Topological Quantum Computing: Plenty of Room in the Middle - Jason Alicea - 5/12/2018

our next speaker is Jason Elisha who is a professor of physics here at Cal Tech and so Jason will be telling us about a different approach to common computation which is called a topological common computation which might circumvent the large overhead a socialist error correction which Chris just mentioned so lets me just introduce Jason a little bit Jason is Jason second as matter theorist and as a conspiracy has made key proposals to realize the idea of topological quantum computation an idea which was originally proposed by Alexey qatayef who is also here Jason's proposal strange from various things from how to realize something called the marianas they're almost as a exotic particle type of namibian danyoung which is crucial for realizing topological computation however using surprising in conventional building blocks like semiconductors and superconductors and so forth and Jason made proposals about how to braid Mariana zero Mo's and also how to realize more sophisticated more sophisticated versions of namibian Daniel's which actually needed for to achieve Universal common computation so these proposals are now being pursued in laboratories worldwide and today Jason is going to tell us about topological and computation plenty of room in the middle [Applause] okay well thank you everybody for being here I'm really honored to be a part of today's symposium I want to tell you a story about a very bold idea called topological quantum computation so the the ultimate goal here is to use very exotic and possible sounding physics to try to build the quantum computer in ways that circumvent the traditional challenges that are faced in this problem I want to emphasize right up front though that the success of this topological quantum computing program should not simply be measured by whether we eventually build a useful technology of course if we do that that's great but one of the main messages I want to convey to you in this talk is that every stage of that journey towards applications really offers exciting opportunities for making profound discoveries about quantum mechanics and nature itself so I'd like to begin the story by going back to 1959 in 1959 computers filled rooms and and evidently the people that use them had to wear fancy clothes so nowadays things have changed in both respects you know small computers dresses much more relaxed but in that era of room size machines Fineman gave his classic lecture there's plenty of room at the bottom so I'd not talk he was envisioning opportunities that would arise if we could miniaturized technology to an extreme degree compared to what was possible at the time so for example for example he says there is nothing that I can see in the physical laws that says a computer elements cannot be made enormous ly smaller than they are now and by normally see smaller he was envisioning circuit em'ly circuit elements being made all the way down to the size scale of individual atoms he goes on to say in fact there may be certain advantages of such ultra miniaturized devices it's interesting to comment a little bit further on what those possible advantages might be there are some obvious things you make your devices more compact improve speed and things like that there's a more subtle potential advantage there because when you get down to those very small length scales the behavior is unavoidably quantum mechanical and so there's a temptation to try to make your information itself in here the quantum which ought to naturally lead to new possibilities okay so Fineman alluded vaguely to those possibilities even back in 1959 and we've come to appreciate those advantages much more deeply later on okay so let's imagine that we follow in fineman's language you know go all the way down to the bottom and imagine in coding a single quantum bit of information or a qubit using just a single atom right so you might imagine for example that we encode our logical 0 and 1 using 2 possible configurations of that atom that might have different energies now because we're in the quantum realm there are new possibilities that arise for example that qubit can simultaneously be in the 0 & 1 state that's a phenomenon known as superposition which is completely inaccessible classically if you have a classical but it's either 0 or 1 but here we have new possibilities okay so with with two atoms we can define two qubits and those qubits can exhibit the phenomenon of quantum entanglement so in an entangled state it's actually possible to uniquely specify the state of one of those bit independently of the other that's also forbidden classically if you have some string of classical bits you can always unambiguously say whether a given bit is 0 or 1 independently of what's going on elsewhere in that string but in quantum mechanics that's generally not possible so if we extrapolate to many many qubits we can process information at least in principle in ways that use superposition and entanglement to solve certain classes or problems that would be completely intractable to any conceivable classical computing machine that we can never construct so we can already anticipate certain applications and things like cryptography simulating nature efficiently designing new drugs artificial intelligence and many more many more things fame famously Fineman anticipated opportunities in simulating nature efficiently using quantum machines it's perhaps less widely appreciated that he was also one of their very first people to ever construct an explicit quantum algorithm and which he was able to do essentially on the fly so I want to go through a brief aside here in light of the occasion for today's symposium and I want to share with you a beautiful anecdotal from David Deutsch about Fineman so as a crisp mention David Deutsch was one of the early pioneers of quantum computing and quantum algorithms he was not so long ago interviewed on a podcast and he describes a meeting that he had with Fineman I presume sometime in early 1980s there's no way that I can do this story justice so I'm just going to play an excerpt of David Deutsch recalling that encounter I think it's quite remarkable it's around a minute long so I'm going to burn some of my time here but I hope it's enjoyable I had constructed what what we would today call a quantum algorithm a very very simple one it's called the Deutsch algorithm it's not much compared to dais standards and so I began to tell him about it and I said supposing you had a superposition of two different initial States and then he said well then you just get random numbers I said yes but supposing you then do an interference experiment and and I started to speak and he said no no stop stop let me work it out hooker he rushed over to the blackboard and he produced my algorithm with with almost no hint and so so how much work did that represent how much work did he recapitulate I don't know because I it's hard to it's hard to say with the benefit of hindsight how much of a clue the few words I said well but you know the crude measure is a few months right but a better measure is that I was flabbergasted I'd never seen anything like this before okay I thought that was pretty amazing anecdote and you know one of many Testaments to how extraordinary finding really was okay so end of my aside let's go back to quantum computing hopefully everyone is is excited about the possible opportunities that arise here maybe not everybody in the audience based on some of the last less questions but I mean almost everybody here so Stachel to now ask you know why can't I yet go on Amazon and buy an intel core quantum qubit enabled processor that fulfills all of this great technological promise so there's two main reasons for this so first of all controlling quantum information in the manner required to fulfill these high-level applications is extremely non-trivial thing to do and a related issue is that quantum information tends to be fragile and easily corrupted by inevitable noise that's acting on your qubit from the environment so faced with those challenges one very natural way forward would be to try to find a qubit platform that you can very precisely control and whose noise levels can be reduced sufficiently so that any remaining errors can be corrected for using ingenious quantum error correction protocols that have been devised so that's the conventional approach in this problem and has seen amazing progress as you heard about in in the previous talk in a variety of systems based on superconducting qubits trapped ions called atom qubits and so on alternatively imagine that you could somehow figure out a way to store and manipulate quantum information and a manner that was intrinsically immune to noise and errors at the level of your systems hardware so I want to stress the philosophy here is completely different from the conventional approach so you don't want to eliminate noise you just try to encode information so that it becomes irrelevant and also you give up on on requiring that you can control those those qubits very precisely by figuring out a way to make the qubit operations themselves intrinsically robust so this is the idea behind a topological quantum computation which I'll focus on for the rest of my time okay so let's think about how we might be able to build one of these one of these machines that's that that's immune to errors at the level of hardware so the way in which this can happen I think is is simply amazing I've been working on this problem for I don't know 10 years or so now and I still find this just absolutely beautiful piece of physics so let's start by thinking about just one atom right so that atom is made out of ordinary electrons protons and neutrons suppose now that we put many atoms together to make up a material okay so this material is still microscopically made up of ordinary electrons protons and neutrons nevertheless if this material realizes a certain kind of exotic phase of matter the system can give birth to new kinds of particles called any ons which look absolutely nothing like those microscopic constituents is it densely you can never create any ons at the Large Hadron Collider or in any conceivable particle accelerator that will ever construct these things can only emerge within certain certain materials okay so any ons are the workhorse of a topological quantum computer they allow us to encode information in a manner that's intrinsically hidden from the environment all right so the idea here is that we don't encode our logical 0 and 1 in properties of individual anions instead we code we encode that information in some collection of any ons each of which is far apart from one another in space and crucially if you look locally at any one of these anions individually you get zero information about that about that qubit so this is very different from the single atom qubit that we looked at previously where we imagine storing our 0 and 1 and just a local property of that atom you know in that case the the information is naturally going to be rather susceptible to to noise so here noise it's it's still there but it's essentially rendered benign because of the non-vocal the very global way in which were encoding quantum information using these anions so this sounds pretty good at this stage we have an internship a secure way of encoding qubits and these are so-called topological qubits the story actually gets even even better at least in theory land so by moving any ones around each other as shown in this animation here we can process those qubits in exquisitely precise ways that that I can control depending on which pairs of any ons I swap and in what order so importantly the qubit operations that are implemented here depend on only very coarse properties of how I move the anions around each other and not on the detailed paths that they actually take so in other words you know I just showed you an animation of moving any ons around each other you can distort the trajectories that are taken and your information should be processed in essentially exactly the same way all right so we not we not only have intrinsically robust way of storing quantum information we also have access to intrinsically robust with operations so these onions also behave strangely when you bring them together they can actually form different kinds of particles when they collide I'm going to indicate that by these blue and green circles now if you're able to detect whether that pair of any ons combine to give a blue or a green particle that allows you to infer the state of your quantum of your qubits which is otherwise hidden from you when those any ones were all sitting far apart from each other so that's the essence of topological quantum computation just to recap if you want to build one of these things you have to first find a face of matter that that generates these anions for you those any ons allow us to encode quantum information than this intrinsically noise resistant fashion we can perform quantum computing algorithms by moving Indians around each other and prescribed in a prescribed way and then we can read out the answer at the end of our computation by bringing out bringing the Indians together and asking what kind of particles they form okay so often we intuitively expect that when we look at a system on larger and larger length scales quantum effects ought to get increasingly fragile but actually exactly the opposite happens here so if you take this the system and then expand it so that the nd onset farther and farther apart from each other in space these topological qubits get better and better more precisely the resilience against noise and the precision of gates that you can generate by moving any ons around each other both improve exponentially as you scale the system to bigger and bigger sizes so from this point of view you know in topological quantum computation you don't actually want to go all the way to the bottom you don't want to encode your information at the level of individual atoms instead you want your topological qubits to be sufficiently big so that you can enjoy significant protection against noise and errors at the same time we don't want to reenter the realm of making room sized machines or worse so that kind of size scales that you might have in mind here or topological qubits made on the let's say tens of microns or 100 micron so that that's perhaps the sweet spot in this problem so there's 40 still plenty of room in that intermediate where you can still fit you know lots of information fairly densely on a chip well at the same time taking advantage of sophisticated fabrication manipulation and readout tools that that are kind of unique to that through that length scale okay so the idea that I have just described this topological quantum computing scheme was invented in really brilliant work by Alexey kitaev who's shown here he came up with this idea around 20 years ago and since then he's won lots of prestigious awards deservingly for this idea I just want to comment on one of them that is especially interesting in in 2012 Alexei was one of the inaugural winners of the so-called fundamental physics prize this is a really nice award to get for a few different reasons so you get this cool-looking trophy you get three million dollars and you also get to attend a fancy award ceremony hosted by Morgan Freeman so I'm gonna play you a very very quick clip of Morgan Freeman talking about elects days work for two reasons first to convince you that I'm not making any of this up and second so you can hear him say in the coolest way possible that only work in a way that only Morgan Freeman could the words fault-tolerant quantum computation or his work in this tradition using topological phases to create robust quantum memories and fault tolerant quantum computation beautiful thing I've heard those words many many times and no one no one comes close to the charisma that Morgan Freeman has there okay so in some sense Aleksei solved the three million dollar question in this field when he envisioned this pathway towards building a topological quantum computer that had this intrinsic resilience to noise and errors the billion dollar question in this field is is still outstanding though which is how do you actually build the hardware to bring Alec's a's idea to to real life so that's a non-trivial question very non-trivial question mainly because faces a matter that support any ons which are central to this entire story are very difficult to find in nature fortunately over the last decade or so there's been breakthrough in how we approach the problem which has provided us a potential pathway forward back in 1959 in in fineman's plenty of room at the bottom lecture he said I can hardly doubt that when we have some control of the arrangement of things on a small scale we will get an enormous Lee greater range of possible properties that substances can have and every different things that we can do so that is very much the philosophy that's now now employed in pursuit of any arms you know people really want to take serendipity out of the discovery process as much as possible and instead systematically engineer phases with any ons by combining things that we already understand in just the right way so by now there's many many theorists who have come up with very clever schemes for for doing just that for instance combining ingredients like superconductors semiconductors and magnetism right so all of these things are very well studied on their own magnetism is an ancient subject superconductors were discovered more than hundred years ago and semiconductors form the basis for our entire computing industry and amazingly in concert those you know well-known interesting things when you put them together in just the right way can furnish hardware for a topological quantum computer ok so I think this idea was a real game-changer and in this field and catalyzed very quickly a great deal of experimental effort by groups across the world so let me show you a few of these kind of engineered devices have been studied in recent years this is one of the original ones this little line that you see here that's a semiconducting wire that is making intimate contact with a superconductor on this side here is a related structure made by a different group using different materials but the basic idea is the same so there's a semiconducting wire which is once again coated with a superconducting shell and either of these platforms theory predicts that if you apply a magnetic field to these structures you should generate any ons that sit just at the endpoints of those hybrid structures so here and here and here and here incidentally one of the pioneers of the proposal that I the theoretical proposal that underlies this work is my colleague Gil Raphael who's probably somewhere in the audience ok so here's another example of a device of a related device this thing here that's a chain of iron atoms that sits on top of a Ledge superconductor in this case the magnetism arises intrinsically from the iron atom the atoms themselves and so you don't even need to apply a magnetic field any ons are expected to appear in at the endpoints of this chain in a very similar fashion ok so these and many other devices have been studied in great detail over the past 5 plus years there's been a lot of measurements performed and those measurements are indeed consistent with the formation of a neon sand these designer structures incidentally I'm being intentionally very cautious about the language that I'm using here but I think even the most pessimistic people working on this problem would agree with with the wording that I'm using but there's still some debate about exactly whether these observations are truly unambiguous signatures of any answer ok so this is more or less where we currently stand in this problem we have mounting and increasingly compelling evidence that any honest can indeed forum in these engineered devices we certainly faced a very steep climb though if we want to eventually get to topological quantum computation so as I mentioned in the very beginning fortunately there's plenty of room in the middle of this journey for transformative discovery so for the rest of my time here I want to just talk about a few big open questions than the problem but I think would be very interesting to explore as we scale up this mountain all right so first I think a very natural thing to set our sights on once you know following any on detection is to try to make the first-ever prototype topological qubit and in fact there is currently an intense experimental effort aimed at doing just this by people at Microsoft so this this goal might not actually be that that far off in the future now you might be unimpressed by this this goal of just making one topological qubit you know you're so far from where you'd like to be at that level but I what I'd like to hopefully convince you of is that you can in fact gain an enormous insight by just making one of these you know so first of all you you can by studying one topological qubit unravel the basic DNA of these any onset that makes them so so interesting and at the same time validate all of the basic underpinnings of this entire topological quantum computing program okay so maybe before I go any further we should pause to just reflect on what kind of information you would like to establish if you're given one of these prototype topological qubits so I would say that there's at a bare minimum three things that you would like to learn so you would want to make sure that you can actually read out the quantum information that's embedded in that topological qubit if you can't do read out there's no hope of progressing forward second you would like to establish that that qubit has some resilience against noise and third you'd like to see that you can actually process the information in this fault tolerant fashion so I'm gonna I'm gonna sketch some some ideas for how you might actually do this in practice I'm gonna you know there's many topological qubit designs out there I'm gonna focus on once per one specific design that I think is visually and conceptually appealing here's here's the theorist impression of what that topological qubit might one day look like this device is actually very close in spirit to this this actual actual experimental setup that I showed you a couple slides ago all right so in this in this picture here the or and blue regions those are superconductors this gray thing underneath is a semiconducting wire and I added these three back three black lines which are electrically tunable switches that allow me to control any ons in that structure so how this works exactly is is not important I'm not going to go into it instead I just want to sketch the kinds of experiments that we can do in these relatively simple looking structures and more importantly what we stand to to learn from them okay so in this starting configuration I'm I begin with a system that has one two three four any ons and together those four any on encode a single single topological qubit so there's a zero and one that can be non-trivial II embedded in that device suppose now that you'd like to read out the state of that of that topological qubit this we can do by closing those those outer two switches that causes an interaction which effectively forces the left and right pairs and yonce together and remember that any ons when they come together can form different kinds of particles so we can get either bluer or a green particle out and this particular setup where you can use well-established measurement techniques to indeed readout whether we get blue or green and that in turn reveals a state of our topological qubit alright so if you were able to do this experiment you would demonstrate a critical critical aspect critical ingredient needed for topological quantum computing namely readout while also validating one of the basic features of any ons which is this peculiar way in which they can come together alright so let me reset the device so that we once again have for any onset encode a single topological qubit we can probe another fundamental feature of anions in the same structure albeit in a more complicated experiment all right so I suppose that we want to we want to explore the resilience of against noise of that topological qubit so it's important to ask you know how you actually do that how do you confirm that the quantum information there is really hidden from the environment in an actual experiment well so to answer this I have to emphasize that no topological qubit will ever be perfect there will be noise and eventually that noise will succeed in in your information you know we hope that it takes a very long time for that to happen but you know eventually it's going to happen so suppose that you measure how long that quantum information actually survives before it it gets destroyed by noise I'm not going to go into how you exactly do that there are concrete protocols for doing that but imagine that you somehow extract that information so then do exactly the same measurement but in a device that is is bigger okay so that the indian's are farther apart so I mentioned earlier that you know the bigger the topological qubit is the better it is they should get exponentially better in fact and that exponential improvement in the topological qubit should translate into an exponentially longer life time for the quantum information in that device now if you observe that trend then you would have indeed confirmed the predicted resilient resilience against noise and so you would you would also establish at the same time that this device is indeed capable of functioning as a intrinsically resilient source of topological quantum memory so I think this would be a phenomenally interesting experiment if you can succeed in demonstrating this if it works out as we hope I think this would go a long way towards establishing viability of these of this kind of hardware for eventual quantum computation now if I dress this thing up a little bit more if I add this vertical leg to the topological qubit then I can I can adjust these these switches over here to exchange to braid these to any ones around each other so here's an animation of how that might look this is very easy to do in keynote by the way not so easy to do an experiment but so I've swapped those two any ons and accordingly I should have processed my quantum information in a very very precise way that should not depend on details so for example if I started in the zero qubit state then after this after this braid I should end up with a very precise superposition of 0 and 1 now you can do this experiment a thousand times under a thousand different conditions and you should invariably get essentially exactly the same result right so if that works out then you would have demonstrated another key feature of topological quantum computing namely the presence of these fault-tolerant qubit operations all right so maybe it's a big gift but you know if you manage to demonstrate 60 a few six we demonstrate all those experiments you would have seen that you can store manipulate and process topological quantum information albeit at the one qubit level and then you can then start to think about integrating multiple topological qubits together so the last thing I want to touch on is some class of problems in that multi qubit arena that's most certainly much simpler than full-blown topological quantum computing but it is also significantly more complex than just doing single qubit experiments so the specific problem I want to I want to discuss in that intermediate realm is performing analog quantum simulation with any ons so to explain what I mean by that I want to go back to the very beginning essentially when I took many atoms put them together to make up one of these materials that I then assumed realizing the exotic phases of matter that harbored antion's all right so again the idea is you take many many atoms bring them together you get new physics in this case any ons so we can play that exact same game but now with any ons ok so let's take this big collection of any ons bring them together to make some kind of a neon soup let's also imagine that we have some control over the interactions among the anions in that soup we can then start to ask you know what what new physics can can you engineer within that and neon soup ok so this is what I mean by analog quantum simulation now you I think this is a very rich problem and you might naturally expect that there are interesting possibilities here there's lots of strange features that we've already seen that these anions can exhibit and so you might imagine that there are certain phenomena that would be much more naturally generated by coupling together any odds compared to let's say coupling ordinary atoms I'm just going to give you two possibilities in this and this and this problem although there's an undoubtedly many other interesting things one can do here so first if you couple those any ons in just the right way you can actually generate physics which is very closely related to black holes quantum chaos and quantum gravity so for specialists I'm referring to the so called syk model firstly I think this is amazing that that there's any link between any ons and these exotic topics but and all this can happen so for my second example I want to imagine putting any odds together to engineer an even more exotic kind of phase in this region that host still better any odds and by better any odds I mean a kind of kind of any on different species of any on that gives you more flexibility for manipulating quantum information through these exchange operations so essentially the idea and the second approach is to take a first generation topological quantum computing hardware and then use that to engineer next generation topological quantum computing hardware I realize that's a pie in the sky especially if you're an experimentalist that that's extremely difficult thing to do but I think it's an interesting possible idea for the future ok so the end game is hopefully to actually build topological quantum computers that can solve certain certain problems that are intractable classically I certainly hope we get there eventually ideally within my lifetime but you know in general I think that the fundamental discoveries that we stand to make along the way provide more than sufficient motivation for we're trying to scale that none by studying a single prototype topological qubit we can explore in great depth the physics of these n eons and glimpse and tabletop experiments new features of quantum mechanics that have never been seen before if you have the ability to interface many of these any ons together in a controlled way you can explore even more out there physics you know related to quantum gravity quantum chaos more exotic phases of matter and so on I want to make sure that I leave you with the impression that every single thing that I've proposed and this talk is extremely difficult to do in practice but a quote from you know yet another quote from Fineman from plenty of room at the bottom I think is appropriate here he said I am telling you what could be done if the laws are what we think we're not doing it simply because we haven't yet gotten around to it so that same sentiment I think applies to this problem people are indeed trying to scale this mountain so we will indeed see how far they can get well thank you very attention [Applause] residence mm so a lot of times biology beats us to the punch in physics by exploiting something that we didn't discover and tell later there was a bit of a flurry a few years ago about entanglement in I think photosynthesis is there anything to that and do you think that this is something that nature might be exploiting that's a very interesting question actually so maybe I you know I have nothing to save based on personal personal experience on that but my PhD advisor actually who is you know collaborating with me on a number of the previous work not exactly related to what I said here but prior work on this topological quantum computing business he is now full-time essentially thinking about whether our brains might actually be able to exploit quantum processing in some form so there are very very creative and very smart people that are thinking very seriously about this and a lot of the ideas that are coming out there are surprisingly testable experimentally so that's that's about all I can say yeah yeah so there definitely is so the question was are there temperature limitations when we wonder we want to explore quantum computing with any ons so this all the conceit all the experiments that I outlined would be very low temperature experiments so very far from room temperature there's a there's an energy energy gap inside of these phases of matter that have any ons and basically temperature needs to be small compared to that energy gap otherwise you start wreaking havoc on your system and then you lose control of everything so in the previous talk there was a discussion of sort of like Co design for like tougher quantum gates anyway you have for classical computing are there classes of quantum algorithms that are sort of best suited for topological quantum computing or does it seem like it's if it worked it's gonna be a catch-all for most of the problems you'd want to work on I'm not sure if there's anything specific about in terms of applications that topological quantum computing would be better to solve than let's say other other approaches I mean the only potential advantage would be if you can actually make the operations and and and more robust than the noise less important but ultimately we want to be any any of these schemes want to have the complete freedom to manipulate quantum information in arbitrary ways and whether you do that with a topological or a conventional on a computing machine at least so far as I know there's no there's no clear difference there everybody's gonna sound a little wacky but I'm really curious about your thoughts on a simulation theory and why do you think that building a quantum computer would be evidence supporting that we might indeed live in a simulation we might live in a simulation well maybe maybe I'll quote I'll use one more Fineman quote I don't know but let's find out [Laughter] [Applause] in principle a very large amount of information could be contained in a topological arrangement so I was wondering why stop at qubits why not store like a larger alphabet of information into a topological arrangement so okay so so it is possible to define actually in a natural way what people would call cued it's with with any arms so this is related actually to the fact that you know when I drew this picture of any ants coming together I said that there are two possible particles that could be formed in general there are not just two particles there could be different you know there could be three four or five possible particles that can form and so it basically the the number of those possible particles that can form if let's say there are n of them then it's possible to define a kind of an end-state qubit i think the there's some some reason to prefer the qubit i mean this is kind of a yes or no sort of thing and i think in general it makes it easier to process and store information so typically even when you do have more possible options you might be able to imprint encode let's say one of these generalized qubits but you still typically want to use a you want to encode the information and qubits but in principle it's possible just amounts to how you know how convenient is to actually actually perform algorithms you you

Channel: caltech

Views: 7,060

Rating: 4.8356166 out of 5

Keywords: Caltech, science, technology, research

Id: qj-w6ISQL5Y

Length: 37min 11sec (2231 seconds)

Published: Tue May 22 2018