Superconducting qubits

57:12with that in mind, let's start with our first big modality, superconducting cubits. And let's analyze superconducting cubits using the FFP criteria. >> Superconducting cubits have made a name for themselves. These are the big players, Google, IBM, Regetti Computing. They had the big quantum supremacy. Um, this is the Willow chip that you see on on there on on on that hand. Um, so what is the cubid itself? A cubid has to be a two-state system that can be in a quantum thingy. >> Yes. Yes. >> It's effectively a fancy LC circuit, an inductor and a capacitor. Um, from classical electronics, we visited this a lot. An LC circuit is effectively a

57:53electronic pendulum of sorts. The inductor gets charged, then it gets discharged. During that time, the capacitor gets charged and then discharged. So you have this back and forth where the energy is moving from the inductor into the capacitor into the inductor into the capacitor. Um and this becomes a harmonic oscillator is what we call it in physics when you've got like a oscillating system that just obeys you know >> a sine wave >> now >> which is what we're seeing in this bottom left. >> Yeah. That's the that's the the current the current is going one way then it's going the other way then it's going one way then it's going the other way. Right? You can also track the voltage. Whatever whatever um variable you want

58:36to track, it's going to look like a >> sign. It's going to have a harmonic. >> Okay. Now, this is a classical harmonic oscillator. >> Yes. >> If I take this harmonic oscillator and I cool it down, I put it inside a dilution refrigerator, then everything becomes quantum. Okay. Everything is actually quantum at the end of the day. It's just classical. There's enough temperature and there's enough modes that you know it obeys classical mechanics. But if you cool it down enough, you're going to start entering quantum mechanics level. And um for those who have taken undergraduate quantum mechanics, there's a famous photo in the Griffiths textbook of a cat going up a ladder. These are the ladder states of a quantum harmonic oscillator where each rung of the ladder is a different state that your quantum harmonic oscillator can be in.

59:17Crucially, the rungs of the ladder are equally spaced. Okay, that um and the the spacing is h bar omega. H bar is um plank's constant divided by 2 pi. Omega is the resonant frequency of your harmonic oscillator. Um the problem here is that all of the rungs are equally spaced. >> Okay. >> Okay. One of the questions with how good is your cubit? it. One of the questions that comes up with that question, how big how good is your cubit is, um, is it really a two-state system that's isolated? >> Mhm. [clears throat] >> Or do can I accidentally go and go and access some other some other spot? >> Is there noise in this? >> Yeah. Yeah. Is there noise such that

59:58like I leave my computational basis is what they call it. I've got a zero and a one and I want to stay within this zero and one. I don't want to go to two >> or three, [clears throat] right? because Q bits bit two two >> um but if there's equal rungs on the ladder and let's say I poke it with enough energy to go from 0 to one I could also poke it with enough energy to go from 0 to two because the the spacing is equal or if I'm at one and I want to get down to zero I could poke it it could go to two and and this comes to the idea of we have these systems at this very low temperature if it was at a slightly like at a higher temperature for example Would that be the equivalent of this poking where it could go from a

1:00:39zero to a two as one that's one way that that it could practically do this? >> Yes, one way. But actually what what's worse is even if that's even even if you're at a low enough temperature, there's something called stimulated emission of radiation. That's the s in laser. >> Um and so you can literally go from like >> one to two even though you wanted to go from one to zero and there's no temperature effect. >> Okay. if the if the states are equally uh the rungs are equally spaced, right? The the photon could just be like, "Oh, I'm just going to absorb this instead of absorbing and then emitting two >> and now now I'm at state two." So you got to you got to do some finickiness to to remove that equaleness in the latter

1:01:23>> because the point there is the equalness allows the easy transition from these states and you basically want to make it so that the zero and one and one and zero is equal but every other state transition is harder. >> It's like not equal. It's like something different. >> Yeah. Yeah. Some something different. >> It's something different. So that I can very precisely control my transitions from 0 to one and back. But I can also very precisely say that I'm not going to go elsewhere. >> Yeah. Yeah, that makes sense. >> So, so in order to fix that, they replace the inductor with a Joseph's injunction. >> Ah, back to our Josephson's injunction. >> That's right. So, um, last year we had a great episode

1:02:04about the Nobel Prize winners in physics. Um, Michelle Devore, John Clark, and John Martinez. They showed for the first time that you could have macroscopic quantum tunneling >> in a Josephson junction at Berkeley. It was a it was a really good episode and I encourage people to watch it. Um >> this sort of started that idea of using a Josephson junction cooling it down >> and using that as part of your cubit. >> Okay. So now if we replace a Josephson junction in in place of the inductor, what happens? Well, instead of a perfect quantum harmonic oscillator, which is on the left, that's a parabola. Yep. >> The that's the potential of a parabola.

1:02:45Um, you know, and on on the right hand side, instead of a parabola, we introduce a cosine. >> It's the bottom of a cosine. Now, the bottom of a cosine crucially kind of looks like a parabola, >> but the farther out you get, it it diverges from a parabola, >> right? What that means is your 0ero to one has a certain spacing, but the other ones >> have different spacings, >> right? And it continues. So because our are >> Yeah. The the it's continuing to diverge farther away from the parabolic. >> Yeah. Yeah. Yeah. In a parabola, it would be exactly spaced. >> Right. Right. >> Just because of how the math works. >> Right. Right. Right. >> But with a cosine now, you've got different spacings. And now I can very exactly hopefully toggle between zero

1:03:26and one. and I don't have to worry about going into two and things like that. [clears throat] >> So this this would be a great cubit, right? If if exactly I could always do 0 to one and so on and so forth. >> Fair enough. >> Um so that that's what we're doing. We're going to replace the inductor with a Joseph's injunction. And this is what it looks like in practice. So this is called an Xmon. The these these cubits are called transmons, the ones that Google and IBM uses at least. Um and under a microscope, this is what it looks like. So on the left hand side we've got like a cross. >> Mhm. The big cross is the giant capacitor. Okay. And zooming in there, there's the Josephson's injunction. >> And um effectively this is your cubit.

1:04:08There's a little circuit that runs inside. It's superconducting, which means that if you let it run, it's just going to keep running, which is nice because you want your cubit to sort of stay cubidy. Um, and that interference device, the squid, that's called a superconducting quantum interference device. It's it's creating the zero and one. This this entire ensemble is creating your zero and one. Now, how do you talk to it? >> This is my cubit. This is the substrate. This can hold my zero, which is one state of the circuit, and the one, which is another state of the circuit. The sort of a little bit higher frequency or yeah, higher frequency. And >> would you say that this is speaking to

1:04:49the cubit uh quality uh variable in the criterion? >> Yeah. Yeah. I'm trying to define the cubit itself. >> Right. Right. So like by defining it now we can then speak to this this we can then judge it against the criterion because we understand its structure and what it's actually doing. >> Made of >> made of and what the zero and the one state is. So then we can begin to as we go through this process ask the questions about quality control. >> Exactly. >> And and scalability. >> Yeah. And the one more thing before we start judging with the criteria is I'd like to talk about how do you actually talk to the thing. >> Yes. >> Right. Um once we define the cubit and how we talk about it or how we talk to

1:05:30it then we can get into the criteria. So that's going to be the format of all of these sort of audits. Yep. >> So to speak. >> So how do we talk to the thing? We use microwaves in the gigahertz range. So here we've got a chip that has four transponds cubits. Those are on the bottom there. Those four, they are connected to um a drive line on the bottom. Those are little lines that send in microwave pulses to change your cubit from a zero to a one. >> And then you see the top squiggles, those are your readout resonators. Okay? And if the cubit is in one state or the other, it's going to resonate with a microwave that's inside that. You can

1:06:12imagine like, you know, in fiber optics, fiber optics like carry light. >> Yes. >> Through it, right? This is a fancy mini fiber optic thingy. Okay. That's going to hold a microwave inside. And if the microwave is exactly the right frequency, it's going to resonate with each of these little squiggly wave guides. >> Okay. And so basically where we read is in these readout resonators. Yeah. If if the if the cubid is in one state or the other, the readout resonator is going to resonate and then my line up top is going to go back up to my electronics and tell me what state is each of the four in >> because we have four cubits. >> And so we want and then we have each of these resonator uh readout like

1:06:54basically line like you know lines that connect to our piece that's going to send it back up to us. So we can independently read each of the four >> exactly >> cubits. And so this is this is a 4 cubit >> system >> transmon um computer a 4 cubit superconducting circuits >> computer [clears throat] right and and the way they talk to each other is just through cross capacitance meaning like the if there's a circuit over here and a circuit over here they're going to affect each other using electric fields >> just by proximity >> just just by proximity straight up right >> and I mean so does that does that kind of make sense the drive [clears throat] line sort of tells you how to poke it >> the cubits are in the middle they can be in either a zero or one and the resonator that's up top is going to let

1:07:35you read >> Mhm. >> what the state it's in. So there's my you know initialize manipulate readout. >> Yes. >> Okay. It's just going from bottom to top. >> Makes total sense. >> Okay. Now we know that how the we know about how the quantum computer works. Now let's do the audit, right? How does it hold up to the FFP criteria? Well, what are the strengths? The strengths are that superconducting cubits have very fast operations 10 to 30 nanconds. You know those rotations on the block sphere that I was showing earlier, those gates, they can happen within 10 to 30 nonds. That's fast. Okay, that's very fast. And crucially,

1:08:16>> um, if you have two cubic gates, it's maybe a little bit longer, like 60 nonds. But the coherence time, how long a cubit remembers itself is quite long. >> Yeah, it's nice. >> Okay, it's nice. We we actually covered a paper by Princeton um earlier in this podcast season where they described a cubit with 1 millisecond of coherence time, >> which is fantastic. >> Which is fantastic compared to nanconds. If you're doing tens of nanconds to to like move stuff around, if the thing can remember for a whole millisecond, that's there's 10 to the six nanconds. There's a million nanconds in a millisecond just to [snorts] give you the like you've got a lot of time to poke around with it,

1:08:57>> right? And basically make sure you like can read what's happening, right? Like the the the coherence time effectively is how long do you have to read >> and manipulate >> and manipulate before the system collapses and you have to start again. >> Yes. Exactly. Um, and that the that Princeton paper used tantelum which is I always find it hilarious that like you know in high school when we learned about the periodic table >> there were all these elements that we were just like who >> who uses tantelum [laughter] >> but yeah in quantum computing industry there's so many exotic materials like tantelum um we're going to get into uturbium later which is you know I

1:09:38didn't think when I was in high school I was like why why would I need to know about uturbium. There's there's good reasons for it, right? So, okay, that's that's a strength. The gate speeds are really fast. The um the coherence time is pretty long compared to the gate speeds. So, you can implement an algorithm pretty quickly. What are the negatives? Well, one, remember I told you about that that harmonicity meaning it's drifting away from harmonic. Harmonic meaning >> the parabola >> parabola. But I've introduced this cosine term that sort of gets rid of that degeneracy in the energy spacing. So only 0 and one is a certain energy spacing. The other ones are not that

1:10:20energy spacing. So when I want to talk to 0 and one, I send a microwave pulse that is exactly that energy and I can toggle between 0 and one. >> And and [clears throat] this is the latter rung distancing. And it's like you want to be able to know which rungs of the ladder you're on. And that's why you want there to be a difference between the different distance between zero and one and others >> and others. >> However, >> yeah, there's a problem. >> Okay, >> there's a tiny problem which is as I'm the gates like how I manipulate this cubit depends on microwaves getting sent in. Right now, if I could send in a pure tone, right? Like uh um uh you know those uh tuning forks that have a pure

1:11:02tone. If I could send in a pure tone at exactly that frequency, that's the difference between the zero and one, then I'd be fine. But a pure tone necessarily means a very long time to send that frequency, right? >> Yes. >> Now, as I start squishing the frequency, right, I I start doing a or a that's a very >> Mr. AC capella, everybody. But [laughter] >> but uh notice over there right what I did was I was trying to access different notes in sound but I was trying to make it very short. >> Yeah. >> Now if you were to take that microphone that that sound readout and then you

1:11:44were to um ask some computer algorithm what are the frequencies in when Krishna did beep versus boop. There's going to be the main frequency, which is the note that I was trying to get to, but there's also going to be off frequencies. Okay? There's going to be other frequencies in there because I'm trying to squish all of the notes into a very short time scale. This is actually straight up Heisenberg uncertainty principle. There is a trade-off between your accuracy and frequency and your accuracy in time. So, if I make the time window smaller, the frequency bandwidth gets larger. That's a problem

1:12:24>> because now >> if I'm trying to only toggle between 0 and one, but I'm sending these really short pulses, there's a chance that I toggle the other frequency like there's a chance that some of the other frequencies have made it in into that short pulse >> and so now I might be accessing the other states. >> Yes, this this this tracks the the idea is because uh we need to communicate at a very fast rate >> because of other limitations of the system. um the accuracy by which we can uh read this between the zero and one it kind of gets fuzzy necessarily needs to get fuzzy because we're trying to communicate so quickly. So it's like this is like a trade-off, right? It's

1:13:05one or the other. You can't have both. >> You can't have very fast and then high fidelity uh like u understanding of the frequency that you're sending like it's it's if you do it very fast Yeah. then frequency is a little fuzzy. >> Yeah. Yeah. And so you need to control it really well. And just to show how much you want to control it, right? The thing the the difference between these states, the zero and the one is at a gigahertz range. >> Okay. >> Okay. That's [clears throat] 10 the 9. >> Yeah. >> But um the difference between So the difference between 0 and one is a gigahertz. The difference between one and two is also in that gigahertz range. It's different from the first one by only like hundreds of megahertz. >> Mhm.

1:13:45>> Right. >> Yeah. Yeah. Yeah. So the two the two rungs of the ladder are not all that different. >> Different. Yeah. Yeah. In terms of how we're able to actually read the difference based on what we just talked about. >> Exactly. So that that's a problem, right? And the other thing is something called um microscopic defect coupling. Effectively, there are these two-level systems in any interface. And this is a problem in sort of any solid state electronics. Whenever you have like interfaces like for example the Josephson junction let's say the Josephson's junction is made out of aluminum with some aluminum oxide in the middle and then aluminum. Okay. Now the aluminum and oxygen they form these bonds but those bonds can be maybe in one of two states like that's the red circle and the pink circle. If the

1:14:27energy between those two states is about the same as your cubits 0 and one then when I'm trying to talk to the cubit sometimes instead of talking to the cubit I will talk to this bond >> and the bond will toggle between one bond and the other and then it's like ah >> so it's like you end up reading the substrate rather than the system. >> Yeah. Yeah. I'm trying to talk to this one thing but like as I send my microwave the microwave is going to spread out because microwaves have a large wavelength. they're going to spread out and maybe it'll it'll like poke this other thing >> and it just happens to be in the right state and phase to send a response back. Okay. And so the point here being um >> from cubic quality we have um

1:15:11>> gate speed is great but the inability to distinguish between zero and one and other states. >> Yeah. >> And it might be interacting with your substrate. >> Yeah. Yeah, some other stuff >> is problematic. >> Is problematic, right? Okay. So, now that was cubic quality. Now, let's talk about control. Now, um the strength is that you've got direct microwave interfacing. Okay. The energy splittings are firmly in the microwave domain. And that means that like control and readout can leverage modern telecom and radio frequency equipment, right? We're we're really good at radar. We're really good at radio and things like that. >> The negatives though, one is planer

1:15:52connectivity. The transmons rely on nearest neighbor 2D coupling. Okay. So the the types of error codes that you can kind of implement here are limited by the connectivity of your chip. >> Meaning only certain types of connectivity can we really effectively use this for. >> And this is this is honestly like I mean it kind of makes sense. This is something that um that a lot of things have to deal with. That's totally fine. Okay, >> the the the the one that I want to kind of focus on is um cross talk and frequency crowding. Okay, here's the photo again of our 4 cubit computer. I want you to notice something. You see those resonant readout cavities, the

1:16:36squiggles, >> they're all different. >> Mhm. >> You see them? >> The one on the left is like uh taller. Like it's like thinner. >> Yeah. Yeah. >> And the one on the right is is larger. >> Yeah. Yeah. Yeah. >> Right. >> Yeah. >> Okay. There's a very good reason for that. The reason is suppose I send in a microwave at a certain frequency at a certain energy difference to the one on the left. to make sure that that microwave doesn't bleed out and talk to the other ones. Each of the microwaves, each of the transmon cubits need to have a unique

1:17:17resonant frequency. >> Yeah. >> Does that make sense? >> It does. No, it does. >> Right. Cuz if I want to talk to to this guy with one language, >> the other ones better not be able to understand me. >> It's like a walkie-talkie with different channels. >> Exactly. >> You need different channels otherwise everyone's going to >> Yeah. Or straight up the radio. Right. There's a reason why 89.9 is uh KPCC and 91.5 is KUSC for classical for those for those who live in Los Angeles, right? Yeah. And and there's a I think there's a 0.2 megahertz like gap between all of our radio stations, right? Because when I tune to one, I better hear the one that I want to listen to. >> Yeah. >> And not the other ones. >> And so you need them to have they're not

1:17:59trying to all listen to >> Yeah. And this is the problem with like AM because AM can bounce from the atmosphere sometimes when you like drive out, you know, you'll get like these you'll get like the the talk radio from Sacramento and also and so depending on where you are in the mountain, you'll like switch between someone talking in Sacramento or someone talking in Los Angeles, right? Yes. >> Um but that's the idea. >> That makes sense. >> Now this this creates a challenge because you've got a certain bandwidth where you can put all of your unique frequencies, right? Like for radio for example, I think it goes from what a like let's say 87 to 106 there. That's a numbers game. >> Yeah. >> And if I've got a spacing of 0.2,

1:18:40there's only a certain number >> that I can put. >> I can't put more >> because you need at least that two mez gap. >> Yeah. So the this this idea is called frequency crowding. >> And cross talk. I got you. >> Now there's ways to fix it. For example, you could have like a flux biasing that like you like pump some voltage into each of the cubits and then that raises or lowers the resonant frequency, but then that introduces like one over f noise and all sorts because you're not introducing more electronics into the system. Right. So, there's ways around it. I'm just saying this is like a kind of a mathematical thing that [clears throat] you need to worry about. >> Yeah. Right. >> Okay. >> Which foreshadowing some other systems