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Universal topological phase of 2D stabilizer codes

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but the political phrases to destabilize of college I don't think that if my Dmitri's this conference Miss about the if 708 phenomena with very fool wouldn't make it this conference in the last minute when the system is the young the lessons who will reunite later though that on Friday this this about the beleaguered cults
and lessons of we have a really have then let me remind you that that too agreeable here it's not in some sort of revolt and that of the Thacker by the listeners had earlier in and look at and the they just FIL language understand that they collaborators have had fat little for that very the offices of ordinary in that that sciences ago aspect of the of the 1 be able to recover any information about that got bit this in this book here I want to take a systematic approach so as this to the coast and died on the sun and the 3rd minus what is the indigenous structure but the I
will be focusing on time as an assistant and with her this assignment enough evidence and defined by well just systems with that both the the electrical so did the beleaguered calls and given then a families of culture and then in a little of that we in the that mean the the goal we live got sound some of and then maybe they would be able son of the facts but there is always the case that this will give surface visionary in man and so approaches to classify goes according to these 2 as with so that it's when you need come from although these different effects so now of
course such goes and it was related to at the Britannia McMullen somebody Blaker I can into that that family then you with this sounds the cell that's and is that the ground state respond to all these guys having 1 so the the guns say that it's a encountered the space non-state it's goes from political subspace and the excitation respond to errors in themselves where 1 of the now the e-mail I have and it's a distance with a with 2 units of time the on the status of all the units just as the gold and from this property of the legal code again that they now states have look into the of so this is mitigated this over the life of a legal and and they surmise perspective on
the blade element this rating 1 1 we may say that the political analyst price the Q and classes the final Lopez yeah they want let's see what they mean by this so the idea is that if you have to
adapt to reinstate they will be in the same phase from live they can be connected the politically with a person is not and then this amount though them being there be connected by look Allianz the formation rest the existence of Samna went into a bit of course that's constant in their in I that this but the size of the system but
itself market directly where they all we are saying is that you know that the justify the reader those of the legal the the window you specify in a longer-range and I'm in but so for them so events that sort rents and diamond pattern is 1 that's a not something some estate that we can transform for local operations into our Apple the stake and all the all the things we have a lot of this is the main thing would be so and it is these London's and then you find by the cigarettes classes is to look at from it so
without further to goes the 1st is to understand the structure of two-dimensional doubling of lexical to including a subsisting goes about was not surprising related to this the political and I was having and in addition for subspace both of which have different than in and we would like to see that I would have the same mistakes in ineffective since we can transformed 1 into another if you look at the as was so I put into this prescription by my women colleges of it so here
that I will that the explain that often use in the very cold their if then I will both laminar Sajudis than the very go the somehow U.S. unfortunate codes and I want them to suffer the goes with half the recognizer direct structure but this this is but I what their surfaces besloten emissions but 1 of them is that so there are 2 anything ways to a sensor particles they they've and the government and so the that facing them in this way and this way I cannot the 2 press is gonna be the funny 1 and the other with other what lies present so this gives rise to the possibility that but there could be some that the boy died the action of the thing is is it in this to and the year but because it suffers that of as subject to sets of the body conduction cycle and so the simplest case is
that of our union which are all as as well as out of this by it 3 of theorem so we cast the 1st of all as before the break out and this this this they can install further of excitations so if I take and even the young and I have a given the little competition of the of phase excitations equilibration and look at and get another at the traditions and the same offer you I say this aforementioned I would move out in the angular last and these suddenly willfully thickness classes so that that is something that this concessionary young elicits issues with similar elsevier so the 2nd the absurd so the 2nd
element will be efficient that that's what they're there Nobelprize threats given the of 2 regions you in the in the light of the the vessel you can get this amount so missing the boat so they they the decision rules with them you would be that about out here in this that then finally that somebody knows that That's what the problem is assume that the Willard and that sometime what when I assumed so used in them in 1 of the 2 possible so that's is there 1 example to the it as they got so I would like to emphasize that in very cold we can size the of invaders Twitter process of X and this necessary so that than actually goes from lower they take and the blah blah link I think in the lattice and this way both the modes of an offense and billion or elliptic operators we can then be together us aspects so there 2 kinds of it it isn't in its citizens in the moment we have exhibitions and look gets the it and by sensors integrated with proto bright here this so is that no place at stream I will not the the even of mammals well it's and and also on a number of sensitive basins and similarly for the light on the disability back at the middle again in any event the police that the 4 centers so they could have and a number of both at this and then I needed to music it might have another member of the loans I say that this stuff on it at that is still at this from a number of bad ones and in this I have made it out and then finally reason but this goes from together with government number of people so rescuers the sobering call their personal recalls any chance most of itself will give me the Atiyah cycle and I am only I only need there there the right and that and so to recover them we can use the fact that this Dennis are by the standpoints of his friends and according to
legal interactions from there with this properties of this in the break so if this is but firm this magnetic students and the 1 who in the community and they can of 2 processes but the growth of this is the way and when seen in bank the Open Bank 1 of the president's this crisis so in both cases that the 2 of the lexicon vectors infinite innocent based letting 1 gave the best aligned saddling into the amount we can see that minus appears differences in there the 2 so the stars that this sooner various profit as the good and then we similarly chemical the the surface of this data the weakest pivotal covered makes sense to to buy the book do to targets of this and that so in this case with the fiercely without 1 point so in the case of elliptic instead the there was an awful lot of time but the Complicite sensibly affirmed in this and we think is way so that the Vatican was read to move from 1 based on tunneling through that chern abraded the of of a link medication medic obvious this and then by that is about half and here once again and my other in this operators and the found I can only in a sense that Gerda Bezos of living with what we have and if again is minus of course would have been the offenders because when this sense the minds of so they may miss it is that without samna from then in sun and vote I would have started an abstract model from me in this case with 4 tennis envisioned those that respond to their at each event at work understand written rules and there's a chemical from this in a paper this is the this demand effects of like and then to the the main results so
1st thing that we need this do as the carousel from a family of the beleaguered goes to our single letter group this air the finding anything you like so you know for the family of calls that would be in the city the constant about and we have a plan the lights now of course
this this is the less it will have some properties perceptron from it comes from at the book from the from if the blade alkyl to cannot be just any violation and we must remember that I didn't really have both we love and that the letters so not vector angular states you know goes in a noticeable in the wake of let's see what that translates into
so if I have some of all agree that the ending lattice and opinions with all the Perlis made us we can find an element of this from even if of gold that is big enough so that this guy sits in there and work and then it will also belong the recent ice of the families from which it follows that from this coding the breakout that know itself belongs to the relation and then well with a binder that it's it's was was so that in opinions with the lesson here or we can assume that in that OK so the message is that we call this condition of this analyzer of the simulator is that the fate of the family itself and this is the the bullet organism wimple so this actually and this name by this the body condition and then we want to justify of so have we
seek to be able to relate to go through a lot of the formation of and indeed how that it's enough to consider the following ones 1st half a clustering of the lattice wits which again muscling nothing is as looking underlies rise from different perspective we have a look on this is my t from others so that we must the body group itself in fact look at this in this case and even let it follows from the translation might even given that I'm only considering the body of the week to consist of a OK does without final support and then finally I would like to be able to add and remove this indignity you it so here is the calf down a single lectures about from the perspective of the political them out but it OK so if this is to say that give industry or 4 from a sounds like money then 1 winner so if if my if michael's has other than any suppose then this animal there will not fair and if the formation injury ghost our it's this cry from with this new breed of appended very Latin for 1 but in destined thing is that the countries of Central and when they're to
both have the same animal as they can be found from 1 1 of the is for these basic then if we rule out the possibility of the vote Banyan's with which we can look at in the back then 1 write on this and that but I will want that to an insurmountable it isolated rope in this sense is not given the high number of copies of the of the legal which is our members have Villani is sent without the proof of this
so 1st of all there too thing I were results but the important so that into for the user study less approach we can't trying as a gofer independent annotators itself the if you translate it into their symplectic vector space a new formalism and as in that there are no clinical signs of another so the thing that into the we can find that the local and of of an innate us and this is actually not true it's the if it is true I mean it in the proof it does so we'll see you the fact that the system is and this and later found naturally of sup so that if a doubling of occasionally it it wanted to but if that if any of the 1st thing think and I think that's a component the of the solid the number of studies if I need was a hobbyist it's very the gas the of the animal like recognition of answer came about it you know envision before this and so on and then once you have these to evade us to construct our framework use of light is the name of the segments with the whole and the framework of a system and there have been that it is the lasers our you've all the the in the full and you've all the other unit before the facilities in the Karstadt's debts and then the rest of you know those a and then there mapping meeting show where goes where we have panel this amount this is the 2nd to the assignments with Internet and all those extra and taxes letters when I'm into I think it would letters so that the couple from and so
some this morning based on the 1st of all we need to the brain it's the at height we can find it was attacked and the whenever we have to to cite some of this attendees and here in the 2nd the site with a given set of is about a week but even then it because the mafia mentally able to construct an operator with so what in this really here the dust everything going about says that it creates a too so this is what we mean for us an operator here with an affine and full I read parts
and once you have to have a there's we can go what are the stakes and the being with a tree of all of his plan for the cycle and to see that this actually make sense consider for example that would have these 2 pairs of this thing so they thought they should have this in common data right and the ticket we gonna extended the victory and now I have
this clauses strings to that of 1 points they produce so the room with the laser but this and therefore the children community it took over the at the same ancestors this this thing
here is for the fight is independent of the choice of the of the streets at similarly for for this 1 but
so was with half a Our new mother and then the body that we can find a set of of the family can in a us for for the for the group of sentence and this is what 1 finds so there will be I didn't president US It's of them so this that's here we'll have some unique models of this would be so a guy and most men of that's within the the unit there and then all the wasn't as that may be rituals that electrons with can be both firms now than it of this bears responsibility and it's in the very cold OK so we have that was a very good and there may be at about which so then the case we can construct the so let
of of the case of these would be a latter readers have the the all the conscript over all the groundbreaking and everything when have the innovators here for mean square layers for its and so this led is so them especially with respect to each other and they had a reason to if we want their their accommodate us dependent the bidding all these effects were 1 and 1 then this can be only on the animal that not on the basis of the of the strict it with other recently that weight so we we are not with the this collection of the same and that have the stuff from data independent of the for you namely that all mother and then you know that the limit means we were
gassed so here we have to both in its of them we need from this persona so we're we're through his lasers and then for its latest so for example you have 1st the say electric test and the
corresponding 1 in there and musical and they will not as things women's listing fragments and then it's so so there there will be about from the families is coming from from pockets of of if the list of a the government out and they can be up to see it with it I would not going to on the debts
so let me move on to the certificates
so what would happen is that they're very fast in an association goes rather than a calling that's based of the premises we will just they gossip system this I would like to attend and and it's with of which we get
and mean there the case of in in the of in the frame of mind we have described our subspace through the license but in addition we have it moves 2nd that's that's another an effect in good effects an important thing is that this relation to get to and the truth commission so that after phase of the variation in the center of of the gage group now that the beleaguered case
what we need for additively gather the lessons of Istanbul will be a family of codes it to infer the relation and it will didn't have a look at him a no again we I want to extract they're the recipients for the world and would in the Finlayson of banks and the relays on Sunday group as before we want impossible that and in
this case what in this if I have by the way here that commutes with all this made us when I carried to our lesson of cold it will also community of and therefore it belonged to the gates group and 1 the again between the the we can assume that the addition empirical sciences this point very so we are left with this condition the ghetto in the center of this tireless and so contains all the by the grade of that community with with the star and that but it was would have this condition we could just as well defined the gets group through it and then we get a a condition on the very laser that's the when the that were what is and we have the number 2 to the becomes audible accompanies right so it doesn't is moving mark and is that isn't isomers and later on the it's a is innocent the fellowship of phrases software these would be trivial in a finite of an enemy of case that is an assessment on the state through in the case of that I need to know that so the
main obstacle to the Morph the to that's a dates goes from 1st cold you know we need to generalize the motion of trapped so the trick is to make it very best actor remember that Gerd that's a prize a given dozens of exhibitions up to do we have set of activism that can be created by applying some of beta and the domestic it by considering that there where the conclusion of a two-day Science actually or if you want this you know was Martins from the laser group total proceed to and material what is the sweetest onto those that kind of thing that the data with some some will break so this plugin with if their group off offended from a from a lesser but not we have this sort of let him after this how can I United immediately debate with it so we have have to deal the and have a new group of status well that that don't have the same sort of all views mean tons of states and Canada that but I really useful and we have the staff the year centers for the for the state and so we have 2 sets of 2 groups of tender and we could not afford like the findable at the body and actually doing them so consider for example phone another number for this and that and that can make sense and I would have the 3 this show opposes the breed of have to commute so that in mother would spare facilitate due to the find this of of interaction so consider for example that have but this the of these things came from there from from that from there from data for its intended to for in that case chronicles a string me that this guy we commute with all the gates operators and therefore you along with this closing we rely on the very relation to nearly I have a stream with that laser in that it the closest thing will commute with a list of letters and therefore it belongs to the metal so in this case that a stream coming up and it should look for data from the we love to be true if I have taken to be telling us that the men will have to assimilate since the community but if I if I laser no information that you have soviet elements of them they than the size so I can define sets of the Boolean that in that case so what we're left with is that for it to be attended would have the when the finer would later this takes with half the pedestrian and we also have when I have a date certain as the LaserJet as 1 of these these would to this that's not so I mean profitably there's been for the lesser charges nor that in them so really I get I come from the new model for the gates this and then I could least as some sort of what Jesus for the sentence so of course I come
up date said this to the relays either simply because amorphous and from the need to sit still and the sticker reason they said to feature I will never forget the biggest this way so that the and it's that is a secular cycle and then the inmates will have a single underscore C and it's well this and what is an investor that's an event on any toes of Canada sleeping but and it will process the this this can be there so that if I guess that have it says and not 1 of them and we had this income data of course I can of the 2 of them because then the of the of the the new site is not not and as in the case of such this skulls
again I can find only go to the Unary those fully this this for the estimated time less the new friends gather data so without 1st the sector that looks very much like we we've having them in subspace goes so that all sounds and then maybe Mikhail spend of actually appear and in a somewhat of something new without there are also some 81 variant all of them when that so they're not they're values the and then for the 3rd this we can find the same number of in this this is because actually this ability in between the 2 so well this ability the way so the thing is that this is the entire it with this kind of with any of the other 1 similarly that with a 1 here FIL holidays and then I have this is the laser tell you that and then it's a funny like here and the love respectively for the so that is there with Sin to them obviously if you want this up to the the periods in so there are many
animals that route but with the past but all of them can be of obtained by combining for basic words so the 1st of them correspond to what we find them in the very breakout with these 2 losses with with the model of thick then and the 2nd 1 is the same with so from Incirlik well they're definitely letters at 4 minutes and this can be found in the blink of you think Oracle that where the where that way I the this we could also have a single wasn't this can where from of the of the 5th and labeled which would be at the Ecole where the study so we have to to to get the get 2 we have all of us ing acute EC sort super for the 1 and we can also have a single fermion and this is what we get if we look at the at it that's honeycomb as a subsystem book so in these 2 cases actually without going good periods OK but it's I mean they this fits into the test data have actually it's important to get the even though it's not useful from from encoding point of view so
once again we can inside the framework of innovators and we would like to go where the by laser and it enables aspect markets of these of these lattices and we
can so so in a guest of their of the gage group this was with the finer said that in the of the for the gates that include these this program so this would be the coming from that is that where things have these types of and this is the the letter at sort of as a bit of a this case and so the thing is that this is the start of the of the spec in the industry in the USA basis of in this set of an admissible theory that Italy for that for the here and then we also have the standard with the the term of music and they come from that it's made up with extremes of the profit out the response to you that that were not well you know the blood of these and similarly for the established so that there may be is that the rest of the neighbors to the the the gates of the paralyzing we have at the delta obvious obvious maybe that with this we put there the calls in our standard form and therefore we can see that all post-communist food in terms of of these anions in addition that we could put this these ladies back into our finances than like those and then 1 sees what would you expect that you have a gain about that the commonly used to the legal operators and so on so it's of these 1st we contributor to commit cynical in there in that arose and is based on the red nothing in a nation that has a problem is that the link with in in a final ladies we need to have in there and gates or the enabled the bad FIL I used to have 1 pair on the 1 of these just and bear and into to a but need of the at 1st we you
DB in his wish to give you that we can understand too there's notably accounts of the thing goes in terms of finance and yes so with that let me ask the
system questions so 1st of all our we have been considered as the boat but we could also look at their defects in their in a cold so we will have this is different market will together pay of these could be just like in but also we have long days and we have 1 effect but we can also classify these potentially using these this though so that we could go but setting where would have to any interventions with the different the recent indifferent but for this decision then we have only this there's agreement and that and then we have point and this way we could testify all such possible things up to love of music especially the but in modern Allatoona's on both and finally there is the most the as there was tried in vain to freely because as we know as we as we learn to be monitored there are must more accept means waiting for others so the be in the modern after all good so that's a pretty at FIL commissions I have a question so what's the what's the defining property of the 2 D topology lies in court so doing assumed the locality of the operator and find the distance because you didn't specified at the beginning so all you both is there but the idea of this violated the neighbors and then that so you have a highly and the new that in the obey so do could do it in different ways but there that yeah there will be always a letter last hold your family right so when you will not enough number where any operator will be look in the sense that it doesn't affect and some of you are your course trained operators are limited influenced by that is so aggravatingly unwilling you know in the lattice and so on yes but they limited in size by the locality of the settlers of generators I mean when there will use the less the limit on the cost required course training all OK so let's see of so this this enemy but the item of like you know there are many things that can approve about does like pocket this is some cost that will give you these but I like it's amazing what so so they steadily 6 and that you can put a bomb on what covering you're going to need the opinion and the depth and size of the universe but I cannot and like expression it is possible to for the standard stabilizer case was the condition that the centralizer of the stabilizes model faces the stabilizer in making that year so yeah that's exactly what I'm asking about sort of the encoded operators I mean what what about us I mean do you put a sort of a size muses on th and the entire group all elements of Parliament's ice so this been at there that angle the bread will appear when you go back to some financial years but not not of course in the light of the villages of the picture that may be of by inclusion in his letter that be everything the catalog so everything is about the kind of castles didn't have to go that way wasn't carefully defined in you know look at it the only thing and you so that the thing is that what they're using today given the sky work and then once linking alleged to this locker and then it says here and OK thank you other questions like the speaker the that
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Metadaten

Formale Metadaten

Titel Universal topological phase of 2D stabilizer codes
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Bombin, Hector
Lizenz CC-Namensnennung - keine kommerzielle Nutzung - keine Bearbeitung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nicht-kommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/35331
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract We show that 2D topological stabilizer codes can all be characterized in terms of a finite number of charges and string operators. This is true either for subspace or subsystem codes, and it has direct applications for error correction. Subspace codes are directly connected to topologically ordered systems, and we show that all 2D topological stabilizer codes are locally equivalent to several copies of one universal phase: Kitaev's topological code.

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