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Fault-tolerant quantum computation via adiabatic holonomies

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but as of a couple of announcements but 1st we wanted to point out 1 the so it's a great pleasure
to introduce the 1st speaker of the session of the ontological FIL you use the element and this is going to talk about fault-tolerant quantum computation the idea but it anonymous but please thank you amendments thank you got a thrill of pleasure provocative seeing the about 4 years ago when I fell here about the preliminary versions of some of this work but since then our understanding has evolved significantly and there is some new results and this is what I'm going to talk about today so here's an outline of my talk how do you leave this introduction of about 2 metric phases of whom on a quantum computation and then I will describe a slight extension of the original model for all the money quantum computation which performs computation in subsystems as opposed to subspace so which should be a killed for understanding how it is possible to combine these geometric ideas for the methods for fault-tolerant competition on the stabilizer codes and then I will describe 2 approaches of 2 fault-tolerant quantum computation all 1 of them is the origin of the 3 proposed its works on stabilizer called as you know it accuses no executed but requires an honor that depends on the Colts reviews and the other 1 is 6 gage units but which is kind of terms which are independent of the call and also allows for reducing the character of the upon to to using with got I will discuss some additional advantages of this advantages of this approach and also some related schemes and then I will conclude with a few remarks and
so home quantum computation is based on genetic traits of genetic traces a phenomenon that occurs on the parallel transport in a curved space for instance consumers sphere and so on vector which loosen in the tangent plane at a given point and if it is by the transport which means in a way that the romance parallel to itself during the of transport along the dotted curve it is going to follow this evolution so that when you bring about the initial point is going to be rotated by some angle phi which is like a long time and this idea is not restricted pool transport the vectors of tangent space but you can imagine any curve any manifold with so where each point associated vector space on even more general space and the parallel transport is a cat some rules which tells you how to transport information in this space as you move along the manifold it is described by a gage potential ants this is actually ubiquitous in physics where the fundamental interactions are described by gage fields interestingly it is the same idea that appears in other biotic on dynamics on which the whole molecule approached quantum computation is based the belonging to acquire in this other cases is actually being proportional to the flux of the kinetochore through the area that enclose so to review diabatic Turin-are here I'm going to use a version which is noncontroversial with the words for DeGeneres ideas spaces of the and is due to proper back in the 19 fifties so basically go through their band depend on come upon in which changes along the curve from a lot of curve of Hamiltonians which is parameterized by a parameter s from 0 to 1 but the dependence of time is given by that so as a actually the current time divided by the total time of evolution let's assume the discovery of Hamiltonians here's a and as dependent space which is separated from the rest of the spectrum by idea and so I assume that this is and the projector onto science basis twice differential then the statement is that's if you slow down the evolution of his sold down the change of the component along the curve in the limit when that the slowdown goes to infinity and are any that evolution generated by the photon will so that any states that begins in the higher space is what remain ironed space during the evolution for all time but for the modest durum also tells us how the I guess in the in the States is going to change within the eigen space this is going in order to express this minute to introduce some as dependent basis for the subspace and was considering an initial states have 0 or it is going to evolve in this transformation will be described the following expression where careful geometric phase which is simply the that all of the energy and there is the geometric quantity which is a sequence of continuous sequence of projectors along the subspace along this curve and the transformation that it that it corresponds to can be the describing this fall what is our G A 0 or R is the basis framing the initial space and GeForce use of the bases for that s and this year we you I J is actually a unit a transformation given by the following expressions of public exponents of of quantity which is given by this of this expression this is actually the wheels a z of connection with describe how animals parallel fashion the states that are in the subspace are going to leave off along the but this year the end of actually is considered bands depends on the choice
of bases soul in which in our case the choice of basis is a gage freedom which is all physical but if there is a mantle plume there is some natural rule that fixes the final frame we actually can get rid of this dish for them and prepare McGeechan enlightened quantity and this is the case when we beta subspace along the loop such that it go comes back to itself the requirement that the bases in the final time is identical with the 1 that we start from removes the gage freedom and worked in this kitchen by and want to call the long associated with the bottle and that data space so in this picture I'm considering apart and what is called a gas money and address monument is is the space of all subspaces 71 dimension think so on what parts of the spine we can take a given subspace depends on the Hamiltonians that we can engineer of course and so but it'll shown by Zainuddin said that in a generic case there are some reasonable assumptions of other your control duties we can actually obtained from so again subspace which can generate then diluted group and their proposes as a metaphor of quantum computation which is what will not quantum computation as of and this idea besides being very fascinating from a conceptual point of view has attracted significant attention due to its but due to the robots is that promises so on 1 hand this is idea biotic than dynamics which gives us some robustness against timing errors so as long as you not about the community in for instance Europe interbreeding between some Hamiltonians he doesn't at the precise at what time you will be able to switch on your interaction or turn it off as long as you're not about thinking that force of satisfactory precision you can you can take a time and Traverse the loop the with so with the timing that you like and also of course since this is out there but I think they use it's the the Hamiltonian itself the gap can protect you from some kind of affairs in addition the dramatic nature of the gates supplies with some additional robustness the audience lost classes affairs which which I changed the the path in such a way that preserves the flux because remember that the long integer generates that is equal to the flux of the curvature area that will link loss but these statements should be taken with care because there are also various errors against was this is not the support among about for instance splitting of this of the ground spaces lumped result in that that errors and if you the specialists' true of doing this evolution slaughtered this we think is going to cause transformation in case which which is going to accumulate and can it invented it but can the detrimental to a computation even if boss if we are able to engineer very well such a system in every system that's variance so we need to find ways to combat terrorists if we if we would like to use this approach to quantum computation isn't really a reliable approach and 1 of the possible solutions is been considered by the London and I'll just to in court decoherence free subspace and they have shown that for some natural since it is possible to whom a competition and clearance for subspace but of course this requires certain symmetries and also in the use ideal so whenever there is there will be errors the direction with the environment and similarly there are errors due to you to control imperfections in addition and scalability if any metal to requires the ability to do fault fault-tolerant this so it is also desirable that who should somehow be able to if we consider this matter as a universal meant for computational combined somehow with fault-tolerant metals for competition in all this is telling us that we need so to somehow our unified approach active error correction and 1 attractive prospect is that assuming that the colonic approach provides us indeed with some control this control robustness to aid the the protection provided by quantum error correction so in order to understand how this works so like to introduce a slight modification of what was already introduces an approach to a lot of computation which is in a subspace so and do it is to develop it so that it can capture the most general form of encoding which isn't of fake 1 going witches and going subsystems this is known as the so called a subsystem principle and this is particularly relevant in the context of the information protection a subsystem use of there's capital subspace such as for instance H with subscript II and superscript may induce the composition talking this decomposition we have a somewhat different orthogonal subspaces labeled by in each of them fuckers into 2 and the 2 factors are in the there is a I'm this particular decomposition is that it is known to be a sort with the structure of preserved information on the open quantum systems the initial by these people in fact the this can be viewed as a hybrid it's a quantum classical cold weather protect its quantum information resides in the subsystem AA and the classical information is associated with the different subspaces when which we have such not called such and subsystem calls she was 1 example that we should all be familiar with the standard quantum error correcting called let's assume there's a court which explores the full Hubert space that the statement that the information if it is you futures remained protected can be found in a subsystem actually corresponds to the fact in this case that but there is a decomposition of the full Huber space of the of this following form where the logical information when from error has occurred can be retrieved it is contained in this factor and all and this other cofactor compares the error syndromes and possibly gage degrees of freedom the call space itself and the 1 which we prepare our information is actually the stuff on his HA then served with the span of some fixed vector which is with which we write this 0 here this corresponds to the to the error syndrome is being initialized to 0 meaning that we're in the cold in the original space the engine from this point of view and the connection can be seen like this I mean we prepare service the the state the logical information in the subsystem and keep in mind that this is a this is a portal subsystem meaning that the observables that the describe that are actually not known local and the syndromes state 0 America part collectible Aracruz what it does is that it simply excites the Gaussian it sends it to some generally mixed states in its being and then the correction is simply to reinitialise that states this concerns correctable errors now it is
desirable no it to to develop the couple of relations as a more general formulation of 1 on the competition which is compatible with this the general notion of encoding which is encoding subsystems and this can be captured in the following come theorem soul consider any the composition of the cubist bases that form will be interested in a lot of the information contained in the subsystems H. K I and the statement is that if we choose a static hamiltonian of this form basically the that's the the only on the subsystems that contain a logical information and Monteria on the Gulf Coast of system and here for different ice of there's a difference of space we requirements have a different spectrum the statement is that if we stop in the scam donor and change its idea about inclusive that on all crossings of energy levels the most efficient control abilities it is possible tool baby subsystems around moves in such a way that we want to generate a university where the transformation of this form where the transformations in the sup the logical subsystems purely geometric ants and he said that we desire and all unwanted dynamical faces can be absorbed in in the course of Interpol subsystems of the level by D. and 1 1 interesting consequence of
this statement is that the when you hear the situation when the Huber space of factors in the tool we can actually implement the Mandatory purely geometric transformations and the subsystem a without getting to initialize the system in this in in a subspace you might have the full you specifically if you're given a system you can best we had some cubits in an unknown state you just don't on a Hamiltonian which acts of Montevideo on that too it's in that gage to you are there but clearly the change it in such a way to end up again with the Hamiltonian acting on that you and you use your original system would purely geometric transformation the way this is not handled showing the proof here but basically it is based on the idea that you perform different computations are in the different ideas spaces of here upon and you do it in such a way that the desired transformation factor result and it remains on this substance on the subsystem aid that you're interested then this approach can be useful that invest in that it saves on initialization procedures so on in the case that when we do do fault-tolerant quantum computation and not as cynical monarch when the dynamical case but we're also moving the logical subsystem around so I think it is useful to get there the focal monarch competition works to also consider a fault-tolerant quantum computation in that and you in that for a picture of from subsystem logical subsystem more for moved around so consider stabilizes cold where logical information is will become contained subsystem AD and bolster Domingos degrees of freedom I I mean I ideally we would like to do all this correction which means that the initializing this so the state of this subsystem be back to the cold space and we would like to perform computations so we would like to to perform some few evolution inside a change but the thing is that for this quantum this part the correction were most works the calls of the logical observables are highly local so this means that you would need to kind local component which this and the analogy would have to implement so the competition is a sequence of music using local on this means that inevitably you have to take the information outside of this called and so it during the original during the Revolution you're wrong to here for the compute time depend on the composition of this type which is related to the initial 1 by some unit that it and this university is generated by the local interactions that you're applying but the question is can this be done in a way that gives information protected because this called might correct errors but during the evolution of my that's the subsystem gets exposed to to errors for which the pope was not designed and that it if you on fault-tolerant quantum computation goes exactly how to so I already a local set about
filtering competitions someone rank going together just to refresh but we say that the problem of connecting said its fault-tolerant different error occurring during its implementation renders the result correctable and if we're able to do this use the powerful Trishul during which tells us that that I do given the dead in which others that if there is below some threshold for information can airport gates then we could the chief of unedited long competition which political overhead so that has been a lot of literature and of how to do that I'm going to here to the reuse simply the building blocks for for our dynamical fault tolerance schemes and I'm referring specifically to the formalism before that you developed by Gosman among which applies for a and theory stabilizer called what and so on since this basic operations will will be needed in our construction and so on you do this by being able to perform transversal the operations which includes a single qubit characters transversal not maybe transversal thoughtfully and the addition we require preparation and use of a cat states of this type with which requires the ability to somehow create to verify that it is well prepared and also we that it transversal signal gets from the logical space for the cat states in addition of course like in a matter of competition required the ability to perform projective measurements in the computational basis in Chile in a man full of the fault tolerance the procedures that smart constructions which tells us how impressive these basic operations to move the subsystem are answers at the immense protective
so coming back to the question of the following problem of quantum computation let's consider our stabilizer court which encodes 1 qubit plan possibly has are engaged units so these are the stabilizer generators and is are the logical operators on the gage qubits so this decomposition if we would like to what they did is that we would like to move the subsystem along the same exact same parts that are prescribed by the standard fault-tolerant procedure so that we're going to keep it protected but if you would like to move the logical subsystem rounds in another about the manner we have to use a Hamiltonian which have period on age be honored this should be our static Hamiltonian and this means that it must be a disk from about another there's a combination of elements of the gage group and the same holds during the evolution if we perform any evolution starting with this final done and the corresponding band band on the composition during the evolution of what will be such that will be such that the kernel gone expressed with respect to its walking that form and this means that it is again a linear combination of the elements of the transform engagement because of the operator so stabilizes or all of the all operators of the gage group get transformed and evolution in the Heisenberg picture so the thing is that operators in the gage group couple qubits in the same block for it this is a non-trivial called which means that our society is impossible I mean we cannot just perform operations that address 1 cure in a cold or the corresponding qubits from 2 different so called worked so fortunately there is a way around this sexually and did transversal operations are not the most general wasn't so the remote call centers to propagate both of which was also unitary followed by summation which is generated by a component of the gage group is also fault-tolerant so it is exactly to this kind of transformations that we're going to drive the subsystem called around in order to generate an cold it's on gates inside so here is the main idea is that abstract forms but did this is what I want to convey to you this is the main idea of this approach basically we are going to idea but the drop the logical subsystem along some sequence of Arts in such a way that during each segment so this part is due and divided by segments and each segment the transformations in the full Huber space that generate including dynamic ON genetic parts are of the type that I just outlined transversal so you there is follow baggage transformation now you will want to follow exactly the prescription of some of dynamical fault tolerance is that if we complete the sequence of these transformations again they were going to get the desired concurrent operation followed by a gage transformation it's by by construction when we when we complete such an operation we have taken our logical subsystem around such a little bit which if exactly opened up along the in its which is the desired encoded gates so the 1st do and by construction will imply fault tolerance whereas the parents of these conditions so ensures that the don't mean computation with with performance purely genetic so how do we do this is the way we do
it is based on the on 1 observation and so we're going to use Hamiltonians for simplicity we're actually going to use it each of if each time only 1 element belies a or digit or the gage group so without loss of generality we can I choose to on that that if we would like to follow this step in the fault-tolerant procedure which in Romance a gates on say the 1st students in the cold war so which was a O'Donnell of that time and equally variates our idea but because in such a way that only the factor on the 1st you changes then the result in units in use of that type up to a gage transformation and all the dynamical effects are compared to the gage transformation so you see that in this way we can actually implemented on a single qubits gates are in the cold and in a similar way though sucking let me give you an example for us that to want to implemented legs gates on the 1st this G Tudor I forgot to say is just the rest is just the rest of the disk is the description of this from the and since it's an element of the gage group at the sun in this thing corresponds to belongs to the following rules so it is something as the product of our mattresses but you can think for instance or some high school such as the such as the Baker Shor called you can figure this is just another Z on on nearest neighbor cure it so all you can think of this as just yet another is on the on the qubit so here's an example for a single committee gate X but what we do is we started this going done and would gradually turn it all off and turn on another from the timing of that and then we go to the initial Canal with the minus so in a similar way we can actually make all the necessary operations in that I which are building blocks for fault-tolerant scheme so do what the conditions that they were short being able to do this as well as the preparation and verification of the cat state we are able to purely genetic terms to to perform fault-tolerant quantum computation but but there are some characteristics of this scheme and the first one is that the threshold all of which is defined as a matter procurement budget is the same as that for all of their articles scheme the command because we simply care for the same set of operations the same number of qubits so they're part of the threshold will be the same if we follow a particular and fault however since the other but the gates a small this is that the the relative from the weight of different errors of law is going to change my presence if if we compare the dynamical on implementation of a gate and it's a whole like implementation to get of 10 to the minus 4 something typical for threshold but we would need full money gates which are up from 10 to 100 times smaller than the dynamical gates this depends on how smooth interpolation it's this means that you're slowing down the evolution significantly so all and during this time there are errors from the interaction with the environment so this means that if this metal the some how useful it must to provide such a procedure in the much in the must Hillview in the procedure in the control procedure so much more than you you lose by slowing down the evolution exposing your information on to possible errors from their environments says that you would remain within the threshold in another future of this of this approach is that it requires at least at least 3 local kernel bonds but this law bound is actually achievable with weeknights nice called such oracle and so unnatural question is is it possible to new universal fault tolerant of caloric computation and grants to local times for instance using the perturbative the techniques to reduce the look out in the upon that for this particular scheme as I just described that I think that this is not possible simply because it relies heavily on the fire the Hamiltonians are elements of the gage group and not when you know our simulates perturbative gadgets when significant only in the integers extra energy levels and so which splits and this is no longer want to preserve this feature now this brings to estimate and
directs metal that I want to describe which actually allows combining with which allows using the gadgets while preserving fault tolerance and this is the concept a much simpler method basically the idea is that in the previous approach we use local wanna computation in the logical subsystem generators to on accommodation in the form system of that describes the original called to do this we need to introduce some external system and desired gage to so we want to essentially and Logitech value with a relevant to or from transversal gates like this simply want through all our make some interaction which leaves the desired on the results due later transformation there and I found this this game here is the future of the the putative assemble never interrupted by construction and so on now we have to use additional curious which lowers the threshold because 1st of implemented to could get to meet the cube but this is are relatively small small drawback that's 1 nice feature is that as I explained to donate to initialize the the gage Committee that's the end of an the donors are independent of the call on the previous always to get to keep track of the stabilizer and an and so the gage group elements as they evolve and again this 1 requires through local interactions but it allows us to to do the work product so how much OK so
I'm this in the way 1 can do is using this so-called perturbative gadgets which were developed by the people in a different context but a very useful and widely applicable tool I'm want to explain how they work in general but rather I'll give an example and here I I will consider the time-dependent Hamiltonian which appears in our construction which of them looks something like that you're operating between a study component which out some of the attributes 1 2 and 3 so because this form that's interior could 2 and 3 and then you're on to turn this off this is described by this function F of T and so you're wrong to I don't know my another interaction which in most of all the all the picture that's the way you do do that for each of these terms you get to the institute which you can consider the local of the 1st ones to log on for each of the stars we introduce the the gadget curious as 1 as a set of 3 for the first one press 2 for the 2nd time and that prepared in that gets states each of them and so what mean is that we turn we use move upon and of the following fact it consists of some of our on silicon upon his undergraduate consumers the ends of automation this population is going to screen bag the this this this component and create effectively leader hamiltonian that would like to extend but selectable has this form it is this this of but in the case of 2 local and here's z z form on the neighboring couldn't so here I can describe a single line that to the pairwise interactions that of that appear in this construction on we labeled on silica bits with this is by S and I ask all response we this as here which corresponds to the to the to insulating whereas I corresponds to the cure it 1 2 or 3 and the that of perturbations you would use in this case if you have a form of this type if it consists of pairwise interactions here described that airlines with ex act se lows for each of these terms and the corresponding advanced the Y or Z acting on the on the on the system on the system convict and similarly for the 2 and there might be I'm not sure about the square root hearing it might be but it's in the 3rd World but the idea is that by doing so you effectively up then the full come upon and the grass you obtain the original and that you like to simulate multiplied by a factor of the land to the 3rd letter that is the perturbations are out in this here and the error the 2 obtained by doing so this lander to the 4th you can see that since this Gonzalo's evolved that Apple Daily other qubits they're all any error that appears on any of the mind this is not long to propagate however you can also see that this
is highly inefficient of all just put the implemented to can get we have to introduce we should use 9 students OK this means that the thresholds is going to be there but 2 times smaller that's not such a big deal that the biggest problem is actually that's and this perturbative approaches to reduce the gap of her from the donor and my significant amount which will require very very of a significant slowdown of version so let's say that you would like to on but the chief of precision nor ever delta so precision one-liners dealt with the original kernel sensible copulations show that in order for it the nor approaching this the precision which the perturbative gadgets you will need to increase the of evolution by this factor of the order of the Légion Altanta to the power divided by the delta to the part is that something like 10 to the minus 4 this is a huge shoots fall down so this is a rather should be regarded as a proof of principle that it is possible with to local upon us little fault-tolerant on the computation however does not seem very very useful so I'll might also comment on a few other schemes and related of very interesting paper by Baker and funnier and we proposed a metal of doing follow me computation by a sequence of operations again driving a subsystem a logical subsystem by different from O'Donnell's very similar to our but what is unique will while the scheme isn't it that use again just by a single interoperation between 2 Hamiltonians now they get the trick is that you actually need your subsystem on another physical system and you keep on doing this by moving your system for a Digital computation this scheme also can be understood as some form of colonic computation but it is an open it's a mobile phone call long which is the basis for the construction and in open colonic can be defined so when you hear about the final space the loss of the initial on so there is a natural fixing of the final frame which comes from the requirement it it is small spiral to the initial France this approach is also compatible with fault-tolerant picnics and working gardens and plan these guys so for the proposed in our scheme inspired by addition while a quantum computing which is why I like computing with without measurements again how particle a driving the subsistence as it implements sort those formations in science another paper that has appeared recently is to local component but we now gadgets so if dreadful monarch the computational ground states of spin chains predicament of logical order which are actually usest local kernel with our gadgets and although I don't know of this scheme being fault tolerance and I would also like to mention another approach which is based on a qualification by the station but in the table with jungle similar work the developed a purified about big particle governments which allows it to move subsystem around and implement on this in it of abuse so compatible with fault-tolerant approach to answer it also is associated with a new type of geometric face generalizes the 2 of them were jigs Equilon me or wants 1 main form public space or any other colonial the states is in fact and so just to conclude we have seen the of that exist the an approach to former computation which is done subsystems which show positive devices schemes that combine the period you might account kind of article approach weeks before the constructions on error-correcting codes which shows that like quantum competition is in principle scalable and it could also it somehow the software protection provided by the quantum error correction we have seen that too could from opponents are universal for fault-tolerant of fission but the gadgets are very efficient so here up a few open problems is it possible to find the what and fault-tolerant realization with the predicament announced what physical the systems will be in a favorable for implementing some of these years and finally get some of these it is useful for finding a fault-tolerant additional thought about a quantum computer and with this I will stop thinking for attention at the under any questions for me this 1st it's an apology and a question apologies because of is the the plate and the question is there if you could expand believed to be more on their last and the dissipate idea but take on scheme if possible in particular I like to know and what can you say about the locality property of the DC Pieterse that would be required in such a scheme and how should I think of these in connection with their yeah hours scheme called the I like to track and frustrated they had the CPT and scheme for the encoded quantum computation yeah so basically the idea of this is that of mean go back to the in the area of this so not the very notion of about might on and I mean that we have introduced in this paper is concerned with quasistatic evolution of the stationary states which in all are organized in analysis subsystem and both up to which is a fixed point show all video this whole monarch in terms of dissipation is simply if it is possible to somehow are engineer on anybody which will drive the subsystem around to to move it in a way that you will depend on to Polonius lasted they get around the loop and I should say that also allows more general armed possibilities than the standard the the standard of like approach based on components because it allows you to move the subsystem along paths that sometimes are not possible to achieve with kernel and also depending on the fixed and the noises subsystem under the state it is in it are you been difference of gage potential that describes a transformation in the more far so here I have flow where we can get on with the currently developing this some idea in that paper with jungle similar we have shoe we have given some artificial example just for the sake of proved that code is possible to achieve on universal computation of for this you would need 1 gage couldn't on which for for that particular example we imagine that to start with that in blood which which acts as the and as the depolarizing channel on that Cupid yes and then changes from bottom and basically you're painted by Senator on to come back so as a rule of various multiple transformations and in this respect I would say that at this the light industry local to achieve to local and how this relates to the power of the shelter and can of on I think it is actually quite different in the sense that their approaches some the closer it applied about a quantum computing and the clock a note on it are they basically the solution there is up then you to simulate the circuits that you'd you designer you design the Ryan which is which attracts into a solution of the problem and how ways and here and there is no solution to a problem we're implementing gates similarly in the spirit of standard the whole monarch approach so if you're worried about the noise that splits the generously since the euro on on these sort of gage operators could use to stabilize of the cold enough to suppress correlated noise as the together about 4 so when you're doing the holonomy right yes you would devote said splits just process so if you assume the noise is correlated I use the stabilizer result the cold like the big ensure called as duty pulses to suppress the bidders is playing on this I haven't thought well that's was interesting in those years at he showed where you were were able to produce any target you on subsystem pay and a science of systems the is there any condition on the relation between sizes the subsystems actually guess of system must deal with the national larger than 1 for the solidity of Montego but they actually qubits is sufficient the is other gets to it can be sufficient for any system the tool in which a contain the logical that is they begin again and and few it but
Resultante
Stabilitätstheorie <Logik>
Quantencomputer
Versionsverwaltung
Quantencomputer
Systemaufruf
Nummerung
Computerunterstütztes Verfahren
Element <Mathematik>
Nummerung
Term
Fehlertoleranz
Font
Informationsmodellierung
Einheit <Mathematik>
Font
Codierung
Maßerweiterung
Phasenumwandlung
Vektorpotenzial
Einfügungsdämpfung
Quantencomputer
Freeware
Extrempunkt
Hamilton-Operator
Raum-Zeit
Richtung
Fehlertoleranz
Polygonzug
Gruppe <Mathematik>
Analytische Fortsetzung
Auswahlaxiom
Addition
Befehl <Informatik>
Sichtenkonzept
Pay-TV
Winkel
Kontextbezogenes System
Natürliche Sprache
Software
Dienst <Informatik>
Forcing
Benutzerschnittstellenverwaltungssystem
Heegaard-Zerlegung
Computerunterstützte Übersetzung
Ablaufverfolgung
Ordnung <Mathematik>
Programmierumgebung
Instantiierung
Fehlermeldung
Folge <Mathematik>
Kontrollstruktur
Klasse <Mathematik>
Fluss <Mathematik>
Freiheitsgrad
Loop
Bildschirmmaske
Geometrie
Datenstruktur
Topologische Mannigfaltigkeit
Varianz
Konvexe Hülle
Orthogonale Funktionen
Schlussregel
Unendlichkeit
Offene Menge
Gamecontroller
Wort <Informatik>
Resultante
Punkt
Natürliche Zahl
Berry-Phase
Adressraum
Gruppenkeim
Versionsverwaltung
Tangentialraum
Computerunterstütztes Verfahren
Ähnlichkeitsgeometrie
Arithmetischer Ausdruck
Einheit <Mathematik>
Skalierbarkeit
Eigenwert
Stützpunkt <Mathematik>
Kurvenanpassung
Beamer
Parallele Schnittstelle
Parametersystem
Exponent
Physikalischer Effekt
Quantencomputer
Klassische Physik
Systemaufruf
Ideal <Mathematik>
Teilbarkeit
Unterraum
Arithmetisches Mittel
Helmholtz-Zerlegung
Datenfeld
Verknüpfungsglied
Verschlingung
Ganze Zahl
Evolute
Phasenumwandlung
Information
Aggregatzustand
Standardabweichung
Total <Mathematik>
Rahmenproblem
Hausdorff-Dimension
Physikalismus
Interaktives Fernsehen
Transformation <Mathematik>
Punktspektrum
Kugel
Symmetrie
Inverser Limes
Luenberger-Beobachter
Zusammenhängender Graph
Einfach zusammenhängender Raum
Fehlererkennungscode
Mathematik
Diskretes System
Thumbnail
Vektorraum
Physikalisches System
Quick-Sort
Schlussregel
Roboter
Energiedichte
Flächeninhalt
Surjektivität
Mereologie
Basisvektor
Resultante
Quantencomputer
Mathematik
Computerunterstütztes Verfahren
Extrempunkt
Hamilton-Operator
Raum-Zeit
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Metadaten

Formale Metadaten

Titel Fault-tolerant quantum computation via adiabatic holonomies
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Oreshkov, Ognyan
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 10.5446/35305
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract I will describe various methods for realizing fault-tolerant quantum computation in terms of adiabatic geometric transformations.

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