're not allowed to measure because then you determine the state and it locks it in but you can still do error correction without doing any measurements but you need it to be pretty good already and so this is a paper that claims yes it's only five cubits but now there have sufficient quality that we've reached the threshold where we can correct the errors that occur using a so-called quantum error correction algorithm it's time to wrap it up but there's a separate subject that I want to talk about and so I'm going to take five minutes or something like that to just to just change subjects which is the introduction of a new idea into physics and into quantum computing namely topology so I think maybe maybe if you had a math class where you've just you know in awake for your lives you've you've you've heard about this idea that say in this case some loop I don't want to call it a circle because it doesn't matter that it's a circle can be deformed you know by going like that into this figure eight design but cannot be deformed into something that has a non-trivial topology so we can distinguish these two from this one by the over-under routes of the string and that branch of mathematics that distinguishes this shape from that shape is called topology and what is it what's its relationship to quantum information or what's its relationship the information processing in general well I think you can imagine that tying a knot in something is a very good way to store information in fact the you know this was done in Mesoamerica for centuries and these things can still be dug up and the knots are also there and there the encoding of how they would how they would hold information in knots lasts for a long time the U in order to get the information out you have to read the knot and take it out and it's you know it's hard to remove that information much harder than destroying a piece of paper for instance so you could ask is there an analog of this can we take the wave function of some quantum mechanical system and tie it in a knot in some way that that knot is hard to remove can we encode topology in the wave function and give it the kind of stability that a knot has and the answer is maybe but first we have to invent a particle that will remember that it's been tied in a knot and there aren't any so far maybe the particles that we live with are called fermions and bosons and that's this thing that I were that I told you about electrons already that if you switch two of them around you need a minus sign those are fermions electrons and most of the particles that we're used to these days if you switch if you take two of them and you switch them there you get a minus of the wave function which means if you switch them twice which is the same as wrapping one around the other one you come back to the same wave function no memory no memory that one particle went around another bosons are the other kind of particles that we live with right now and in either case if you surround one by the other nothing happens but in lower dimension there can be particles that remember when one particle has encircled another and in so doing changes the wave function it's as if they have like a string hanging down in the third dimension below them and when you move them around each other it tangles the strings around each other and in a way what we would like to try to invent would be a system of all of these particles and they're all moving around each other and what's coming down below is like weaving and that the cloth that's produced from the memory of the particles going around each other is the memory of what what computation has been done if we could only make particles that do this and so the last bit of my talk was to talk about this I'm a little shy on time so I'm probably not going to spend that much time but it is interesting that if you did see who won the Nobel Prize in Physics this year and what it was for these guys Duncan Haldane David Salas and Michael costal it's got the Nobel Prize for studying topological states of matter and if that didn't make any sense to you there's a nice description and now you see why they're talking about flatland because it has to be in this reduced dimensional space so that the string can hang down into three to the imaginary string can hang down into three dimensions and it's interesting if you read the citation on them on the Nobel website it says topological insulators topological superconductors topological metals are now being talked about these are examples of areas which over the last decade have defined the frontline of research in condensed matter physics not least because of the hope the topological materials will be useful for new generation of electronics and superconductors or in future quantum computers so what's that all about how do we compete with them well that's what I wanted to end with I think that in this for the sake of of time because I'm probably pretty much out of time holiday yeah so then I'm gonna skip forward and not tell you a long interesting beautiful fantastic history of these devices unfortunately but instead to say that that they look like this these are wires nano wires made out of a single crystal of material with aluminum that has been grown on the surface and the aluminum at low temperature superconductors and the combination of super conductivity the material properties of the semiconductor which includes something called spin orbit coupling an applied magnetic field can produce a particle that theoretically has these so-called I'll give you the term for it non abelian particle statistics meaning they remember when you move them around each other and so we're now in this game where we're actually much more primitive than than the rest of the qubits because we're trying to do it in this crazy topological way this is also going on in the lab and we hope that there are these so-called Meyer onna zero modes these particles that have these statistics located along this wire and I just wanted to give you a little tour of what this thing looks like in the lab that's what the device looks like we use these things to measure where the my Arantes are and they live at the boundaries of the superconductor that's the device right there it's connected via all of these wires that when you zoom out let me go back one when you zoom out it looks it's connected here that goes out to the edge of the chip here's what that chip looks like on the refrigerator on a circuit board that lives inside of a copper box the copper box lives at the bottom of a machine that goes to 10 mili degrees above absolute zero so we take the entire device down eventually it gets all buttoned up here and there's a sign on the outside that says caution strong magnetic fields but inside of there that little chip is sitting at ten million degrees one hundredth of a degree above absolute zero with these new non-abelian particles that remember when they've been wrapped around each other as possibly the basis of a future technology now life is gonna have to get more complicated and the theoretical results that say how to move these things all around each other each one of those X's is one of these topological properties and it's all happening right now it's all happening now that the theory is coming out and saying if you can make these non abelian particles if particles can remember that they've gone around each other here's how you can make the fabric of a computer that will remember and will be as immune to decoherence as a knot tied in a wave function now that's pretty exciting if it works to me it feels like pure physics but to the technologists that support it and I have to say Microsoft supports a huge effort in our lab to do this is this idea that maybe this is going to be the answer to cloud computing this or the spins in the semiconductor or the the superconducting qubits that Google is making all of these are interesting technologies and I want to end with this slide which is the response if you haven't been browsing the NSA website lately I'll show you this page from from the National Security Agency which is they are worried about the existence of these machines I'm worried about the failure to make one of the machines but they're worried about the non failure and so you can see that what they say is below we announced this is an announcement on the NSA website below we announced preliminary plans for transitioning to quantum resistant encryption algorithms algorithms that are provably immune to quantum encrypt to to having a quantum computer what's the mathematics of proving that it's not possible it's also an opened beautiful math problem without I'm going to end I've given you a little taste of an advanced technology that stick around let's see how fast it develops thanks [Applause]
And so here we are at the end with one last question. How will quantum computing change our lives? if our desktops and our phones are not going to be quantum machines any time soon what will the quantum revolution mean to us? Richard Feynman once said you can't truly model a quantum universe on a non quantum machine and the ramifications of that are profound. Optimists posit that quantum computing will revolutionize everything from engineering to medicine, consider the field of chemistry if we could model things more accurately at the molecular and quantum level we could better simulate how chemicals interact with the human body. We could better understand how the medicines we take get distributed at the lowest level. We could remove the veil from neurochemical interactions and come to a better grasp on how the complex chemistry of the brain really works. Or we could combine quantum computing with earth sciences and agronomy, over 1% of the world's total energy is used just to produce fertilizer every year, this is because most of it is made through a complex and inefficient process that we haven't really been able to improve on in the last hundred years. But with quantum computing we might be able to find a much more efficient catalyst and save the world literally millions of tons of natural gas every year and along those lines if we want to talk about the environment, right now we don't have a really good catalyst for simply capturing carbon out of the air. When people talk about carbon capture and using it to lower the amounts of CO2 in our atmosphere right now they're basically only talking about doing it with bulky systems at power plants themselves, if we could use quantum chemistry and quantum computing to help find a way to do this in the ambient environment it would be a major step forward towards solving our CO2 build-up crisis. Or in the material sciences realm one of the greatest quests of the 21st century is to create a superconductor that doesn't require serious sub-zero temperatures to action superconduct. If this is possible, it will require an exploration of materials at the quantum level, something quantum computers will be far more suited to handle than today's machines. Now more immediate realistic things that quantum computers will provide us our advances in areas like machine learning and data handling. Many of you have probably heard of MARI/O, it was an attempt to have a computer learn how to play Super Mario World simply by telling it that the further right it got the better it was doing and then just leaving it alone and letting it play Each time through it would just press some buttons and see how far to the right it got. Less successful attempts were discarded and more successful button presses were integrated into its next run, eventually it learned how to beat levels in Super Mario World That basically is machine learning but instead of running the first level of Mario a ton of times, most of the time modern computers are fed gigantic sets of data, told what success looks like and then set about trying to learn from any of the success cases. They find within the realm of data they've been given and eventually if all goes well, they produce algorithms. That should help us create or predict future success. City planning, cancer metastasizing, movements of the stock market… All of these are problems that we might be able to crack with machine learning, and heck we might be able to build cities that avoid getting major traffic jams, predict much more accurately when a patient's cancer is going to spread or see a likely stock market crash far enough in advance to mitigate it, if we could really sort through, compare and analyze the data we have. And quantum computers are far better at this than the binary computers we have today. Sorry guys! But quantum computing doesn't come without its dangers, I mean just consider security encryption Right now, most of our encryption from our email encryption to our private social media data to our Amazon shopping, All of that security hinges on one straightforward idea, they all depend on how difficult it is for modern computers to factor the product of two enormous prime numbers, the staggering computational requirements of that task are what make modern encryption secure. But quantum computing by its very nature makes that impossible problem: soluble. Quantum algorithms ability to assess entire ranges of possibility at once rather than having to check each possible solution individually. Changes everything and I'm not saying the unbreakable cryptography of today will become child's play but it sure won't be impossible anymore. Modern encryption won't truly be secure once quantum computing becomes a reality which will expose our data to a whole new wave of security threats. Allowing governments to spy more efficiently not only on each other, but on us. And forcing us to rework how we do some of today's most routine internet-based tasks Of course, at the same time it also opens up new possibilities for improving encryption creating a whole new field of quantum cryptography. Which could potentially allow for new approaches and enable brilliant minds to fundamentally change how we think about security in the modern age. Quantum computing also presents a massive threat to cryptocurrencies like Bitcoin, most of today's crypto currencies depend on a security protocol that could easily be overcome by quantum machines. And even if quantum computers weren't used to actually overcome the systems that keep cryptocurrency secure, they could be used to mine cryptocurrency far faster than the fastest computers set to the task today potentially flooding the market and dramatically tanking the currency's value. So thanks to those theories that Einstein and Bohr debated not a hundred years ago We will soon have safer and faster air travel with routes built to make it easier for humanity to connect across the globe, we'll be able to detect cancer sooner through machine learning And solve even more complex problems of protein folding and DNA interactions to create yet more effective drugs. We'll be able to better forecast the weather preventing deaths from flash floods and freak storms, and we will be able to better anticipate market crashes and potentially prevent the loss of hundred of thousands of jobs We will even be able to better understand the stars as quantum machines help us sort through the enormous pile of data our modern telescopes provide. Yet at the same time the quantum revolution may fatally wound our nascent cryptocurrencies. And create a new battleground for cybersecurity potentially putting everything for a military hardware to eBay purchases at risk. But all of these ideas are in their infancy. Right now, in Universities and laboratories across the globe people are building the algorithms that will make these things possible. Because to take advantage of the potential of quantum computing we have to think with quantum mechanics, we have to build whole new algorithms to tease out answers from the quantum superpositions or the space of possibility of our qubits. And even for problems we've already addressed through traditional means we will have to find new ways to address them ways that involve realigning our thinking and approaching computer science in a way that most engineers out there haven't even begun thinking in. So will quantum computing revolutionize the world? Maybe. That's largely on us. Can we learn to think in this way That was once so disturbing, so counterintuitive even to Einstein? Can we make the theoretical a reality and then build off that reality? Can we work with abstractions so complex that even the greatest minds couldn't agree on what exactly they meant? And if we can do all that can we do it in a way that's positive for Humanity? Can we do it in a way that doesn't simply enable governments to more closely monitor us? Or allow advertisers to better target us with their ads? I don't know. All I can say after having wrestled with this for so many weeks. Is that the potential is there, And that makes this a very exciting time, because knowing the potential exists one simple question remains… That's right Zoe. Can we seize it?
you can use topology to make a quantum computer work now topology is the word that mathematicians use when they want to describe the properties of objects which remain unchanged if we smoothly deform the object without tearing it topology is irrelevant to quantum computation because we would like the way a quantum computer processes its protected information to remain invariant if we deform the quantum computer by introducing some noise or error now physicists have known for a long time for decades that there are physical interactions that have a topological character for example I can transport an electron around a tube of magnetic flux and that will modify the quantum state of that electron even though the electron never enters the tube in a way that depends on the enclosed magnetic flux and that modification of the electron state is unchanged if I deform the trajectory that the electron followed all that really matters is a topological property that the electron wrapped once around the flux tube now we know more exotic types of such topological interactions that can potentially occur for particles in two-dimensional systems which we call we call these particles non abelian anions so it turns out if you have many non-abelian anyons there is a very large number of possible quantum states for those particles and all of those states locally look the same they differ only in the collective properties of many any ions and that's just the type of encoding of physical information that we would like to hide the physical state from the environment so quantum computation can work and not only that we can process this information in a simple way simple in principle by exchanging the particles which changes the many particle quantum state of many any odds so we can envision operating what –get I have called a topological quantum computer we would initialize it by preparing pairs of any ons and then perform a sequence of exchanges of the particles so that the world lines of the antion's would trace out a braid in space-time and to read out the computer we would bring the antion's together in pairs and observe whether they annihilate one another and disappear or not well what's beautiful about this idea is that the information that's being processed is very non locally encoded and therefore protected from the damage that could be caused by decoherence in principle as long as the braids traced out by the world lines of the particles is the right braids will do the right computation and get the right result well at least that's how it's supposed to work now the plight of the any on has been noted by the poets who have said you and your buddy were made in a pair then wandered around braiding hair braiding there you'll fuse back together when braiding is through well bid you adieu as you vanished from view alexey exhibits a knack for persuading that some day will crunch quantum data by braiding with quantum states hidden where no one can see protected from damage through topology any on any on where do you roam braid for a while before you go home and this poem goes on to but you get the idea so this is the theorist version of computing with any owns can we really make it work in a real physical system well here too there's an interesting story that involves three members of the Cal Tech faculty Alexei Gil Raphael and Jason Allison Alexei again started the ball rolling with a very stunning idea some time ago he pointed out that it's possible under the right circumstances for an electron in a wire to split into two parts for an electron in effect to be sawed in half well what he told us was that if I have a wire in the quantum regime there are really two types of wire an ordinary garden-variety superconductor and what we call a topological superconductor and at the boundary between these two types of wire there's an object we call a Meyer on a Fermi on what you can think of it as being like half an electron and if we allow an electron to be absorbed by the topological superconductor it sort of dissolves away and disappears and thereby changes the state of these my Arana fermions so in this way there are really two different states one with the extra electron added and one without and locally these states look the same this is a topological encoding of information the type that we can hide from the environment that we might want to use in a quantum computer well originally in qatayef psy.d a– was a rather mathematical proposal he had a model in which this phenomenon would occur and what Raphael and Alice say and others explain is how we can really make this practical by combining a semiconductor wire with a superconductor and some other clever tricks and just in the past year or so we've seen the first experimental evidence that an electron really can be absorbed by a topological superconductor and disappear as I described but the experiments are still not definitive and more experiments will be needed if that is achieved it'll be a real milestone for physics apart from any long-term potential technological implications now can we really use these Bionic fermions for computing well here – I will say and Raphael and others had an interesting idea which is we can imagine a network of wires in which there are T junctions and if I want to exchange the positions of two of these my honor fermions I can do it in three steps first by using electric fields move the meijer on a Fermi on around the corner of the teeth Junction and park it then move the my Renault Fermi on that was initially on the right over to the left and then unpark the first guy and by that way we have exchanged the positions of the two particles without them ever coming close to one another that's just what we need to do to perform an operation on topologically encoded data that hasn't been done in experiments yet but we're hopeful that it can be in the next few years