Correcting noise in optical fibers via dynamic decoupling
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Noise (electronics)Self-organizationTransportation theory (mathematics)CodeLevel (video gaming)FehlererkennungLogic gateForm (programming)Computer simulationMoment (mathematics)QuantumResultantAreaServer (computing)Operator (mathematics)Linear subspaceError messageCommunications protocolObservational studyStudent's t-testThresholding (image processing)Dynamical systemType theorySurfaceLecture/Conference
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Execution unitAddressing mode1 (number)Analytic setPolarization (waves)Integrated development environmentCartesian coordinate systemStatisticsRotationDynamical systemMathematicsOrder (biology)Noise (electronics)Phase transitionIntegrated development environmentState of matterWage labourSphereTheoryResultantDivisorBasis <Mathematik>CASE <Informatik>Error messageAsynchronous Transfer ModeNumbering schemeDistribution (mathematics)Parallel portStandard ModelCartesian coordinate systemDirection (geometry)MetreQuantum computerQuantum cryptographyEndliche ModelltheorieFiber (mathematics)10 (number)Block (periodic table)RotationDigital photographyRight angleDiagramOpticsRing (mathematics)QuantumRoundness (object)Sound effectComputer animation
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SphereBloch waveAerodynamicsSequencePulse (signal processing)Phase transitionError messageHill differential equationDiagramDynamical systemSequenceGraph (mathematics)InformationNoise (electronics)Statistical hypothesis testingFloppy diskDialectFlow separationConstraint (mathematics)Mathematical optimizationState of matterArithmetic meanBeta functionForm (programming)Computer simulationSphereMereologyResultantNumberMixture modelData modelAreaLogical constantDistanceParameter (computer programming)Error messageMetropolitan area networkPulse (signal processing)Point (geometry)WaveSet (mathematics)Cartesian coordinate systemGraph (mathematics)MetreAlpha (investment)Endliche ModelltheorieFiber (mathematics)Key (cryptography)MedianBlock (periodic table)Element (mathematics)Particle systemLengthMultiplication signStandard deviationBounded variationRight anglePosition operatorMathematicsElectric generatorMultilaterationRoundness (object)Different (Kate Ryan album)Computer animation
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Dynamical systemQuantumError messageWaveEndliche ModelltheorieFiber (mathematics)LengthTelecommunicationSuite (music)Computer animation
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AerodynamicsOpticsSequenceNoise (electronics)Sheaf (mathematics)Matter waveResultantError messageSocial classGradientMetreFiber (mathematics)Standard deviationFlow separationArithmetic meanWaveComputer animation
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Menu (computing)AerodynamicsBloch waveNoise (electronics)Sheaf (mathematics)Standard deviation1 (number)Graph (mathematics)Computer animation
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Total S.A.Fiber (mathematics)Arithmetic meanNoise (electronics)Thermal fluctuationsFiber (mathematics)LengthComputer animation
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Error messageAerodynamicsOpticsComputer-aided designPhase transitionNoise (electronics)Thermal fluctuationsLengthFiber (mathematics)FeedbackPhase transitionPhysical systemDependent and independent variablesControl flowWaveDirection (geometry)Module (mathematics)Dynamical systemArithmetic meanPolarization (waves)WhiteboardContext awarenessService (economics)Computer animation
Transcript: English(auto-generated)
00:00
All right, so our last talk for this session is Correcting Noise in Optical Fibers via Dynamical Decoupling, given by Katherine Brown. Okay, thank you very much for the conference organizers for letting me give a talk. As you can tell from my accent, I've come from Louisiana, and I've got – I'm going to give a talk then along with our PhD students, Bosca and Manish, our former
00:24
postdoc, Peter, who's now at Stony Brook in New York, Cody, and our two professors, Huang Li and Jonathan Dowling. And I'm going to be talking about correcting for depolarization of a photon in an optical
00:41
fiber. We've – our work is simulations rather than analytical. So I'll begin with an introduction. I'll then introduce dynamical decoupling again. I know you've had several introductions this week, but one more can't hurt. I'll then introduce the CPMG, the one we're using, and finally show our results, and
01:03
then some conclusions. So dynamical decoupling is a type of open-loop quantum error correction. It's not going to replace the closed-loop error correction protocols that we've been discussing a lot today, such as surface codes, but the hope is to introduce it before
01:24
we perform these operations to get the errors down to a suitable level for threshold, because at the moment most of the errors sent in transportation and moving gates are far too high for threshold level, and we can't even begin thinking about performing the quantum error correcting codes.
01:40
There are several forms of this open-loop quantum error correction. Dynamical decoupling is one example, and the other one, which I think you'll hear about, is Dicke-Heron's free subspaces. So there's been quite a lot of previous work done on using dynamical decoupling to correct for errors, O-TOMs.
02:01
Wu and Lydar did some key work on proving that you could use dynamical decoupling to correct for dephasing in optical fibres. That was some analytical work driving worst-case scenarios using a regularly pulsed scheme. Other work has looked at correcting for mode dispersion in optical fibres, and interestingly,
02:26
experimentally, there's been work done looking at photons in ring cavities. So it's a different scenario to the optical fibres, but that's actually demonstrated the effects of, or the effectiveness of, dynamical decoupling for photons.
02:41
So we're going to consider sending a photon through an optical fibre. There's two particular reasons you might want to do this. One would be for distributed quantum computing, and in that case, you're wanting to send a general state in the HV basis. The other reason may be for quantum cryptography, and that's slightly simpler, but going to send your zero, one, and your plus-minus state, so you don't necessarily have to
03:03
correct for all states. And we're going to model our noise as being changes in the birefringence of the fibre caused by changes in the environment of the fibre, and these changes are going to happen on the orders of tens of metres, and because we're using a polarisation-maintaining fibre,
03:21
we're only going to be correcting for depolarisation in, defacing in one direction, and that's going to be our z-direction, so that's the standard model of noise that's been being used throughout most of these dynamic decoupling talks, although it's slightly simpler than the more general model. So our defacing can be seen as being a rotation round the z-axis of the block sphere, and
03:44
as a result of this, we can see that the zero and the one state only acquire a global phase factor, and therefore don't need any correction at all, they're perfect, but any other state will gain an error, which can be considered a rotation round the block sphere.
04:05
The simplest example of dynamic decoupling, again, as you've all heard this week, is the spin echo, so we're going to introduce a slightly different diagram from the runners, which also gives an idea, intuitively, of why this works. So in diagram A, we're considering letting our state evolve under the defacing, and
04:25
it evolves round the z-axis of our block sphere for a set amount of time, d. In diagram B, we then perform a pi-pulse, this flips the qubit, as can be seen here, as it moves from this state to this state.
04:40
In C, we allow it to continue rotating round the block sphere, so defacing, for the same amount of time as in diagram A, and this begins, this continues to incorporate defacing, but now our defacing is moving our state back to its initial position, so it's beginning to actually correct our error. Finally, the last pi-pulse brings us back to our initial state.
05:05
So, different forms of dynamical decoupling are useful for different purposes, so we've all heard about the URIG dynamical decoupling being the optimal pulse separation, but that worked, and we did some initial simulations on that, and we didn't get very positive
05:21
results, and the reason for that is because it works better when the noise has a sharp high-frequency cutoff, which we don't have in our noise model, so instead we moved on and looked at a CPMG sequence, car, my boom, car per cell, my boom, and gill. Instead of using regularly spaced pulses, we used a sequence where we're placing
05:44
them along an optical fiber, so we're now going to go into distance instead of time. Our first pi-pulse is placed distance L into the fiber, the second pi-pulse is a distance 2L, the third one a distance L, fourth one another distance L, and then 2L again, and repetitions of this sequence throughout the fiber.
06:06
One advantage of this sequence is it's supposed to be resistant to errors in the wave plate if we send through a plus or minus state, and the reference for that is paper by Morton. We haven't incorporated errors into our wave plates yet, that's something
06:23
we hope to do in later work, and Dieter Suter gave us quite a good idea how to do that yesterday, so we're hoping to incorporate that in the next few months. We, so we modeled our fiber here as regions of constant birefringence given by
06:41
delta N, and delta N is a constant here, not the change in birefringence, for constant noise regions delta L, and these delta L here, these one, two, three, four, five, we have more than five in our total model, are actually different lengths, so the idea is that it's, we have, we set the mean of this distance
07:02
and the standard deviation, so the idea is you've got your fiber and the length of each region of constant birefringence is fluctuating, and you don't actually know how long it is. So this is trying to get a more physical model, and the birefringence here we set with some parameters, we set it as zero mean, and we set the standard deviations,
07:22
as you'll see in our graph. So a region of, after us traveling a set region, we get accumulate this noise given here, and that's for one region, and then we run our simulations by sending a photon through several regions, generating this delta L and this delta N parameter at random,
07:44
given our constraints each time, and we ran this for several hundred simulations, and then plotted the graphs that we'll see. One key thing about our graphs is we plotted the fidelity of the plus state, and we justify this by saying it's the worst fidelity possible,
08:04
given that we have no errors on our wave plate, and the reason can be seen for that is if we consider sending a single photon through our fiber with a collective dephasing of theta, which is the collective dephasing of all the noise regions, then we get the final state, we'll take this form here.
08:23
When we have alpha equals beta, so when we have our plus state, then you just get cos squared theta, so this is the worst possible scenario, and in the best possible scenario where we have alpha is one or beta is one, so our zero and one states, we get perfect fidelity every single time,
08:42
and we're going to move on to our results now. So this is our first result, is how the number of wave plates affects our resultant fidelity. As we can see, as we increase the number of wave plates unsurprisingly, the fidelity is, of course, if we take into account errors within the wave plates,
09:00
then we'd actually expect this to level off and possibly go down further at the top. Here we've got a fiber of length 10 kilometers, and a main noise region of 10 meters. The standard deviation in our noise region to the variation in the noise region is 3 meters, and we can see, you can't probably read off the point, but to achieve 98% fidelity, we need 610 wave plates,
09:26
which would involve placing them roughly 8.2 meters apart. So that's a realistic distance apart to begin placing our wave plates, it's something we could actually consider doing. We'd be using passive wave plates, we've modeled it so far as X pulses,
09:41
but obviously there are advantages to using a mixture of X pulses and Y pulses, as we found out yesterday. And here we hold, that we take 500 wave plates on a fiber length of 2 meters, and we can see how much defacing we can correct for. So we see we've got this region here, where we can correct up to 98%.
10:07
So we begin thinking about using this region for quantum communication, we'd probably need to get some further improvements. And we've got this region here, where we've got above 89%, which should be suitable for BB84. So hopefully for a reasonable error model in our fiber,
10:22
we should be able to use wave plates and dynamical decoupling to correct for defacing. And it's a brief talk, I'm afraid. So what we showed in our results is that we can use a CPMG sequence, a dynamical decoupling, to correct for defacing in optical fibers. When we've got a mean noise region of 10 meters,
10:43
standard deviation in this of 3 meters, and a standard deviation in our birefringence of 100 radians for 10 kilometer fiber, 610 wave plates are required to achieve a fidelity of 98%, and we're going to go on. What happens if we introduce errors into these wave plates? Thank you very much.
11:00
Any questions? Thank you, that was crystal clear. And are there any questions? Just a clarification on the technology side,
11:20
what do you mean when you say you put a wave plate in a fiber? So that's something we've got, or we've put several proposals in our paper on how to do that, but it's not going to necessarily be easy. I think there's some suggestions of using twists and other techniques, but I'd have to get back to you on the details.
11:44
Could you give us some further details on how you model the noise on the fiber? So, what happens is in each section of noise, in each section of noise we generate a value for delta N
12:03
with the standard deviations given by the ones on our graph, with a mean of zero, and we have that delta N lasting for a length L.
12:20
So the noise is basically a fluctuation in the length of the fiber? The noise is caused by fluctuations in the birefringence along the length of the fiber.
12:43
Coming back to the technology side, you talked about only using passive wave plates, but there could be electro-optic modulators instead of phase plates, and it would be a system very amenable towards, what, dynamic feedback to work out the optimal dynamical decoupling based on the phase response
13:01
of a polarized light going through that fiber. I'm wondering if this has a future direction in this. I think it's a good idea. It's not something we've had a chance to look at yet, but I think it's something we want to move on to look at because we've certainly seen other papers on that work. Okay. Any more questions?
13:23
All right. If not, then thanks again. We have a 20-minute coffee break.