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Towards Optimal Constructions of Dynamically Corrected Quantum Gates
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00:00
but thank you can unifying or is it to close the fire I it I can finally say OK the instability telling us about the 3rd pass that idea Newell Darden to name the corrected gates OK so I like to start off saying that it is the pleasure for me to be back here 4 years after and the 1 from my point of view and obviously I like to tell you something of the work that I've been doing I in between and that the is about trying to extend the principles which underlie than me because you how to connects a nontrivial quantum theory so that's probably something that you can guess already from my title and that's what they want to focus on but these people that are trying to describe a lead at the top the contest let me just say a few words almost this morning nonindigenous tutorial on what I'd like to consider the simplest possible setting of not exactly we see that the fetus meant to distinguish it from this band that you see on reach we also had a beautiful tutorial this morning and so I think I don't want to have action stands for Papua on this but the the form of an errorcorrection and from the point of view of of control and this is not as bad idea already emphasized purely by an open loop engineering off typically an open system it that we can do in the simplest possible case by means of a finding that 2 are all you entirely operations policies that we applied to us sees them and leave the environment untouched on I would like to stress once again because it's a very easy to let the goal of to forget it when we get that immersed in them I won't be the principle that enables all of these in the Q E C but techniques of reach dynamic of the company and now but it soon dynamically correct date but they're not going the dates as well as our altering upon and that physical principle is essentially a separation of time scales are that means we have at the ready about the importance of frequency cutoff that means that I have that not only is the noisy degrees of freedom that we are trying to remove the influence on our system from that I associated with a finite correlation time scares all which basically they can be considered as being approximately 4 allsinging type so that the whole evolution can be seen as a coherent evolution and as such we can intervene actively from the outside and we can use coherent control methods to effectively undo the bad things just like in the spacing our picture that Valiant was showing an adult coherently over time the unwanted effect so from mathematical point of view seems pointed out if you do on page and that was being there is going to be a natural smart metering the problem which is the ratio between that kind scared for the correlation of the noisy degrees of freedom versus are the time scale that they become a time scale of the control going to art and that our enables a lot of the perturbative analysis upon which we are relying on to be proper form so the kids see that that's the broader context I actually started working in dynamic recovering quite a few years ago only 97 on those days have about the emphasis at least for me and many people were like a lot of understanding how in principle it could be done not so much a not anymore ideas that is where my effort that we want what the what's trying to make this method practical and that it is in this spirit that I like to our food but
04:09
I talk about before but let me say a couple of words and another related top many related 1 by the time I could just we also here in the audience and also my insect is here and so I'm mentioning of well the goal to try to close the gap between theory and experiments and making DQE see as practical as possible and in the process of doing so what we have to face is unavoidable limitations due to system unknown etiologies due to control constraints and so on and so forth so here is the 1st set of of golf that we looking at in terms of how to better address past timing and sequencing cost that I present you learn in those controls scenarios where oxidation all the having purely instantaneous passes reach as we refer to as are benign approximation and you know can still be considered as occupying so is that you can the scenarios where that can be actual in this the year I a factor that there are classes cannot be applied infinitely fast so that is a minimal as switching time there is a fine at the repetition rate and then readings along a lot of questions on which we are starting to have answers so in particular question is like what are the ultimate even in the absence of any kind of of imperfection but just in the presence of these fundamental limitation how well can't have very biased they're gnomic the government to do so that's 1 question that have been addressing and similarly once we are able to find out the fundamental limitation or at best possible coherence 11 for these they can reach for actually put a system of Chinese character that of coherence 11 be achieved for no matter how long we would like it to this so how important is the final storage time in indices and that can we therefore have also arbitrarily good long kind of storage and the type of constraint reach actually I am I have to be very thankful to my party where it might be different for bringing this up to our attention because I think it doesn't being considered are sufficiently so far is that as the implementation will scale up that complexity our sequencing will also become an important consideration and so will have to decide on the sequences and so on down the line also we can see schemes in such a way that they will be as compatible as possible with the constraints imposed by our beaches God atomic clocking and all of that so this is not going to be my talk of my talk is going to focus instead on another of constraint which is unavoidably present in practice because it is true that even though it may be the bend bang based on the news control approximation can be at relatively good approximation of realistic control amplitudes and then there are infinite sorry alive control action they have fun at the energies of life policies they always have a duration and these introduces from the design point of view from the control point of view a whole new set of challenges by new not that they haven't been looked out before because in Minamata is always there is a lot of legacy coming from the Unimind experience they have been considered but from the point of view of wanting to really have a systematic and general approach that's what I want to look at so the issues that comes about when they're looking at bound so it wants his life and we have clearly speaking up and at the behavior of the coherence happens happens also during the execution of a gate so we have to devices strategies which are not only going to give us a protected or be coupled the memory but also we we have to come up with ways foreign moving decoherence as it happens in the moment we are processing information so that is going to be of my main the for the rest of the top and I want to stress that I mean a lot of related ideas and and I will be inspiration to take inspiration buff from from modulating balloting composite busses techniques in NMR we have in the referring to these approaches dynamically connected game and I apologize if some of you might be in the ball and workshop you will hear some of the background all dynamically correct the gate the how to construct a half and was given a 2nd time but it is necessary for me because what they want to ask the next is that once we have these 2 which is pretty versatile in general how can we make it even better than it is now namely how can we make dynamic collecting data more efficient and also much flexible in accommodating different but of other constraints and what like to to mention it is not inconclusive but just are in progress worry don't want to try to merge our formalism of dynamic we can correct the gates with 2 were from optimal control theory so that we
09:38
start by giving the essential that dynamic regret the day not really a lot of elements have been already and you this morning for me so I am going to concede the target system which is in general an open quantum system name is going to interact with 1 so that it's 1 that I have with consist of system component on the about component on in the system are about the interaction and we can always expand these without loss of of generality in terms of system and by opening and and it was any note this this morning in darkness tutorial in general in the juicy approaches we try to go with a Munyemana are essential as in regard to the noiseless trying to find and read and this land and I'm not going to assume much on these operators for the bus fare out and then they are bounded in some of appropriate norm and then you you operate the norm of because that was just many matches the environment is uncontrollable by definition they're going to introduce operational controlled by the action of certain control inputs which are coupled to control at the time and you will hear a lot about this all happened that the conjecture but in the coming from the time of the exponential of the Consortium for now what I want to stress because this will become relevant at some point in my talk There's system and phoneme then going and that the system would have even if it would be isolated from the back out so that the as up to fund role because depending on the type of data that we are performing it can on be an unwanted contribution finding that the environment we think we just created there's another 1 another type of error even though it induces coherent than 1 which you know this this summer it might be that that the very same policies that limit on it is necessary for us to have complete control of unity in the 1st place so keep in mind these as we would go through and so I I am talking about being undercut action so and amount that we have to define on the other he visible and can include any deviation between the actual control of evolution we would like to impose on the system and that we have on the system and the intended evolution that we would that not to get for that so if the system and the boss would be uncoupled we would that we would go out and get a certain you need time propagated given by the exponential of this but the the unwise the action of the same control in the presence of the error Hamiltonian which is due to the company's with about results into the osmotic complicated object here and what is going to become a very important and probably the most important I'll element for constructing or but for analyzing what is going to come next is that I know how complicated is unitbody propagator is we can always view we as a certain isolate the parent component by expressing in terms of the idea of a target date that we would like to achieve times are neither you entirely operate there which is going to college is we have 1 to going option is the exponential of animation system by opening that up here see it and physically of what these of effective and Estonian is is not embark on their effective a thorn in that we obtained by our affecting a canonical transformation into the bargaining fling with respect to the applied control now I'm going for the moment to stick to to simplifying assumptions are for constructing the BCG's and while the 1st assumption is like the controller is not going to be out there to me is not going to introduce additional errors my only source of error is going to be the coherence here and so I will if we assume that our water when the system Estonia and at the last act I don't need it for controllability and therefore I would delete that as yet another unwanted piece of evolution so for automatic output was is I will go into the and will refer to these as a belief less system no I had this is simply find my life because in this case out there have controlled the propagator is exactly what the target date and he just comes from the application of the controller now that is not due to the system at the Indian and as it was referring onto to before he sees the error Newtonian which is modulated by the control properly now have full and completeness many focuses on my target system consisting of on set of puberty which I have eaten at the of this is the the new market errorcorrection set in the coupling with about and the possible copying of those are going to be arbitrary single cubic operate of this is the genome the coherence model that has been considered a lot of time is just a typical 1 so the sign of an error predators we wish to suppress notice that in this framework the error operators is the and operator on system times but I i is of having that poly operator in the system component and arbitrary operator in the book OK I having defined and I don't know that I also need some sort of Ameritech of performance and having the animal data embrace good but basically gives us a natural way to quantify the deviation between the actual and the intended that will show that we would like to have for that system we call our and on the side is the norm open it the nominator here which she is the area action not to relevant pure bluff contribution that we just the removal of the project them away because they do not have a direct effect on the evolution that interested so given this definition of the other delegate it is possible to prove that that this this this is that our place all the distance between the actual state at the end of some evolution versus the ideas that we like that is actually bounded by how large this model the our ears so I will assume my task here is going to be and and I have other possible given that I have the possibility to affect universe science center of gates of you know for all the way up or basically and the way that the number imitation that's it I might task is going to be to be and to devise a better way to verify them so that start are having access to a set of single qubit and the in into to cubic the very this is just an example I don't have to stick to those but it's 1 that you can keep in mind for completeness so I we let on ways and work we've controlling inputs we shouldn't have rebounded amplitude that was my premise so terms of the control assumptions that have element once the 1st as they said bounded control and it'll there would never allow out that the functions of up to appear and what will turn out to be a very important and design principle for the C. I will allow myself the possibility for a given date to be incremental let's say we difference be the end of this can be dropped these by for instance imagining that given at control profiler shape that we like a tandem that are used the simplest 1 but we don't have to be in fact we might want for practical reasons to have finite the rise times and so on and so forth but the important thing is like I assume that we are going to be able to stretch and the scale of the amplitude our by achieving the same day out that that 1 OK alright so once again the objective envisaging construction the is composite quantum gates so this is very much in line with many other construction of budget and full of tolerance we have far too components that we call primitive gates and we have putting them in sequence back to back so that if we are doing these things right than
18:46
that all that we are going to have from the decoherence acting we at the end of the sequence with be smaller and then read this back to their origin and had a backup primitive implementation without suffer from so I don't think it's appropriate for me to become a very technical area but the basic idea is like what I've done it was stunning us about by some serious moderns expansion is of the same tools that are going to be used terms of our understanding how the given the individual blocks with their error propagate began to cascade these blocks together that we can compute the all along and the date of the sequence and assuming appropriate convergence condition for happen was that we kind of do estimates having in mind the intuition that the basic idea that they're going to follow is the fact that the error gates as we are cascading far blocks belong to add up plainly otherwise they would be all but the fact that I within this formula to show the fact that the regional and the date that each are modulated by the action of the control after that point and because presumably we know what the control that has this is something that we design are being used to vise that modulation so that we can gain at the end of the day so 1st on and anomaly correct gates are so designed in such a way that we want to start from an uncorrected Arab but did that typically when standing at with the how long that date with take to achieve and I was saying that firstorder correction has been achieved the scaling of the gate rather than the linear as we broke down to be quadratic read that basically land that I'm going to call dog so that's the objective and that well there's out I wanted the time to do all the technical details but the basic idea or the 1st step rather it is to learn how to do these by having in mind the simplest possible quantum gate which is that I get the gate which is you know that it's quite distracting me back to the mapping control here and so on how to perform an effective now OpenGate we only outbound that control which means having access to creative segments out well that actually have real you before I started I actually working on this problem I had already solved this problem with money and this has to do with a form the copying we'd done it didn't have the time to call it unfortunately which is binary and dynamic and the company and how well the still uses groups but it also makes a reference to the generator of the group and here is the fact that the creative gates are that dolls I think of them as the views of science you add in the lab and the ones that you can implementing a fault the way that correspond to the generator of a certain copying group and the reason think recipe which has to do with up lying these generated by following a certain part also that Cayley graph with 3 % grew so that was the the the 2nd explained it about so that if this is the right on the head of energy and all of that turns out to exactly do I what we wanted to do so so namely that 1st order there is constant and we are left with secondorder contribution this picture here is the most important 1 as far as we are considering adding coherence so if we consider only undergoing and some Gilbert that group is the 1 that Daniel mentioned the power the latter imagine that of each of the body operation is applied collectively as a product like Explorys dummies text long pants or X R N and N is the number of 2 between how and there are these generators can be implemented by having access to to the collective limit on it in this way it turns out that this is the all of this is that Cayley graph at each advertisement pools and and element of the group and then we joined is of the edges of the graph are meant to be like the control operation that take us from 1 continent that they passed from 1 element to the other so my wait to read this graph at least in or control recipe is that we have given here 2 sets of Hamiltonian that the collective along and the collective and even I applied that in this order so at y y y x y axis this is not a cycle which uses each edge once and only once by this symmetry property we can prove that the area is of 2nd order with respect to their duration of their individual said when we started off from of course the land is multiplied by 2 so the is that were set and then take but we can do this but by keeping their power control amplitude finite at all times now and that's exactly what you want to do here at all because at the end of the game I have done as free of what I have done and all we less error what they want to achieve is a generic gate and in the beginning Thom and I were scratching their heads because there we were kind of thinking that maybe this wouldn't be possible to achieve our so it is possible to prove the fact that the 1 property that the company has is the fact that the cancelation of the IRA happens as long as we are using the same are generated to implement are given onion along the cycle it doesn't really matter our how the generator is implemented so basically it's a controller previous implementation for which the cancelation happens promise of war this kind of control of Bolivia's cancelation unfortunately doesn't extended to marginalize quantum gates so for a while thought that maybe that was wanting however on them but the thinking into the problem it is possible to made these not go of fear and for black box of air cancelation realizing that it is still possible even though we might not know and in fact we want to know the individual and at the gates of operating segments there's going to be willing to enforce relationship between the between them and this is the idea that path leading us from not to unmodified construction for constructing the synergies and it has to do with finding out the basic intuition here is like I suppose we succeed and I will show you that this is possible in the next slide so low that we succeeded finding to a particular sequence of primitive gates that we call balance bears on that for a given target we want to achieve a have the property that they share this saying ever up to the 1st part of that not 1 of the does achieved the target date the other how does nothing is a special identity date up but not is that it carries a matter and this is the same manner that you start carries so if we succeed and finding such a construction to imagine I think they could that aren't enough I had before and that on the floor the vertices I attach an identity while in that case and will still have done an identity overall by just taking longer so that doesn't seem as marked idea however if at 1 of these are and she's I going after wards and instead of doing 1 of these haiku again I performed you by definition or better by the fact that I have chosen this balance bear to share the same area I will not change the Arab cancelation properties of this construction but not all the negatives out of the game is going to be that they will affect the target date we unless syntactic idea underlying these genes and I apologize if this is very great
27:53
in any case the key constructing ingredient is the most through that balance bears exist and the fact that they exist the key insight is to realize that other that that basically the parent gate is going to depend upon how we are going to implement the gates and how we can not go out and explore the relationship between primitive and operates in such a way that we do succeed the finding I communication with saying at this tool has specific constructions which are out there we just described briefly about our naive stressed that me as a college in this case the we assume power access to stretch all and in addition on our control refined where I can also minus if this is the case and the basic mathematical factors that if I considered a controller MacDonald and then I the step and stretch the actually gets to be scaled by exactly the same factor that's the key thing while in this case if you can't see them up to it and prefinal each of which take to but 1 of them is this useful and these other ones status while I'm they share the same error to leading order in the duration tau however this 1 achieves nothing it doesn't identity this on log achieves 2 so this is the 1st example of naive about spare naive because we use that I find that the controller reversible this construction can be improved at the expenses of allowing 3 control as slots for a 1st order correction out by how what we call our portable set off balance pairs and the common that out we are going to use instead so the bottom line is like if we are willing to make the sequence number we can succeed at getting 1st order have corrected data and with the agenda of construction of about spare time overhead that we have is Hey that was the length of the cycle and then we have a the for each transform which becomes 20 I time style but in the presence of an arbitrary linear the coherence Island this is the most technical part and I would just the state that results in case you are curious well it is possible to achieve correction be the 1st order and the technique of concatenation was mentioned already quite a few times the idea is the same although there are some technical steps that I mean by on but basically it is possible and we call native the gnomically corrected gates it is possible to recursively bad law the as components for the cycles and balanced there and by following decidedly there's come we've constructions of which are able to I Mr. include support to arbitrary suppressed the effect of the coherence we are generating gates now the empire boundaries and it'd be that you got to derive but the message is that after level of concatenation as we would like it to be the all overall error of the sequence scares as there basic is a combination of the norm of the error on times the basic duration and plus 1 and it was you use the physical layer as we were last seen this morning in some of the 240 talks so just like in the cabinet and indeed also no action that is an optimal concatenation level but let me move on and the well you stationed here this is a single cubic case and that we had the study it's a single to be coupled to a simple I'll see it's been by and we have exemplified in here I would do that for the uncorrected gates which are of the blue line 1st or the 2nd or the 3rd 1 there and the only thing that I want to emphasize aside from the technique leaders fact that as we increase the of that initial landed in a system that slope although not the smoke is a logarithmic out plot but how we are getting more and more error cancelation spite of the fact that the length of the sequence becomes longer and I would like to point out in particular that this point here that improvement of the dialectic between this block and the blue money as the orders of magnitude in spite of the fact that their life has been going up quite a bit because I don't like you can read about this is that the end of that and it's more than a thousand durations with respect that after the primitives segments I would also
33:02
like lymphocytes and this guy is indirectly we've John's previous talk and Mike's comment by actually had the same problem and I wanted to make on that being not an recent experimental being performed in the group by and David are high is is not here about me in the office of the of the statement here where basically there's been a composing day sequence aimed at obtaining better but Minnesota gating trapped ions and that meaning of to our the that work to achieve more robustness in the presence of an unknown out better meet at the end of science and being inquiry and in this case and whose consequence that amount the consequence would be to call the the shot in tandem and at the end of the gate between this being an emotional degrees of freedom now what I want to say and that the side while they didn't do this experiment having the C. B. C. G framework in mind but it turns out and the in these joint open here that this is an experimental implementation can be interpreted in fact as a step toward implementing the BCG's are in the presence of a particularly favorable our we just nice properties nice algebraic properties and the data that you see in this state the that clearly the video change of slope even though there is still a lot of Scott that are in the number data via a change in slope from the uncorrected versus some form of what composing out of sequence gate designed having this type of radius of modulation in my OK on
34:53
that list get to the beginning of
34:56
what would be your power then next steps that they are summarized on what we have so far so good that they did they not candidates then a lot of the feature right I believe in so in particular they give us a proof of principle of construction that of Italy Oculink decoherence oppression during its is possible and the this is based on completely on openloop control it doesn't require the that doesn't require ancillary resources actions that very portable it because I haven't made a specific assumptions on the environment then they have of course and cut off and they unbounded in on the construction of fully analytic I we could even considered to concatenate father with consequences so that we can fight simultaneously the coherence and systematic control so that's the process but their minds and undermine diseases like place because I have forgot what I have I assumed that the system Newtonian cold we are ignore that was my belief this assumption turns out that the season an enormous simplification of the problem because so the peak hour contours and ideas we actually need the system I'm inclined to synthesize the primitive gates in the 1st place so in those situations where the this is becomes itself on complex on their challenge of becomes also to construct a balance pairs so how do we go about it that's bad but not so bad and then how bad of course is the fact that I have mentioned concatenation concatenation also in these country overheads which can be and typically will be exponentially in the sense that even for a single you'll be the lack of the sequence grows exponentially with Gonvick at initial level and they haven't shown that to you but if we want to concede I many you read with an adversary model where in that case we would also have all adult 1 could argue that the study of model is not exactly realistic in many situation but in that case we will also have an exponential growth which sees themselves no problem there are ways
37:19
out of that we can try to mitigate these factors and the startingpoint for that these tools are realized that basically what and then framework afford economically correct gates is in a constructive masses recipe for that I meaning a solution to pool targets simultaneously so a lot we want to be able to a control on it on your own that generates the desired target data up to a certain phase which is invalid so this is a great synthesis constraint and secondly we want to do that Our depending on which on that we want to suppress and we want to achieve we want what she perceived as his wife canceling this and up to the desired by and this is a different process to do so as long as I we can achieve the effect of seeing this in the absence of the and environment I think that we are able to identify the key point a systematic relationship between the control and the yeah for each sector however here I think he is also true that there might be that we have about the model and the control specifications then made that I have emphasized a not for portable construction that make me that specific of the system can be the and the space the way for optimizing this construction for a specific error scenario and sees them on so basically and this will underlying 0 mean it's negative look at this will underlie poured would underlie the 2 example I wanted to show it is to when I on medical search methods to solve 1 or both of these problems by restricting their control variables are we being that symbol of our domain that we have so well I would not I don't pay so the time to tell you that they that but the 2 problems for which we have I would say encouraging our results along this way it is I and II I think this step is I've left trying to talk their these 2 problem of the 1st assumption being that construction and also improve the efficiency 1 at that so it is possible to have 1st of keep the drift this assumption and then try to use numerical search algorithm to get more efficient dates and by the fact that I had the data that they wanted to show you on the CBS control scenario which is simple cubic but purely facing and the result that the generative recipe was 365 power for 2nd order that and the Regional Medical search it can be brought down to less needed s 21 I durations here and that's that medically optimize performance with respect to the unconnected and the 1 that the 1 which you so before and lastly and it is also
40:38
possible to act accommodate that but of a nonzero out system is Tonya so this term so much we had started looking at this problem focusing but going back to 1st order dynamic and collected data and the power I also wanted
40:55
to showing the salt but probably I can do this for our discussion given
41:02
that there is no fun but it just conclude read set of remarks that they want the less I think that although this is not a fullfledged art solution to fault tolerance dynamic approaches to quantum errorcorrection they do have the potential to physical date there's been no the letters that that acquired by photon constructions and there is a lot of work that is our on going in this direction I didn't know how much of a chance to show you the numerical results however I want to stress that that is really plenty of room to make this induced terms of optimizing their performances against specific error modeling specific Contra scenarios and up from that point of view 1 of the steps that I think is to really necessary to make is to make more contact with optimal control theory approaches and for many give setting also to better incorporated there are physical properties of the error models such as localities sparsity and all of that last 3 and this is where the conclude we have seen and not an impressive number of experimental on our demonstration regularization and benchmarking of dynamic that the company I I think it's really important also that we're going to have a look carefully advocated experimental realizations of dynamic regret the gates are we have already had mentioned 1 even though that was not intended but turns out to be an that context I like to
42:39
well this is just advertising are working together with the my obvious economy you probably not about an hour for the plan is to really try to investigate as part of this collaboration and scrutinize the viability of this approach wasn't at variance and the quantum dots and we don't like to conclude and thank you for your attention the devil water at most 2 questions I and so have you considered the possibility of combining the Orrick dynamic the company in ways that is and so that is can suppress to highlight the wireless setting some nontrivial contemplates you are referring to the fact that the procedure we have used use exponents land because of the compact and well yes know we have been thinking tool back to the problem right now is that even for just the out the target of doing an arbitrary order the arcuate not so forget about the genetic just wanting to do our identity and to the best of my knowledge we know how to extend that to arbitrary or so all I let the coupling can be made into semantic ordered the companies also work by would concern at all in our realistic Europe dynamic of the company but that goes out to suppression of 2nd order there have rebounded amplitude so we don't have an answer before that yet so that would be the 1st step and probably if that can be achieved the next challenge would be asked to evade the no go an and come up with with good balance there's if any thank you so to answer 1 more question OK most of us think tolerance again
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Punkt
Quantenfeldtheorie
Gruppenoperation
Physikalische Theorie
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04:08
Einfügungsdämpfung
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Gerade
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Funktion <Mathematik>
Nichtlinearer Operator
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Nebenbedingung
Gruppenoperation
Implementierung
Zahlenbereich
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Term
BSpline
Physikalische Theorie
Framework <Informatik>
Task
Inverser Limes
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Quantenfeldtheorie
Speicher <Informatik>
Grundraum
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Relativitätstheorie
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Physikalisches System
QuickSort
Objekt <Kategorie>
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Bus <Informatik>
Normalvektor
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18:45
Randverteilung
Bit
Punkt
Quantenfeldtheorie
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Element <Mathematik>
Gesetz <Physik>
HamiltonOperator
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Addition
Zentrische Streckung
Nichtlinearer Operator
Konstruktor <Informatik>
Dicke
URN
Sichtenkonzept
Kategorie <Mathematik>
Plot <Graphische Darstellung>
pBlock
Biprodukt
Dialekt
Teilbarkeit
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Randwert
Generator <Informatik>
Lemma <Logik>
Verknüpfungsglied
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Rechter Winkel
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Ordnung <Mathematik>
MessagePassing
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Lesen <Datenverarbeitung>
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Ausdruck <Logik>
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Primitive <Informatik>
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SchreibLeseKopf
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33:02
Algebraisches Modell
Radius
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Mathematisierung
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Datentyp
HillDifferentialgleichung
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34:55
Resultante
Nebenbedingung
Folge <Mathematik>
Punkt
Prozess <Physik>
Minimierung
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Snake <Bildverarbeitung>
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Framework <Informatik>
RaumZeit
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DomainName
Negative Zahl
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Konstruktor <Informatik>
Konvexe Hülle
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40:36
Resultante
Vektorpotenzial
Punkt
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Term
Richtung
Fehlertoleranz
Quantenelektrodynamik
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Regulärer Graph
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Benchmark
Leistung <Physik>
Umwandlungsenthalpie
Konstruktor <Informatik>
Sichtenkonzept
Kategorie <Mathematik>
Stellenring
Optimale Kontrolle
Physikalisches System
Schwach besetzte Matrix
Kontextbezogenes System
Verknüpfungsglied
Menge
Lesen <Datenverarbeitung>
Fehlermeldung
42:38
Summengleichung
Kollaboration <Informatik>
Quantenelektrodynamik
Exponent
Wasserdampftafel
Nichtunterscheidbarkeit
Mereologie
Güte der Anpassung
Automatische Handlungsplanung
Firmware
Ordnung <Mathematik>
Algorithmische Programmiersprache
Varianz
Quantisierung <Physik>
Metadaten
Formale Metadaten
Titel  Towards Optimal Constructions of Dynamically Corrected Quantum Gates 
Serientitel  Second International Conference on Quantum Error Correction (QEC11) 
Autor 
Viola, Lorenza

Lizenz 
CCNamensnennung  keine kommerzielle Nutzung  keine Bearbeitung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nichtkommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/35330 
Herausgeber  University of Southern California (USC) 
Erscheinungsjahr  2011 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Informatik, Mathematik, Physik 
Abstract  Dynamically corrected gates (DCGs) provide a general perturbative framework for boosting the fidelity of gating operations in a large class of noisy qubit settings. While original DCG constructions rely on fully analytical control design and aim to maximize portability with respect to the underlying error model, realistic applications may call for DCG sequences that are both more efficient and more flexible in accommodating control constraints. After reviewing the standard DCG framework, I will show by example how numerical optimization methods can be successfully applied to this end. In particular, I will address a practically motivated scenario where the presence of an alwayson drift Hamiltonian mandates numeric search in order to allow robust gate synthesis. 