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Dynamical decoupling noise spectroscopy

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the foreigners nurses because of and all the people that we see more in the the up sequence by using and is the earliest mention them a like so the when the the modulation more common for all of us what we want to bring to the list to try to reduce the level of noise we want to write in here you know and to be able to apply quantum error correction coils so embrace indignities and we still need to fight the egg is equal he had to die but the the the level of noise required for quantum error-correction 1 of the ways to do that is by using the coupling me and died to the cup and the environment from the the 1 promising beneath these being undergo the coupling of 1 of the properties of because the coupling that we need access only to this system so we need only to manipulate it sees them to that victory reviews interaction with that with them by in order to find the optimal anemic sequences is very important to know what is the vitamin D. does and is our motivation what we wanted to do was to try to to to make sure the characteristic of our my so when in I will briefly
because it was really refresh still they what is the use of you know that got in for example the pioneer here sequin that can be identified as having democratic up sequence was the echo experiment and if we have a 1 we cover as being and this is the thing that an environment we look at this 1 by the probability of our initial estate as as a function of time when the the cis interacting with an environment we see that this thing is that we can we time but if we apply bypass that that the but the negation of this being what with incentives to change this system about their actions the sign of the memory that we we we will see an equal so is what with all these 2 guys in the fiefdom environment there and what what it keeps is the mean medical of the environment the environment it's difficult we we bear effect but it's the environment have something I mean the people will not we will not be bathed again and the of people with decay so essentially in the picture of the writer but is that is that the all the
right if we know that light at the same time so the idea now was likely to die to be me any of these equal with the get their mind by the expected properties of Biderman and this is what they want to try to measure so where he
for example you can a for motion of policies then called the survivor brewery he gave as a function of time and we have applied I have a kind of sequence and we may show the object of the whole we get the black is square some we can see that we can improve the cookies so in in order to cut it I
say what it mean in the environment it's assumed that we come up you're the face interactions so the only thing is this able operator and it's assumed that when some kind of semiclassical picture is where the effects of the environment on the on this being of some kind of random I he even babies form the font so this is some kind of function that depend on time and we can that the saved through these through plating feel the prose is right environment by correlation function and produce hundreds of the correlation function we can get this because this city of our environment that we give the the promotes that I would by them so they now and we live
on Futuna we haven't had a few but of 2 passes and lives of on the the the sign of the system Biderman enacted at the beginning the sign would be both cities so this said would be equal to 1 but when we apply a past what we which the chief effect effectively the sign of this by the way the action of this 1 and we have like this income ETA assigned to the 1 it was shown is some years ago by like Goffman putting the that we can work out what we did is something of the different in these graphs and also I could be equal was talking about that yesterday you made it so that if we look now now and it's a lack of libido following the and they want to add that the gate with a and exporting test functions VN woman of that exponent function is given by the overlap of these make that this city of Biderman times before had time for all and function of this eastern Biderman deduction so that is what is called the field the function of our chemical makeup sequence and in this field there is very little that will read really that we feed the sum frequency more of our environment of that that you know that was discussed yesterday there was a man I can be so in in in we use the southern that we can enhance the codon we can optimize the and because sequence the the the the the the we know they think the density we can find what is a suite of to the function of the bride to reduce the spectral density the so I'm not warrior local to optimize that was that was tied to always like to be a we think that this is the function for that it's be expression so the 2nd continuous indeed and they who I want to go to the scene version ECE said difficult task so what we do is to use some kind of it's so
just to give you an example that confuse the evening line is the spectral density function we found kind of culture and a speculative people I I would assume that they are blind to bonds is seeking sequence and building heating up black line which is Diffie the function of thing in the so you can see the without some kind of elation of me because I believe your love the that line and the green line we we get the decay of our signer after 1 site but this is a cycle of of 2 baths at what happened now we repeat that cited bit you can in the final thing if we repeat that us and API as cited in of in a number of time we will get copied here function so if we had planned for of the sign of this is the member invention we give function so the downfall of the before it comes with the to the 4 you see it so for example here and looking the field of function after 40 cycles and we morally the reading that before you die of recent years you knew that the the red line he thought it was is that is they have seen functions that same data that their mornings over the the sequence so he's really to Wikipedia of living in the trees so you can see that the things that you know you function except some money to only for these good values of the aid of a frequency that they are really with at 1 frequency of the universe becomes sequence so instead of having the continuous expression the data the sort women without the song of prospective in cities for this good values of on excel in terms of another important property of the inflation when we are in the ravine that if the functions of some of the the functions what happens now Now the decay of the survivor brought with the and exponents said so we can all that we are reading that we see when we start to see that this available everything that the exponential so now where they can do is to chose the feminine and up sequences of what they can use to change the relating by in such a way that they for all the even in the face and the state budgets of frequencies and I had to choose If I choose say meaning a with 4 people in the name of the Captain sequence and can be some kind of in a system of equations so the idea I'm blocking different fit the function for different and government sequences exactly so all of them cut different differentiating like this and with in doing that with all the elements comments were dated between different anemic and got so the then current I mean come on if I a lot I can be this expression I can write like adding a system of equation work can block the rate that they get for the phenomenon that the Governing sequence he you this because this is the function and I can be demanded that is related the the 2 of the field the function of the of the morning of the of Of course it is assumed that having find that members so we need to make some kind of some of our solution to try to to make the final abuse and respected is functional with the K with the frequency of phenomena can be delayed the completion of the day or even if I know if I can get and minorities that they can use that that solution the type to to in this expression I so this axiom about the meaning that we neglect the contribution of the day when we can link that we can make a fine at linear system of equation so that we can do about that and we don't find the is that this is a function from each of the rate for the Framingham you can do that in the so these the ideas in the middle there and this is how we can go months a spectroscopy using dynamic of the cup so now I I will give you some examples that we
perform in in in in my so in the in the here I show you this by the probability of of phi he said it's the as a function of the number of cited of CpG sequences in different quarters at different delay between balances so the bending of the leading up to that indicator rates you can see here in Sandel a lot so you can see here that we have already seen exponential decay so we are going to reading what the model that I showed you and even the nature of the game for the food and the lady in Basque I look here the relaxation time of the decoherence time as a function of course the place of the forensic in the sequences and against the way the mean of the squares in Louis and you can see it with that reduce the ports the point in the course the day the fantasy that cooking by accepting I suspect this region that this is because of the fighting is of of the real answer that we can expand so it's forget about the spot because the society this because of the we'll have ideas on the within of by the way I see it but these regions the we policies of the past a moralist the idea so now we use relaxations I can be the linear system of equations and then I can that it and
it can be a difficult density function so this is the that word here in the in the so here we have the density of the culture the frequency in investigating now I think we can think of this because the function have always loaded is it in fact the factor of the poorest cities almost 4 how we can see that the man of the people all that we have in the thing of frequency is sort of the same that we have in the relaxation time as a function of the was the late so I'm really from here for a polar or for a polar low in inspector function we can give you the date of the of of the relaxation time but I want to show you novel something more there in the examples and what we do is now totally totally fighters because
they follow him by the Soviet Union and he had the relaxation time as a function of the relating by this this is the penis got that they show fall and then what we know is to apply at an outline frequency feed to our environment so what we we're vitamins as being but Unwin we applied that field to the environment what we've always believed in Princess without even frequency they have a meeting with them not there in the laser so essentially what let is to book of and frequency now aspect of this function and is the the dominant frequency that it's been a precise so the different colors on relaxation times that the function of the fate of other US evolution of the maize if invited for the fair will leaking frequencies of on our life so you can't see now that the relaxation time T shot Arctic according to the model eating frequency the going away but I think 1 of its the black line here you can see that for these need devices in the book and I was very short so what is happening here is that it was indeed what we're looking at in this eastern on recent with the environment so instead of that environment but we are doing is to optimize the exchange with so the the condition that a blending and captain with this condition will not be a useful tool so it's very important that we show you very important to know this because this city of our environment to I we describe it so now we have all these relaxation time we can be the historic equation we can embark a we can
get the spectral density function for the which so different colors of indifference picked this function and you can see that in covering bombing of the and on the frequency of of of of of the spin of the environment as the they but something that I want to show you here and there you see there some solid seen worse and in the scene so that focus on the black line you get to hear that they can be seen without some kind of in the sea moss at doing gas solution as they should do for the day you the field that function couple intuition for different harmonics of anemic the what the in the scene was and consider that the main of how our freedom function even though he gave me but it's still here is that holding for the formation of all their money coming in if we don't go and see that the condition for the 2nd 1 sitting here that we have some kind of maximum using these matching the scenario that doesn't belong to the realistic in the course we have the information that is here is not because of the main morning because of the secondary harmonics so if we get the contribution of the 2nd but getting information of our respective is there is not free but if the policy that they don't mention we unit and the foundation for what I want to cite the recent progress that these Andresen what's that they were also would expressing the antibody we're within the last war was the 1 that was given by the induced so with all
of these say I show you how we can use and that the captain famosa spectroscopy and sing during the the when the 1 s the
there's so we saved the the the time is the winery uncle time scale for the same thing and was their reporting perfection being in the experiment that they show you we use SET in the sequence for the the the so the short thing he stole that sea BMG sequences for putting perfection is the state is logically notably bounces so if we know that we can remove the puts perfection and and essentially we never did something relational and we can see that the behavior of the Grigori he saw more compatible with the idea parts the actual they're dangerous because there's this concert show I Gray talk thank you and I had a question that's a little out of sync with most of what we talked about in this conference and you go back to the early in your talk you showed characters ation and the natural spectral density of your of your system I think it had 1 overall negative 3 point 6 or something and don't that's very similar to what we saw using a superconducting magnets for penning topics permeable over the force and curious I was curious if you know where this comes from this it's this flux diffusion and the magnetars I mean if you think I know that the this is not this being the fusion because it has been in covered through I don't remember now exaggerating is there he is there a polar exact square border of I with know exactly what is that you have some feedback from it what fairly among different form the remember but there are some some people that the cover some purely become more this the fate of the people they could be described explaination times have all along about but that I don't know exactly where he's coming up with of 1 last question before lunch in the last case that you have earned shown all that deep and environment basically to show that if you don't know the location of the you know the spectral density the coupling can be harmful I did try that to me seems a very nice of setting foot find out those randomize the coupling schemes because the backing 2005 with many and also we made for me was the best scientist I was arguing that 1 instance we're randomized gene can the beneficiaries that your taking you out the vastness in the presence of uncertainty in our theories and so on and which you could see the head for you mean the is the but you been on I would have to be very effective and useful not work on on on out there that is there for months over a randomized to copy you minimize the thinking I knew that I had not applied in you know the automotive is high for the new exactly you think of of OK let's thank the speaker and all the speakers of the session at the
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Metadaten

Formale Metadaten

Titel Dynamical decoupling noise spectroscopy
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Alvarez, Gonzalo Augustin
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 10.5446/35301
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we generate effective filter functions that probe the environmental spectral density. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.

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