Panel -- Will Quantum Computers Ever Be Useful?

okay Thanks so we were talking last night about what to say and the Seth pointed out well no one really knows what quantum computers will ever be used for and I said well okay but wait a minute I mean we know far far more about this than we know about almost any of the other questions that will be discussed at this conference so so maybe you know I would be good if I start by just you know presenting like something about what we've learned from the last 25 or 30 years of quantum algorithms research and by the way we know a lot more about what quantum computers could ultimately be used for than we know about what they could be used for within the next few years ironically enough because for the only for the former question you know is it a question of pure theory really and so you know the applications of a quantum computer are that have that have been discovered to date are more specialized than many people would like them to be they're certainly more specialized than popular articles would give you the impression that they are ok but you know to me what's you know miraculous is that there were sort of any interesting applications at all for this right really bizarre hammer of you know interference of amplitudes that a nature makes available to you so you know I would say that there were really five main classes of applications that have emerged over the last few decades the first one is simulating quantum physics and chemistry themselves that was fineman's original application when he proposed this idea around 1981 in some sense it's still the best application it's what a quantum computer in my opinion it's what a quantum computer would do in its sleep but it's actually useful for material science may be designing high-temperature superconductors better batteries solar cells chemical reactions like the one that makes fertilizer at least you know given a candidate you could simulate it and have this facility that you know that would let you see what's going on and we're much more confident there than we are with many of the other applications that a quantum computer will actually be giving you a speed-up the second is a breaking cryptography you know that's the famous application that put quantum computing on everyone's radar with the discovery of Shor's algorithm 25 years ago so we know polynomial time quantum algorithms for factoring discrete logarithms elliptic curve problems a few other problems in number theory in group theory which together a break almost all of the public key cryptosystems that are currently used to secure the Internet and these are problems were the best-known classical algorithms take exponential time I should stress that these speed ups are for extremely special problems so not np-complete problems it's the ones that we happen to base crypto on ok but even within crypto there are candidates for quantum resistant public key cryptosystems that you know in a world with quantum computers we could switch to those systems now number three would be combinatorial search and optimization problems so there's another important quantum algorithm called Grover's algorithm that can solve almost any search problem in about the square root of the number of steps that would be needed classically so it's not an exponential speed-up like Shor's algorithm but on the other hand it has a much much broader range of application unfortunately we also know that in the sort of generic case that square roots speed-up from Grover's algorithm is the best that even a quantum computer could give you okay which means if you want like an exponential speed-up for a combinatorial problem you have to exploit structure somehow there are candidate algorithms that you know try to do that like the adiabatic algorithm something called queue AOA okay but even after years of study we still don't really know if these algorithms will give a win for any instances that matter in practice we might have to try it out on a quantum computer before we know fourthly machine learning there's been huge excitement about quantum machine learning in the last decade a lot of it originated with an algorithm that Seth was a co-discoverer of in 2007 called the h HL algorithm unfortunately expirience is shown that it's really challenging to find real-world cases we are these quantum machine learning algorithms work and there were not comparably fast classical algorithms that do the same thing until a year ago one of the best candidates we had was for recommendation systems like recommending movies and Netflix unfortunately that algorithm has now been D quantized actually by E Wynn Tang who was an undergrad who was working with me and you know I think the challenge remains open to find an exponential speed-up for machine learning that's going to matter in real life we don't know if there is one and then v there's a very recent class of applications that involve not using a quantum computer to do a classically infeasible calculation as much as using it as a prover in some interactive protocol to prove something that a classical computer would not have been able to so I proposed the protocol a year ago for a quantum computer to generate random bits by itself not impressive but then you know prove to a skeptic that the bits really are random so that they could be used in proof of state crypto currencies for example I expect that there will be a lot of other applications to be found in that sort of space of you know the quantum computer using its quantumness to prove something about what it's doing so surely there will be more applications that no one has thought of yet but you know if they see more you know limited then you might like well part of the problem is coming up with enough candidate problems and part of the problem is that we don't know the limits of what classical computers can do and you know a secret of this research is that sometimes it's much easier to come up with the quantum algorithm than it is to rule out that there's a classical algorithm that could tell you the same thing thank you we go now to Michel so I also agree that some of the most exciting applications would be simulating sort of knowing more about strongly coupled many-body at quantum many-body systems with an eye towards gravity this is one of these very exciting potential uses and you know we we started we're starting to know more and more about this you know not to sort of exhaust the the duality arguments and people they roll their eyes and like we were tired of talking about this but but really there there's been some exciting ideas results from Dan Harlow and and garnet chan around you know fully commuting Hamiltonians and and that that could potentially reduce the resources down that the resources are still a massive problem but in terms of why do we want to to do this this is this is a strong motivator so there were some results from sach dev in Boston I think and he's he's looking at sort of the Miss Dictionary correspondence on again the physics of 80 Kelvin is is pretty questionable when we're talking about this this kind of thing but you know there's it in a case where you know conformal field theory doesn't have a simple quantum gravity tool but then we sort of say let's modify it and go to a large n limit and it does have a gravity dual what if you had a quantum computer this would you know you you you you you the sort of problems with the physics on that level that they're looking at or not as they're no longer the same and and so yeah so that's that's that's one thing I think it would be very useful everybody's talking about sort of n is Q there's a lot of marketing around this but it would be very exciting to see if we can sort of pull out of one dimensional problem that that sort of a small 1d problem that a quantum computer can calculate oh okay near near-term near-term no no a noisy noisy intermediate scalable quantum algorithms so there's there's a search for you know this sort of quantum supremacy regime within within a lot of corporates and within startups and the idea there is you know in my opinion I you know I'm a little bit concerned about this because I feel like that's that's not really good enough sort of counting the qubits you know it's one thing to sort of onboard academic research programs but you really need a sort of a systems view to get to to get to a architecture that's that's going to do some of these things that we're so excited about you know in in the first place so for example Google now has this sort of 72 bit 72 qubit physical qubit Bristlecone architecture that they say costs a hundred K per chip so ok willing to take them on their word but it's 100 K what does it actually mean you really have to take into account sort of the classical peripheral overhead of the system so you know for for that hundred K chip you have maybe a dilution refrigerator that's 500 K we know it's more than that but I'll just be generous here you have these sort of amplifiers attenuators 9i probiem coax cables that need to go across fridges to manage the signals in and out and let's say that's 400 K so all in it's a million for the 72 qubit chip that's 14,000 per qubit if you are actually engaging with the numbers that would be needed to scale you know quantum algorithm and and and for a cloud we're talking about on the order of you know 10 to the 6 cubits so so the LHC did not cost did not cost a hundred and forty billion and you know there's some question as to the cost-benefit around that but so I think I think you know the to two main points that I'm turned about our the focus on the lack of focus on logical computation and what I now started calling digital error correction for quantum computers because I think I think that I started calling it this to distinguish it from the control level hardware error correction that that people do which is sort of this like you know one-shot measurement readout kind of thing and people ask your favorite experimentalists and they all say that they have this this sort of error correction right but really what's needed is is is is a much more complicated in-depth higher level engagement on the fact that these machines are not standalone devices and we have error rates we you know they're basically our correction machines right so you have you need to be optimizing and programming and managing the the classical data that's coming out of these machines okay so I guess we're gonna pose this question last night one of our initial reactions for is how to generate actual controversial statements is a question like this since if we went through just the basic applications of quantum computing I think we all agree here and Scott has done an excellent job introducing all the basic applications that pretty much I think everyone in the family is in agreement so I thought I would extend this to say things that are a little more controversial in the spirit of the fqx I so I'd like to think about this question more in the far distant future so in the sense of their world quantum computers ever be used for focusing on the ever part of if we had quantum computers and if we were for we were able to overcome the monetary and resource constraints in the far distant future what sort of other interesting applications currently have and of course we have a lot of the well-known computational problems but now I would like to focus on some potential interesting questions we may be able to answer on the more foundational side I think one of the key questions term from the quantum foundations community is of course a measurement problem that that when we have observer whatever it means for something to be conscious or something to be observer the action of observer observing auxilary system collapses wavefunction and you're certain instance route interpreted as a raising entropy in this incentives process is irreversible we have seen other instances if we look at phenomena witness friend one of the postulates is that the measurement can be reversed and I think this is one of those deep philosophical questions that years that we cannot answer with near-term technologies but as we gain progressively better and better control of largely of quantum systems we can begin tackling this so over breakfast today I was actually talking to Erica Cavalcanti who recently had this very nice paper about building a stronger than bell inequality constraints for looking at sort of exactly looking at this vagueness friends an arrow to ask whether or not a wave function actually collapses or whether we can sort of reverse this collapse in the future and to answer this question of course we can simulate the predictions of quantum mechanics using systems of one two and three keyboards but this is not very convincing since if we believe the laws of quantum mechanics help us review birds then we are going to get our experiments is going to align with the predictions of quantum theory and the interesting thing comes of cards once the systems that the measurement system we control becomes progressively more and more macroscopic to progressively more and more simulate that of an actual practical observational system so we can think about as we going better and better controlling quantum computers to better and better model what we expect intelligent agent or intelligent conscious system to have obviously there is no fine line of where we would say something's intelligent and there's no fine line of where we would classify something between sort of an inanimate object and something that has consciousness but we have properties that we may expect the conscious system to have for example the ability to learn or the ability to adapt and if we could begin to be progressively more and more sophisticated quantum networks that can imprint a lot of these behaviors that we expect intelligent agent to then we may be able to view the Similan of a conscious thing and observe if at any stage sort of the collapse of the wavefunction actually occurs using these testable inequalities that's akin to bearing qualities but rather to measure measurement collapse and I think this is one of the most striking things to me as a physicist for what having universal large-scale quantum computers can do and of course this is by far something that what will not happen in the next five or ten years this requires us to be able to view the essentially macroscopic quantum systems to the level that we are able to reverse every interaction inside them and this is something that perhaps we will something that quantum computers will in the far distant future be useful for but it's something that I find personally exciting one other thing I want to mention is if we go back to the more pedestrian thing I think the one last thing I want to mention that I don't think has been discussed so far is that the classroom we know that the classic amount of information that's required to track a quantum system even if it's just to track a sequence of stochastic observations can grow and bounder despite the fact that the physical system itself is bounded so how it wiseman for example is dark or number of papers looking at the amount of classical information needed to track the observations of open system so this tells us that certain stochastic processes to sample them efficiently may require unbounded amount of classical memory so if we can find interesting processes to sample that people out there actually care about then that could also be a near-term application of quantum computing I'll leave it there for Seth to talk about some adventure stuff or things so I actually want to talk about something much less adventurous I I think Scott did a great job of summarizing what quantum computers might be good for let's just say where we are which is an extremely exciting time for aquatic computing if you look at the devices made by Google IBM or iron trap devices made by inq they're between 50 and 100 cubitt's and their current coherence rates for multiple operations is something like a factor in error rate of one and two hundred to one and five hundred and if you could actually extend that so it's an error rate of one in a thousand to one and ten thousand which is a difficult but by no means impossible plot a mechanical engineering problem which we hope will make a lot of progress on the next couple of years then these applications like quantum simulation will be we could we can do them pretty much right away in fact already in quantum simulation if you build special-purpose quano devices that have tunable hamiltonians right now you can use them with you know twenty to fifty cubits to investigate things like many-body localization which are very important things in solid-state in fact whatever one thinks of the d-wave device for you know whether it solves hard combinatorial problems or not it's a very beautiful tunable transverse Ising model model which is a very hard problem to simulate so that's great possible applications include quantum machine learning I will actually talk about that in the future so we won't talk about anymore now and then there's Shor's algorithm which is you know the killer app for quantum computers but it also happens be in some sense the suicide app because if tomorrow we build a scalable quantum computer which would factor large numbers and break all these public key cryptosystems then all you have to do is demonstrate it once and nobody would use those public key cryptosystems any longer really the only way to make money from it would be to you know to keep it secret and sell your services to the NSA and to international criminal organizations so anyway that says as you mentioned that michelle mentioned the the technological problems in making a scalable quantum computer would say with a million qubits and able to do 10 million or billion operations that's very daunting you might need with current technologies your superconducting chips would have to be the size of this table that's hard to do so i would say that the projection for that is somewhere in between 15 years plus or minus never for a building distance anyway our esteemed moderator asked us to sing a song together and there was reluctance on the part of my co-panelist to do this so i decided to to take the bull by the horns and i volunteered to do this so with a with apologies to Gilbert & Sullivan I will now sing you a song that to me kind of well it's a sad song but it it states them kind of where things are with quantum computing right now in a superconducting circuit a little qubit sang entangled entangled on entangled and I said to it qubit oh why do you sit singing tangle entangled on entangled unentangled is it just decoherence qubit I cried or a nasty quasi particle in your little inside with a shake of its poor little head it replied entangled entangled on entangled its flux fluctuated as it sat on that ship Oh entangled entangled on an entangled it's Josephson junctions were having a pip entangled entangled on entangled its side and it's sobbed and a quantum jump it made as it lost all the phase of its debroglie a wave and a spin echo arose from the suicides grave entangled unentangled entangled that was a spin echo joke by the way now I feel just as sure that I'm sure that my name isn't entangled entangled unentangled that it was not spontaneous collapse of the wavefunction that made it exclaim entangled entangled unentangled if my neurons interact with the universe I shall decohere as it did and you will know why but I probably shall not exclaim as my coherence dies entangled entangled on entangled [Music] thank you very much so actually I was launching this idea and saying is that for taking youth the most important thing I forgot to say before is that for me sort of you know I talked about five different applications you know maybe you know you heard from the other panelists about some others for me none of those are the main application the main application of a quantum computer is to disprove these people who keep coming to my blog and saying well quantum computing will never work I thought about it for 30 seconds and here's you know you know an obstacle that no one in this field you know it must never have occurred to you right that it's basically just an analogue computer right or you know like they've never heard of our correction or anything or you know what makes you think this quantum mechanics is true anyway right it's just it's just something some physicists made up and you know I would I would like to sort of rub these people's faces in the reality of you know the the exponential wavefunction and for me everything else is icing on that on that cake I feel like we're we're all you know there was one fqx eye where people somebody said we're all Alan good so I feel like actually my answers were sort of distributed over this table and so there's not too much to say but I I agree that for these two two other reasons like that those are my top three and I hope there are no investors in the room but that's that's definitely the most exciting aspect to me and yeah I I kind of call what you were talking about like deutsches parable right so like can you can you run an AI and and and sort of check it's also Wagner's friend right so yeah these are cool ideas so I guess one last comment I thought it's quite interesting it may not be exactly what quantum computers are useful for but I think an interesting application is the exponential increase in capability depending on the size of the computer which I think it's one of the things that is quite unique among other physical resources so usually when we think about classical computers or any other resource when two countries combine their resources together the capabilities that they do is generally scales linearly was with a combination of resources and this certainly applies with physical resources and to extend classical computers as well and one of the interesting things about quantum computers is that when we add our fixed number of qubits to a quantum computer it seems that for certain problems and certainly for the ability for us to classify simulated the complexity seems to grow exponentially and this means this has some interesting sort of social political implications and this is something that Peter ODI believer has spoked about spoken quite a few times about is that you can have instances where there's a strong incentive for countries and other entities to collaborate with each other assuming that we had a coherent method of transferring quantum information and I think this you know itself is a it can have dramatic ramifications in what our quantum computing devices how people use them as it creates a strong incentive for entities to work together to do something greater than what they can do themselves even if say even if it's just collaborating with a relatively entity was relatively few keepers or relatively small amount of resources even as modest contribution can greatly improve the sort of the class of problems that we can tackle and I think that's a interesting property of quantum computers to point out so I'd actually like to say something about quantum information theory as opposed to building quantum computers now if note that what was Touring's amazing contribution he took curdles undecidability theorem ii so this applies to a computational device so he made the model of a Turing machine of a machine that does computation in order to talk about what is computable and what is not computable now the world is quantum mechanical and our devices and our computers our bottom quantum mechanical so if we want to know how information can be processed in the universe as a whole we have to look at quantum information processing we have no choice and it's a bonus that we can actually build these devices and we're in the middle of a very exciting time of building more more powerful quad computers whether large scalable quantum computers well world or be built but let me just say something in favor of quantum information theory which is a theory that came out of foundations of quantum mechanics during the 1980s prior to quantum computers being you know thought people felt prior to be able even thinking who might build a quantum computer look quantum information theory is a universal language for discrete quantum mechanics and it tells you how entanglement works it tells you how you can compute things it tells you how communication works quantum communication by the way limits the the communication capacity of fiber-optic cables which are which are actually quite close to their quantum capacities and it's now gotten to the point where my god even people who do a DSC of T theory and string theorists are now doing quantum information there goes the neighborhood I say and that's exactly because you know quantum information theory tells you when you have discrete quantum systems how they can behave so as a way of understanding the way the universe works I'd say that's the most important application of quantum information theory we can't actually understand the way the universe works unless we see how it processes quantum information just as Francesca Vedado from Western Ontario just a short comment since you were mentioning a DFT to me the most interesting reason well the reason why I want quantum computing to work is because it makes a fantastic quantum simulator for the loopy quantum space-time so there are already work ongoing work to do this in partnership with IBM and with also people in guadeloupe let me comment on that that you know the the the reason so the history of applying quantum information to a DSC comes from Brian Swingle who was when he was a graduate student at MIT noted that there's a connection between quantum error correcting codes which allow you to store quantum and nation in a distributed fashion in a system so that you can recreate it over here from these bits over here and you can also recreate it from this these bits over here and that gives you insight to how you could have the same quantum information in the bulk and on the boundary of anti-de sitter space so it's a remarkable insight I don't mean to diss it I think it's completely cool so my question to you is do you know of any of the often talked about interpretations quantum mechanic today that have stuck their neck down and said that if you can build a really large quantum computer that seems to obey the shortening your equation they will consider their interpretation ruled out max the thing that you're asking for it would not be an interpretation it would be a rival physical theory I mean I mean I mean it would be making a prediction that's different from the prediction of quantum mechanics you know and so so I mean you know there are quantum computing skeptics who think it can never be built right you know either because they don't believe quantum mechanics or they just believe that there will be you know some noise you know some principle on top of quantum mechanics that will sort of censor quantum computation or prevent it from ever scaling you know that itself if that existed I think would be a revolution in physics you know and that's not you know sister so that's not attached to any interpretation like you know Copenhagen you know Bohm many worlds and you know to you know to the extent that any of them you know that you know made sense to you before I think they still make the same sense to you in a world with quantum computers because they all predict exactly the same thing about their functioning grw I would precisely regard as a rival theory but by the way a super cool observation is that even if grw was true and there were like real spontaneous collapses you might be able to treat those as just another source of noise to be dealt with by quantum error correction and just go go right on building your quantum computer actually say that the the to the extent that grw has been falsified right so that it's limited to spontaneous wavefunction collapse to a very small level and those are already things that you could deal with with quantum error correction because the actual noise that people are looking which is on air in one part in ten to the fourth or ten to the fifth is much much larger than you'd get from grw so then for to have G or W prevent quantum computing from happen it would have to be different up to some scale actually I'm working on that trying to falsify on gr W okay it regarding regarding they sort of Brian Swingle stuff and the error correcting codes I mean it would be nice to to sort of that there's a naturalness argument there right that okay we live in a we live in a quantum universe and there's these are topological qubits and and we need a lot less error correction and it would make all of the work that we do on error correction completely irrelevant and so it's not like this sort of forcing mechanism of let's just force the noise out and in this little fraction of a Hilbert space so that would be cool if Microsoft should stop slacking what is the most destructive counterproductive and destabilizing outcome of developing quantum technologies that you could imagine might happen well final computers are not very dangerous right now the worst thing that can happen is if you drop one on your foot so yeah and and of course as you're suggesting Lee of course the the primary application of quantum computers right now is to put them in your funding application to get money which is a very near-term application for quantum computing I think in some times this is it's a sociological thing so it's almost like the US government has decided we're not going to pick winners the UK is decided we're we're you know we don't want to hurt anyone's feelings and we're gonna sort of fund everybody and China is just massively doubling down on all budgets and having the government build the qubits whereby you know the startups get to sort of capture the crops get to work on on some of the problems that are really really important to get these machines to run get to capture the value of subsidized qubits so what's going to happen in terms of being able to collaborate I think I think that's that's something that that could become yeah somewhat somewhat even tragic if things go fighting can I ask if this is what you have in mind when you ask the question maybe I misunderstood the question I thought Matt was asking for the most destructive application that you could imagine yeah I mean the obvious thing to say about that would be you know the use of Shor's algorithm to break public key cryptography and you could imagine all sorts of things falling out from that like maybe someone would decrypt some emails that would you know sway the outcome of a presidential election or you know lead to lead to some clowns being elected I mean you know obviously that could only happen in a world with quantum computers but I mean yeah you know there's all there's also there's all sorts of mayhem that could ensue yeah I think everyone has pretty much summed up on my views I I can't see anything particularly destructive about quantum computers at the moment other than perhaps decrypting some since the messages in secret when incest sells is content computed to the black market which is happening anyway which is happening right now other than that were obviously our knowledge of the applications of quantum computers is fairly limited the moment and just like I think classical computers in 1960s where we could only think about decryption as their major use and now we use them to watch videos of cats from the perspective quantum computers I think it's a very similar regime we're currently at the level where we don't have a function in quantum computer you know to the sophistication that would like so we don't really know as applications but I don't believe that there is any particular application that would be catastrophically destructive in the sense of being able to because I can't see solving a problem as being catastrophic late destructive at least from a naive point of view at the moment I'm curious this is maybe just a silly question but could a quantum computer at some point in time be used to prevent decoherence and an external system so I have some thing in my lab that I don't want to decohere I plug in my my error correcting quantum computer and I prevent the decoherence in that external system is that a possible thing that could be done I mean I mean at that point the other system that you've prevented from dqo hearing I would tend to think of it as just itself a quantum computer right I mean you know it's been said like like if you actually wanted to build a Schrodinger's cat in reality and you know have it remain in the alive plus dead without the Co hearing your best bet is probably to build a simulated cat that is inside of a full power and quantum computer right but you can extend that reasoning to all kinds of things and yeah and there are recent protocols so I think by Magoon of askers that looks at at sort of restoring certain open system application open quantum systems by continuous measurement they happen with a probabilistic success rate but but I think that's what you would do short of putting a virtual cat in your quantum simulator which is probably your most stable solution hi so as Scott touched on one of the problems with demonstrating quantum advantage is not actually finding the quantum algorithm but finding what the best classical algorithm is as often it yeah as he said it's just that you find a quantum almost better than the existing classical and this is like this D quantizing of algorithms so let's suppose that practical useful quantum computers aren't built in the next several decades and the field dies but in the process we're left with several D quantized classical algorithms that be the presently known algorithms would you then class quantum computing to have been useful even if we don't have a quantum computer just because it improved classical algorithms so the question was if quantum computing merely leads to sort of spin-offs for classical computation is it a success I would say you know depending on how good the spin-offs are sure you know I'll take that I mean you know no there already have been really exciting spin-offs for classical computer science that have come out of quantum computation you know if you know new algorithms and also new impossibility results you know because this has just put this new and unusual set of demands on you know theoretical computer science and so great stuff has has come out of that I hope that will continue to happen but it's kind of like you know string theory right where you know like is string theory a success if all that comes out of it is new insights for condensed matter physics or quantum field theory right well you know depends how good they are I guess when Charles Babbage was funded by the British Admiralty to build the difference engine in the 1830s it was a Manhattan Project size a scale of funding and it failed and the reason it failed was because he discovered it trying to build it the the machining techniques were insufficiently precise to machine the gears of the difference engine so that they could actually turn and wood could overcome friction and so they spent you know the equivalent of a billion dollars or more trying to build this device and it failed but the results were that they didn't get a mechanical computer but they were able to machine gears to ten times the tolerance as before and this had a tremendous effect on the Industrial Revolution so this was told me by one of my colleagues in mechanical engineering so that and of itself would be great and if of course you already see remember that the that for the last 20 years now for 15 years the world's most precise measurement instrument has been Dave Winelands quantum logic autonomic frequency sorry optical frequency atomic clock which operates by exchanging entanglement between hyperfine levels and optical levels of atoms and explicitly uses quantum information so this has already happened with quantum information and is likely to continue to happen one remark I mean I think it it would be fantastic to have better multiplexers and single photon sources and a lot of that is what this this in part I think is about you know it's a little bit like at the moment having a Bacchae but you really want to have sort of a a a quantum computer you need to put forth sort of conditions on architectural designs and have have many people talking about about that in terms of footprint and and although size may cost may sound like a hollow argument it there's an implicit kind of request there too for miniaturization and densities to get to something that could do quantum simulation for get to get to logical qubits in the first place so I think there needs to be a focus on that if we're going to see these these kind of more sci-fi applications like what we've been talking about great so let's thank to Polina and [Applause]

Channel: FQxI

Views: 3,985

Keywords: Scott Aaronson, Seth Lloyd, Miles Gu, Michele Reilly, Catalina Curceanu, Quantum Computers

Id: zW6ZtIPCPEs

Length: 40min 6sec (2406 seconds)

Published: Sat Nov 16 2019