Quantum Conversations By the Bay I: Oxford and U Chicago

Quantum Conversations By the Bay I: Oxford and U Chicago

Recording: Quantum Conversations By the Bay I: Oxford and U Chicago

my research is centered on condensation phenomena and also on quantum computation and kind of the integration of both of those fields and like David said we'll be given a talk in a little bit later so I'm excited for you all to hear that and oh and I'm an Indiana right now that's where I'm calling from thank you mom oh I see Alex joins Alex gonna hear us yes yeah welcome Alex just give us a 30-second introduction about yourself hi yeah I'm Alex Kissinger I'm an associate professor at the University of Oxford I'm calling you from beautiful Oxford where it's sort of late in the afternoon now I'll be talking today a little bit about quantum software particularly about compiling quantum software on a circuit optimization very happy to be here and and excited to chat with some people that I might not have normally seen before so yeah looking forward to it so we're going to spend a few minutes going around and make introductions before we start your talk is that if that's ok so everybody can can meet others so uh alexandra raber's next Alexander can hear us going once going twice ok I'm gonna just follow the list Alex C Golda if you could introduce yourself hi my name is Alexa Golda I'm a research assistant professor all studies Chicago calling in from Chicago I'm a condensed matter theorist by training and lately I've been working on quantum computing era mitigation techniques specifically targeting superconducting systems like IBM really looking forward to this this these Doc's thank you thank you Alex hey I like your background it's a nice tent overlooking I wish mr. Balaji ramamoorthy yeah I'm a software engineer interested in quantum I have my own meetup called Zen for quantum and I do host some meetups like that hi yeah so yeah I I'm doing a small study on Sanskrit as a quantum language and quantum computer language and my own interest some hobbies I have encounter thank you that's great thank you so much Konstantin Jung coolican color is next I saw I worked for JPMorgan Chase I'm leading a group called advanced computing part of it is quantum computing so we have some public work I won't be able to talk too much about anything else the boss's Banerjee hey my name is Debashish Banerjee I am a particle physicist who's based in Berlin so I'm trying to use quantum computing to solve some of the particle physics problems but yes thank you yeah it's a good I'm coming right after him because we're collaborators I'm at the Perimeter Institute in Canada and yeah I have a background condensed matter and lattice field theory so we're working on simulating these models on circuits also thank you Eric bond Eric going once twice ok let's get to it would van den Berghe hello everybody i'm eric van der work I'm a research staff member at IBM TJ Watson here in Yorktown Heights and dialing in from New York I'm currently looking at error mitigation techniques so thank you Thank You Gavin Jones and Gavin Jones I'm a research staff member at IBM as well I work in research lab and in San Jose now actually managed the qualifications before they work on quantum applications in chemistry thank you Kevin goooal wonk hello my name is Duane I'm currently doing research in dr. Matthias group and I'm currently working on using the current constraining zyr DM to study molecular currents thank you a Harshita gandhi hi i'm dan from india I'm an undergraduate student just exploring this field and thank you I got your notice about recording so we will be doing the recording of the public talks but thank you for joining us in person for me it's exciting thank you thank you Julie right Julie rice hi I'm a quantum chemist I work at IBM Research Center in California in San Jose and I've been working on quantum computing with the larger quantum computing team and in particular on quantum applications Jeffrey corn sorry yeah I'm a little late we introducing yourselves is that correct tell us about yourself and your interests and okay I work on a quantum applications team and I'm with an under Gavin Jones and my interests are mostly just in all aspects of a quantum simulation state preparation time evolution and imaginary time evolution and measuring other other properties of quantum systems great Thank You Jeffrey Matthew Roberts hi i'm matt roberts i'm a postback I was recently admitted to University of Pennsylvania I'm interested in exploring how category theory and quantum computing connect also excellent I haven't haven't got there yet because with situations that delay my plans a little bit but I was admitted and decided to go in and I'm interested in eventually get a PhD connecting category theory quantum computing I hope you get to work with Benjamin peers I was his one of his first TAS and he's a great authority in the category theory field so that's exciting I will be looking forward to see how you connect this issues fantastic Miriam beckons hi I'm Miriam I'm a lecturer at the University of Birmingham in the UK I welcome those that X calculus so this is category theory and quantum computing and I also work on applying methods from quantum computing in theoretical computer science more generally great thank you thank you mate Ernest noble yeah hi my name is Nathan Ernest noble I'm a quantum computing applications researcher at IBM really focusing at how we can make use of pulse level applications on our software and access to the backends great ah Thank You Nicholas Avaya I am a researcher in Intel Labs I focus mainly on quantum algorithms for hamiltonian simulation and new applications in material science and chemistry thanks for putting this together Alexey thank you welcome to Eagle is great to have you finally we made them the virtual space after the physical space no ha ha hi um I'm a diesel student and Oxford University working with a quantum group mostly relating category theory with descriptive complexity great welcome New York des care PhD student at Edinburgh I'm also doing category theory and trying to find connection to a quantum stuff thank you welcome if you guys can just a turn on video if you're it's easy for you during the introduction would be great so folks can meet you I think it really helps to kind of feel that we have almost like we're in the same room if that works for you Oh Marsh Shehab hi I am recently joined IBM as a quantum computing applications researcher previously I worked on quantum complexity theory on programming language and near term quantum algorithm thank you for granting this absolutely welcome core long one Oxford University I'm working on zs cactus and condom so to the optimization yeah that's it welcome Rena our stalker hello I'm a PhD student at Q soft in Amsterdam and I currently work on protocols for cryptography welcome Scott smart hi I'm a student at the University of Chicago with Professor Gianni we're looking at applications of reduced density matrix theory for quantum computing for molecular simulations and just all different applications there great welcome good morning Alexei Sebastian has here I'm with IBM I run the academic partner program in the quantum team and I sponsored this event so I'm hoping it goes very well and thank you for organizing that's amazing like a few weeks or a little math and actual coffee shop and the existence of this an hour all here from around the world thank you thank you let's see Scott smart oh I think I just introduced myself you here yep sorry I'm going down to this mother this is fluctuating Simon doing hi my name is Simon Ewing I'm a PhD student with David Maserati lately I've been working on introducing periodic boundary conditions to the variational to idea method that I'm sure you hear more about today I'm looking forward to it Darryl front hi folks good to see some of you I know I made an associate professor at Harrisburg University in central Pennsylvania my research is generally on organizational networks and I study mergers and acquisitions from that regard I'm transitioning from classical to quantum to see how quantum will work in that space but for most of my time recently I've been focused in on workforce development kind of like Nate except more on the outside of IBM world great welcome hi hi I walk in IBM research and I'm a developer and Chris key which is great Alexander Bolton mark here yeah hi I'm a grad student in Applied Physics at Stanford and I'm very interested in both the experimental and theoretical sides so looking forward to hearing more about this talk welcome Andrew Eden's hi my name is Andrew I'm with IBM out in California and I'm working on quantum simulations and demonstrations Thanks hey morning everyone I'm postdoc at Los Alamos National Lab work in quantum chemistry of the heavy elements welcome Ferrari hi I'm a student from Parma Italy I work on compilation and ultimate working welcome welcome so I'm glad we set the tapas in the morning so your folks in Europe can can join this great Benitez as Retta hello everyone Wayne's Bonita I work with Sebastian messenger on the IBM quorum academic team great welcome so let's see my list is actually fluctuating that's very interesting it's not a trivial task we need some quantum computation to do properly if I missed anybody please just introduce yourself let's see if if first of all raise your hand let's do this if you haven't introduced ourselves yet there is a feature in somewhere you can raise your hand I will see that I can call for you know and I probably can just call people who have their hand raised okay so if you so raise your hand if you have not been introduced yet okay great jin-seok him hi my name is Jin sonken I'm a researcher with IBM I work in the demonstrations team welcome to soon and now you can lower your hand so I see that okay great Alexander Raber hi I'm Alexander River I'm a graduate student in David Mathias research group at the University of Chicago I'm working on sitting modular conductivity using the one majority of reduced density matrix methods great welcome now we can lower your hand and then I will see the okay Jonathan Candelaria yes my name is Jonathan Candelaria I'm executive director of a system X program at Stanford but I'm also the interim chair of the Workforce Development Committee in the QED C consortium this is great it's great to have locals because I need an implant this will be quantum conversations West and will join the you know West Coast in solutions but we expand at a global meeting of course hopefully once the restrictions are lifted we'll be able to host local meetings so it's great to have folks from Stanford let's see is there anybody else who have introduced themselves yet if so raise your hand or you can just do it now in the open floor okay so I think everybody introduces themselves it's great it's great to have a few guys it's really amazing how we can have the global community together in this time so I think it's a silver lining and I think we now can proceed with with our first talk we'll have Alex Kissinger from us of Oxford I put the description on the side so Alex I have made you the host so now you should be able to present and I let you introduce yourself and the research group in more detail welcome Alex okay hi everybody thanks thanks again Alexi for for setting this up this is I think we're all trying to get used to this this new format and it's and it's nice to see that you know along with a bit of the the weirdness there are kind of some new opportunities for doing stuff that wouldn't have been so possible before right so I already introduced myself I'll say it again for people that came late I'm Alex Kissinger supposed to get professor at Oxford in the computer science department in the quantum computing group which which is a sort of an unusual quantum computing group in that about half of us or more or category theoreticians so you might have noticed a couple of them sort of speckled amongst the group here I mean I won't talk too category theory today actually not at all but some of these ideas sort of sort of grew out of that and that that explains at least kind of half of my top title let me see if I can share my screen Shh share okay and I guess that sort of explains the structure part of the title of my talk so it's it's quantum circuits from structure to software and well maybe I should maybe I should just rather than waffling about what that actually means just kind of dig in so this is a talk about quantum software and if you see people saying quantum software you often often they mean one of two quite different things on the one hand someone could mean the code that runs on a quantum computer right so quantum algorithms and you know there's the famous act algorithms for factoring and searching and these days lots of lots of other stuff I have a question which is which is maybe a bit of a generational divide or maybe a western hemisphere versus eastern hemisphere to buy does does anybody know who's pictured in that in that factoring picture there Polly short that's yeah that's polish or so so you the kenai would catch that this is not in fact Peter shor but Polly Shore famous for his roles and numerous stoner comedies in the 90s anyway that's that's kind of one meaning of quantum software's is algorithms another meaning is is not really the code that that runs on a quantum software on a quantum computer but the code that makes that code or rather the code that makes that code better so by this you can mean compilers so things that turn say high-level software into something that's actually runnable on a machine something me and my students think a lot about is optimization so making making computations run faster verification here I mean verifying that the codes you got is actually doing what you think it's doing and and and things kind of in that general genre so so this is really thinking about kind of the structure of software and how can we make it I knew this fast and efficient and correct as possible okay so until recent years if you worked in either of these areas a common criticism would be that this is pointless there's no quantum computers now by now we all know that that's not true anymore there are quantum computers but they're a bit rubbish so you know we have this catch phrase now misc which is we're just somehow a handle for these not very good quantum computers that we have these are these noisy intermediate scale quantum computers of short coherence types small amounts of memory typically operations say gate level operations measurements very noisy and we have limited connectivity so if for instance I want to do something involving two qubits I can't do it between an arbitrary pair of qubits I really have to do it between things that are neighbors and this is definitely true for superconducting devices and for most of the kind of ion trap type type proposals but I think this is this is actually a nice place to be if you're working in quantum software because you can come up with a small kind of kind of stupid idea and if it makes the software just a little bit better this is actually increasing quite a lot which you can do with these very limited devices so I've been talking kind of about code and about software but really really what I'm thinking about when I'm saying these words is quantum circuits so quantum circuits are kind of like an assembly language for quantum computation they consist of sequences of primitive operations which are which are kind of run in order on some register of quantum memory right so so you can really think of this as sort of an assembly code like this but we also get used to thinking of it more as this kind of 2d notation where you see your memory here and and time kind of flows this way as different operations get applied right so so now let's let's think about this little circuit and think about how we could make it run faster or better right so running this circuit with with with fewer Gates's is just going to be better because these gates introduce noise and they take time okay so a very simple thing we could do to make this circuit smaller is if we know a little bit about how these gates kind of interact with each other we can start to transform this circuit into something that's equivalent but runs faster okay so a very simple thing that we might try is these things so these see not gates interact with Hadamard gates in a certain way which is that I can take a pair of Hadamard gates and sort of push them through a scene on gate and it kind of flips it around okay so let's see that I push those hata more dates to the right and the sinon flips around okay so when that happens now I have a pair of seanut gates and these things cancel out with each other okay so now by doing some little simple moves on gates I have a simpler faster circuit all right so you can you can start to come up with a lot of these identities and so here's a pair of sinon gates equals a C naught and a swap and here's the thing I showed and here's some Z gates other things about C knots and so on and then maybe you would come up with some more of these identities if you thought a bit longer and then you'd come up with some more and some more that's more and at some point you start to wonder when does it end when do I know that I've got all of the right identities to really do a good job optimize my circuits and I mean the answer is you don't it's it's it's a purely a heuristic thing you just keep kind of throwing in the kitchen sink and seeing how well it works or at least that's kind of how this kind of optimization is done these days however you can also do something that's a bit more clever which is I can look at this circuit and think of these gates not as primitive things but actually is built out of even more primitive stuff okay and now there's there's a few definitions for what might be more primitive stuff the kinds of things me and my collaborators like to work with are these things which are called spiders so so these the these red and green dots which are labeled by angles like this are called spiders this this green one is called a Z spider this red one is called an X spider and put together these things make what's called a Z X diagram okay so I'll explain a little bit about what these things are so there's a few perspectives you can take on these things and actually if you go way back to well I say way back about ten years back the perspective might have been something about category theory perspective one is the X diagrams are really just like circuits but instead of being made of unitary gates they're made of these special gate like things called spiders okay and there's two kinds of them as I said there's the Zen spider which if I draw the matrix of this thing it looks like it's got a one right up here in the top it's got an e to the I alpha right down here in the bottom and it has zero as everywhere else okay so if it's got one leg in and one leg out okay so I suppose I should say this is a two to the this has a min puts and this has an outputs and this is a 2 to the M by 2 to the in matrix okay and if this thing has one input and one output then it's a tune to the 1 by 2 to the 1 matrix and it's actually this matrix which if you are used to playing around with circuits is just a Zed phase gate which sometimes you see written as our Z alpha okay so you can see this is a kind of a massive generalization of these kinds of phase gates okay so that's the Zed spider that spider is almost the same it's just rather than doing everything with respect to the standard basis we do everything with respect to this Hadamard basis the plus and minus basis okay so really this thing is just the same as that thing up to a change of basis okay so so that's one perspective I heard a couple of people mentioned they're there in convinced matters so maybe perspective to you is something that they can appreciate maybe some others as well ZX diagrams can also just be thought of as tensor networks but whereas tints are usually the way we think about pinzer networks as some black boxes kind of wired together and we don't really say what's in the boxes these things we use two special kinds of boxes which are parameterised by a single angle so we have the Zed boxes which are kind of like a Kronecker Delta x times this phase and the X boxes which are which are this this other kind of thing okay so so you know you could you could say well I'm not I'm not sure these don't look that natural so so why would we want to fix these as our choice of boxes well maybe I should say one thing before I get to that so so the difference really in a Zed X diagram and a circuit or I'd say the biggest difference is is FX diagrams like tensor networks or friends are bendy in the sense that they're they're they're very flexible so you tend to think of a circuit as this kind of rigid thing where I have a gates kind of happening in sequence and in parallel whereas EDX diagrams if I take this this picture here and I deform it to something where the graph is the same this is actually still the same linear operator so it inherits this nice property of tensor networks that the only relevant thing here is the graph so it's what is connected to what okay so this thing is equal to this thing is equal to that thing because they're all just deformations of each other okay so so now here's the here's the thing I was getting ahead of myself to say a reason to look at these generators well one one reason to look at them as they are universal in the sense that they actually generate all linear maps or at least all linear maps on powers of two-dimensional space and they're handy for building most of the common gates that you would see in the quantum circuit okay so these we already I already showed you how is that phase gates are written as just these one input one output spiders some familiar special cases or the s gates and the T gates the Hadamard which we often draw it's just a little yellow box like this can be written as a green red green sometimes called the Euler decomposition if you're familiar with these things see knots just look like a kind of more colorful Cina and see Zed's look like a pair of green dots connected by a by a wire okay so these are these are very common gates in the toolkit of somebody building circuits they're easy to express the spires so so that's nice but what's nicer is that these fighters satisfy some algebraic identities which together are called the ZX calculus so here we have 1 2 3 4 5 6 7 8 laws that the spider satisfying and these eight rules actually imply all of those pages and pages and pages of gate equations that I showed you before okay so there they have a very nice compact structure that that lets you work very effectively with these kinds of interactions between gates okay so let's see this in action so here's here's our little sample circuit we're gonna take these gates and slice them open and we see that there's actually spiders inside and now we'll apply some of those rules and now I have to anticipate what I'm going to do I believe the first thing I'm going to do first rule is that spiders are the same color so those are the green ones and these red ones confuse together to make bigger spiders so that's what's happened there so you can see that these actually four spiders here have all squashed together and they fuse together and their angles have added all right so here's a PI by 2 pi by 2 the blank ones count of zero so if I add all their angles together I get a PI here a few more things are fused and then the next thing that happens is if I have a red spider and it hits a green spider it actually copies through okay so if I look at this if I look at this Doc hitting this this other doc it copies through and it makes two copies of itself okay and then we can fuse these red dogs some more and yeah we fused some dots some more and then confuse some dots some more another thing that happens is if I have a pair of parallel edges these things disappeared or I haven't done that yet yeah there we go a pair of parallel edges disappears we can fuse some more and at some point we get a much simpler diagram okay and this if it has a nice enough structure I can pull a circuit back out this obviously has a very simple structure which is just some product state of my outputs right so I can prepare that state using the quantum circuit this this way for example okay so now a question becomes how can we do this by hand calculation which was involving about 30 spiders on thousands of spiders okay and you might you might say well actually you know current current hardware is pretty small-scale still you know we're talking about 10 to 50 cubits but as soon as you start talking about say 50 cubits and a gate depth of honey or something like that you're already getting into the regime of thousands of spiders so so it's not not practical to do this kind of thing by hand so how do we scale up and the obvious answer is we need a tool for doing this some software for for working with these things okay so we have a tool it's called physics all right so so some people say PI Z X button but according to us the developers it's pronounced physics which is like if you say physics but then you don't pronounce eh it's physics okay and this thing is a Python library which you can use from Jupiter notebooks and you can sort of interconvert things to kiss kit and well do do quite a few different sorts of stuff which I'll which I'll show toward the end and and give you some more details on how you get this tool okay so maybe I should let the slide do the talking for me so physics is an open source tool for quantum circuit optimization verification and classical simulation using the Z ax calculus okay and the main idea it uses for automation is actually quite a simple one so if you're a human and you're you're clever you can work with these things right equals means that I can use my human cleverness to decide whether I should replace this picture with this picture or if I should replace this picture with this picture all right and you know maybe a machine can have some kind of strategy of knowing which way to go but you know it needs to use some smarts but one thing that the machine is already capable of doing is if I just tell it which way and this rule should go okay so so clearly this thing with one dot and it is simpler than this thing with two dots in it so I'm just going to direct this thing okay and that's effectively the difference in what's called equational reasoning versus rewrite theory okay so the idea is to turn some equations into rewrite rules or derive some rewrite rules from equations and now just tell a program which is called a simplifier to just apply these rules until it can't apply them anymore and then when that's done so so at some point as long as my rules are always making this picture smaller this thing will terminate and when that's done try to extract some meaningful data from the simplified thing so so often that's just either a smaller circuit or some simulation data like amplitudes or probabilities okay so the first thing we tried this technique out on was something called T count reduction which is exactly what it sounds like it's reducing the number of T gates in a circuit so in this see X diagram notation a t gate is just a green dot which is labeled by an angle which is a multiple of Pi by 4 so I guess technically this thing is a is a t dagger gate but but anyway we call these all T gates so why do we want to reduce the number of TJ's well one reason come from fault-tolerant quantum computing so so we have these sort of long way off schemes for doing harm competing fault tolerant lis and what they tell us are at least almost all the schemes that people have studied but they tell us is that if we want to do clifford gates which are basically everything in this picture which is not a tea gate these things are easy and if we want to do tea cakes there some something like a hundred times as hard as the clifford gates okay so if for instance we can get rid of sixty days here that's as good as getting rid of a hundred of the other gates so this motivates why you would want to get rid of them okay and the way we do this with physics is we take some circuit like this and we compute its reduced to ZX diagram which in the process has eliminated some t gates ok so some of these t gates sort of finding each other and fuse together or cancel out and then from the simpler diagram we extract a circuit account again ok and if you're not so good at counting on the fly i think there's about six fewer t gates down here so like i said that's that saved about the effort of six hundred of these say seen on gates or something okay so we tried this on a bunch of benchmarks and in the particular case of what's called an sila free tikal reduction so this is without using extra memory we did pretty well and that we matched on something like seventy two percent in the circuits we looked at we matched the state of new york and on about seventeen percent we actually did better with this kind of technique so i when we first got into this actually a Earl Campbell who's the Campbell here emailed me to say welcome to the tea wars because because there's actually quite quite a few people working on this and pretty much immediately after we reduced we produce these results another group came out using a different technique and matched all of our numbers but then later in 2019 so this was in spring of 2019 and winter of 2019 a couple of Oxford folks so Hardy Wong have introduced himself about thirty minutes ago I guess 20 minutes ago produced another technique based on Z X calculus which which then got ahead of the state of the art again so this is really kind of I think the team Wars is the right word for what's going on this this at the moment okay so that's kind of what I wanted to say about about T count so something that was kind of pleasant about this kind of technique and actually you can use this for a lot of techniques based on simplifying circuits is that they are self checking so what does that mean that means if I have a circuit like this and I optimize it to a smaller circuit well then the smaller circuit better be doing the same thing as my bigger circuit otherwise I've introduced some errors into my code so one way I can check that is if I have two unit Aries which are equal to each other then doing one and then undoing the other should be equal to doing nothing right which which in this kind of language is the identity gate which I've just written is one here and it turns out the simplifier if it simplifies C to D it'll also simplify C and undo D to nothing so we were able to run this kind of checking procedure on all of our optimizations and it did say yes thumbs up but I should mention this well I should say one more thing which is which is so yes it thumbed up kind of all of our outputs actually along the way we found quite a few bugs when this thing was giving us a thumbs down and we fixed them but interestingly we ran this on some circuits from the literature and it actually found some bugs so this one here was a circuit that was actually published in a peer-reviewed journal and it was it was just wrong so so our verifier found it and we were able to - well what it said is this thing might be wrong and then we were able to use a different technique to prove that it actually was wrong okay so some one little caveat here this doesn't prove that our code is correct because our optimizer and the thing that checks it could both be wrong but it's lightweight and that we didn't really have to do any more work to do it so it didn't cost us anything and it actually builds confidence that our techniques are working correctly because it's actually quite unlikely that these two quite different procedures are sort of conspiring to convince us that they're both correct if they were both wrong so so I think these kinds of techniques are actually really useful especially here in these early days of developing quantum software especially because it all happens before we fire up the quantum computer all right so if you if you know the kind of frustration of getting something to work right when you're and you're sitting there waiting in a queue to run it on a quantum computer you can appreciate doing as much kind of offline as possible okay so so that's what I wanted to say about verification the the last thing I was going to mention a little bit about is circuit routing so I mentioned a little while ago that these misc architectures have limited connectivity which is something I guess a lot of people here will be familiar with so if I want to do a two qubit gate say on this this is a I think this is a Righetti architecture if I want to do a two qubit gate between qubit 14 and 13 that's fine but if I want to do a gate between 13 and 6 that's not fine so naively what I would do is I would to swap this thing around and I'm gonna bring it over here do my gate and then maybe even if I'm super naive bring it all the way back here all right so I'm doing one two three four five six and then my gate seven eight nine ten eleven twelve thirteen games to do a single game so this is obviously never going to going them to be the right way to do this okay so so there are a lot of techniques for actually turning your logical circuit into a routed circuit one that we've been thinking about exploits thinking about this circuit extraction procedure so I didn't really tell you much about how we extract circuits from ZX diagrams for people that are interested I'm happy to explain some more but the kind of basic idea is is that it's it's a sort of Gaussian elimination type procedure and the way we do it is not unique so actually if you choose which row operations let's say in the Gaussian elimination you do if you choose which scene on gates you do respecting some constraints you can actually extract the circuit in a way that only produces sinon gates or to qubit gates between neighbors okay so if you think about this as a kind of nine humid architecture here in this sort of 3x3 grid and each of these is is a time step then you can see that the sinon gates are getting applied only between neighbors at each at each time step okay and this is the kind of extractions we can do and actually for seen on circuits this works very well so so comparing this kind of technique to more general-purpose techniques so here's the here's forget ease kwill compiler and that they at the time it was doing a lot better than kiss kit even at these things but but you know this is changing fast so I don't want to make any any twenty20 claims about this but comparing to Righetti at the time we were doing up to five times better routing seen on circuits using this kind of technique okay so so that's that's about it for the the kind of talking part of my talk I also wanted to give a quick a quick demo of the tool and just show you some of these things in action maybe before I do that I could ask if anybody has any questions or comments or things that they want to pop in and say give me a minute to do so because sometimes it's hard to find for the mute button yes this play by ear so just unmute yourself folks and ask a question if we see too many people asking we will try to sequence it but for now I think we'll just open the floor you can always type at the speaker in the child also to ask your questions let's let's start with energy and then scale that from there exactly exactly so I have a question about a little bit tea gates on the IBM hardware you a basic gate is rx 5 over 2 right which is not RZ you wanna is actually considered kind of free so they are swapped right so the tea gate on IBM would be our X PI over 2 okay yeah because the because the Z rotations are a purely a classical update is that right that's my understanding ok yeah yeah and so so a nice thing about this choice of generators is everything is color symmetric so so actually if you flip all the reds and greens everywhere which is the same as flipping the role of Z and X everywhere everything still works exactly the same the same way thank you okay maybe I'll just start the demo but but feel feel free to jump in anybody who wants to say something or ask something okay so so here I am in a Jupiter notebook normally if you if you want physics you can just pip install physics not worry about this stuff so I'll just import physics a ZX now a very simple thing I can do I guess some of you will recognize this this chasm format this is just a very simple text format for writing circuits so here's a register for qubits getting C knots between some combinations of them and then a T gate which if I draw that looks like looks like this okay and another thing I can do is I can actually turn that thing into a graph or is the X diagram like draw that as well and it looks identical but one thing you should bear in mind is that this thing is kind of more than a circuit it really is a graph so if I just pick these things I can sort of move them around and I can see that this is actually just some graph which encodes this circuit okay and here's a here's a simpler thing and if I look at these circuits before turning them into a graph then this is just a list of gates which is probably pretty familiar if you're used to working with something like iskut this kind of circuit format if I turn it into a graph it really is a graph so this thing is the graph with 14 vertices and 15 edges okay but but the way we draw it of course it looks identical now a very simple way I can simplify this graph is to use what's called the spider sin so so simplify and see if I can get it to complete here yeah has a bunch of simplification procedures but all it was just called the Spyder significant G and what this will do is just fuse together dots of the same color all right so this didn't do very much in this example I believe it fused this one and that one together to make that infuse this one and that one together to make that but it couldn't do anything else so it didn't it did the rule once and then once again so that was in two iterations now if I call a full reduce which is our sort of kitchen sink simplifier then what you see is that this thing reduces all the way to a swap and if you if you look at this circuit you can see that I kind of contrived it that way because these things are seen on gates which it kind of exercise you learn and quantum info 101 as if I do 3c not gates in this setup this makes a swap and then I can see that this red pi by 2 which is like an X pi by 2 rotation goes and cancels with this 3 PI by 2 and this pi by 4 cancels with the 7 PI by 4 and leaves me with a swab okay I wonder so I'm going off-piste here this might not work if I turn that off no it didn't work so never mind I was thinking that that might get me this kind of output but anyway this this sort of thing always happens when you're getting a live demo so it supports input in a number of formats something that is a bit hackish is this thing called squaws M which is spider chasm which is if I just make a register with a capital letter that will plug in a dot of the same color to the to the left and plug in a dot of the same color to the right and already knew all the fusions that it can okay so so I use this kind of squeeze em thing I think I can actually turn off simplifying first you can see what happens then this bit is just a circuit right and that made this middle park and then it plugged in a green into the front and the red into the back and then if it if it does do the simplification which is the default behavior I get me this thing which is not a circuit anymore or at least it doesn't look like a circuit anymore right so I can also make more complicated looking things it should be just the extra draw okay so so here I've got a pair of these things hooked on now these these are a sort of thing that we that we study quite a bit called a phase gadget which what this actually does is it applies this face whenever the parity of these inputs is equal to 1 so if it applies that phase whenever the parity is equal to 1 and then it undoes that phase whenever the parity is equal to 1 then the total effect of these two things is to do nothing okay and if I I think if I apply the Clifford simplifier it can't figure that out which is a kind of simpler simplifier but if I apply the kitchen sink one it does and it reduces that to the identity okay so as I said this thing loads in quite a few different formats to their varying levels of success so sports chasm is dock you see format the Q sim format which which Google published its supremacy circuits in so here's what one of them looks like okay and this is this is their F sim gate which is a sort of a swap anon and I think a poly poly Zed Zed with with a given phase something like that ok so here's just here's what it looks like drawn flat okay which is just some big circuit I can also draw in a kind of a three-dimensional way and what you'll see is this circuit is actually involving a register of qubits which is 2-dimensional it's three cubits wide and four cubits tall so this is one of the smaller ones it's not the full-size ones and what you'll see is that the f sims are actually only happening between nearest neighbors ok so here's here's a qubit and here's the one directly below it in essence happening and then and then so on so this is happening to the middle layer and then this is happening to some other configuration of them this is happening to some other configuration and so on and if you go read this paper you can you can see that they explained how these um how they how these different iterations are done and if I apply full reduce to that I get something that's that is somewhat reduced but not that reduced because well if I'd come up with a way of reducing these things very small then I could classically simulate them and then I wouldn't be telling you all about it before I wrote the paper and got all the credit so so that's that's a bit about kind of the basic features here's a little tea optimizer that I've just wrote by chaining some of the built-in functions together ok here's a here's a smallish circuit I think this is a this is a 5 cubic Grover maybe it has some in sylla's as well looks like so that's 336 cute tea gates in it if I apply this tea optimizer another circuit comes out with 166 ok and now I could check that this thing is in fact equal to this thing by calling this circuit dot verify equality and I give it another circuit and it says true but but you know I could have just waited for a few seconds and printed out true so I'll show you what's kind of going on under the hood here I've made a copy of my simplified circuit and I've hooked the adjoint of my original circuit onto the simplified one and then I've simplified it that's what this full reduced in and I see what came out is actually the identity which is in circuit language is just a bunch of wires with nothing on it okay and if I take this thing and if I mess it up a bit so let me show you see one gates 10 is actually a seen on K okay if I change that to something different here's a T dagger and I verify equality says false and if I kind of do the same thing as I did before and see what's going on then my reduction actually didn't didn't terminate with the identity and didn't terminate but a government gave me something which was not an identity circuit okay so that doesn't tell me that they necessarily are not equal to each other because in fact this is a this is a hard problem this is a QM a hard problem actually to determine equality but what it does tell me is it wasn't able to prove that they were equal to each other which is a sign that something might be wrong okay and here's something obviously is wrong that I've messed up this this circuit okay so another another way you can use physics so this is running on my machine hopefully this hasn't just hasn't died in the meantime is on the on the quantum experience so physics is available over pip am i discovered quite interestingly that I can just hit install things inside of a QX notebook okay so we got piss exhale damn Oh is going to run but it's not it's not too much of a problem if it doesn't so here we already have physics just load this I'll load pics and here's a very simple little little wrapper for turning a ZX diagram into a kiss kid circuit okay so that's that's a bit of glue that I did I kind of hacked together in a few minutes and now here's here's Burlington let's see if this will this will come back to me in a reasonable time here I'm gonna build a little Z X diagram okay so so what did I do I created some vertices here I hooked them together with some edges and I drew it so here's this thing this thing is not a circuit but I can turn it into a circuit by doing the circuit extraction so here's what it looks like is kid's circuit and now here's the here's here's the part that you know let's see if this will this will come back and in time the little job is actively running yes I guess nobody watching right now is sending jobs to Burlington which is good job is successfully run and I get the results and and the the Z X diagram so this thing if I plug in zero zero zero I should get zero zero zero out of it and Burlington agrees well seventy five point four percent of the time okay so so that's that's about it that's what I wanted to say so so thanks everyone I'm happy to answer questions yeah I have a question this was great and I'm wondering if there any companies using this to your knowledge not to my knowledge I think I think so so Cambridge quantum computing plays with physics I think but but I don't think they're I mean I I know that their compiler doesn't actually use physics under the hood but we talked to those people quite a bit but yeah yeah I don't know I think maybe some of these ideas from it are starting to kind of get out there into the end of the vials which i think is which is nice maybe I can comment Alex yeah so so this is Ross Duncan from Cambridge quantum computing the ticket compiler doesn't actually use physics itself but it has some of our own implementation of some of the parts which are in physics so we used some Z extract those things and slightly differently cool I'm glad you're here so you said he didn't force me into a situation of saying something that was maybe wrong about what you guys are actually doing so other questions I can I can hear you very softly yes blue speak up there alone okay is there any way to put in like say additional constraints such as like you know right now two qubit gate errors or like the highest source of error so post a single qubit gator so to kind of like add additional structure to this kind of simplification so so one thing we're thinking about a lot is is this this extraction face is it's actually it's not unique and it's quite sensitive to in a clever way and if you do it the wrong way it actually ends up generating a lot of to qubit gates so we're thinking about how to get that number kind of as low as possible so that sentence it's kind of always the goal to produce as few two qubit gates right for like current state-of-the-art superconducting qubits like two two qubit gates are kind of the main error you know I would say T gates are for error corrected for an error corrected quantum computer so each each each kind of system has its own kind of thing you want to get rid of yeah that's right I think ions would be different from superconductors because you can use the motional degree of freedom to entangle so I was just I guess interested in a little bit more hardware structured simplifications yeah so we we just we kind of started with the T stuff because that's that's what we what the people around us we're talking about at the time but these days we're thinking a lot about two qubit gates as kind of the main the main next target for this for this kind of thing something I didn't mention actually a useful application now for getting rid of T gates is a classical simulation of circuits so there's these these stabilizer rank techniques which go exponential in the number of T gates in your circuit rather than the number of qubits in your circuit so there it's actually useful to do a little bit of simplification for him and get rid of the T gates cool thanks other questions if not let's all think Alex was a great presentation thank you thank you feel free to unmute and clap around like so just show you no clapping that was great and you know great screen sharing it's it's it's really great to see Jupiter and everything works smoothly on my own hope everybody was able to see it well as well so that's that's that's awesome I see we have some some more folks joined us after the initial introductions so in case you just joined us or joined here at the talk thank you for joining we did quick introductions when we started about 30 seconds per person just to say your name your affiliation and your area of research and your interests if anybody is here who didn't do that I would like to introduce themselves please raise a little hand using the zoom raise hand feature I can see you and I can I call your name to to give a brief introduction I'll give you a few moments to find that we just feel free to go okay we'll Swope please hi my name is Bill Swope I'm in California I work for IBM in the research division I report to Gavin who's uh was introduced earlier and my background is quantum chemistry basically a general computational chemistry and mostly statistical mechanics but lately I've been working in the quantum chemistry area yes I'm thinking I'm working in Cambridge in the UK my background is from categorical theory and the xanax calculus particular and nowadays I'm mostly interested in compilation of quantum software thank you great welcome Ross I think let's see Kevin crystal ish have you been able to introduce yourself yup [Music] let's see we can't hear anything okay great so we still have time you know after the second talk to add more introduction and so the plan is just to recap during the talk which is on the agenda or any any other talk feel free to chat basically the chart is structured so that the host will see your questions and the host is the current speaker so that way the speaker can decide if they want to answer the question during the talk or they want to defer it to the end and obviously after the talk is done there will be Q&A so it's really up to the speaker how they want to manage it so feel free to use the chat feature for this if there is any problem on the around please email me my email Alexia chief scientist of orc it is at the event web page quantum dot SV so I put it there for the whole world to see and use so if you for instance decided that you want to give a talk at the next meeting which will hopefully will hold monthly as a structured agenda part just email me there with your ideas or any any other suggestions right so basically creating this format as we go so it's very exciting I'm open to all kind of suggestions and certainly appreciate your feedback all right so let's see I think if there are any questions suggestions about the running the meeting itself yes somebody just made a made a good point which is I didn't mention the github link for the tool so I'm just gonna check oh yes please do so and everybody can see that yes and also what I'm gonna do if you guys want to share I will copy this and I'll put it on the event page as a follow up right so that that way folks can can always go back so if basically if you miss something go back to the web page quantum dot SV and and see if it's there if it's not there email me I will be able to recover in your links and share it with you great so our next talk is from University of Chicago and there is monsieur t will star so David I'm gonna make you host right now okay great I'll do that alright so now you're the host and now you should be able to share a screen and welcome David alright excellent Thank You Lexi let me come down here get the screen sharing started and feel yourself again because I think some folks joined us during the initial bar saw some comers okay certainly just get this started here all right okay great all right so I'm David Maserati from the University of Chicago Lee Anne and I will be presenting some of our recent research today I want to thank Alexi and Sebastian for the invitation to the meeting I think this is great quantum conversations by the bay it's really great especially in these times for all of us to get together and enjoy science so definitely if people have questions you know during the talk that's great too you can use the chat or you can also just save your question up for the end as well so alright let's get started here I hope everybody's having a good day and staying safe so the talk today is preparation of an exit on condensation on a 53 cubic quantum computer so the outline of the talk we're going to start actually by talking about a couple of other things and then build our way up to talking about the exit on condensation so we're going to start our talk by talking about strong correlation problem in quantum chemistry we're going to look at wave function theory reduced density matrix Theory error mitigation via and represent ability and talk about a novel and efficient quantum eigen solver and then we're going to talk a bit about verifying generalized poly exclusion principle and then we'll talk about exit on condensation of photons on a 53 qubit quantum computer and then we'll wrap things up by talking about the coexistence of exit on and Fermi on pair condensations and then just a few final remarks ok so let's get started actually so just a little bit of background so again we work in the area of quantum chemistry and many electron quantum mechanics and let's just start actually with some very basic ideas of the representation of quantum mechanics so essentially on the left here we have the classical computer and of course the classical computer works by encoding information as ones and zeros as we all know in terms of bits and I think we often hear about the quantum computer in terms of of course key bits where ones and zeros are entangled together and the qubits obviously being an important generalization of the bits when it comes to quantum mechanics I would say another aspect of the difference which is probably the most important is that on a classical computer we have really an abstract representation of quantum mechanics in terms of vectors and matrices where is on a quantum computer we have an experimental representation of quantum mechanics in terms of prepared quantum states and it's actually this distinction that really drives the advantage the potential advantage of quantum computing so in this talk we'll talk about some of the advantage Vantage's of an experimental representation so again the key aspect of course is that on the quantum computer we're not just representing the abstract we're not just representing the abstract information in quantum mechanics as vectors and matrices but we're actually preparing those States on the quantum computer so in the strong electron correlation problem one of the difficulties is that we need to solve the Schrodinger equation for let's say very complicated materials that can show long-range order and other exponentially scaling phenomena in the wave function and the traditional approach we take of course is to take our Hamiltonian write down a Schrodinger equation with that Hamiltonian solve for the wave function sy and then from that many electron wave function which can have many electrons we extract descent one or two body observables from that and unfortunately the process of computing the wave function is where we have an exponential bottleneck so as scaling essentially on the classical computer that scales exponentially with the size of our quantum system and the quantum computer then offers essentially a different approach where instead of actually computing the wave function we're preparing the wave function on the quantum computer and because essentially of the ability to entangle the qubits into the bits and two qubits we're able to represent an entangled quantum state on the quantum computer in a way that does not scale exponentially with essentially the size of the quantum system that we're studying the quantum material or molecule so in principle quantum computing could essentially allow us to take a Hamiltonian write down a shortened your equation prepare a wave function on the quantum computer and then abstract abstract abstract observables at a computational cost that does not scale exponentially so the traditional approach on quantum computers is to think about the wave function and in wave mechanics we have our traditional expression for the energy as an expectation value of the Hamiltonian involving the wave function here we have a molecular Hamiltonian involving an electrons with the one body kinetic energy and nuclear electron attraction terms here we have the electron electron the two body repulsion terms and typically we prepare the wave function on the quantum computer and measure the energy probably the most popular way of essentially solving the eigenvalue equation is to use a variational quantum eigen solver developed by a sphere of gusik in 2014 and the idea basically is that it's essentially porting the idea of the Rayleigh Ritz variational principle where we essentially optimize a wave function a trial wave function subject to certain parameters to a quantum computer so essentially parameters in the wave function are varied to minimize the energy okay so basically that's the background there now one of the difficulties of course that we heard in the previous talk as well is the near term quantum computers of course have lots of errors due to noise and therefore the energy energies we compute in quantum systems to study quantum chemistry and materials will have errors so what you know what can we do to and to improve this type of situation what can we do well one approach forward is to think a little bit about reduced density matrix theory and to develop a reduced density matrix theory on quantum computers so on our left we have wave mechanics where we have the energy as a functional the wave function and on the right we have reduced density matrix or RDM mechanics where the energy starts off as a functional the wave function however we replace the Hamiltonian by an effective two body Hamiltonian without changing the expectation value because the two body Hamiltonian essentially the Hamiltonian itself has only two body interactions so we can actually just rescale that Hamiltonian so that our Hamiltonian depends only on two electrons we can integrate over all the electrons except for two of them inside okay moving that inside K 2 and now integrate sy sy star over all the electrons except for two okay that defines what we call the two electron reduced density matrix so the energy becomes a linear functional of our two electron reduced density matrix d2 and our two electron reduced Hamiltonian k2 so in our di mechanics we essentially have simplified things down where when how we write the wave function in terms of the two RDM so one question of course is well how would we implement our DM mechanics on the quantum computer well basically we can the two RDM from the wave function and then compute the energy so why could there be an advantage here well in terms of thinking about reduced density matrix theory one of the things is that actually it turns out that not every two electron density matrix actually represents a wave function so a two electron density matrix needs additional constraints on it additional conditions to ensure that it actually represents an electron quantum system and these constraints or represent ability conditions are called the n represent ability conditions okay because we essentially want to represent the N electron quantum system in terms of just the two electron reduced density matrix and these conditions are very strong and powerful to give an idea of the entire set of two electron density matrices is both the blue and the red then essentially the set of two electron reduced density matrices that are n representable would be just the blue okay they actually correspond to n electron wave functions or density matrices and the interrupts edibility conditions are essentially the boundary conditions sort of in a hyper dimensional space that separates the red region from the blue region now why is this useful for quantum computing because on some level well we'd say well if we can prepare the wave function on the quantum computer then perhaps we obviously should be representable but the key basically is that we can actually use the unrepresented bility conditions to mitigate some of the important errors that are developing on the quantum computer in the two RDM okay so indeed we're extracting the two RDM from a wave function on the quantum computer however the entire process of preparing the wave function and essentially measuring the two RDM of course will introduce errors and we can use in principle the interrupts edibility conditions as a physically motivated error mitigation or error correction on the quantum computer okay let's try it let's take a look and see how this works okay so here's a picture of one of the IBM quantum experience computers so it's of course an is and one of the IBM computers using superconducting qubit technology and we're going to go ahead basically and look at the dissociation of h3 on five cubed IBM quantum computer and what we see here basically is the blue represents the energy computed classically using a method called full configuration interaction which is where we just solved the Schrodinger equation in a certain finite basis set to full precision okay so here's our potential energy curve in blue and you can see these X dots here represent the calculations on the IBM quantum computer and you can see that - all visual effect here we're essentially tracking the full CI both actually in the region around equilibrium as well as in the dissociation region and it's important that actually as we pull the Aged 3-chain apart so we're actually just pulling all - chemical all of all the bonds equally okay it's a hydrogen chain we're just pulling that chain apart where everything just equally pulls apart at once as we essentially end up in the dissociation region the electrons on each charge and become highly entangled and so we actually have some strong correlation in this region and yet the quantum computer is basically oblivious to that producing an accuracy essentially 1/10 of kilocalorie per mole which is about one tenth of chemical accuracy in this basis that at least throughout the potential energy curve okay so we're basically able to treat strong electron correlation as we essentially pull this chain apart and the reason we're able to actually end up with such good accuracy here is because along the way we're essentially using the interpretability conditions to correct the two RDM that's being computed on the quantum computer okay so it's an RDM quantum computing algorithm that essentially then allows us to use the interrupts and ability as error mitigation and you can see the mitigation works not just for the energy but also for properties as well so here for example we're looking at the sum of squares the off diagonal elements of the one electron density matrix in the atomic orbital basis and that gives us a measure of essentially how how localized this is and here is a function of the separation so initially the system is highly delocalized representing a metal and then as we pull the chain apart the electron densities become localized okay on the quantum computer with the full CI and showing essentially a metal to insulator transition however you can see as it goes down to zero everything is isolated whereas hartree-fock theory which is the mean field theory in quantum theory electron Theory pretty much shows a metal the entire way okay so it is the strong correlation that drives the localization of the electron density and essentially the metal is insulator transition so we're able to see this transition in a ch3 which cannot be described without strong electron correlation so in addition to that we'd like to essentially look and see can we develop for example based on some of the ideas and reduced density matrix theory can we also go ahead and those calculations we just presented we're using a variational quantum eigen solver but can we come up with essentially other quantum solvers that could potentially be more efficient for molecular simulations so we recently developed a quantum solver of contracted eigenvalue equations for scalable molecular simulations existing existing methodologies using phase estimation or variational algorithms have drawbacks such as deep circuits or high dimensional classical optimization in particular the variational quantum eigen solver often is used with derivative free optimization that works well for small numbers of electrons but essentially will become intractable as the size of the quantum computer as the size of the quantum system being simulated on the computer grows larger we would like to be able to deal with some of those challenges so one idea is we introduce a quantum solver of contracted eigenvalue equations which is the quantum analog of classical methods for the energies and reduce density matrices of grounds and excited states by solving essentially something called the contracted Schrodinger equation so the solver does not require deep circuits or difficult classical optimization and it achieves an exponential speed-up of the exact classical algorithms okay so how does this exactly work let's take some example so in particular we're going to solve something called the contracted sure injure equation or the anti-hermitian contracted Schrodinger equation physically this is a projection of the Schrodinger equation on to the space of two electrons and we're taking its anti hermitian part now why is this equation so important well the equation is very important because for a couple of different reasons so it basically represents the Schrodinger equation on the space of two electrons so it's sort of the sort of the equivalent just as a Schrodinger equation is the engine for solving for wave functions the contracted Schrodinger equation and the anti animation part can be viewed as the engine for solving for the two electron reduced density matrix and we can solve the AC se by a series of two body unitary transformations which are shown here okay so we iteratively apply a series of two body unitary transformations to the wave function to produce another wave function at the n plus 1 Federation and an important part of this is if we look at the energy as a function of these two body iterations two body unitary transformations we find that the gradient and the energy with respect to this driving transformation is this quantity here which we can see is actually just minus the residual of the AC se so actually the contracted Schrodinger equation or the aunt even AC se is really critical because it actually represents its residual or it's like it's it's it's deviation from zero actually represents the direction to minimize the energy as a function of these two body unitary transformations so as we follow this gradient downhill eventually when it goes to zero the residual will go to zero and that will correspond to a solution of the AC se as this equation is set to zero okay so let's sort of take a look at the algorithm briefly and then we'll look at an example to get a better physical feel for for what we're doing here so the quantum jcic algorithm for Chi RDM optimisation here's kind of just a formal sketch and what's important is we can actually prepare an auxiliary variable a wave function called lamda and when we prepare lamda from lambda we can actually take measure it using quantum tomography on the computer and taking the imaginary part ends up giving us the gradient information so it's very important about the algorithm is we don't need derivative free optimization we can directly extract a gradient at each step of the algorithm then we apply that transformation that unitary transformation to the wave function and produce I of n plus 1 from that we can do tomography and extract the two RDM and then we just repeat these steps over and over until we reach convergence in the system at each step obtaining the gradient that we need for the optimization in terms of advantages so essentially it's the classical AC se or the AC se algorithm for conventional or classical computers poured it over to the quantum computer the classical algorithm actually also has polynomial scaling but it basically requires a reconstruction of higher reduced density matrices from lower ones and that approximation essentially introduces error whereas on the quantum computer we're actually able to achieve the polynomial scaling and do it in a way that's in principle exact its exact up to the noise essentially on the quantum computer okay so our algorithm is essentially exact up to the noise on the quantum computer so let's take a look at a couple of examples so we'll actually start off which is a really simple example and this is fun because this is on a one qubit quantum computer called IBM Armonk and what we're going to do basically is we're going to optimize this one qubit hamiltonian we're on the Bloch sphere here this blue vector represents the ground state of the Hamiltonian so this point on the Bloch sphere is the solution that we want to achieve and we're going to start with an initial point up here at the top okay at the top of the plus C direction and we essentially take a gradient direction down and you can see our first iteration takes us here now essentially what we're doing is we're we're rotating by these transformations as we solve the ACS see each iteration is rotating us around the Bloch sphere okay and as we rotate along the Bloch sphere and about nine iterations we essentially converge to the ground state of the Hamiltonian which is right here on the block sphere so essentially our algorithm for solving the AC se corresponds to performing a series of two body rotations okay in this case because we're in three dimensions we can look at it as a rotation in three-dimensional space but if we're essentially at higher dimensions we have a rotation in a hyper dimensional space so let's take a look at a more challenging molecular case okay so here's here's a case that's got smart and I developed on the quantum computer for looking at h2 on a five cubic quantum computer we're using our ents the IBM computer five qubit and here's the full CI is in black down here so this is the sort of the exact reference value and in red we have essentially a quantum simulation of the solution and you can see we just sort of marched right down here and we essentially converge to the exact solution now performing it on the quantum computer of course we have some error so we march down here and then essentially in about about nine or so iterations we stabilize at about this value so indeed we stabilize at a value that does have a difference from the exact solution again all of this is due to quantum noise and here we can extract the potential energy curve okay for pulling apart the hargeon molecule and you can see that our full CI is here and we have the quantum simulation in red here and then the on the quantum computer we have the blue curve now it's important basically is where we're essentially doing this in a way that is essentially not using any special symmetry so we're essentially using kind of all the traditional mappings of the fermion system onto the quantum computer and so doing it in the most general way possible is what's introducing to some extent some of the error here because of the large numbers of dates but the result basically is showing and importantly that even as we essentially pull apart the chemical bond both at equilibrium and bond breaking we're getting an accurate representation of the information now here on a quantum simulator we went back and looked at breaking apart the h3 molecule and what we see basically has a function of pulling this apart again this becomes more strongly correlated so if we solve the a CSC classically you can see here in red that essentially we shoot right up above chemical accuracy as we pull this apart where is essentially the blue which is the quantum algorithm for the a CSE essentially as a virtual it's basically exact this is just the degree of convergence we converged it to ten to the minus ten and so we ended up with ten to the minus ten accuracy throughout the bond breaking okay so in principle as we essentially remove some of the error in the quantum computer we can essentially we can actually recover essentially strong correlation regions equally well as the less correlated regions by solving the a CSE on the quantum computer with significant advantages over the classical solution okay so before we get to the exit on condensation okay which will be a good test of some of our ideas for a more complicated molecule err material I want to talk about an experiment that we did I'm one of the IBM quantum computers to investigate essentially the validity of an N represent ability condition so indeed and represent ability the idea that we need conditions to constrain the reduced density matrices to represent the many electron quantum system it's a bit of an abstract notion and it's something that's always been theoretically developed but it but basically there's never been a really simple way of actually demonstrating an interestin ability condition experimentally and so we realized there was an opportunity to do that using a quantum computer and so we ended up picking a special set of Emerson ability conditions which are called colleagues highly generalized highly constraints and so basically what they are is a generalization of the poly exclusion principle so probably many of us are familiar from premise or introductory chemistry that the probably exclusion principle tells us that the orbital occupations must lie between 0 and 1 ok so what does that mean well basically obviously the orbital cannot be less than filled and it obviously can't have more than one electron because essentially the electrons are fermions but is that actually the entire story it turns out there's a analyze poly exclusion principle that for wave functions with more than three electrons there are additional constraints okay so if you actually have a pure quantum system for three or more electrons it actually turns out the Pauli exclusion principle is not the whole story and so these generalized poly constraints can be viewed as a class of n reps and ability conditions on reduced density matrices okay so in fact the Pauli exclusion principle itself is an arab stability condition and these generalizations give us more and so the experiment that we'd like to do is to verify the generalized poly constraints experimentally we to do that we're going to prepare and measure a random sampling of quantum states on IBM's quantum experience okay so I think the idea is to just use a series of unitary transformations that can actually drive us anywhere essentially in the space of three electrons okay so we basically have our three electron wave function we have a series of rotations and C not gates and a couple of different angles here alpha beta and gamma and we're going to use that to sort of move around all different parts of our three electron wave function and here are some results then the occupation numbers it turns out the occupation numbers for our three electron system can actually forms a three-dimensional polytope it's three dimensional and not six dimensional because three of the occupation numbers are redundant with the other three so if we have three electrons and six orbitals we actually only need three orbitals to represent the information so we end up with this nice three-dimensional polytope and it turns out so this poly tope I'm giving it two different colors we've ordered the occupation numbers from largest to smallest and so because of that folding the poly exclusion principle actually ends up being this entire object now if the generalized poly constraint is true if there are generalized poly conditions then there's an additional constraint this hyperplane in green separating sort of the yellow region in the front the yellow greenish region in the front from the purple blue region in the back and this hyperplane basically can basically separates the allowed region in the front from the forbidden region in the back so the back is forbidden because it violates the generalized poly constraint that's been derived theoretically interestingly the the constraint was actually derived theoretically who actually computationally motivated for the first time in 1971 by two scientists Borland and Dennis who were actually working at IBM and they were doing quantum chemistry at IBM and they were doing some calculations and in the process they recognized that there were certain additional constraints beyond the poly constraints that essentially were never violated when performing full configuration interaction calculations so it's kind of exciting that basically many years later here we are with an IBM quantum computer and we're going to now test whether the quantum computer agrees that these conditions are essentially if we actually look at it experimentally do we verify that these conditions really exist okay so again the quantum computer is an experiment so we're gonna go ahead and do the experiment check this out again this boundary is the boundary between the allowed and forbidden region okay so let's go and see what happens so we're gonna basically suppose for example of both regions were allowed ok then by random sampling of 60 States about half should lie on one side of the condition and about half should lie in the forbidden region it's kind of like all the air in the room you know wouldn't just go to one side of the room the probability of that is miniscule so we don't have to worry about you know essentially any kind of catastrophic event there and so in the same way here if we randomly prepare the states they should lie on both sides if the constraint is not true but they should lie only on one side if we actually have the constraint so voila here's the results from the quantum computer we find that all of the randomly prepared states lie in the yellow region so the result verifies the generalized power constraint to one part in one quintillion so two to the 60th is about one and one quintillion essentially showing that indeed the theoretical ideas that motivate generalize probably constraints do hold up when we essentially perform the simulation on the quantum computer and that these conditions indeed are shaping the quantum reality that we have providing supports and hyperplanes that shape where we can essentially drive our quantum system and these constraints become more numerous as we go beyond three electrons and more complex of course as well but are very important for shaping the landscape of what quantum theory can do okay okay so this now brings us to the next part of our talk where we're going to talk a little bit about something called exit on condensation and to motivate what is exit on condensation we're going to back up a little bit and talk a bit historically about condensation phenomena and how that has led to some really recent and exciting research in the area of something called exit on condensation so let's start off with both start off with bose-einstein condensation so we go back to the work of Bose 1924 deriving photon gas statistics the work of Albert Einstein also in 1924 applying the statistics departed khals of arbitrary best and then the very important paper by Fritz London called on the bose-einstein condensation from 1938 and so basically London recognized that these bosons and their statistics would allow essentially any number of such particles called bosons to essentially condense into the same quantum state into the same orbital ok and so bosons basically violate the Pauli exclusion principle and we can have any number we want in the same orbital so from an electronic or fermionic point of view it does seem strange but it pretty amazing that essentially we have these two classes of particles fermions and bosons where the bosons can essentially act so differently just from a difference in statistics okay so is also recognized by its itzá in 1947 and then in 1940 we had the connection between spin and statistics from Wolfgang Pauli okay so historically you might think well this is something then they should have been experimentally realized early on however kind of the early liquid helium experiments didn't really show pure bose-einstein condensation because there was no way to separate the attractive forces in the helium gas from the statistics and so when condensation was observed it was being driven not just by the statistics the Bose Einstein statistics but also by the attractive forces I wasn't actually until the night 90s that VEC was recognized was realized in his pure form by using essentially very dilute gases of alkali metals okay so basically the first realizations were done in 19 1995 in rubidium and sodium metals by Cornell vmon at Jilla and ketterly at MIT using rubidium and sodium respectively and so here we can actually see a picture of the peak emerging so the idea is you basically four kind of like cooled down using evaporative cooling and a heart and basically a magnetic trap we essentially cool the quantum particles down they go into the quantum well and we end up getting our bose-einstein condensation so I'm always excited about science on condensation for me is also very kind of like just exciting for in my own formation as a student I was a graduate student at Harvard shortly after this experiment and I do remember Wolfgang ketterle coming to Harvard to give a talk and just the excitement of just seeing how he had used essentially fundamental science to just you know expressionist copy techniques to really visualize something just so fundamental as these statistics in the particles and also the time my roommate Dave land ice who is actually now at Google working on quantum computing was working with kleppner over at MIT and collector was pursuing essentially bose-einstein condensation in hargeon atoms and I still remember just the you know took took months and years of work to essentially get that to work and I think it was 1998 or 1999 when it you know finally was realized in the atomic hargeon and I just remember Dave land ice coming home and the excitement of essentially realizing bose-einstein condensation in his lab with the hargeon with the hydrogen atoms okay so back to our story here so of course OSI sign condensation is sort of the quintessential condensation phenomena we also of course don't know superconductivity is also a condensation phenomena here we have the Meissner effect observed by Meisner in Austin Feld in 1933 basically later determined to basically be electron pairing so electrons of course we know we can't put more than one electron in a spin orbital however we can actually put many electrons into essentially a global quantum state by pairing the electrons to form essentially quasi bosons okay and the theory of superconductivity was developed by bardeen cooper and schrieffer in 1957 here we see phonons mediating the Cooper pairing okay and so that's the basic idea of beö of the bcs theory for superconductivity and we of course can also have high-temperature superconductors which also function by Cooper pairing even if the exact mechanism is different from the BC phonon induced mechanisms we can have iron based superconductors okay with temperatures around 55 Kelvin or copper oxide superconductors like the ones here on the right and again in these high temperature superconductivity as the standard theory does not apply okay but we still have Cooper pairing and here you can kind of see as a function of the critical temperature for super conductivity as a function of time how we've been able to achieve superconductors at higher temperatures the important work in the mid 80s which led to the whole family of the copper oxide family here reaching higher temperatures and you'll also see the important iron family okay in the mid 2000s also point out the hargeon sulfide here at very high pressures 155 giga pascals okay so basically we've seen bose-einstein condensation of bosons we see essentially a kind of condensation of Fermi on pairs to form superfluids superconductors but what about a bose-einstein condensation of something called exit ons so this idea was first put forward by black power and Brant in 1962 or at least this is one of the very earliest papers to look at this and one question is well why do we care about this phenomenon first of all what what exactly is going on with exit ions here and and why do we care okay well basically exit ons are particle hole pairs so an exit on is formed for example if we take a Fermi on and we pair it with the hole the absence of a Fermi on then essentially they compare together to form an exit on and it turns out we can take a large number of exit ons and we can condense them at low enough temperatures in certain materials to essentially create in principle a exit on condensation and we obviously know that superconductivity is important because it leads to essentially friction free flow of electrons but it turns out the analog for energy is actually exit on condensation so exit on condensation leads to a frictionless flow of energy first recognized in principle by Keldysh in 1968 okay so for example if we have electrons flowing from left to right on the top here we could have essentially then the holes have to flow from left to right meaning particles now flow the opposite direction and so if we induce a current on the top we essentially get a current in the opposite direction for free on the bottom okay and so and essentially it's showing here that how we essentially have a friction free flow of these exit ons in the material so it turns out though exit on condensation historically was very hard to achieve it was only achieved in the early 2000s by essentially using strong magnetic fields or strong interactions with light and polariton so here you can see using the B field on essentially two graphene layers so we take two layers of graphene we match them we put a strong B field and the particles in one layer line up with the holes and the other layer in a checkerboard like fashion and then essentially people were able to measure scientists variables measure the maximum inter layer tunneling conductance so essentially at sort of the zero bias voltage here they're able to get di DV to have a strong peak showing essentially sort of a friction free flow of electrons through them through the through those few layers implying the exit on condensation now my research group got interested in exit on condensation with this paper which appeared in physics viewpoint one of ApS is publications and it's called chasing the exit on condensate and in 2016 when this came out the exit on condensation had still not been realized without strong B fields in in any material however some new signs were emerging that that might happen soon and so indeed actually we got into started working on it theoretically and then essentially in 2017 basically exciting news out of Harvard where Halperin and Kim announced essentially achieving exit on condensation in graphene by layers for the first time without strong magnetic fields and they also found that the exit on condensation was extremely robust to essentially changes in geometry and modifications of the material okay later in 2017 we also had exciting work from AB amante at the University of Illinois he announced in science signatures of exit on condensation in a transition metal die chalcogen I'd so here we have a picture of this transition transition metal complex and indeed it's basically involves molybdenum tungsten titanium and basically they were able to use momentum resolved electron loss spectroscopy to essentially confirm the existence of the exit on condensation around 200 around 180 Kelvin very recently in October of 2019 there has been evidence of exit on condensation now in two dimensional atomic double layers okay and this opens up some new possibilities to look at exit on condensation in these van der Waals hetero structures and this was done at temperatures a little bit above 100 Kelvin okay so this basically brings us to some of our research and so one of the things we were thinking about is how do we come up with a bona fide signature for quantum condensation exit on condensation well the bose-einstein condensation signature is a large eigenvalue and the one boson reduce density matrix so essentially here's our one boson reduce density matrix and second quantization it has a large eigenvalue that represents the number of bosons in a single orbital now offer me on pair condensation FPC the signature for that occurs in a large eigenvalue of the two Fermi on RDM because we need two fermions two electrons actually have the condensation so they're the natural quantity is the two RDM this was first recognized in 1962 by CN yang working at the advanced Institute at Princeton and we were wondering then well can we come up now with equivalent exit on condensation ICI signature it must be a large eigenvalue in the particle hall reduced density matrix okay so my postdoc she vas a fee and I recognized that basically it's the G matrix that should have a large eigenvalue associated with it and it turns out there was some earlier work from the 1960s also recognizing in the reduced density matrix field that one could have collective excitations of boson ik systems or collective excitations through essentially large eigenvalues of the G this work had been largely forgotten and so Shiva and I were able to sort of bring it back and and recognize that we should be able to use this as a powerful signature or exit on condensation so we got interested in looking at molecular scale exit on condensates we took a model system essentially taking some harsh and atoms and putting them in a in a line and then essentially taking another hydrogen chain above it essentially varying the distances between essentially the hydrogen atoms within a chain and the distances between the two chains okay represented by L and D respectively and we found that if we tuned L and D to the ratio that essentially is predicted to be to be essentially the regime for exit on condensation in the theoretical physics literature we indeed found in this molecular scale system we found the emergence the beginnings of exit on condensation so as d goes to about 2 angstroms we see the large eigenvalue in g go from 1 which is its value in the absence exit on condensation the large eigenvalue of this modified g goes up and essentially reaches a maximum around 2.5 angstroms and so this is exciting it's showing essentially for the first time that we can actually get exit on condensation potentially not just in large scale materials like graphene by layers but also essentially in smaller molecular scale systems as well so for example if we put a hole here at the red dot the particle essentially ends up on the other layer across from it likewise if we put a particle over here on we put a hole over here at this layer then the particle will be over here for the bulk of the hole over here then the particle likewise will be over here so indeed the particle and holes are matched essentially in the in essentially the eigenfunction associated with this large eigenvalue we can show this in more interesting systems as well so for example if we take hexa scene which is an a scene chain like a little patch of graphing a linear patch and we essentially pair it with another hexa scene molecule so we have a hexa see an electron double layer EDL then around 2.5 angstroms to separation we see the large eigenvalue emerge and when we see the beginnings of exit on condensation in this molecular scale system so this got us thinking a little bit about the idea of well could we actually use some of these ideas to prepare an exit on condensation exit on coggan set essentially on a quantum computer when can we actually prepare the condensate itself as an experimental realization where we actually would have not essentially just well that we actually have not just a sort of an abstract representation the exit on condensation but to actually prepare the exit on convince it on the IBM quantum computer ok so at this point actually I'm going to transition to Leanne so Leon Sager one of my graduate students at University of Chicago is the first author on this paper on exit on condensation on IBM's 53 qubit quantum computer so okay so we're going to basically do a little trade off here so I'm going to go ahead and stop screen sharing for a moment and let me just see okay so I'm going to stop my share here and I'm going to turn it over to Leanne to tell you a little bit about the results here that we obtained Leon are you ready to screen share I know it's not looking like it's gonna work right now I think I need to be mean host okay okay so we're doing a little bit of a okay so Lexi's gonna become the host and then he's gonna make you the host and we're gonna change hats here so just area oldham yep all right all yours thank you that was awesome it was great okay so as David percent was saying we were thinking about how to prepare some exit ins on the IBM quantum computers and we noticed that the transman cubits were basically composed of photon whole exit ons so the first thing that we did was we looked at a three exit on system which we knew would could show exit on condensation and we did multiple preparations of three exit ons using different input parameters for the preparations so we used three different angles to repair this and we buried them all from zero to PI over two and for our simulated results the the graph that I'm showing you here is a heat map of what happens as you vary those parameters specifically varying theta2 and theta3 with theta1 being set to zero and as you if you recall from what David was saying the signature of excellence ation is that large eigenvalue in the particle hole reduced density matrix and anything above one demonstrates exit on condensation and for actually for an a system of three exit ons the maximum value that we can get there is n over two or one point five so the simulated results here not only demonstrate exit on condensation but they demonstrate maximal exit on condensation with an area around that maximal preparation that still demonstrates very large excess on condensation for a three exit on system which was super exciting so then the next step was to transition from simulation to running the computations on IBM's devices specifically we ran experiments using IBM yorktown for this the three cubed three exit on results and we do indeed see exit on condensation pop up on your coun in the region exactly where we would expect it again it's rather robust region right around that PI over 2 PI over two zone we did a complement we did perform some error mitigation but we were interested specifically in the non mitigated results because that showed the true noisy quantum experiments and that those experiments were able to achieve excellent condensation which showed us that we did indeed have exit ons on the quantum computers okay so another way to visualize our results was to go back to that the generalized poly poly tope that Scott used in some of his work that David was talking about earlier so as you can see we're still demonstrating here that we are in the allowed region but moreover we notice that there is a trend in how large those the signature of exit on condensation is the darker the color the higher the signature of X upon condensation so when you're on that hyperplane that boilesen is hyperplane between the allowed and not allowed region we don't really see X's on condensation we see like a bright red it's right at one so that's not really excellent condensation but as you get closer and closer to that point five point five point five region you get darker and darker which indicates a larger exxon condensate signature in fact we see the largest one point five at that point five point five point five vertex which we recognize as there are several preparations that have that point five point five point five value but one such preparation is the GHC state which we'll use i'll show you after the next slide we to extend from just three exit ons to n exit ons we use this preparation first we also have these results in some experimental data okay so we started just looking at three to five cubits or three to five exit ons on Yorktown because that's what Yorktown can do and as you can see as you increase the number of qubits you increase that signature of excellent condensation which means we're getting more and more exit ons condensing into that single quantum states and almost in a linear fashion here so in order to go to hierarchy bits we also looked at data from IBM's Melbourne computer which goes up to 15 cubits and we're still seeing more and more exit on condensation as we go to higher and higher cubits and then we wanted to see what happens when we go even further to higher cubits does it keep increasing do we keep getting higher and a higher exit on condensation so we looked at Rochester which has up to 53 cubits and indeed we're still seeing some growth in the number of exit ons that we have condensing as we increase the number the system size here's a nice little summary of all of the data that we we gathered and as you can see even for the 53 cubits we we have demonstrated excellent condensation so we have prepared an exit on condensate on the quantum computers an experimental exxon condensate on the quantum computers for systems of up to 350 3 exit ons up to 53 cubits ok so we wanted to to look at the why we didn't necessarily get the X the maximum and over to values for the quantum computers experimental simulations we do get X's on continents it but it's the condensation but it's not the maximal exit on condensation so we thought that what might have been happening is that we were having some sort of decoherence on the devices which didn't allow all of the qubits to become perfectly entangled with one another so we thought ok let's look at all of the the eigenvalues of the two are the the particle-hole artyom that signature anything above 1 shows that there are multiple qubits interacting with each other and looking at the sum of all these values tells you kind of how the how many exit ins are interacting with other exit ons but not necessarily all in one global state but rather in islands of of correlated States so the way that we visualized this was to look at the sum of all of the eigenvalues above one first is the number of qubits again the maximal exit on condensation that one would expect is that diagonal line there the dotted diagonal line and we're still looking at the Yorktown experiments and Lauren experiments and the Rochester experiments and as you can see we do seem to approach that dotted line so we are getting close to the maximal axis on condensation but they're just in different islands of condensation likely due to the decoherence on the quantum machine okay with that I'm going to turn back over to David for the last little bit of our talk let me do the same dance one second so I'm getting hoarse snarl and no I will make David hosts done all yours oh yeah all right I'll come back to screen screen share here hold on a second okay I'm gonna do a little fast-forward here all right right to the hold on a second okay so coming back to okay here and we come back okay so here we are so to a little kind of time travel forward here so the anted an awesome job telling you about essentially the work here on the exit on Condon sit on the IBM quantum computer and so one question that came up in our minds we've been thinking theoretically about of course the idea that we have superconductivity has a large eigenvalue in d and exit on condensation has a signature and large eigenvalue in chi and we started thinking theoretically about this question is it possible to essentially create a material that actually would show dual fermionic and exit on condensation at the same time so essentially a state that would actually have kind of both of them both condensations occurring simultaneously and so the goal is basically to computationally demonstrate the existence of a Fermi on exit on condensate in a molecular system okay so here's obviously the Fermi unpair condensations and we'd like to add that to the exit on condensation to really have both of them present at the same same time in a system now one question of course at first we weren't even sure is it possible to even have a large eigenvalue in both D and G at the same time so really when we started the project I don't know we weren't really sure about the answer and so we're excited we wanted to figure out you know can we actually have both condensations so Leanne basically looked at three electron systems and we plotted basically the lambda so that the axis here the y axis should be lambda sub D the large eigenvalue for the d2 matrix and the x axis is the large eigenvalue for the G matrix and what we see basically is all these X's represent different states that were computed for different three electron states that are being computed and we're seeing essentially how those states essentially can go from the largest possible lambda D to essentially the largest possible lambda G now for three electrons is actually not possible to have essentially Fermi on pair condensation so the lambda D does not get larger than one however we can have a large eigenvalue in g and we can see that largest eigenvalue is 1.5 which we observed earlier in the talk as well so essentially it turns out that as we look at different states that are allowed we see that those states have an elliptic trade-off between essentially large D and large G so essentially you can kind of see here here you have large D but now essentially D gets less but now G is getting larger okay so there's an elliptic relationship between the two and so maximum exit on condensation in this case has essentially has no Fermi on pair condensation okay so that's the maximum exit on condensation over here and over here we have the maximum fermium pair condensation but in this particular situation we don't see any of that okay so now we basically wanted to look at a 4 electron system and in the 4 electron system now we can see that we are getting Fermi on pair or kind of superconducting type condensation in the system for some states and other states are showing the maximum exit on condensation which is 2 in this case but what is really interesting and exciting is that in this region here in the middle we actually see states that actually have both a large eigenvalue in d and a large eigenvalue in g simultaneously so these states are realizing realizing essentially a state that has both exit on condensation and it's undergoing exit on condensation and firmly on pair condensation simultaneously ok so we can basically a coexistence of Condon set so again maximum there and there but now we essentially have this new region where we actually see states with both exit on and Fermi on pair condensation in the same state so we can actually summarize this in this figure here we're down here we have no condensation phenomena up here we have a state of matter which is Fermi on pair this is the traditional superconductors here we have the state of matter that's exit on condensates which again have only recently been realized in the last few years without large magnetic fields and now in this new purple region here we have the prediction that we can have a coexistence or States a new state of matter if you will that actually shares both be essentially the properties of the fer para condensation but also potentially the properties of exit on condensation and so the state basically has both of these simultaneously and this is just the elliptic trade-off between essentially maximum hair condensation and maximum exit on condensation okay so that's the region there and what's really important is you might wonder well when you actually create a quantum state that actually shows both pair particle or both essentially particle particle condensation and the exit on particle hole condensation are we actually just getting two separate Condon sets and so importantly our calculations show that actually we're not that actually the two are actually non-trivial enmeshed and you can see that because these squares here represent it's a little bit of a complicated representation but we've essentially unrolled the orbitals one through sort of one through eight in this direction and we've unrolled them in this direction and the squares represent essentially the interactions between essentially a particle in this orbital and a hole and that or a particle in this orbital and a particle in that orbital whereas here this represents a particle in this orbital but a hole in that orbital and so where the squares are more colored you're essentially getting a greater contribution of that particle particle pair or that particle hole pair and so just comparing squares you can see that there are squares where you're essentially getting both particle particle condensation and particle hole condensation at the same points in our lattice and that essentially shows that we're essentially getting firma on pair condensation and exit on condensation in a way that's highly a meshed or if you will entangled and so we can actually formalize this more rigorously in the large number of particles large and thermodynamic limit and what we do basically is the following we theoretically write down a model system that shows basically Fermi on pair condensation and so one example of that is the anti symmetrized geminal power model a GP model those Hamiltonians and wave functions exhibit large eigen values that represent fermi or essentially super conductive for me I'm Pierre Cooper pairing and we also can write down a model do the lipkin that has a limit in which it shows exit on condensation now we can actually do this in general while we're using these two models to kind of motivate the idea we can actually use a wave function that exhibits these characters from from any general model that shows essentially exit on condensation and fermium pair condensation and it turns out if we take an entanglement of these two wave functions this one showing essentially Fermi on AG AGP showing Fermi on pair condensation and the wave function showing exit on condensation if we entangle these two with the appropriate sign of entanglement etc etc what we can find we can prove basically is that this new wave function created by the entanglement okay is a Fermi on elect exit on condensate and its eigenvalue in d is actually bounded okay it's always greater than equal to this relationship here which is equal to n over 2 minus the square root of n so for large n we can see the large eigenvalue of D for this new wave function is going to be essentially a large eigenvalue likewise the maximum eigenvalue age of G has to be greater than essentially n over 4 minus the square root of n over 2 so therefore as n gets large this also has to have a large eigenvalue so basically we have a proof that entangling essentially a wave function that exhibits Fermi on pair condensation with one that exhibits exit on condensation produces a new wave function that actually will have both condensations at the same time so that's exciting because it shows basically we can generate a very large family of quantum states that actually exhibit both Fermi on pair and exit on condensation and this new state of matter has the potential to have properties that are associated historically both with superconductors and exit on Condon sets so in principle we can have we can generate materials that have an efficient flow of not just electrons not just superconducting in terms of electrons but also superconducting in terms of energy okay so that pretty much brings us to the end of the talk so I just want to acknowledge everyone in the research group here so a picture of the group I want to in particular highlight Scott smart who's over here on the right so Scott basically had a hand in all the work you've heard today on the quantum computing he's doing just some fabulous work on quantum computing all different aspects of things and Scott's been involved in all the coding and all the details so a lot of the work I talked about all the work really I talked about today Scott was instrumental in doing and doing all of that and none of it could have been possible without Scotts work on all that so the two of us have been partners in all this and lance ager so Leon just talked a little bit ago and LeAnn basically was involved in all the work on the exit on condensates on the 53 Kubik quantum computer as well as the research of showing that we can have potential coexistence of exit ons and fermium pair condensation as well and I also want to highlight Shiva sathi Shiva was involved with me on the work showing that we can actually use large eigenvalues in the particle whole g matrix as a signature for exit on condensation finally a big thanks to IBM quantum experience we couldn't have done they qubit the 53 qubit calculations without Sebastian's help getting access to Rochester and it was it was really exciting to be able to run calculations on that and see the emergence of the exit on condensation thanks to do e NSF and aro and finally a big thanks to everybody tuning in today I really appreciate this this new series is exciting and it's been a real pleasure to present today and discuss our research all right thank you thank you David in the end we have time for questions so folks feel free to just go and ask your questions directly and David and I can answer can I ask a question 20 I think mostly towards the end about the different between the different machines that you saw so when I was looking at your your plot I could just about believe that the Rochester and the Melbourne series were the same series and then they it seemed to drop down quite a lot when you switch to Rochester is there some feature of these devices that can explain the difference well yeah the connectivity is a lot different between all three devices as well as the error rates especially the C not errors so they probably just had differences in the decoherence that was happening in the ghz state so I would have expected Rochester to know better decoherence since it's a newer machine compared to the other two I don't have the numbers um I have the numbers in the SI for the paper that we have out on this that it might be beneficial to look at those but I do believe that Rochester has higher error values okay thanks all the questions going once going twice if not let's thank their attorney on for the great talk and now we have an interesting bar so we still have I want to thank 130 people we I think it big we had about 57 and and actually it's interesting a lot of folks sign up you know during the night of my time some data I'm European type so people still sign up substantially do you know during the first part about 20 sign up so there look at about 75 signups from all around the world so I want to thank everybody we would try to fill up with the assembly right on the websites a lot of people just join us so thanks guys so very interesting to share with you what we wanted to do so this is very typical in computer science conferences now we're have a lot of topics and a lot of people so what what we do we basically create a spreadsheet it's called on conference so people just triple stops and this is a good way for the group to self-organize make the most use at that time by seeing the talks then we let everybody who propose the talks in the spreadsheet pitch it for a minute and then with votes if the number of drops exceeds the number of available times laws or is the physical conference you can have venues right you can have room so you basically you know schedule talks on two rooms we actually had to sign ups for the lightning talks called the lighting with a shirt fall in the main program and I think we just can let folks tell us what they're going to talk about and then we can go into the top so it's up to you guys to stay obviously so I want to see if John Candelaria and Terrell are both here if you guys here if you can say so I'll meet yourself if you're on it I said John's here yes this is John ah yes and Tara like here not sure if they're all still here so we'll see so John proposed a talk entitled QDC workforce DAC introduction to the QE Dec quantum Workforce Development Committee activities so yes I just have a couple of a couple of slides that I wanted to go through ok sounds good so let me make it hosts and then please introduce yourself for the folks who let me see one second to see if I can do that ok first no I do that I make it host yeah please introduce yourself again for those who join us later and the floor is yours okay well thank you very much Alexia we appreciate this this is a great event that learned a lot today so appreciate that my name is John Candelaria I work at Stanford but and we also are doing quite a bit of quantum research there as you know and I'm leading a program that is funding that research with funds from industry but I wanted to talk today very briefly about another activity that I'm involved in called the quantum economic development cuts for shuttle so this is a consortium that was formed in the u.s. under the National quantum initiative that was started a couple of years ago it is a consortium that is made up primarily of member companies but it has a very broad Charter the Charter is essentially to identify and develop strategies that's here to address the gaps in the enabling technologies and supply chain as all of you know there's there's a lot of work to be done in developing the supply chain for the hardware that's involved in quantum computing as well as communications and sensing we're also chartered to start developing some performance metrics trying getting people together and agreeing on what the common benchmark should be in all of these quantum areas and lastly the part that I'm most directly involved is developing the workforce so trying to connect industry with academia and as well as a government agencies in order to provide curriculum development advice to two universities and get the connection made to industry at what their needs are in skill sets that that are needed so there are advisory committees that I invite all of you to to take take a look at and enjoin it's open to to anyone whether they're in academia National Labs or or industry these are the the technical advisory committees there's one looking at use cases there's one that's looking at the enabling technologies formats and metrics and in the work force committee that I mentioned before that's again developing curricula in universities these are the Sinese these are the companies there's there's almost 150 signees now in companies in all different aspects of computing sensing and communications there's a number of universities academic institutions that are also members and other national labs that are also participating so for for anyone who is interested in getting more information about this they can contact me john candeleria at stanford or they can contact the two leads of this consortium general bras sue who is the director and Celia Merce Walker who is the co-director of this consortium and here's the address for the for the organization the consort org and you can learn a lot more about it there but again I I urge you if you're interested in participating we are looking for people to contribute ideas to technical roadmaps for the technologies and in computing communications and sensing and also ideas that they might have about benchmarks and how to develop the benchmarks common but benchmarks that we can use across all of the research areas and entities that are participating around the world in this space so again it's it's a great activity it's a critically important and hope to have as many of you as possible consider joining this effort thank you thank you Jonathan does anybody have questions for Jonathan about the construction I think it's the great development and certainly brings people together so we we really love to ally you know with other communities and create kind of how were multiple communities can share what they're doing so this is great any questions for John can I ask John my own question so is this when you said the workforce is the idea basically to to raise talent to to basically track education and and tailor kind of programs encouraging students to learn subjects which are then make them horrible by the industry partners Cobra is that the idea yes that's that's exactly one of our key goals especially in the in the work force committee that I'm that I'm leading right now so yes we want to get a two-way conversation going between industry and academia for instance in order to help academia develop new curricula in the quantum area that we need directly into to industry and again industry obviously making direct connections with the students and the faculty to fund their research while they're still in universities in do so for instance right now a lot of students are looking for summer internships you know for internships graduating PhD candidates can find jobs is this the hub story there how do they find the jobs and internships yes well I'm glad that you asked that question actually because we're in the process now of adding that to our website so there there is going to be a place there for a two-way connection so members of the consortium will be able to advertise their internships and job openings and students can go there as well as we're also going to be following that up very shortly with a site where students can upload their resumes so that the members can actually search the resumes using the same website so that one will probably be coming within the next month or so but probably within the next couple of weeks we will have the site available where members can advertise their job openings and again this is the address got it not a great know that I actually receive already you know inquiries from students around the world and so that would be great if you would like us to share using you know our website and mailing list would be happy to do so so it's it's great so thanks for sharing this and you know if anybody knows folks special students I think now well looking for internships this is a great place to directly write well thank you very much absolutely thank you John so let's see I'm not sure we have others does anybody else want to use the floor for announcements for discussions I think we have some time about 20 folks left feel free to say you know what do you think about this format what would you like to see we'll share a feedback form with brief question you know how did we do what was good what can be improved so please when you get this email please spend a few minutes maybe one minute less than a minute to share your feedback with us so now it's basically it's all yours the floor is open for anybody you can ask questions so what we had an interesting topic we we had a talk solicitation so you instead of given a talk you might ask for a talk maybe for the future serious I would like to invite speakers so if folks want to learn a topic or they want for instance a new one on one introductory talks to an area way which is not your primary area that's also one way to use this format so you can ask basically teach me teach me X so anybody feel free to unmute yourself and say anything you'd like I know it's been a while so I'm not sure how well this is ecology here I would like to know the current situation co 819 how quantum computing is helping to find solutions for that what are the research done in the question for anybody I mean I see for sure that people are at home well that's that's lettuce clear and I understand that remote access it's possible so the part of the thing is unimpeded can anybody talk to any covered 19 applications I guess not so but it's a good question so we'll make a point of sharing this question because I think it's every community got together to help the fight I think I think there is a lot of modeling going on right now in the conventional Big Data space Pharma I know personally firstly the bricks the spark company they make up health science vertical right so which was I think previous is doing protein folding for farm and I think they're kind of making it available for vaccine I don't know what the quantum state of practical application there is so if anybody knows please share it with us Balaji will forward it to you if we find out thank you for the question thank you any any other questions thing I was going to suggest I think it'd be fun if we could have some interactive sessions because we all have probably computers too in front of us and you know we learn about the physics package and whatnot and I think it'd be kind of fun to follow along with some sorts of applications so you're looking like a zone tutorial yes Alex I see Alex is still here Alex can anybody from your group basically just leave the class and we all learn and friends on keyboards and you can grade it if you like what was the question again basically you know for you to teach a class on physics as a structure tutorial you know maybe if you have a Jupiter notebook people can follow right and learn learn by doing I'm a huge fan of this just going to have more things like that right now since we all have our computers with us yeah yeah I think it's a good idea maybe we could also get somebody I mean Ross is left from now but but but I think he can also get access to ticket and maybe somebody from the Kiska team to do yeah something I think would be would be quite cool maybe we could organize a few of them kind of as as quite short things in in a row and a block or something like that mm-hmm that's a great idea I'll take it as a actually a point for maybe the next one right because we want to do this monthly so now folks are all at home talking with computers all the time so if people can prepare tutorials we can just indeed you know sequence that might be half an hour each right and just do them boom boom boom one and like one after the other and so everybody can get kind of an overview of tooling and learn awesome I'll try to set it up and also guys if you you know have an idea for a talk going on my - on the site so Justin mail be and we can work through you know sequencing right because we want to do it monthly so we can basically structure and we will collect the feedback you'll see we don't want to make it too long so I guess we we've had a pretty good-sized meeting today right pretty kind of same number of people most of the time so so yeah so if you'd like it to give a a full length talk as well let me know alright any other questions or suggestions well it's not I want to thank everyone it was really good to me one more thing to mention I don't know who started these things but it's quite interesting there have people seen these quarantine talks or the queue - Oren team talks it's it's a sort of self-organizing quantum talks series so there's just basically some Google Doc somewhere on the web where people are typing in if they want to give or see talks it might be something people here are interested in I just I just dug up the link for it I can't I I can't for some reason I can't type to everyone so I'll just type it to a Lexie and maybe you you might be interested to put that on the website or to pass it to the other people that are here the costs each the top of the chart that you can only shuttle the host from now that will make it easier yeah I got the talk I'll say thank you for bringing this up I'll see what listen my goal is basically you know connect as many people as possible working on the field so I'll definitely we will reach out to this folks and see if we can you know join forces in bringing more talk to people so that's great thank you Alex I said a quick question before we go I wanted to ask you I really enjoyed your talk it was really awesome and I have some questions about historically it seems like the gates are rather arbitrary in quantum computing and I was just kind of wondering when you have something more definitive like essentially this Z X calculus is there is there a sort of a way like would it be helpful if kiss Couture other programs if the final computer could be programed directly essentially in more fundamental quantities than let's say the gates that are used traditionally or I mean is there a way of understanding that that process at the end of essentially extracting the the gates that are normally used in quantum computing from essentially the more fundamental spiders is there something to be said for I don't know is there some way of maybe is it is there a way of systematizing that historical legacy or is it just not really an issue I don't know yeah I don't know yeah I guess when it when it comes to you know thinking thinking about theoretically building circuits there there were you basically any combination of gates you'll come up with it's it's very hard to find a set of gates which is not Universal I mean it's it's right I think it's true right you can get missiles and yeah there is an arbitrary nature to them something that it does seem more natural to work with are our gates that look much more like kind of poly type interactions or something so the multi qubit gates or something you know to think of something like exponent of some phase parameter times that Zed or something is much more natural than a control not gate or or or a sees it or something that sort of shows up in this Z X notation I and I guess that that is also kind of buried out in the hardware I think not being a hardware person myself but but yeah I mean I'd I think it is useful to think in a way that's not kind of married to a particular set of gates so yeah I guess I'm just wondering is there a way of translating like spiders more directly into sort of what's available on the quantum come ughter in terms of its is it I guess are there some lessons in even the compilation for essentially those sort of building the fundamental gates on the quantum computer as well yeah maybe so I mean the the our our extraction is is still very very tied to control not gates in the way that it works but I don't think there's any particular reason it needs to be that way so ok ok so that one could in principle as you said go to a more natural structure if this was more natural one could could migrate to a more natural way of coming up with a different set of Universal gates essentially mm-hmm ok cool it's really it's really interesting it's fascinating stuff that's it is there a one more question is there is there a good paper that you would recommend to review some of these things just to get a better understanding of the basic ideas yeah so the the kind of the the best paper for for what specifically I talked about is there's a paper on the archive ok I think if you if you look for my name of the archive it's called graph theoretic simplification ok something something using ZX calculus it's it's also appearing in quantum quite soon so if you if you watch quantum journal org it should show up there within a couple of weeks ok there's most of a big a big pink book with a dodo on the front which I which I meant to plug called picturing quantum processes written by me and Bob cuca which explains kind of a whole lot of this things around that isoprene also also I mean something that might be interesting there is we spend quite a lot of time looking at density operators and mixed states and stuff in this kind of more diagrammatic language so ok nice that would definitely be interesting to take a look at ok cool is that like Amazon or just unit on is it available at Amazon or something like that to just get a copy yeah yep awesome all right thanks guys any other questions or suggestions as as always you know the information on the website we'll post the recording a lot of people asked for a for the recording of the talks will post them under the same entry once you know down it should be very easy and so hopefully more people will learn I will share the links there there is a feedback form quick questions just let me know but thank you very much it was really great so Alex David Leon you're the pioneering speakers no no girl serious and John pioneering lies lightning speaker I hope more folks come forward hope to see you next month we'll publish to the next date on the same site want indatus be and we'll mail you guys thank you very much and they say thanks I Lexie thanks a lot you should thanks Rama hi everybody you