WEBVTT

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330W: you I don't know.

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330W: Pleasure to have Jay Sau with us today. Jay was telling us about his PhD today at lunch with Marvin Cohen at UC Berkeley. And then he went on to a postdoc at University of Maryland with Shankar DeSarma.

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330W: Where he and Roman Luchin proposed a novel way to produce Majorana zero modes on the edges of nanowires, which subsequently led to a lot of

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330W: A lot of experimental effort and theory effort. And he also spent one more postdoc at Harvard before moving back to Maryland as faculty.

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330W: And he's also now the director of JQI and other responsibilities as well. I'm happy to hear what you're working on today. Towards topological qubits and semiconductor nanowires, challenges and updates. Thanks for coming, okay. Hey, yeah.

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330W: Thanks, okay, yeah. I assume people can hear me, but, so, thanks for, the invitation, Jed. It's, great to, visit Rutgers.

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330W: So yeah, I will.

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330W: There are about… I mean, as any theorist, there are a bunch of things I'm working on, but this is, still, like, from my postdoc, one of my favorite topics. I should say it's, from a pure theory standpoint, maybe it's a little bit.

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330W: a little bit, I don't know, scale is the word that's coming to my head right now, but there aren't… the theory questions are maybe, not necessarily as fundamental, but the possibility that this is one of the ways to realize this idea, still one of the most.

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330W: near-term ways to realize topological qubits, still keeps me following the experiments kind of closely, so I'll kind of tell you about some theory and experiments, sort of, together.

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330W: experimental progress. So, again, I just… just for, I guess, more amuse… education and amusement for… and for some of you, I mean, the…

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330W: The… not… the motivation, which is not very…

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330W: Okay, I'll explain the connection to our Majoranas in a while, but… in a little bit, but the idea of Majoran fermions really came from high energy physics originally.

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330W: And the puzzle started with Dirac trying to write down a relativistic covariant equation for to describe an electron.

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330W: And, the amazing con… the amazing prediction, I think one of the most fascinating predictions to come out of theoretical physics, was that, there was… he had to predict positrons, or conclude that there must be positrons in the… just from consistency, trying to get that to work, and

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330W: Turned out positrons actually existed. Itori Majorana was sort of a quirky genius at that point, according to Fermi, who was

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330W: who was really trying to find a way around Dirac's argument, and he concluded that it was also possible to have a variant of Dirac's equation where the particle, the fermion, was its own antifermion. So, in the sense that the solution would be, like, self-conjugate.

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330W: So, and, so, and he, he wrote down this Majorana equation.

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330W: For a little while, people thought that neutrons would be a candidate. That disappeared relatively quickly, but then neutrinos remain a candidate, and people don't know for sure if neutrinos are these, are Majoranas, but that's not the question that we are directly interested in. This is more for, like, a historical.

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330W: perspective. So, we'll be interested in Majorana fermions, or actually, I should put fermions in quotes here, which are emergent in a solid state sense. So, what that… we actually… they're not really going to be fermions, because they don't obey the fermion commutation relations. So they'd be called Majorana zero modes.

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330W: They still are, actually. If you take Majorana self-conjugacy relation and demand that the objects be spinless, which in 1 plus 1 dimension, this is allowed for the fermions to be spinless.

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330W: And, and localized, they turn out to be topological, and that's really the object that we will talk about. So.

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330W: to now come into what I'd say more conventional condensed matter language.

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330W: we don't have particles and antiparticles. For us, antiparticles are really holes, so, right, so if the electron is described by a creation operator C dagger, that's the particle, and then C is, that's… that's the hole. Whether or not that's a positron, that's a…

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330W: separate question. So, by that analogy, a self-conjugate fermionic operator is just an operator which is a Hermitian fermion, otherwise anti-commuting operator. That's what we will be calling a Majorana zero mode, and that's really what we're after.

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330W: And if you think in terms of, like, number operators of some kind, you realize, just by comparing with the particle hole case.

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330W: Well, one operator was… the creation operator was supposed to increase number, and the annihilation operator was supposed to decrease number, so now this gamma sort of toggles between left and right, so that's kind of weird.

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330W: And it'll turn out… so, okay, so then how do we make sense of this? And the easiest way to make sense of it is to think of the Majoranas as the real and imaginary parts of a usual fermion operator.

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330W: Right? Just mathematically speaking. And that's going to be… but that's kind of weird, because a Fermion operator is a two-level system, right? It only can be occupied or empty by Pauli Exclusion Principle, so splitting that up is weird, and

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330W: I'll explain, exactly what that means, but it's telling you that that's why it's going to be special and topological. So.

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330W: Let's, for now, for this slide, just assume the

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330W: part… one of the things I will explain later on is how to get Majorana modes, but let's say we got Majorana zero modes from somewhere.

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330W: And they're at the ends of some one-dimensional system. Let's say… let's say this just happened.

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330W: And we want to ask, what are the quantum states of the Majorana?

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330W: And so the way to do that would be to construct

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330W: This Fermion operator, gamma 1, plus I gamma 2, and now this Fermion operator, which is like a fictitious one in some sense, it's just a mathematical superposition, this operator can either be empty or filled, and those are going to be our two states.

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330W: The fact that to construct, have these two states, I needed a pair of Majoranas, that's the hint that this is a topological object. I can't have a system with only one of them that's made out of electrons. That would not be a physical system. It must always come in pairs.

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330W: One can also use a locality argument to say that these would be like have to be have to be zero energy operators.

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330W: Which would mean that the two fermion parity sectors would have to be degenerate if these existed.

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330W: That degeneracy tells… gives you one hint for what system could have this. Superconductivity has to be an important part of this discussion, because without superconductivity, two different number of electrons, whether they're degenerate or non-degenerate, that's the…

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330W: definition of chemical potential. So it's an arbitrary, you can't compare those degeneracies in a meaningful way, but when you have a superconductor.

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330W: That's a condensate, it has a reference chemical potential of zero, and in that sense, it is, degenerate. So ultimately, when you have these Majorana zero modes, you have this parity-protected degeneracy.

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330W: By the way, at this point, let me just state the obvious. Please feel, we have a manageable number of people, so please feel free to interrupt me at any point.

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330W: with the question. Since you invited a famous model with a Majorana zero mode is the 2 Channel condo model.

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330W: Yes. Is that an example of parity-protected generosity? I… that will… I would like to… I should chat with you about this. I do not completely understand that model well enough, unfortunately, to, I… the… I have, the answer is I don't quite know. Maybe the symmetry of the two channels.

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330W: Yeah, yeah. Kind of a parity. Could be, yes. Yes, it could be. But here, the parity, I mean, it's fermion parity. Yes.

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330W: So, it's the statement that two fermion parities are degenerate, so the nice thing about this is This is…

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330W: not a breakable symmetry. Like, you cannot…

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330W: It's extremely difficult to break compared to the parity between two channels. So it's a degeneracy between

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330W: Zero particle and one particle. It's more like there's no matrix element that can transition me from 0 to 1.

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330W: Whether these two are degenerate or not, that depends on the Majorana topology and the existence of a superconductor, but…

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330W: But on fundamental grounds, I can say there cannot be any matrix elements transitioning between these two.

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330W: Whether they're degenerate or not, that's a little bit, yeah, more complicated.

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330W: Okay, so now that we have that conceptual point out, and we even had some discussion, it's great. Now I'll go get to more practical, like, okay, what were… so this was…

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330W: how do we make these things? This is… this was the original idea from one of my postdoc works, where we said, okay, you sandwich a semiconductor, superconductor, and magnetic insulator together to get this.

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330W: That turned out to be difficult for… and the experimentalists are still working on it, materials people. But, after that, shortly, we realized that if the system was in one dimension.

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330W: then, actually, life is much simpler. We don't need that magnetic insulator, because

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330W: We can apply a magnetic field along the wire and not kill the superconduct… parallel to the plane of the superconductor, not kill the superconductor, and still get exactly, the same… same math, really. So mathematically, it's identical, but physically, it's very different. And we have this condition where Zeeman is greater than square root delta squared plus mu squared.

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330W: We would have this end minor mode.

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330W: And there'd be a tunnel probe.

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330W: So, so because this is a zero-energy state, we could pro… we could tunnel into it and look for it. This was our… our, vision at the… at the end of the… back in 2010. It seemed all easy.

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330W: So let me just quickly, so in a hypothetical world, what we imagine, how we had imagined this would go in terms of detection.

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330W: One can use STM to detect the measure the quasi-particle gap as a matter of principle, if you could just tunnel into the middle of the wire.

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330W: Unfortunately, that experiment turned out to, be not very doable.

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330W: But, and the prediction was that because it's a topological

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330W: transition from… sorry, as we increase Zeeman field, from Zeeman 0, no magnetic field, that would be topologically trivial. Large magnetic field would be topologically non-trivial. There should be, like, a gap closing in between these two, and then, and that should be one signature. The gap in the reentrant phase would be proportional to spin-orbit coupling, that's what this was showing.

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330W: you

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330W: And then, if we plotted the end conductance. We should have seen this gap closing as well, and then…

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330W: in the topological phase, there'd be a quantized zero bias peak that would appear. So, those would be… so zero bias peak, it would be quantized, and this would be a nice story with not a lot of controversy. That was our imagination originally.

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330W: Okay. Well, it's 16 years after I'm talking about it, so clearly it didn't go that way. So…

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330W: Okay, so the good news was, again, and this is how I, I guess, this paper was enough to, this paper and the follow-ups that I wrote was enough to get me a job, was two years, two years later, these experiments are actually done. These are very doable experiments.

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330W: Not…

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330W: Okay, what I mean is that the device could be made. This is a nanowire with epitaxially grown aluminum.

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330W: And when the aluminum is connected to that other end, like it's shorted to that other end, and then you're tunneling from

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330W: the left end through a tunnel gate and measuring the conductance as a function of magnetic field. And what you see is an example of that data from the experiment. Looks reasonably nice, and then…

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330W: And, and there's, that's the theory. One thing that you see is that the, conductance here is actually 0.2, so this was not particularly quantized.

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330W: Later on, people, saw… sorry. People saw closed to quantized.

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330W: tunneling measurements.

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330W: At that point, experimentalists who had done superconductor tunneling started warning me, like, like, look.

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330W: You see zero bias peaks when you travel into superconductors. The thing that just happens

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330W: And then I ask why, and they're like, well, we can't… there are theories, but we don't know which one fits, but it just happens. So you should be careful. Stop a second, so the exuberance is, like, one superconductor. Correct, yeah. So a magnetic field doesn't…

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330W: Do anything to it.

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330W: No, that's correct, yeah.

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330W: Oh! How are you inducing your mind? Thank you, thank you. So…

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330W: One… it's in the semiconductor, so the soup… so… so… this is great.

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330W: I guess that this is one of the slides I would have typically had, but

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330W: So the idea of this, having multi… like, the nanowire on the superconductor is that the nanowire is a proximity-induced superconductor from Cooper-Pierce tunneling. Yes. So… and it's important to have the semiconductor so I have the electronic control. For example, I can tune the chemical potential

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330W: And also tune the spin splitting, because the semiconductor is a large G factor.

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330W: And without affecting the superconductor very much. So even though the superconductivity doesn't actually penetrate the aluminum, it penetrates the proximity region, is that the idea? No, so even the magnetic field, even though the magnetic field does not

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330W: Exactly. It affects the semiconductor a lot. Which has Cooper pairs inside it. Which has Cooper pairs inside it, exactly.

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330W: Very good. Thanks, actually. Question? Yes. So, maybe, like, explain this, but why is the conductance supposed to be quantized, and why is it not quantized in the experiment?

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330W: A.

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330W: it's, okay, why… so it's supposed to be quantized… okay, this is, again.

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330W: No, I'm actually not going to go into it. I mean, we can… I can maybe explain it to you more later, but it turns out that it's actually a fundamental, like.

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330W: particle-hole symmetry… it's a consequence of particle-hole symmetry, the fact that the Majrana particle and an antiparticle are the same. If you think in terms of, like, Bogolibov-Dizhan, what that means is it turns a problem into a

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330W: symmetric double well problem, where you repeat the same barrier between particle and hole, and it's forced to be exactly symmetric and on resonance, from particles. That's one way of seeing it.

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330W: So it turns out that it's actually, like.

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330W: That's actually one of the nice things about Majorana, which is intriguing. You can make the barrier… you can… and then you can result… make paradoxes that you can think of resulting. You can make the barrier as high as you want.

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330W: All that does is it makes the peak narrower, but the height of the peak is still.

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330W: Fixed that quantized. Well, the right side is… the right side is theory, right? Yeah, right side is theory. Why is there asymmetry in left and right? Minus one, one… Oh, yeah, yeah, yeah, yeah, no, no, no, that's right, that's right, thank you, thank you, thank you, that's a great question. We actually put some, extra dissipation in there to make that happen.

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330W: Basically, and also this… the theory… even theory is not quantized, you… Oh, that's exactly because we… we… we… we want to test for this theory modeling, we wanted to make it look as close to the experiment as possible, so we put dissipation in there to make it work.

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330W: Thank you.

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330W: Okay, so now let's sort of jump ahead and ask, like, okay, because we're gonna get to… the field has, like, there has been a lot of work in it, even though, like, things… there's also a lot of controversy. Yeah, so, so just, like, going back to what would a Majorana qubit actually look like, right?

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330W: So it would basically be two copies of what we… the setup we talked about.

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330W: So the… so there'd be a left

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330W: pair of Majoranas and a right pair of Majoranas, and

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330W: As a result, there'd be a left fermion and a right fermion, and our qubit would basically be… one way of thinking about it is just a two-well charge qubit, or a two-well system, electron on the left side versus electron on the right side.

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330W: And, and so that's what you would… you would look for. That's… that… that would be… that… that would be your two-level system. Or you can think of it, because the superconductor, you can also imagine having fermion parity, so 00 and 11. One of these… these scenarios. So, back in 2016,

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330W: So, Charlie Marcus's group in Copenhagen just decided to make this system.

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330W: and try it. Despite the fact that there were a lot… I'll explain what the… what the confusion is, but… or why people weren't… or people still aren't sure that there are Majoranas in here, but he said, let me try it anyway. And if it works, that would be proof for Majoranas. So what he did was, again, make two of these nanowire systems.

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330W: But then he put to.

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330W: I guess these two. These are about like a micron and a half.

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330W: Yeah, and yeah, there should have been a link scale somewhere. And, there are two… I think these are the ones… two charge sensors here.

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330W: that are sensing the charge on the… on each of those electrons, and this here is the sort of Coulomb diamond diagram of changing this left plunger and right plunger voltages, and then looking at the charges on each of those, those wires.

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330W: And what he was hoping to see was the following, that

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330W: So you're going from, like, 00… I think this is, yeah, 00 and 11, these are the…

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330W: Sorry, 1, 1. I think these would be the two column diamonds, 00 and 11, and…

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330W: there's a tunneling matrix element between the two, because there's a barrier that I can turn on, so… so, going between the two, there should be an avoided crossing, going from 00 to 11. And… and that should, that avoided crossing would tell you what the tunneling matrix element and some kind of coherence

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330W: Would give you some measure of coherence.

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330W: And unfortunately, in this case, the lifetime… the measured coherence was terrible. It was in the 10 picosecond range. Question? Yes. So 00 and 11 represent, like.

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330W: electron in the left wire and the electron in the right wire, or my arms? No, no, no, sorry, the electrons. So zero, so, so, well, or yeah, the C left and C right, those would be the… Right, so what… if you have a tunneling of an electron, why is it coupling 0, 0, and 1?

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330W: I guess we're… it's a superconducting, right? So, when an electron tunnels, then it forms into a Cooper pair and goes into, so it's easier to think about from, like, 01 and 10, which is also another basis state. That's also a fine place to think. Then it's just tunneling. Otherwise, you have to count. Zero means.

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330W: You know what I mean? N equals zero? N equals zero. Like, it's not… you should think of it more like even number of electrons, because it's really parity.

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330W: All right.

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330W: Okay, so… so then the next… okay, so now I get… so that… so this was the vision back in 2016. We will come back to this at the end, where we have gotten.

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330W: Okay, so in the meantime, what happened was

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330W: we had… we came up with at least one scenario for we and others, also, for what else could be producing zero-bias peaks in these systems. And this really came… was motivated by this experimental observation, where a…

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330W: pair… a pair of conductance peaks seem to merge into a Majorana. So, and, Charlie Marcus would call this, like.

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330W: Andreas states morphing into Majoranas, that, for theorists, send off, like, alarm bells, because this is supposed to be a topological transition, if a local state just can't turn into a Majorana. This is just not supposed to be allowed.

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330W: So, but on the other hand, with the student Cho Cha Liu, we just did a simulation with a larger chemical potential.

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330W: with everything is non-topological, and, we were like, okay, we can see something like this, so what's going on? And then, a bunch of theory papers figured out, sort of, it's not an unfamiliar story in the

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330W: context of quantum hall edge reconstruction. So, basically, there are a pair of Majoranas, one in each spin.

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330W: Because of the Zeeman field is large enough.

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330W: That.

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330W: you have split the two spin sectors that they don't couple very much, but each produces Majorana, and that's

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330W: pair of Majoranas, unfortunately, is a conventional fermion. But they're still at zero because, like.

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330W: The the splitting between them is still small. That's that's at least.

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330W: That was the belief, and most numerical simulations seem to be consistent with it. Okay, so that's our alter Majorana, or quasi-Majorana, however you want to call it.

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330W: Okay, so… now, yeah, so in terms of… I'm okay with time. So now let me come fast forward to…

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330W: 2023. This is Microsoft's… 2023 data. So, so now let me just…

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330W: Experimentally and sociologically in the field, a lot of

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330W: At this point, by this time, a lot of stuff has happened, so…

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330W: In 2012 there was a lot of experimental activity in the field.

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330W: And Microsoft was kind of, like, corralling it, and funding some of it. And 2016.

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330W: some combination of Microsoft Brass and Charlie Marcus and Leo Covenovan.

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330W: Decided that, okay, this is now time to go big, like, this can be a technology.

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330W: And so they started so so then they limited funding to like Charlie Marcus and Leo Cole. They concentrated all the funding there.

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330W: But that led to some controversial papers in 2018 that people… that sort of overclaimed. We can talk about what the issues were in those papers. But an electoral retraction from Covenhoven, Microsoft did not like that, that press.

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330W: So they dissolved the… they got… they kept the labs, but got… but, disconnected with Leo Kovanovan and Charlie Marcus, and so…

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330W: But the experiment… the finger… the hands in the labs were still kind of, like, still the original group, a lot of the original group.

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330W: And they spent more time optimizing their device, and this was sort of one of the results. One of the criticisms that they were…

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330W: trying to work their way around was that the question of when… the criterion for discovery. When have they realized, like, when is something a Majorana fermion?

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330W: They came up with something, and that's called the Topological Gap Protocol. I will… at…

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330W: talk about it briefly, but that's… that's… that was this experimental paper. So, I think the nice… the thing that is great, which some of… sometimes not appreciated, is a lot of

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330W: They invested a lot in terms of cleaning up the device and making higher mobility, more reproducible, less glitchy, like semiconductor, superconductor systems.

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330W: So that's… that's definitely nice. And the other thing that they did, which was nice, so again, here… here is… so this…

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330W: this line in between, that's the wire. And the way it's made is it's a 2D electron gas, a neomarsonide, and they put a strip of aluminum on it, which then dopes

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330W: the underlying indium arsenide forms an electron gas. They gate it from underneath to form, like, a single channel-ish… I mean, actually, I think the evidence of single channel is fairly strong. So, single channel wire underneath, right? That's, and…

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330W: The other thing that was nice in this data was that they were able to measure conductance

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330W: the non-local conductance, from the left to the right end. So, which is, if you think about it, kind of interesting, because

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330W: The superconductor in the middle is shorted out. It's a 3-terminal device.

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330W: And you're injecting electrons from the left end, and you're… or you're… and you're catching them at the right end, and goes past the superconductor. Why is the superconductor in the middle shorted? Oh, oh, you… you just… there's a third…

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330W: Which is not shown… it's not entirely visible, but somewhere in here, there is a contact to that aluminum.

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330W: strip that is, yeah. So this is, like, kind of different from the previous architecture? Yeah, the previous architecture, they didn't know how to actually contact the aluminum strip in the middle without… in the middle, so they were always, like, using the second lead as the contact, like, the right lead as the contact.

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330W: So, no, this was a very nice… Tunnel splitting you were seeing between 00 and 11 are the two different parity states. Like, that was a tunneling across an insulating gap, right? Correct, yes. But let me…

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330W: you should compare this with the original transport measurement, the qubit part I'm going to come back to again. This is a transport device, not a qubit device, so it's… you should think of it compared to the first, like, zero bias peak measurement.

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330W: So… When you say not a cubic device, you mean not two wires. Exactly, not two wires, and not being measured in the microwave domain, being measured in, the real transport domain. So, yeah, this is actually one of the challenges of this business.

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330W: You want to take a semiconductor device that are usually characterized by transport, but then ultimately you want to get to a qubit, which is characterized in the microwave.

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330W: And, Can you explain the device again one more time? You said it's shorted in the middle, meaning the voltage at the middle is zero. Zero. The approximatizing aluminum is grounded.

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330W: Grounded at the center. At the center, yeah. Now you're applying voltage on the left and the opposite voltage on the right. It doesn't have to be the opposite. It can be… and there are two independent voltages on the left and the right. The grounding in the middle is strong enough that

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330W: Why should we just regard this as two separate conductances, one of the left and one of the right? It is, and indeed, these two plots are two separate conductances on the left and the right, but

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330W: There's also, like, you can apply a voltage on the left and measure a current on the right.

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330W: And those are these two plots.

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330W: I see. So no voting on the right, just. Yes.

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330W: I project. Okay. You just measure the current on the right, voltage on the right is zero, but there's a voltage on the left, and you measure a current on the right. That is another measurement. So it's an interesting physical system, independently of whether you… Exactly, that's what I'm talking about.

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330W: technology. Exactly. Yeah, this is… this is… this… this… this was my… Yeah, right. Exactly. Sorry, one more question. Yes. So, in this case, you have the indium arsenide, just 2D sheet. 2D sheet. Yeah.

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330W: And on top of that, you have like a thin aluminum. Yeah. Exactly. Yeah. Yeah. Aluminum film, actually. Yeah. Yeah. But it's a strip.

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330W: And, so you said that there's a gating, that's… Underneath, on the side of the… next to the aluminum, it's all gated.

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330W: So you're squishing in the electrons. What does this one D thing do in the normal state?

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330W: What does the

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330W: Oh, it's just… Is it insulating? I don't know. No, it's just metallic, like aluminum. It just behaves like aluminum. Some kind of…

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330W: single channel-like conductance, even though… Yeah, so I'm not, so, so, no, it's not single, it's hard to see a single… no, essentially, I do not remember this data, they have some of it in some of their papers. There are interesting…

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330W: Let's see, that's a…

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330W: That's an interesting question. I… I think the tunneling between this aluminum is strong enough that it just broadens out.

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330W: this… I don't think these channels retain their identity.

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330W: in the normal state, because the aluminum

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330W: tunneling… like, the tunneling between the semiconductor state and the aluminum is large, and once it goes into the aluminum, it's basically, like… So then what happens when it goes superconducting to that picture? Now the electrons can't escape into the aluminum. They have to come back.

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330W: of Andre, reflect and come back. And that's the Cooper pairing.

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330W: And it's… and somehow it becomes a single channel Cooper pairing. It's single channel, yeah, yeah, so… so the way… okay, okay, now, so I think, I have to… I don't remember this data too carefully. It might be even in the normal state, but what they can see is.

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330W: as they… they can… they have some way of measuring the density of states. I think the tunneling itself from the end tells you about the density of states, and as they change the gain voltage, they can see subbands as peaks, like, the bottoms of the subbands, there'll be vanos singularities there, and they can see

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330W: individual peaks, and then eventually the wire is depleted. So… so when I say single channel, it's the first… it's after the first vinyl singularity.

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330W: from depletion.

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330W: So, yeah. We have a single aluminum wire, that wire. Yeah, it's a single, I mean, it's not a single… From where to where? Where does it start? It goes along the entire… It's a single aluminum, just wire from… Yeah, here, along, yeah, all the way. Yeah, exactly. The single wire. Single wire, yeah.

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330W: Okay, so they see zero bias peaks, like, in the… at each end, as you expect.

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330W: But the other thing that they see, which is nice, is that… Yes, sir. They can see a gap, like.

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330W: They see where the zero bias peak opens.

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330W: the region of non-local conductance seems to come down like a gap closure. This is…

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330W: This is one piece of evidence that they use.

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330W: And then they have a… Can you say that again? So, so, where the zero bias peak appears, like, there's a zero bias… they're not the same amplitude, but the zero, but there's a zero bias peak that shows up, like, at some same amount.

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330W: And at the same place when they measured the non-local conductance.

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330W: They see, like.

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330W: This conductance come down, like, this gap.

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330W: From the non-local conductance seems to collapse.

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330W: Right? I should say that there are… there's a lot of… And okay.

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330W: the part of the problem is this data is actually very faint and needs to be anti-symmetrized, so there are… there are fine prints to this story that we can get into later. But based on that, they concluded that there is… they suspect there is a region of a topological

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330W: Small topological region in their device.

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330W: Okay. We expect, the, MARA0 mode at the end of the non-Y. Correct. At the end, here. Oh, oh, and, and… Yeah, yeah, yeah, yeah, yeah. Here…

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330W: That's one end. And the other one. Is that where the… the plunger… Okay, I… Yeah, yeah, yeah, yeah. Those where the probe is. Probe, exactly. Right, the probe is right there. And these are the zero bias peaks from…

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330W: So, good. So, so now, let's see, how am I doing?

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330W: Okay, in time. Alright, so…

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330W: We had a puzzle… there was a question that we were trying to… as theorists.

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330W: We were puzzled by what does it mean to have a topological patch, which is, like.

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330W: really small, like, a topological region which is really small. What does that even mean?

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330W: And.

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330W: So…

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330W: And maybe here, since we have some experts about topology in the audience, let me clarify a little bit what the topological invariant even is here.

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330W: Umm.

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330W: So, at least for these kinds of devices, our choice of topologically invariant is a scattering matrix invariant. So basically… and this… there's a whole formalism

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330W: from, I think Baynak… Carla Baynak's group from Leiden, really, where you reform… you can formulate

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330W: a topological invariant… we're used to topological invariants from the bulk, like, looking at some winding or invariant or something, but at the end of the day, many… most… but you can also

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330W: By analogy with the Talos pump.

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330W: think of topological invariance in terms of the scattering properties of electrons from the end. So in this case.

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330W: You can… you have a finite chunk.

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330W: Let's say semi-infinite, let's say Majorana, you ask, what is the scattering matrix of the electron from the end

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330W: from this…

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330W: topological superconductor. Well, okay, what can it do? It basically turns from an electron into a hole. You have a 2x2 scattering matrix, which is particle-hole symmetric, and unitary, the reflection matrix. And from that.

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330W: if written in the correct basis, this reflection matrix here, R, is supposed to be real, so you can take a determinant of that, and…

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330W: If you say that this R is supposed to be unitary, then this determinant can only be plus or minus 1, and that sign is a topological invariant, in the sense that the only way it can change is by the bulk gap closing

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330W: breaking the unitarity of the reflection matrix, and then, so, so, so, so that, so, so that's the, that's the story. The… but there's, there's, there's a, there's a catch.

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330W: One is that for any finite system.

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330W: this will always be positive, it's always trivial, the two Majoranas cancel out, because whatever reflection you get from the Majorana at one end, there is a resonant process from the far-end Majorana that ruins the thing. So… which is what you expect. A finite system cannot actually be topologically non-trivial.

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330W: So, in some sense, it has to be, like.

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330W: infinite. So, the way we deal with it in the theory is we say that the other Majorana is already coupled to some semi-infinite lead, so it's broadened out.

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330W: The price that we pay is that then this determinant R is not.

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330W: unitary. Sorry, it's not… R is not unitary anymore.

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330W: It's plus or minus 1.

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330W: And so… sorry, it's not exactly plus or minus 1, so there's a value now. So there's a… so topology has a… we call it visibility. It's not black and white. It… it also has information about

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330W: like.

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330W: Degree of which something is topological.

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330W: And you can ask, how does that make any sense?

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330W: so it's basically a measure of how the Majorana splitting… in an infinite topological system, Majorana overlap should be zero, so how does that compare with, yeah, it's a measure of that.

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330W: So, and…

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330W: So we get a scenario where we can then calculate this. With this order, we can get these small patches. So the subject is quantized in some cases, or… This will be quantized in the thermodynamic limit.

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330W: But for a finite system, it is not quantized. But because that's what we're interested in.

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330W: In the experiment. Yeah, how much is it reduced from the quantization, like, relative to the size of the gap, or relative to the size of the overlap? Yeah, relative to the size of the overlap, exactly.

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330W: In the position, position, where is this, where is the end of the non-wire? I'm… Zero and… zero, the zero, the zero and 300 in this simulation. At the end? Yeah. Oh, this simulation? Yeah, yeah, yeah. Oh, oh, this is… All the simulation, all the simulation. Yeah, this is, this is, this is theory work that I did, yeah. No, no. Can you measure the…

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330W: Q?

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330W: Yeah, so the… so this… We are treating this.

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330W: Measurement from the… this… an app did this.

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330W: analysis of the topological

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330W: graph protocol that they're producing from their data as a substitute for Q. That's… that's the motivation here.

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330W: To, they… that's… they have… they claim that they have done this over many models, like, and it seems to.

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330W: B. That's how they calibrate. Let's put it this way. You can think of it a little bit like machine learning. They have some…

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330W: This is…

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330W: This… Q is sort of generated by a function with a whole bunch of parameters that they optimize so that it matches their simulation queue.

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330W: That's… that's one way to think about it.

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330W: But then you can ask you how realistic the simulation was. But the point here was that… the point we were trying to do here is trying to understand, can a realistic model, like, can a theoretical model produce these kinds of small topological patches? And the answer was yes.

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330W: But then, one thing was that if you took the thermodynamic limit with the same level of disorder, it becomes topologically trivial.

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330W: And…

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330W: the wave functions for the low-energy Majorana states are completely delocalized to the wire. So this was… this was one of the main conclude punchlines of this story, is that

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330W: At least in our simulations, when we have, like, very small topological regions.

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330W: What that really means is you're… you should think of them as critical fluctuations. It's not really topological. It's, well, okay.

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330W: It's a very delocalized Majorana, maybe. Let's do it this way.

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330W: Okay,

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330W: So… Sorry, question? Yes. If it's highly delocalized, then the original assumption that two Myranas have to be separate… Yeah, that's right, and I should… I should… but I should… I should clarify. This is the theory we don't exactly know. This is a scenario that could be happening in the experiment, and it would be

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330W: And unfortunately, there's, like, a whole gradation going from localized to… to, like, very strongly overlapping. And, yeah. So…

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330W: Okay, right.

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330W: So I will actually skip this in the interest of time, and just.

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330W: get to the… that was some theory inspiration for

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330W: for this next, Microsoft result, which was they trying to actually

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330W: do a cubic measurement, right? This is the first… it's still a one-wire device, but the important thing is now that this is in the microwave domain.

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330W: Not in the transport domain anymore. It's the same device.

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330W: Like, say, nanowire, but now, instead of connecting to… well, they disconnect the leads from the sides.

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330W: And instead, they have, like, a… Long quantum dot.

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330W: which allows tunneling from one Majorana at one end to the Majorana at the other end, assuming that there are Majorana.

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330W: Right? So… so there… so the Majrana at the left end goes through this quantum dot 1, quantum dot 2, quantum dot 3.

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330W: And gets to the Myran at the other end.

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330W: Or, if you want to… if you want to not believe in the Majorana and believe in the delocalized fermion picture, then you can just think of there is a delocalized fermion at… on this wire, and there's an Arnav-Bohm-type loop.

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330W: That, like, where it allows it to see a flux.

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330W: Right? And what they do then is measure the capacitance, they wiggle this dot to measure the capacitance, which is basically the second derivative of the energy level.

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330W: And,

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330W: when they do that as a function of flux, there are two things that they see that are interesting. One is that

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330W: In many regions of flux, there is a bimodality in the distribution. You see two values of capacitance, and you kind of go telegraph noise between the two, which suggests that there is some low energy

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330W: The most reasonable explanation for that is that there's a low-energy fermion, or low-energy state there.

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330W: Probably has to be a fermion, and this state is sensitive to flux, so with rough… with the correct periodicity corresponding to this loop.

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330W: So…

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330W: So, so… Just to clarify. Yes. When you say Fermi, is it just 1E or 2E? One. One E. Yeah, the most period… No, not the Cooper pair, not the Cooper pair. Yeah, good point, that's very important. Not… the periodicity doesn't correspond… okay.

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330W: This is a subtle point.

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330W: The assumption here is that these are actually crossings, not avoided crossings.

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330W: Which that… that's actually a little bit unclear from the data. But assuming that those are crossings, then this corresponds to, electron, that this periodicity going from here to there to there, that would correspond to an electron plus one.

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330W: Right? So, good.

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330W: It's alright, so… so we… Yes. I just understood, like, the size of the capacitance difference, and, like… There… So… When I should I… Yeah, yeah, no. … signal, are you gonna show me? Yeah, so…

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330W: There are a lot of, sort of.

294
00:44:55.500 --> 00:45:13.929
330W: things like lever arms in this device that are a little bit, like, require detail, like electrostatic simulations, and we get from them. But if you, with those, and assuming, like, the right… you get the right order of magnitude. That seems to, seems to, work out.

295
00:45:15.500 --> 00:45:33.270
330W: Sorry, yes, question? Yes. Sorry, can you go back to the previous one? Yeah, absolutely. I just want to understand, so the, the, in the picture, like, you have this dashed black line? Correct. That dashed black line is indicating the loop? Exactly. And the top is the nanowire? Perfect. And you have two, and you have two

296
00:45:33.270 --> 00:45:47.680
330W: sort of islands, superconducting islands? No, no, they're actually semiconductor… semiconducting. They're just part of the two deck. Okay. Where… and the dot 1 and dot 3 are just, two…

297
00:45:47.900 --> 00:46:01.179
330W: modulate tunneling, they should think modulate… they're actually column… they're all column located, actually, but dot 1 and dot 3 are more for, our barriers, really, and dot 2 is the one where you're actually, like.

298
00:46:01.790 --> 00:46:21.410
330W: going through. And, I'm sorry, you're, you're, you have an electron tunneling… An electron tunneling, exactly. One end to the other. One end to the other, yeah. So dot 2, dot 2 does not have any aluminum on top or bottom? No, no, dot 2 and dot 1, none of the dots have any aluminum. There's no aluminum on that.

299
00:46:22.520 --> 00:46:26.179
330W: Okay, so… right.

300
00:46:27.460 --> 00:46:32.520
330W: Okay, so, Umm.

301
00:46:33.950 --> 00:46:39.780
330W: Right. So, so, so, so again, we can, one can do some, analysis

302
00:46:40.260 --> 00:46:47.209
330W: of… of this… this kind of experiment. One way to think about it is it's an… it's an Andrea state.

303
00:46:47.900 --> 00:46:53.179
330W: Which may or may not be made of a pair of Majoranas. And…

304
00:46:53.300 --> 00:46:56.599
330W: And then coupled to a quantum dot through a flux.

305
00:46:56.880 --> 00:47:11.390
330W: And then all we're… so… so, in terms of a Hamiltonian, you just have, like, a quant… so… so the C dagger is, like, in the, the, sorry, sorry, sorry, not C dagger. So… so there's a gamma left and a gamma right.

306
00:47:11.580 --> 00:47:23.150
330W: And C dagger is that combination of gamma left plus I gamma right, like we've had before. It's the fermion that's shared between the pair of Majoranas, or you can just imagine that you took the

307
00:47:23.910 --> 00:47:29.180
330W: fermion and split it up into a pair of Majoranas, but the…

308
00:47:29.750 --> 00:47:34.589
330W: Majrana are not… so D is the fermion, or state in the quantum dot.

309
00:47:34.810 --> 00:47:40.010
330W: And… Now, the extent to which… if…

310
00:47:40.120 --> 00:47:44.870
330W: system is ideal Majoranas, then delta is zero.

311
00:47:45.220 --> 00:47:50.190
330W: And then Zeta left and Zeta right are also zero, which means that the right Majorana

312
00:47:50.530 --> 00:48:05.119
330W: like, tunnels only to the right, and the left Majorana tunnels only to the left, but if it's non-topological and delocalized, then you have, like, this Zeta left and Zeta right, and so on and so forth. So, turns out that if you can see, like.

313
00:48:05.290 --> 00:48:08.729
330W: Very nice HC over 2E periodicity.

314
00:48:09.280 --> 00:48:18.739
330W: And… Sorry, AC over E periodicity, and the fact that the two fermion parities.

315
00:48:19.500 --> 00:48:34.700
330W: Like, I guess what I'm saying is that these oscillations were perfect, which means that it's… you have electron periodicity HC over E, and then the two parities exactly pi-shift from each other. That's a very strong signal of Majorana.

316
00:48:35.010 --> 00:48:44.790
330W: but at this point they don't really really know that the the next store next step is you can try to build a qubit from here like put

317
00:48:45.010 --> 00:48:47.180
330W: This data is…

318
00:48:49.500 --> 00:49:06.999
330W: the periodicity is not very good here, right? Whether this is AC over E or AC over 2, I mean, this is not just not very periodic. Yeah, yeah, exactly. So, so… Yeah, so it's hard to tell from… How confident are we about heading weird by runs here?

319
00:49:07.220 --> 00:49:21.139
330W: No, so what I'm saying is that… People are confident, or… No, it's very controversial. It's still controversial. Yeah, yeah, yeah. Move on to Cuba. If Marana itself is controversial, please move on. Yes, this is part of the…

320
00:49:21.550 --> 00:49:32.900
330W: problems with, with corporations. Because the thing is, corporations have a… there's a timeline for a product, and whether the scientists are convinced or not is…

321
00:49:32.900 --> 00:49:57.219
330W: sort of, there's money coming in, so just keep moving. You keep moving, yeah. So, like, in superconducting systems, like, you know, if you have, like, a cooked pair box or something like that, you know, you have this offset voltage is fluctuating from, like, background charges that are present. Yeah, yeah. How do you know that, like, these… like, firstly, like, in this, like, even if you had a fixed magnetic field.

322
00:49:57.250 --> 00:50:10.039
330W: Does your capacitance, like, fluctuate, and… I think, so… so, my understanding is that they have worked to make these devices somewhat stable.

323
00:50:10.280 --> 00:50:16.830
330W: etc. So, yeah, and I have to say that From…

324
00:50:17.540 --> 00:50:22.060
330W: like, these data keep improving at some level. So the latest

325
00:50:22.090 --> 00:50:32.780
330W: latest versions of these are more periodic-looking and so on. So there is continuous progress. They have a team of, like, a hundred and some people.

326
00:50:32.780 --> 00:50:42.280
330W: including Mike Monfra, who is a very serious grower. So… so they are… yeah, it's work in progress, so…

327
00:50:42.630 --> 00:50:50.450
330W: So while that data is definitely not convincing, but I think it's… it's getting there. It's approaching that. Okay.

328
00:50:51.480 --> 00:51:01.909
330W: Eight. OK, I'll try to wrap up soon. So again, you couple two of these to make a cubic, right? MS. MS, it's OK? All right, MS, that should be good.

329
00:51:02.020 --> 00:51:07.919
330W: 2 qubit, And then again, at least.

330
00:51:08.080 --> 00:51:16.870
330W: Sorry, let me just quickly… oh, yeah. So, so the picture, we…

331
00:51:17.640 --> 00:51:29.900
330W: to us, what is the most natural thing to do? Okay, so firstly, you combine two of these to make a qubit, you have… and then you have a tunneling, then in principle, you can have this, and then you measure

332
00:51:30.190 --> 00:51:49.839
330W: the parity, or occupation, using this… the measure… the setup I just told you, that same exact measurement. You can… that capacitance tells you which state you are in, and so ideally, if you can… you measure, and then you turn on the tunneling, let the electron hop back and forth.

333
00:51:50.060 --> 00:52:05.890
330W: for a while, you should be able to see, like, a Rabi oscillation, or a… and measure… measure dephasing. This is sort of the… the picture… that's one picture, and then one can then extend to say how

334
00:52:06.070 --> 00:52:16.230
330W: But on the other hand, Microsoft's plan is to do something called measurement only, and the way that would work is it doesn't actually have that tunneling

335
00:52:16.740 --> 00:52:18.810
330W: Turned on at any time.

336
00:52:19.000 --> 00:52:21.090
330W: You just do…

337
00:52:21.840 --> 00:52:38.049
330W: So this is the nice thing about having a Majorana cubic, like a pair of my wires as a cubic. You can measure the parity along this pair, that's measuring the parity of this pair of Majoranas, but if you're in the topological regime and you have 4 Majoranas, then you can measure…

338
00:52:38.170 --> 00:52:51.240
330W: the parity of this one, that's X, and measured the parity of that pair, and those are 3 anti-commuting measurements, so you get Pauli measurements relatively easily from this

339
00:52:51.480 --> 00:52:53.830
330W: this, setup.

340
00:52:54.120 --> 00:52:59.019
330W: And this is enough to generate like Clifford, the entire set of Clifford gates.

341
00:52:59.150 --> 00:53:05.349
330W: So… so this is… this is what's underlying Microsoft's optimism that this is a

342
00:53:05.500 --> 00:53:12.800
330W: good way to go. A single qubit Clifford. Single qubit Clifford gate. And for 2 qubit, so.

343
00:53:12.940 --> 00:53:20.660
330W: If you… if you… Connect two of them and do this, we're a joint.

344
00:53:20.860 --> 00:53:27.660
330W: pair of wires, then you can get a 2-qubit entangling gate. The entangling clipper gate. Yes?

345
00:53:27.850 --> 00:53:32.490
330W: Why do I need a quantum computer to do the Clifford game? Sorry? Oh!

346
00:53:32.840 --> 00:53:45.030
330W: No, so you don't need a quantum computer to do Clifford gates, this is correct. But, once you… but if you do have a quantum computer with Clifford gates, and then you add one crappy gate.

347
00:53:45.330 --> 00:53:56.530
330W: then you can use Cliffords to distill and work your way through. But that's the story for surface codes and a whole bunch of quantum computing strategies anyway.

348
00:53:56.960 --> 00:53:58.939
330W: That's at least one strategy.

349
00:53:59.610 --> 00:54:17.970
330W: So, what we did was we, as theory, we, did this Robbie simulation for the Robbie, and I'm not gonna go… What are you simulating? Basically.

350
00:54:18.080 --> 00:54:31.100
330W: This device? Oh, okay, okay. That device, and I'm… and it's just this Rabi oscillation. And calculating what is the frequency and the decay time. Lifetime.

351
00:54:31.280 --> 00:54:36.209
330W: Like two tight binding models. Two tight — exactly, two tight binding models.

352
00:54:37.760 --> 00:54:56.460
330W: I mean, I can get into details of it later on, but it's not… but the main point was, we can do, Majorana on the top layer level, Andrev, and, also, like, these two

353
00:54:57.250 --> 00:55:08.889
330W: this delocalized Andrev with different levels of separation. One is kind of topological, and the other one is non-topological, and

354
00:55:09.780 --> 00:55:26.779
330W: And the main conclusion is one gets various levels of decoherence times. So the Majorana decoherence rate is 38 hertz, which would be a beautiful qubit if that happened.

355
00:55:26.820 --> 00:55:37.290
330W: And, some of these are… and this would be pretty terrible, 0.2444 GHz, and so on. So, so depending on the quality of the Majorana, you end up with different

356
00:55:37.390 --> 00:55:47.210
330W: times. Now… So, what is the explanation for the… so this, like, beyond, like, some topological protection or whatever, but how… how do you…

357
00:55:47.510 --> 00:56:01.719
330W: Why is there my… the lifetime in the Mayan understanding? Yeah, so what's going on… the main… in this, the main noise that we're considering is the… the gate… the… that the, I don't know, some two levels of… some charge noise.

358
00:56:01.720 --> 00:56:10.879
330W: in the wire, and if it's Majorana and very well separated, then that charge noise, you get basically insensitivity to that charge noise.

359
00:56:11.030 --> 00:56:14.949
330W: And that's… that's what exactly… that's a good… that's what this is buying you.

360
00:56:15.290 --> 00:56:20.450
330W: So Microsoft, again, has tried not this measurement.

361
00:56:23.360 --> 00:56:29.560
330W: So, they don't have the Z and the X, so they have done the X measurement, right? So just to remind you.

362
00:56:30.370 --> 00:56:34.720
330W: So… They're continuously measuring this X.

363
00:56:35.210 --> 00:56:43.990
330W: For a pair of wives. And… They see… a bimodal distribution

364
00:56:45.290 --> 00:56:52.169
330W: And they see a lifetime, which is 15 microseconds for a certain value of flux, which is respectable.

365
00:56:52.600 --> 00:56:53.740
330W: The…

366
00:56:54.050 --> 00:57:03.040
330W: Problem is, they don't have any dynamical control, the measurement is continuously on, so the lifetime is in the presence of the measurement, which is then not a…

367
00:57:03.590 --> 00:57:15.829
330W: it's… it's hard to think about what it is. Okay, so… So, so this is, this is a qubit with what frequency, or… No, so this is all zero. Well, okay, no, no, no, sorry.

368
00:57:16.340 --> 00:57:18.689
330W: There is a frequency, because…

369
00:57:19.020 --> 00:57:36.729
330W: I don't know what the… the frequency is actually reasonable, substantial, it's a micro-EV, you can convert to… So it's substantial, but the qubit should not have… Majrana should not have a frequency, because everything is zero, but because of this measurement.

370
00:57:37.220 --> 00:57:42.319
330W: the quantum dot measure is produced, creates the frequency. It's like a tunneling, creates a frequency.

371
00:57:42.460 --> 00:57:56.799
330W: And this is what they're measuring. We are… anyway, so this is one set of results. They're trying to improve on this, but the main goal would be to actually be able to switch between X, Y, and Z. Right now, their electronics can't let them do that.

372
00:57:57.040 --> 00:57:58.420
330W: So, in the…

373
00:57:59.660 --> 00:58:07.110
330W: I want… okay, I'm almost out of time, but I just want to… maybe this is more like an advertisement than going to be an advertisement. One last…

374
00:58:08.160 --> 00:58:10.190
330W: set up. So…

375
00:58:10.350 --> 00:58:23.200
330W: Again, after writing those Myron Nanowire papers, we were very worried about disorder, so we came up with an alternative proposal to… where to say that, okay, let's just say there's a lot of disorder, but we just use a bunch of quantum dots.

376
00:58:25.170 --> 00:58:41.419
330W: And then we gate-tune our way out of the disorder. So we tune our gate so that all the dots are resonant, and in some sense, we build ourselves way out of the disorder. It can… turns out that that can be matched to a cute-type chain in the right scenario.

377
00:58:42.980 --> 00:58:46.469
330W: Leo Kaufenhoven, after kind of getting

378
00:58:47.690 --> 00:58:54.460
330W: left out of the Nanowire project, he decided to pick up on this approach instead.

379
00:58:54.960 --> 00:59:01.980
330W: Which is, so… and again, the idea was, okay.

380
00:59:02.510 --> 00:59:07.029
330W: Two dots here, but only, like, a two-dot version of the chain.

381
00:59:07.270 --> 00:59:08.380
330W: And…

382
00:59:08.990 --> 00:59:15.620
330W: Each dot you can think of as a… just like in this picture, actually, back to this picture. So, imagine just…

383
00:59:16.120 --> 00:59:19.569
330W: Two of these dots, each dot is a pair of Majoranas.

384
00:59:19.760 --> 00:59:26.860
330W: But then you use, Andrev, coupling and Zipper to gap out these two, and then you have

385
00:59:27.380 --> 00:59:40.530
330W: those two Majoranas left over. So… so he's done some measurements. of that kind, and again, measured parity, very analogous to Microsoft's measurements of capacitance. He sees the telegraph noise.

386
00:59:41.090 --> 00:59:48.299
330W: But more interestingly, just this year, like, just a few months ago.

387
00:59:49.100 --> 00:59:50.349
330W: Two months ago.

388
00:59:50.610 --> 00:59:55.050
330W: He actually also did this experiment where he turns the tunneling

389
00:59:55.820 --> 01:00:02.989
330W: He has tunneling and then looks for the Rabi oscillation, and he sees some Rabi oscillation in this with the

390
01:00:03.140 --> 01:00:04.170
330W: 26.

391
01:00:04.280 --> 01:00:06.279
330W: nanosecond time, so…

392
01:00:06.420 --> 01:00:14.229
330W: I would call this a Majorana qubit demonstration for the following reason. I mean, okay, there are people who disagree with it, but

393
01:00:14.910 --> 01:00:15.850
330W: It's…

394
01:00:16.350 --> 01:00:26.010
330W: he definitely tunes himself into the regime. With quantum dots, you have a lot more control, and you can see, like, it's very easy to check that these are Majoranas. Much easier to check that these are Majoranas.

395
01:00:26.210 --> 01:00:33.419
330W: It's almost too trivial, and then he's splitting this inner Majrana with the tunneling, and then…

396
01:00:33.680 --> 01:00:41.760
330W: seeing this, oscillation. I wouldn't call it topological, because there's no notion of length.

397
01:00:42.090 --> 01:00:46.460
330W: You… if you perturb away from certain sweet spots, these Majoranas mix.

398
01:00:46.780 --> 01:01:00.039
330W: But anyway, so… so, but this is encouraging. So now, the question is… What's the sense in which they're Majoranas? The sense in which they're Majoranas is in the sense of this, like, if you match their…

399
01:01:01.570 --> 01:01:07.099
330W: So they can actually, like, basically the system is simple enough, they can measure all these couplings.

400
01:01:07.230 --> 01:01:15.159
330W: And they can check that, really, like, their Hamiltonian is this. So it's the… it's by construction, like, the math tells you that they should combine.

401
01:01:16.240 --> 01:01:21.810
330W: And, okay, we can, yeah.

402
01:01:22.240 --> 01:01:28.920
330W: Anyway, but let me just, because I'm done, so let me… I'll just put my conclusion slides up, and then… oops, sorry.

403
01:01:29.050 --> 01:01:34.550
330W: So, yeah, thanks for your attention, and then I can take my question.

404
01:01:39.520 --> 01:01:48.580
330W: Actually, following up in the last question, so what does protect that the left and right majoranas with the same quantum dot do not mix? Because before I understood it was the length.

405
01:01:48.910 --> 01:01:52.779
330W: No, so the same one does, it's… okay.

406
01:01:53.030 --> 01:02:08.940
330W: Yeah, so you literally have to… so it's a com… so the parameters are you have chemical potentials of the two quantum dots, and you have a normal tunneling through the… this guy, and you have an unraved tunneling through this guy, so those are your parameters.

407
01:02:09.080 --> 01:02:15.169
330W: The two dots… okay, you can tune them by gate. Turns out you can tune this one

408
01:02:15.380 --> 01:02:20.320
330W: by two gates as well, independently. So you're literally…

409
01:02:21.920 --> 01:02:29.209
330W: You have enough knobs to tune all four, and they go through this exercise, all these plots.

410
01:02:29.320 --> 01:02:48.409
330W: Which I can, like, these kinds of plots of transport, they monitor the transport as they're varying various parameters, and check that, really, they're in this regime. So, but on the other hand, you're right that it's not protected in the sense that if any one of these parameters drifts, then you mix everything up, and yeah.

411
01:02:49.370 --> 01:02:57.539
330W: But while it's not… so it's not scalable, it's not topological, but I think if you ask whether or not it is Majorana, I think that is correct.

412
01:02:59.120 --> 01:02:59.939
330W: Yes.

413
01:03:00.050 --> 01:03:04.820
330W: Isn't Marana… Kind of intrinsically topological.

414
01:03:05.170 --> 01:03:10.580
330W: No, that's what… so, I don't… no, I don't think of my… that's the thing. In Majorana by itself.

415
01:03:11.030 --> 01:03:16.849
330W: Is If it's truly isolated, then yes, I think you would call it topological, but if it's

416
01:03:17.790 --> 01:03:23.729
330W: If it's not isolated, then… and then there's a question of what do you mean by isolated, unfortunately.

417
01:03:23.810 --> 01:03:42.789
330W: So, are there… is the data what you're seeing, is this simply some kind of boundary localized edge flow? It's not even a boundary, look, it's worth… there are only two… two sites. It's a two-site system, so I don't know even what a boundary precisely means. That's part of the problem.

418
01:03:43.050 --> 01:03:52.359
330W: That's why I say it's, so… that's why I call it Majorana, but not topological. I don't even know how to start to think about what is topological here, because it's, like.

419
01:03:52.890 --> 01:03:54.070
330W: Four sites.

420
01:03:55.560 --> 01:04:03.489
330W: But their plan is to go to larger chains and show that its coherence time becomes better.

421
01:04:03.600 --> 01:04:14.440
330W: And yeah, we'll see if that happens. Or Microsoft's Nanowire strategy gets it better like to hire. Maybe I have a more generic question. Why do we want power on that?

422
01:04:15.380 --> 01:04:24.560
330W: So that, I think, is related to this kind of simulation. If you ask about the lifetime and the decay rates of the various parodies.

423
01:04:25.630 --> 01:04:27.270
330W: So you can think of.

424
01:04:28.680 --> 01:04:38.900
330W: This as, sorry, sorry, yeah, this system with two… if you didn't have superconductivity or anything, this would be what people call a charge qubit.

425
01:04:39.100 --> 01:04:54.629
330W: That is susceptible to any kind of electric field fluctuation and noise. With superconductivity and all of these things, you build protection against more and more of those noise, and that's the… and so Andres takes, I think, gave you some protection, and Majorana gets you even more.

426
01:04:55.460 --> 01:04:57.329
330W: It's harder to control.

427
01:04:57.600 --> 01:04:59.790
330W: Corner view control.

428
01:05:00.020 --> 01:05:05.290
330W: Not… once… if you could enter the topological regime, then it's less… then it's…

429
01:05:05.560 --> 01:05:08.179
330W: more. But yeah, at this point.

430
01:05:08.420 --> 01:05:26.969
330W: Anyway, yeah, it's complicated, yes. But the ideal dream is, if you have nanowires, let's say this DOS scenario, I'm not so sure about, but the Microsoft scenario, where we have clean nanowires in the topological regime, or let's say even better, some topological insulator-based material, etc.

431
01:05:26.970 --> 01:05:30.080
330W: So actually, from the broader standpoint, I actually think this is int…

432
01:05:30.220 --> 01:05:33.800
330W: So that was where, sort of, I…

433
01:05:33.970 --> 01:05:38.810
330W: ended. My… my… in some sense, my vision is that there are other

434
01:05:38.980 --> 01:05:44.309
330W: Other roadmaps towards topological superconductors, which involve more topological materials.

435
01:05:44.570 --> 01:05:51.940
330W: And then you build in more and more robustness. It's a path where topological materials can help you get a better qubit.

436
01:05:52.100 --> 01:06:06.189
330W: My understanding is that these topological things are good because they are robust, kind of robust to this noise protecting this. Yeah, correct. But as long as when you're trying to control these qubits, you are breaking that.

437
01:06:06.630 --> 01:06:13.180
330W: No, no, no. So, no, so the… you… you enter… you control to enter

438
01:06:13.490 --> 01:06:19.570
330W: the topological regime, and for that you need good control, and then it doesn't seem very robust. But the point is, once you're…

439
01:06:20.380 --> 01:06:32.320
330W: you find the right regime, and if you have good material parameters, then this regime should be big enough. So I guess maybe another point is, yeah, if you have a small topological region and it's fragile, then there is no point.

440
01:06:32.360 --> 01:06:57.109
330W: That is correct. But if you… if you… let's say… let's say Microsoft manages to lower their… they're already switching in their new paper, they're switching to lead superconductors. That gets the superconducting gap energy scale bigger. If they can control the disorder as well, then that topological patch, instead of being stable over, like, let's say, a quarter of a Tesla field, becomes stable over half

441
01:06:57.110 --> 01:06:58.270
330W: Tesla field.

442
01:06:58.270 --> 01:07:04.200
330W: And you get a gap which is now of the order of a Kelvin, then you're actually in a much better shape.

443
01:07:04.580 --> 01:07:06.270
330W: That's kind of the vision.

444
01:07:08.010 --> 01:07:08.830
330W: Yes.

445
01:07:08.950 --> 01:07:18.569
330W: I actually have a question in similar lines. So, the existence of isolated Majorana zero boards, you said it is for Q less than 0.

446
01:07:18.680 --> 01:07:20.750
330W: But what happens if you add disorder?

447
01:07:21.180 --> 01:07:23.500
330W: Does that still… happen.

448
01:07:23.500 --> 01:07:44.559
330W: Yeah, yeah, no, this is for… this was for… yeah, yeah, yeah. So, so this… the invariant, the topological invariant, that's one of the nice things about scattering matrix invariant. It doesn't… it's agnostic to disorder or no disorder, it doesn't care. It's… it's… the… I mean, its value depends on whether there's disorder or not, but what I'm saying is that you compute it with the disorder.

449
01:07:44.560 --> 01:07:47.019
330W: In there, and you get what you get.

450
01:07:47.120 --> 01:07:53.789
330W: Is that how, looking at the value of Q, you know in what regime you are, and then you can do control?

451
01:07:53.930 --> 01:08:00.540
330W: So let me… so, yeah, so let me, clarify a little bit more. If… For theorists.

452
01:08:01.120 --> 01:08:09.390
330W: We would say that we are in the thermodynamic limit, Q is plus or minus 1, none of this intermediate value really shows up.

453
01:08:09.770 --> 01:08:16.720
330W: Then you are clearly topological or trivial, and that's the end of that story. But for a finite system.

454
01:08:16.859 --> 01:08:24.320
330W: Q will be in some intermediate value, and what that's telling you is how much Majorana splitting you have.

455
01:08:24.450 --> 01:08:27.320
330W: Relative to how much coupling you have to the tunnel.

456
01:08:27.880 --> 01:08:36.499
330W: to the… to the splitting and tunneling. Like, the… so the Majorana splitting, you should think of the uncontrolled part of your Hamiltonian, and the other one is the controlled part of your Hamiltonian.

457
01:08:36.950 --> 01:08:44.140
330W: And, yeah, if you're… if you're much closer topological, the control part is much bigger than the other piece.

458
01:08:44.880 --> 01:08:45.700
330W: Okay.

459
01:08:46.910 --> 01:09:01.090
330W: Yeah. I have a question about the Rabi oscillation part. So that's what… I should think of that as tunneling when two levels are brought close together, or is there a microwave drive applied to… No, just tunneling.

460
01:09:01.710 --> 01:09:25.830
330W: just tunneling when you're you're you're black. And this point you made about like switching to lead. And so like in these systems or in supernatural systems, we have, like, you know, IR, you know, noise that like creates quasi particles. And so is that's what limiting these experiments. And and are you going to hire Tc. To and have gap frequencies to mitigate that? Or is this something to do with like

461
01:09:25.830 --> 01:09:28.990
330W: the topological gap. Oh, that's that. Yeah, yeah.

462
01:09:28.990 --> 01:09:38.990
330W: No, we don't know, it's both. Basically, the superconducting gap, in some sense, sets the energy scale for everything, quasiparticle gap.

463
01:09:39.319 --> 01:09:50.209
330W: But also the length, the coherence length. Because that's also determined by the… yeah, so… so it's…

464
01:09:50.399 --> 01:09:51.589
330W: Both of them.

465
01:09:54.290 --> 01:09:57.149
330W: I'll try it again. All right. Yeah, thank you.

466
01:10:05.430 --> 01:10:13.029
330W: Sean, you want to take over here? Yeah, yeah, yeah, yeah, I will.

467
01:10:13.760 --> 01:10:20.629
330W: Yeah, just a bunch of meetings, and then I'll just send you an email. Okay, perfect. Terry, is that good? Yeah.

468
01:10:22.310 --> 01:10:26.120
330W: Yeah, I'm optimistic about… Save it.

469
01:10:26.720 --> 01:10:37.870
330W: Yes. People are still pushing in sales. No, no, exactly, that's, that's, that's the reason for optimism. The management code should be. But there are many uncontrolled…

470
01:10:38.050 --> 01:10:43.620
330W: The fact that there is only one effort.

471
01:10:43.660 --> 01:11:02.729
330W: That's the… so they're actually… there are two efforts. One's in China, and the other… There is one in China? There is one in China, but again, it's moving slowly. It's a tricky deal. The reason it's a tricky deal is because it's by the first author of the retracted paper.

472
01:11:03.290 --> 01:11:13.230
330W: Haozang. So, I, I, I don't actually… he, he gets… I feel he gets unfairly villainized.

473
01:11:13.470 --> 01:11:19.340
330W: For this, including he… I think he, he was…

474
01:11:20.210 --> 01:11:30.089
330W: He was not allowed to go up for tenure at Tsinghua. He was hired there, but he was not allowed to go up for tenure. Did he go somewhere else? He had to go somewhere else, and we sent his group up.

475
01:11:30.270 --> 01:11:36.279
330W: But I think, at the end of the day, I think he's reasonably good, and he… this guy…

476
01:11:37.570 --> 01:11:44.549
330W: I have trouble with Chinese names, Kohe, or how to say it, but he is a very good grower.