Christopher Monroe - “Quantum Computing with Trapped Ions”

today to the day going on and I guess to follow up on Karl's quip it's true that when when I graduated with my PhD here Cornell it simultaneously took a position at Jilla the University of Colorado and he begged me to be his postdoc I I thought it would take them ten or fifteen years it took them only two or three so there was a dubious move dubious move for sure in any case I've since then while since about the mid-90s have been working I'm still an atomic physicist that's my native hat I guess but I've become a little more generally involved with computing and quantum computing in particular and the cross there of course is that atomic systems individual atoms one at a time a bunch of atomic clocks if you will are the leading candidate to build a so-called quantum computer and I want to in the colloquium spend a few minutes defining some very basic terms and motivation behind it and then talk about some experiments recent recent developments in the field and I presume most of you have heard the term quantum computing or quantum information and right now it still is a rather speculative field and it's it's scary having a company also and my co-founder John st. Kim is in the audience here he's a stanford product at duke university he waved your hands and so it's just it's a scary position having a company that's building devices where we don't even really know what they're going to be useful for it's very interesting time but we are going to build it nevertheless and it will we do feel that it will do something so hopefully I can tell you that story so the field has some hype there's no doubt and even the motivation there's always there's always something hiding under every piece of good news you see in quantum computing and the first piece of I won't call it hype but we know Moore's law very well especially in this part of the country this is the number of transistors on processors throughout the years from both Motorola Intel this Moore's law says something like the transistors are shrinking by a factor of two every every every couple of years or the number on a given chip is growing by a factor of two every few years and the common thought here is that that can't continue forever and if you try to stay on this exponential over the next few decades you find that you run into some interesting roadblocks that is the transistors are getting so small right now they're you know seven to ten nanometers in size the features if they get really really small they're going to you know come to the boundary of individual atomic structure and at that point you probably can't shrink the information storage in the usual way of making the transistors smaller now I don't want to say that means that we have to go to quantum computing but quantum computing does offer one potential to stay on a certain type of exponential not exactly the number of transistors on a chip and this was first pointed out remarkably about sixty years ago by richard fineman in his very famous APS speech this is at an ApS meeting there's plenty of room at the bottom most mostly probably no this one lots of cool quotes in that lecture but the one I like best is that he's speculating after the advent of the first solid-state transistor which was a big thing it wasn't ten nanometers it was more like ten you know ten inches on the side or something the idea of shrinking that thing down and he imagined the pasta Majan the possibility way back then of Moore's law shrinking down to individual atomic scale and he has this little zinger that when we get to that level of a few atoms per circuit there are completely new opportunities for design and it's just amazing he had no idea what that opportunity would be but he knew there would be an opportunity because the laws of physics are different when you have fundamental constituents of nature like atoms these are the laws of quantum physics and again at the time there is no nobody knew that nobody talked about quantum computing back in 1960 but let me not now now step back and tell you a little bit about how you the the the finding terms of a quantum computer from the bottom up and we'll go from there in terms of its potential opportunities and I think since the last 20 25 years I would say that this opportunity has shown itself to be the quantum computer ok so quantum computers are very much like classical computers only they operate not with bits but so-called quantum bits so instead of being in a state definite state 0 or 1 like a flip-flop a quantum bit can be in a superposition of 0 and 1 and so as Shannon and touring taught us bits are abstract you can represent a bit in any physical system that can be used as a computer well qubits are the same they if if you have a quantum system whose superpositions follow a wave equation as is quantum mechanics then you can have a quantum bit now of course this quantum system has to be very well isolated to maintain its coherence and so a typical example might be two states in an atom this is this is an atom with one electron that has ignore this complex nucleus with one electrons but one electron is in two states at the same time we're comfortable with that it could be states of spin or orbital Liang or momentum whatever but we can encode a qubit in those two states of a single atom and the problem of course is that if the system is not isolated or it's measured the superposition collapses into a definite state 0 or 1 with probabilities so often often when I when I lecture to a public audience about quantum computing or even quantum physics it's very simple to state what quantum physics is we have a wave equation over here and we have probabilistic measurement over here that's pretty much all there is to it because all the math and quantum physics comes from how alpha and beta the the coefficients of the supervision how they evolve in time that's a wave equation and if you're comfortable with wave equations in math there's nothing that's not necessarily a quantum concept the wave equation that's fine the weird thing is of course that we have probabilities that have to be in the theory so when you look at a quantum superposition it randomly pops into one or the other based on those weights now another concept with quantum bits that that's a little more subtle is the concept of entanglement and that is if you have multiple quantum bits they can be prepared in interesting super positions when you consider the measurement process here's an interesting super but it doesn't look very interesting it's just two quantum bits prepared either in the state 0 0 or 1 1 I should say and 1 1 with these weightings and of course when you measure this system it pops into one or the other and what's interesting about this measurement is that whatever you do those two qubits are correlated perfectly and by the way before you make the measurement these two qubits could have been in principle separated a very large distance in which case when you measure one the other ones perfectly correlated it seems like there's a wiring there it seems like there's faster-than-light communication well there's no communication of information but there is something interesting by the entanglement you get these strong correlations without real wires to be there and sometimes I tell this correlations without wires again I'm being a little fast and loose here because correlations are not necessarily useful and to make use of them you have to do some other you have to do you have to make bigger entangled States and do interesting things with them so let me try to tell you that story so my last couple slides on general Kwan confusing well clearly a quantum computer is going to involve lots and lots of quantum bits lots of qubits and we're going to throw all them together and make very complex entangled states so if you have n quantum bits there are 2 to the N possible states 2 to the N and bit binary numbers and you can in general in principle store a superposition of all those exponential binary numbers so I like to think of how quantum computer works and again this is very fast and loose it's it's sort of a good news bad news good news story the first piece of good news is maybe evident this that's this sort of exponential growth you get just because the size of the space spanned by all these qubits grows exponential there are exponentially many amplitudes or weightings that you have to ascribe to n qubits this is this is just three cubits so there's only eight of them but if this were 300 cubits this would be to to the 300 weightings that you would have to use to describe that quantum state to to the 300s big it's it's ten to the ninth er something like that and that's more than the number of particles in the entire universe so by some argument if you need to do something that involves 10 to the 90 pieces of information you have to use a quantum computer you have to use a qualm system there's not enough space in the universe using classical computing to just deal with that amount of information okay so that was itself a little bit of an overhyped statement because to use the informations really tricky how do you get it out and that's the bad news of course if you this is sort of a it's hard to draw a parallel this is a parallel processor where we have multiple inputs at the same time so here's a three bit processor and we have different weightings of those eight states and then after the quantum process happens which is maybe mysterious maybe it's computing the logarithm of all those inputs the good news is you get to have this massively parallel processing the bad news of course is that when you look at it when you measure it you only get one answer at the end and we're still you don't know what answer you get at the end because it's ran it's probabilistic so in fact this is worse than a classical computer I think because if you're computing a one to one function you don't really know what output you got so you might as well just do them in sequence one after the other but we can do that classically right so quantum computing for one-to-one functions are probably no better than they are no better than classical computers which is too bad I think most of the computing we do is one-to-one most of the computing not all of it and that's the final piece of good news and so this so I'm sure Fineman had reached this conclusion in 1959 and didn't really know where the opportunity was but in the late 80s and early 90s this fellow David Deutsch started toying with storing information and quantum systems and he came out with some interesting ideas that involved interference of these of these weightings or these amplitudes before measurement remember these these amplitudes follow a wave equation and like any wave property sorry there's like any like anyway they can be described by the wave equation there's the process of interference and the idea in a good quantum algorithm is generally for all these interferences I've it's hard to draw this but these red dots are sort of interferences between pathways if you want all the almost all the interferences are destructive where there's only one or a few a very small number are constructive and then when you make a measurement there's very low entropy here there when you make a measurement you can get information on all the inputs okay so there exists the good news is there exists applications where this works and the tricky thing is what are these red dots these are quantum gates these are similar to the NAND and or an XOR gates we have in classical computing but they involved quantum bits and quantum interactions I've drawn them as binary interactions between any pair of any pair of bits okay so I'm not an algorithms expert but there are a few very popular algorithms you probably know about one of them is factoring large numbers if you take a number with a thousand digits and if I give you that number and ask you to factor it there is no known fast algorithm for that it's exponential in the size of the input in fact you can't factor a thousand digit numbers too big well Peter shor in 1994 showed that a quantum computer if sufficiently large to store the big number and do have work space it could factor that number fast and he basically realized a very old result in number theory that if you find the periodicity of a certain complex function involving the number you want to factor if you find the period of that you can show how it's related to the factors of that large number and find the period the period of a function is exactly of this type the period of a function is it it depends on all the inputs so it's a global property and that's what we look for in just quantum algorithm property and that's one example it's a killer example because the inability to factor large numbers is behind all popular public key encryption as you probably know so the fact that quantum computers could if they could be built would factor numbers was very important to certain three-letter agencies and in fact these certain three-letter agencies were in a position 20 years ago of funding fundamental quantum science research to see when and if one of these things could be built so we had our own Moore's law in the field and here's here's one expression of that in publications this is over the last 15 years or so the number of from Google Scholar the number of articles per year with one-one of it with any one of these three terms in it so it's a huge field now lots of its most of its theoretical which stands to reason because we they're not a whole lot of known killer apps like factoring but they're they are out there and in fact before I start talking about experiments and in physical platforms one very general application out there and again it's I can't really point to exactly how this is going to work but the idea of optimizing is just like one of those global outputs right if I ask you what the tallest peak in the rocky mountain range is that's a function of of the entire landscape there's only one answer so if I give you a function that's very spiky this is only two variables it's very easy to identify the minimum but I think give you a function with lots and lots of inputs it's very hard you there's exponentially many configurations you can't test them all but the ground state is in fact a unique a unique property of all the inputs and it may be true that in certain cases a quantum computer might allow us to find those minima and this this can apply to all kinds of different examples and again I want you get into details this again this will look overhyped but I have to tell you optimizers right now our approximate s-- they're heuristics the best classical optimizers we can't prove why they work and why they produce the best answer and I think probably the first application of upon computer will be some heuristic that you can't prove that that it'll beat anything classical but it does beat everything we know classically and my favorite example is actually the Traveling Salesman problem which we know to be an np-complete np-hard problem that is what's this identify the shortest path between a bunch of cities that scales exponentially with the number of cities now you can apply classical on this and get the best answer you think you have and if a quantum system can somehow find a better answer even though it's not the best if it's better than a classical optimizer then it's useful and so it remains to be seen whether a quantum system can can model the Traveling Salesman problem but you know the Traveling Salesman problem to me is just an energy landscape and you're trying to minimize some energy function that that depends on lots of variables that's what we do in quantum we have Hamiltonians which are energy functions if we can carve out and control that Hamiltonian us with with sufficient accuracy to our underlying problem maybe there's some headway to be made there and there's other work of course more in the physics side of things magnetism is very interesting even classically it's interesting but quantum magnetism having bar magnets effectively that can be both north and south at the same time that's like a qubit and if you get a bunch of qubits on a lattice how they interact and forms exotic states of quantum magnetism is very interesting it's also related to an optimization problem that looks like a nonlinear spiky function with lots of variables and another example of optimizers involves simulating complex structures where I mean this is probably way too complex for the next many years but even a simple molecule with maybe a hundred electrons there's there's too much there's there's too much configuration space what is the ground what's the binding energy of that molecule it's very hard to calculate we can approximate it using many numerical techniques in chemistry but it may be that if we can model this as a Hamiltonian a coupled fermion Hamiltonian map it on two qubits and it may be that this this will be an interesting application so again a little bit on thin ice I'm starting to learn about these things but I'm more of a hardware guy coming from atomic physics and I'm glad to say that right now there are a couple of platforms out there physical platforms that are looking really interesting to build so this is a figure I stole from an article in science a year or two ago and so there are a couple of platforms and I would say superconductors and trapped ions are by far and away the leading candidates to build small quantum computing devices and there's some other very interesting ideas and this will you know the research in these and other platforms will continue I think to to evolve and I think one that's missing here maybe I'll comment on that later neutral atoms that are popped into rid berg states has over just the last year it's looking very interesting but trapped isin superconducting loops the reason i guess the reason they're they're very interesting now is if you look at remember the gates that show the interactions between qubits with these systems we can control those interactions with the sufficient accuracy over the last several you know decade and a half or so the civility or the the error rate per quantum gate is getting better and better and by quantum gate i mean a gate sort of like a NAND gate between two qubits it's a two qubit gate so it's nonlinear and that allows you to make entangled states and in both these platforms things have gotten better and better the one thing i want you to keep in mind i'll return to this later is that all of these data points every one of them involved exactly two qubits so that's why this this plot is sort of irrelevant entirely irrelevant i mean it's good to know the fundamental limits of a gate between two qubits but if you have lots of other qubits around they'll almost certainly not help the gate you're trying to do between those two qubits crosstalk and other aspects will come into play okay but this is again sort of a i come from a background in metrology and atomic clocks we like to know what the fundamentals are and both these systems are very good so atoms why atoms well atoms in a sense are nature's qubit because they're standards in fact we use energy levels within an atom that are defined by the hyperfine levels in the ground state of these atoms these are the same levels that are used for a ton of clocks and they're they're incredibly coherent very long lifetimes and even more importantly the atoms their standards so they're reproducible that's that's what makes a good clock you can reproduce it an atom of you terbium here is the same as an atom of ytterbium in washington exactly the same well to a part in 10 to the 12 easy if you want a part in 10 to the 15 we can do that too but it's it's much better than we need no solid-state platform can have nearly the rep replication of individual atoms well the great thing about solid-state platforms you can print zillions of them on a chip and that in a sense is one aspect of scalability you can throw lots of them and scale it but because every qubits different in these other systems and those differences can even drift over time that's a big problem when you try to scale things up now in atomic physics we don't have that problem in scaling up the problem we have in scaling up is controlling the system and that means that we have to resort to techniques and cold out on physics laser cooling these atoms are in a vacuum chamber and then and they're probably they're trapped in three dimensions in in the case of the platform I'll talk about atomic ions they're held in an ion trap this is a chip trap that is made out of silicon at Sandia and I'll show another picture later individual ions form a linear crystal and it floats above this surface this chip has I think I think forty eight electrodes you can see these little piano keys to detail there but the idea is we can trap individual ions and they stay there for a good long time and they're all identical and our wires are provided by lasers and let me talk a little bit about that so now diving down into an individual particular atomic clock qubit and in this case I'm going to use you terbium 171 plus but there are a handful of other ions that are equally well they're there they're also appropriate it comes down in atomic physics you choose an atom and that chooses your host of lasers and so forth and so the ytterbium is particularly nice in terms of the lasers that we need as I said the qubit is stored in the hyperfine ground state these are so these are sometimes called clock states in atoms because they're so stable and I've written this frequency it's a microwave twelve twelve point six gigahertz I've written it all the way down to one Hertz I could write a few more digits if you want but that's kind of boring we don't need that resolution but every qubit has this frequency now there are a couple of other levels here these are daemon levels they're shifted with a magnetic field but these two their clock states meaning that they're there they're not perturbed by external magnetic fields very much that's what makes them good now the detection of when we want to detect a qubit so we can store a superposition using microwaves or lasers I'll show you in a minute when we want to detect this qubit in atomic physics we almost always use cycling transitions optical transitions to excited States and in this case when we shine light in the near UV we know this wavelength to about nine digits it couples to excited state and this excited state can only come back down here now in fact it can come to these two but we can clean those out easily just a detail but this is a cycling transition that goes up and down really fast the single atom will emit ten to the eight photons per second so it's a very bright source in fact here's here's here's real data on integrating single atom prepared and I call it spin up sometimes you call that one and zero bright dark spin up spin down in the spin up state in 50 microseconds we collect roughly 30 clicks so we get a click every microsecond well I said it was ten to the eight photons per second we're only collecting ten to the six per second so that means we're only collecting one percent of the light but still a pretty healthy signal even after integrating for a few tens of microseconds so this is a repeated experiment or many times you see the post audience statistics now the whole point here is that that's an image by the way of that single atom under the same conditions the whole point here is that if the atoms in the other state same experiment the only difference the atoms in the other state well now we're 12 gigahertz away from a line that is only 20 megahertz wide so the atom is transparent to that light and this is the data we see nothing we see darkness mostly and the point here is that these two are so well discriminated that even in a single shot we can detect with very high efficiency and I would say dung sightings in the audience here but I didn't plant this he this is this is the kind of world beating data here on hyperfine qubits you can easily get three nines of detection fidelity if you have good detectors and good collection optics so we have really good detecting by the way in a quantum bit when you want to measure it you need to measure it with very high fidelity because you might need to measure million of them so that means you better have lots of nines in your fidelity per qubit and okay so how do we make the cubit to begin with in a coherent state what we actually do this with another set of lasers that that drives two photon transitions and the reason this is important is that this is a coherent process because each of these two lines from the laser is very far detuned from any excited state so it's dispersive the interaction it's coherent and we can drive so called PI pulses like from NMR language and make super positions and we can eventually do gates here and I would say the single most important feature of your turbine 171 is that there is sort of a magic wavelength where this is best and it turns out to be 355 nanometers which is an important wavelength is it's it's a third harmonic of YAG it's easy to get that kind of a laser as much power as you want this this is a pulsed laser which is technically this is a little bit technical but that's good too because if we have a frequency comb so we can drive these transitions and control the rep rate we can control what we're doing in the atoms so I said you can buy as much power as you want this is a similar this is 351 nanometers but the same type of the laser that's used in inertially confined fusion up at Livermore well the one we use is quite a bit smaller but the important thing about this laser again mobility computer but you have a laser well this is actually a good laser it only has one button the on button this is made for lithography it's made for the upper levels of CMOS lithography and the shell Herron makes 200 of these a year and they're turning heat literally so when we turn these on they work for years that's the I mean I'm very comfortable inside any laser that's why I've done most of my career on but I'm just as comfortable not doing that so the laser is sort of now a black box that we can use to control our qubit it's important because this is going to drive all of our gates it's going to drive all of our operations it is the bottleneck of everything we're doing with these atom these trapped ion quantum algorithms so how do we entangle them this is this is sort of an old story I mean it's the the fundamental way that you entangle atomic ions was put forth literally weeks after serac and Zoeller Ignacio was actually in the building earlier today but Alma think he's here now Ignacio serac and Peter Zoeller literally weeks after they heard of the algorithm for factoring numbers they came up with this idea of how to do gates and how to build an ion trap quantum computer it was not at the system level it was just how to get the fundamentals how to do entanglement between any pair of ions in principle and it was refined later by several others especially mullmer and Sorenson and that's kind of the version everybody uses now and this is a basic idea of how it works it's not hard it involves laser forces if you know what optical tweezers are we're going to do this with individual atoms the idea is we can use those 3:55 lasers if these are your terbium ions to apply a force on any one of these atoms and the force is interesting because it depends on the qubit state it depends on whether you're spin up or down and that can be done through selection rules and polarization and so forth I want to get into the details but suffice to say that if I shine a laser from below it can you need a pair of lasers actually from blowing and above you can transfer momentum to the atom in such a way that if the atom has spin up it moves up if it's spin down it moves down so if you want to do something between these two atoms you simultaneously illuminate those two atoms and only those two atoms now if you do that you'll note that there are four possibilities of these two qubits if they're down down they both move down together and note their Coulomb interactions are charges remember I didn't talk at all about the trap is these a linear crystal of charges if they're both down they move down together and their their Coulomb interaction is exactly the same as it was no change they're both up it's the same but if they're down up if they're in hick states down up or up down then they're a little further apart and that that little extra distance due to the diagonal connecting them amounts to this amount of energy they're further apart they're in a lower energy state you can see it falls off like 1 over R cubed it's a dipole-dipole interaction because you're making if you have up plus down here a superposition you've been a little a little electric dipole you've separated the charge and so there's stands to reason you expect are cute potential here these dipoles are pretty big they're in if you familiar with the by units these are big these are big dipole moments because we can we can move these guys several nanometers the atoms and of course they're much smaller than a nanometer each so these atoms are they're separated a good distance now Mark can separate atoms by 50 centimeters so we're not going to compete with them but those are neutral atoms they don't they don't follow this interaction either but it's the same idea you Mark also applies to spin dependent force in his atom interferometers and he can let them fall ten meters in there they're really far apart here the atoms are fixed but we sort of the same physics now if you look at these four possibilities only the states with different spins find a phase lag in their quantum state that's just the wave equation if you change the energy of these guys then they they have a phase lag and this gates very interesting because it's nonlinear what happens to up up is not a product of down-up and up-down okay so when when this angle when this phase angle is PI over two that's equivalent to making full entangled state between those two ions oh one thing I wanted to hide I didn't want to hide but I kind of had to is that this only works if this operation is really fast so zip zap them and then they then they return otherwise is it's it's like a rubber band or violin string there's all kinds of modes of motion that's indeed a problem but we deal with that by I'm not going to get into too many details but we can shape the laser pulse to take care of all those normal modes of motion and keep that in mind because we're not going to be doing this with hundreds of ions but maybe dozens of ions okay so keep that in mind but the same it's it's a very similar physics it's still a Coulomb interaction that's mediating this entanglement so we're mapping spin to motion and then motion to spin that was the original serac consoler idea now in fact the the native this is actually called an icing gate if you want there's a Z Z type interaction effectively in fact in the lab it's a little more complicated we actually have an X X Ising model it's a different kind of gate and this is the evolution operator that gate using NMR language and these gates aren't fast they're in microseconds or so for a computer you want fast of course but this is a quantum computer we don't we don't need fast we have we have an exponential entanglement in our back pocket um in any case because atoms have inertia and we have to push them around the gates are relatively slow compared to superconductors the fidelity is so far again with just two and exactly two we can get three nines so far but that can probably be even better with lots of ions were in ninety-eight ninety-nine percent right now and again it's all about the lasers and controlling those lasers you know I should comment briefly that in superconducting circuits I didn't talk much about them their gates are about a thousand times faster so that's good clock speeds a lot faster there decoherence is about a million times faster so anyway it's the ratio that sort of matters here and the superconducting decoherence is a big issue just the fundamental qubit itself losing coherence so as long as you have some time to wait depending on the depth of your circuit how long your quantum computation is the AIA system will be able to go for a long long time all right so using this basic idea we started from the ground up with just a few ions and we actually learned something very interesting in doing this it might sound trivial but this is a schematic of an experiment with just five just five cubits here and these three five five nanometer laser beams the one coming from from the backside is global it's big and fat very easy to deal with that one the hard one is this one where we have individual beams that can be turned on and off with a very fancy optical switch here we can turn on all five at the same time we can turn any single any pair any triplet whatever and it's all from electronic controls on this multi channel all the cousteau optic modulator and of course this Coulomb interaction is long-range we can apply a gate between any pair and we do it you know I should say this this was a 1 over R cubed type of distance dependence but we in fact are better than that because we do gates that couple to all the normal modes of motion and the normal modes of motion are long range they're not one of our cubed so we actually can do gates that are independent of distance with a system of five and probably a few dozen we think we can scale that so we can do any of these with five cubits there are 10 pairs we can do any of those 10 gates we actually have to pre calculate the laser pulse schedule to do that there's some classical physics involved it's not hard and then we program those pulses and we're off to the races and what we realized in this system is that it was stable enough that we could just run it for hours and hours without thinking about the atomic physics and the vacuum system and the laser we were at the PC running circuits even though it's just five cubits and so we had to develop a system that I call it a full stack but this is a I should say a full university stack as best we can do at the bottom is the hardware we're returning all the knobs but then there's the pulse shaping making these lasers we pre calculate them but somehow they have to be called from above which ions do we want to do a gate on these are xx gates and rotation gates from an mr but if you look in the textbooks there's something called the C not gate the Hadamard gate which is sort of a square root of not gate and we have to come we have to we have to convert the textbook gates into what we have in the lab and that's sort of a level of compiling we're starting to look like computer scientists here and now at the very top we have algorithms somebody says Oh run the run the short factoring algorithm on five cubits I mean I don't know why we'd ever do that that's a pretty small number but they're there there's a circuit for that and we have to go through this entire stack of processes and almost none of them are really physics so this is an interesting exercise in I don't want to I won't call it systems engineering but this full stack idea is something that will have to play a role in the future as we build bigger systems so I want to go through a few again these are toy algorithms on these five cubits the first one in fact this was among the first ever demonstrated it's called the Bernstein buzzer Ani algorithm and this is one of the so-called Oracle algorithms that is sort of a toy means it's kind of useless it's like the game 20 questions right I think of a concept and you can I can you can ask me 20 years or no questions what is that concept so you have to somehow that the Oracle is mana the concept I'm holding in my head and here the Oracle is a function that has n bits on the input and it produces one bit on the output so this is a dot product of two n bit numbers and it's just a dot product so it's only one bit and the question is what is seen what's the hidden and string in that function well classically you have to evaluate it at least n times to find out what C is right you would evaluate it for input of 1 0 0 0 0 and then 0 1 0 0 0 0 0 1 0 to get every digit of C classically it requires n queries of that function and that's the Oracle the function evaluation quantum mechanically you can do it just once so somehow it's very expensive to evaluate F then you get a a win by doing this in a quantum way and the reason this works of course is that we're going to be able to evaluate a superposition of the input and process it in just the right way where C is the output of the circuit now I won't go into details this is just a 4 qubit circuit we use we use the fifth qubit as a ancilla working space and these are called Hadamard gates these are called controlled-not gates so depending on the state of that that rail you flip this one by the way this is a spacetime diagram all quantum circuits are space-time space vertical and time goes from left to right so you apply these gates so they're in superposition than you do the circuit itself has the vector C encoded in there so you can see wherever a bit of C is 1 you have a controlled-not gate between that and the insula and then you do further rotations than you measure these 4 and you basically measure C you have to read C right out in this operation and you've only computed F once because C is encoded in that Oracle you've only used the circuit once so here's the results on our 5 qubit I on track on a computer sixteen possible Oracles for four bits and this was the detected state it sees about ninety percent eighty five ninety percent well each gate is about 98% good and each of these controlled-not gates has a bunch of xx's so there's a lot of gates here so it stands to reason it's not going to be perfect the important thing I should mention is that we can do a gate again between any pair even though that's not really exercised in this algorithm so as it happens IBM around the same time we started this experiment IBM unveiled their quantum experience superconducting quantum computer and to their credit they put it on the cloud and it was looked at by some of the community as being a stunt I thought it was great because the amount of engineering to to to get a system and stand back and let people dial in their instructions and actually run very hard to do that I don't want to say it's gonna be the five cubits you're not going to do anything interesting we all know that but Jerry challenge a Gambetta are sort of the leads on the technical team at IBM and they have the system all hardwired so we ran this algorithm in their system in fact they had very similar fidelity stars 98 99 % 5 qubits and we got similar results not unexpected now what is different in their system is that their qubits are connected in a different way it's a 2d it's a 2d square lattice but they only have 5 so this is the unit cell I guess it's not very well connected they can't do a gate between these two for instance but for this algorithm you don't have to as long as you're smart about qubit assignment now you clearly pick this fifth qubit to be the middle one because it's the one that has to interact with all the other yeah and that's why it works pretty well well it doesn't work for all algorithms though this is the hidden shift algorithm that was first pointed out to us by Martin rattler at Microsoft he called us up and literally called us up and he said you know I've been running the IBM system and we've been testing this hidden shift Yaeger and it doesn't work very well on the IBM system I heard you have a five qubit system coming running on yours he said sure send the circuit so they sent the circuit and the hidden shift algorithm by the way it's another Oracle if I give you two functions F and G they're identical except for an unknown shift in the input it takes exponentially many queries to find that shift you have to evaluate at least half of the inputs to find out what that shift is quad mechanically just one so this is actually even better than the Bernstein buzzer on its exponential gain in the number of queries here's the circuit for a particular function I won't even say what it is in a particular shift and it's you can see this is a more complicated circuit it's more connected and when we run it on the two systems we see a definite degradation in the IBM system it's not about the qubits in the supercute exists it's about their connectivity and maybe this is obvious to you but it's it's interesting that if you're going to run an algorithm you'd better have a system that's that's appropriately connected to run that algorithm and so there's there's lots of black art and how to do that it's more computer science again how do you assign qubits in the right way how do you make the connections and so forth so we didn't have a cloud we had grad students taking orders basically on the phone and this this is this became a little bit of a it's been a little bit of an issue in the lab we've had lots of orders over the last few years we've been running lots of algorithms again these are only these are only a few qubits but you can see that there's one simulation in particular this was communicated to us by an MOT service team up at Intel until desperately wants to get get some kind of hardware working so that their their their theory team called us and wanted to work on some very small Fermi Hubbert simulation just a to site model but in fact this is the deepest circuit we've ever demonstrated only five cubits but it had 160 gates most of them were entangling gates and actually I want to I want to comment on one one particular experiment that has sort of stanford fingerprints all over it's scrambling tests that talked a little bit about this this morning which do with lending Susskind group so the the concept of quantum scrambling is more than entanglement quantum scrambling means that a system of qubits somehow samples the entire space spanned by the qubits the entanglement is sort of complete I guess technically if you look at any we were just just talk talking about the definition of scrambling if you look at any subsystem then that's smaller than the overall system then it's entropy is greater than zero so there's sort of massive entanglement and what's interesting is qualm scrambling is thought to model what happens in a black hole because a black hole is is is it's it's isolated and therefore it could be described by a some monstrous unitary operator and the question is how do we differentiate a scrambling unitary operation from a non scrambling one that might be entangling but not fully scrambling and this this is relevant to the the the black hole information paradox Patrick Hayden and John Prescott spoke about this while ago dealing with his information actually lost in the black hole what if you have one half of a entangled pair and you throw the other pair into that black hole is that information lost well the pair that you threw into the black hole will get scrambled and if you can observe the Hawking radiation from the black hole is evaporates you can make correlations with the one you kept behind and in fact it seems like you can you know this is the black hole information paradox and I think Lenny Anna's group talked about how this connects to you know wormholes being able to travel travel through space time and again I'm on thin ice talking about those but I do know about quantum circuits and here's a quantum circuit what does this have to do with scrambling well this is a seven cubic kilometer c't and what I'll note is that there's a three qubit unitary remember this is time in space and there's you the unitary and there's its inverse u dagger to me that's just a circuit but the property of that unitary that whether it's scrambling or not is is rather tricky and the connection to black hole is that those are the black holes this is a very minimal black hole of just three qubits and this one is I guess spinning backwards because it's the reverse black hole so but you know this is a three cubic quantum circuit we can apply u dagger it's just it's not hard to do that now what this circuit does it's really cool how this works and there's a nice interpretation in terms of wormholes and so forth the idea is that all of these qubits are initialized except an initial one which is prepared in some random state a known initial state we of course prepare many different states and we entangle pairwise these two these two these two we run U and u dagger in a sense we're running forward and backward in time and then we make bail measurements what that means is that we do it we see whether these two are in a particular entangled State and based on a positive measure of any one of these pairs in a particular entangled State this this unitary is scrambling if and only if that state gets teleported here and so we can directly measure this state here and say well was it a replica of the initial state and we're previous parent many times and do tomography on that state and show whether it is or not and by the way we can we can apply any unitary and I won't get into the details here this is a three cubic unitary it has lots of gates you recognize X X and ours there's a parameter in these rotation gates when theta is 0 there is no scrambling when theta is PI over 2 it's complete scrambling so we actually have a variable scramble unitary here and here's the data when theta is 0 the teleportation Feli is 1/2 meaning you know no scrambling and when it's 1 it's not perfect but because the teleportation is bigger than 1/2 and we see unambiguously they're scrambling and importantly we can separate the effects of decoherence in this unitary from masking a scrambling signal and again the this was we worked in collaboration with Benny o sheet at perimeter in Normal Berkeley on this experiment and Brian Swingle by the way again stanford stamps all over this he's now at Maryland and we talked to him all the time about scaling this to bigger systems and taking further measurements so I talked about quantum computing but let's step back a little bit we can also trap lots and lots of ions even if we don't poke individual laser beams on each ion and weave in one of our experiments we have you know between 10 and 50 atoms along a line and instead of doing discrete gates X X gates we can apply this overall Hamiltonian to the system this is an icing interaction between all pairs and j IJ is the icing coupling matrix it's long range and in practice it falls off with a power loss not nearest-neighbor it's not the one you learned in in stat mech 101 this is long range so it's very even though the ions are in d the interaction is not 1d necessarily now we can apply a competing transverse field to this Ising model and I won't get into too many details here but we can do all kinds of experiments in the dynamics of spins undergoing this type of interaction because these two parts of the Hamiltonian don't commute there's lots of entanglement and very rich structure in in the states we measure so with 50 or so ions here's a string of them all prepared along one direction the the spin up state along Z when we measure them as we increase B or J and we quench this Hamiltonian we turn it on suddenly after a certain amount of time we measure we wait wait for some amount of time roughly 10 1 over J times any way that looks like to go but as we increase B over J there's it's a little hard to see here but the and we take lots and lots of data the size of the domain that's formed along the x-direction reaches a minimum and then it comes back up if we plot the mean domain size as a function of B over J we see this kink that's called a dynamical phase transition it's not an equilibrium phase transition it's a weird system but I guess the only point I want to make is that you can't calculate where that's going to be the system is too complicated there are too many spins there's 2 to the 53 configurations of these spins and even though most of them you can rule out it's still a really hard calculation we use a long-range interaction I don't want to say this is a quantum computer I don't even want to say it's useful but it does show you something you could argue that this is something that says that dealing with qubits is something that you maybe can't do using classical simulations what's even more fun I promise I'll talk about Rehberg atoms at the same time Missha Lukens group had a similar experiment with 51 atoms prepared in Rehberg states with very short range interactions and they see interesting order emerge there as well these are neutral atoms they don't have very long lifetimes where the interactions are very strong kind of a complementary hard work if you're wondering why we stopped at 50 well the vacuum wasn't good enough with if you trap bigger crystals than they the background gas collides with them and they melt so one of our projects a lot of the community's going this direction is going cold I hate to do that especially on a system you want to call a computer but everything we've done so far the system is at room temperature even though the atoms are laser cooled this is this is not a dilution refrigerator but we get the electrodes that hold the ions in contact with a four Kelvin reservoir and we can hold big iron chains pretty much forever there's a little kink in the imager here positive said but there's an there's a missing tooth here this is a different isotope if you terbium and the impression is that that gap stayed there all day meaning that there was not a single melting collision so we're gonna continue to do simulation experiments on much bigger systems here so let me start to step back and I the next plot I started I stole from Google but I acknowledge them this is from HAARP in Devon and this is an interesting plot sometimes it's called the the NQ plot where the number of qubits if you want to build a big system what's interesting where should we go for what should we shoot for what what trajectories of our technology should we go after well the number of qubits we clearly want lots of qubits but we also need lots of gates if you have a million qubits you better be able to do well if you can only do two gates it doesn't matter how many qubits you have so if you want to go up here you're not going to get anything that you can't simulate classically likewise if you only have two qubits you don't need eight nines of fidelity if you only have two qubits so you clearly want to move up here and I didn't talk at all about error correction that's a colloquium in its own right but but when you get a large numbers of gates on large numbers of qubits you can do error correction to stabilize the entire computation which is a fascinating subject but fortunately really far from there so what I've plotted here with a little bit of license the black dots and this gray dot R this is existing data in trapped ion technology and we have ideas on how to how we're going to move up here and I'll just share very briefly with those plans now it's very hard to measure what's going on in superconductors this grape blind by the way is courtesy of D wave because we we're not sure really how to say what they're doing is even quantum so I gave them I gave them 10 to the minus 1 gates times but the super the superconducting systems that we see out there it's not clear how many what the gate depth is and as they grow the number of qubits it appears that their gate depth gets smaller but again not not a lot of this this data is somewhat projected and so forth so some of the latest data I don't say it's not interesting but it's not clear that those are on the correct path of scaling you really have to go up into the right this dot is great this this point is grayed out because it we don't have full control this is the data I showed you with 53 qubits but we can extrapolate that into how many effective gates that are but we don't have individual full control of them so it's not really along the path we want there's five and seven if you're asking you know a tiny bit tiny bit of a movement but we're going to make it bigger and I wanna I'm gonna since I'm running out of time I just want to skip and and have you know that you know it's a typical amo you see sorry a typically amo experiment looks like this of course and this is probably why it's very hard to make it bigger this this is in fact an experiment where we where we where we entangled to two separate ions in two separate vacuum chambers based on photons I didn't talk about that but this is how we hope to scale up in the long run by having a modular architecture where we have maybe 50 here 50 here 50 here and use photons to scale to to bridge the gaps that's in a very expensive process it's slow but it's still at least it allows you to make the system bigger without having a huge crystal in any one spot but of course the problem in all atomic physics is this in fact the atoms are only you know they're right here and we have you know all this is many of you will recognize the lasers that we have there and so forth and you know to me it reminds me of the old ENIAC picture the vacuum tubes and and this is this is definitely not good so on the other hand you know Marc Marc Casper's in the front row here I think his his company AOSS was the first to really attempt to engineer atomic systems for instruments for instrumentation and so with Johnson Kim in the audience we've collaborated for about 10 years now and at the University of Maryland we have this system the black box inside this black box is pretty much everything you saw here I'm exaggerating only slightly it's all in there it's about a cubic meter two things I'll point out one it's got a Santa very fancy Sandia chip that holds we have a template for 32 qubits but we could probably hold more if we want to this is room temperature so we're not going to go much more than 32 but we have 32 laser beams our acoustic modulator has 32 channels and we have control of all of those and also the CW lasers that do the detection and readout indeed came from Marx company AO sense and this is all of the CW lasers here and that represents pretty much half of this entire table all in a drawer it's really amazing but one you know is junk saying always says when you know what you want to build you can make it really small and the the added benefit when you make it small it will perform better so kind of double feedback there so if this looks like by the way this project is funded by ARPA it's a fairly outsized project and we are afforded to have relations with with with strategic corporate partners that provide some of the key technologies including the CW lasers the acousto optic modulator from Harris and that laser I talked about from coherent the 355 laser and of course Sandia makes makes these silicon traps we integrate it all we don't make a very fancy software stack we don't put it on the cloud that's that that's action that should be done at a company and so Jung saying I founded this company inq and we're we have 30 employees now and this this is a picture of their of their first prototype system not really up and running yet but it looks sort of exploded but this is the same cube that I showed you is opened up and all this stuff we haven't we haven't need to condense it but it's all electronics and and CW lasers so I think with that I had a few other slides I wanted to say one that's one that's a little cute is from my colleague Bill Phillips and stepping back this has a couple of meanings for me he's fond of saying that a quantum computer is more different than a classical computer than that classical computer is from an abacus and his his meaning here is that the classical computer in the abacus are both touring machines in the abstract you can model them as moving classical information around even though they look quite different but these are quite different beasts this is not a touring machine it works with quantum superpositions and entanglements it's totally different and I think it's important to keep that in mind theoretically but also experimentally there's no reason that quantum computers gonna look anything like this why should it it's so radically different so even though well to this this friendly crowd atomic physics is not weird its atomic physics systems aren't have not yet found their way into into the behemoths corporate structure in quantum computing I'm including Microsoft Intel IBM in Google they're gonna they're gonna try their hand at superconducting circuits because you can print them on a chip and design control systems but my bold prediction is that they're going to be if they're in the field at all they're going to be investing in atomic physics in the soon future okay in the last slide I stole from the latest issue of MIT tech review it's about blockchain actually but I took that off to Mequon computing is maybe captured here I think there's a lot of hope but you know some of the hype a lot of it is a lot of it is kind of ridiculous but there is something there and I think as an experimentalist I'm comfortable to say that we need to build it to find out where that something is so with that I'll conclude with a picture of my group and always interested in good people who want to move to the Washington even in this day and age so please let me know if that's you thank you thanks Chris for a breakup I'm sure Chris would be happy to answer questions oh yeah good question I almost comment so so this is yeah this is not really accurate because it looks like we're not conserving entropy I think that's what you're getting at this is not decoherence this is all coherent and unitary and the way you the way you preserve unitarity and i didn't show it so you have to have some workspace and so with with all these qubits I think you need at least two n you need another n qubits that keeps track of the input statement that's basically what you do so you take that input state you make it twice and one of them goes this way and the other one keeps this information it should if there's a tangle meant it will yes the the if you take a subsystem in a quantum this is a definition of quantum mechanics if you take a subsystem the entropy is bigger than the entire system so yeah I mean if you have entanglement that will come for the ride it's almost a definition of entanglement oh I think I see you're saying that's probably true and I don't know I'm a little bit on thin ice there but indeed the the simplicity of this output means that somehow that entropy went elsewhere in different entanglements and that's that's why you need these all right that's a good line of question here that's why you need to have that work space oh I think I see you're getting to I guess the answer is yes it is difficult it's almost like an analog computer that as you grow you have this exponential cost to pay instability and what I didn't talk about at all except for five seconds is the idea of error correction and it's more redundancy not just to em but you might need you might need a hundred N and if you can redundant Lee encode things you can pump out that noise from the instability it's called quantum error correction and it perceives exactly like classical error correction number the old parity check in memory you waste a little bit of space to store redundant information but it can check and in fact even correct for errors that occur that's fascinating subject in its own right and I didn't talk about it at all sorry but indeed to do that you need millions of qubits to begin with so we're not even close to doing that so up until we get to tens thousands or up to millions of qubits we're not going to be doing error correction for useful computation so we need to do our job right and if it's ten thousand gates that's only four nines in atomic clocks four nines is easy all right yeah I'm being very optimistic here but I don't worry about four nines I worry about six or seven nines I guess in the fidelity of all our operations here but I don't know where that endpoint is I guess and that's sort of what I meant we need to build it and maybe ten thousand is not enough for something interesting maybe a thousand is enough so we'll just have to see Thanks well we can borrow ideas from classical computing there are universal families of gates if you can apply a NAND gate on any pair of classical bits you can do absolutely everything in fact that is the native the native gate and CMOS the NAND gate so it turns out in quantum computing there are also families of gates one of them are the rotation gates and the C not gate if you can apply the C not between any pair and rotation of arbitrary angle of any single qubit then then that's universal you can you can reduce any circuit to that yeah oh sorry I don't have I don't have that slide but the XX gate if we surround it by five rotations on the two qubits why would it be five maybe it's just it's just four I think yeah so we have two rails two qubits and there's an X X gate in the middle and we put two rotations on the input and two on the output and we can tune those angles we get to see not hit the XX gate is as expressive as the see not gate so it's that like I said it's of similar power it is part of a universal family and that's where the art of compiling comes in and there's no it's

Channel: Stanford Physics

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Keywords: stanford, physics, colloquium, christopher monroe, quantum computing

Id: 9aOLwjUZLm0

Length: 63min 14sec (3794 seconds)

Published: Mon May 21 2018