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Rm 330: Natalist, we… So, I haven't yet connected. I see, can I just connect my HDMI to my…

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Rm 330: You don't have to connect any cable. You're just gonna zoom. Yeah, I'm just gonna zoom. Okay, so, I guess I can go back to… Somebody ask a question? Oh, let's see…

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Rm 330: The microphone… yes, yes, now it's, unmuted, but I muted it earlier, so that way you don't get the extra chatter before I start.

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Rm 330: You must hear my voice. Okay, so my computer is being… Okay, we still have…

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Rm 330: So, my audio is down, and my video is off. And then hit the mute button.

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Rm 330: There we go. And share your screen whenever you're ready. It's going well with you? It's going well, things are going well. I'm learning a little bit of sword fighting.

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Rm 330: Any fun trip with that plan? Well, either this upcoming weekend or next, I'm going to Pennsylvania for the first time. Oh, for the first time! That's what I hear. I don't know if it's still…

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Rm 330: There's the theater there, Bucks County Playhouse.

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Rm 330: It's really… they do a pretty good job, you know, I mean, some are better than others, obviously, but they're… they're all good, right? And the ticket gets us, like, it's only a 300-seat theater, so…

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Rm 330: I mean, I don't know about right now, generally, yes. Yeah, yeah, it's your helpless. Did you know that? I've done that email. She reads her email, she's just busy doing things that she's not always on campus. Okay. I think today was an off-campus thing.

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Rm 330: Bush. Oh, no.

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Rm 330: somewhat pricey, but pretty cool, place called the Nectar Pine Bar, which, it's got those small plates. It's really… it's a cute place to hang out over the river a little bit. It's got a

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Rm 330: Agreed.

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Rm 330: Treehouse. On the weekends, it gets pretty busy.

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Rm 330: I don't know if we're… Friday evening or Saturday morning? Or you can stay overnight? Yes, yes. Oh, okay, where are you staying? I'm not sure if he's making all the plans. Oh, okay. Which I'm not used to, because I'm used to…

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Rm 330: My prior relationship having a lot at this point, but he's taking charge. Well, basically, there's a woman that I have, which is a kind of a D…

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Rm 330: plays.

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Rm 330: Occasionally move on to plays in the space.

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Rm 330: That's pretty… it's pretty nice.

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Rm 330: Sort of.

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Rm 330: They have a couple of different areas. I mean, there's an old part of the hotel, you know.

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Rm 330: thing, you know, but depending on what part you're in, it's more goldy or gooey. The new one's… well, the new one is kind of got some pretty cool…

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Rm 330: We stayed in the Newport Park. Yeah.

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Rm 330: through the Honors College, so it's officially introduce them. Brewery, you said a restaurant there, which we always liked. Yeah, I actually… there's a textbooks, I don't know why they're good.

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Rm 330: There are a few, there are several smaller shops, and also…

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Rm 330: Walk over to… across the bridge, and that's a…

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Rm 330: It's a moderate walk. I mean, it's nothing, you know, nothing…

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Rm 330: Just across… just across the river. Lambert Piers also does.

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Rm 330: It is unfortunate, it is… It was cooler before the pandemic.

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Rm 330: But that killed a lot of the cops, and so, not as… not quite as scary as me, but it's still fine, it's still good, but it's… some of the…

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Rm 330: Some of the places that we're cooking were having delivery, so…

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Rm 330: And please come at your list.

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Rm 330: Nice. I really can't wait to see your work.

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Rm 330: Like I said, I don't know… We do sellouts.

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Rm 330: It's not very big. Take a look and see. Hutts County Playhouse. I think rent is… We went to see South Pacific.

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Rm 330: Have you ever heard of South Pacific? Oh, there's a huge play.

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Rm 330: I don't know, like, credit history.

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Rm 330: Anyway, one of my teachers loves it, so he's like, I knew I had something, right?

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Rm 330: We saw Rocky Horror there. Yeah. We saw… they've had a few things, like bio, everybody…

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Rm 330: Okay, yeah. But here, it's already kind of, you know…

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Rm 330: They won't let you go off the stage, or… There we go.

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Rm 330: You know, it's not the movie.

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Rm 330: So they're kind of limited, because it is a small business.

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Rm 330: Although, the thing you'll see… You'll sit there, and it's a speedy degree.

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Rm 330: Because, like, everyone who's there competing.

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Rm 330: There are a few… oh, we saw a grease, and I took my grass. So glad you could hit it.

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Rm 330: Yeah, well, and my control mean that I'm actually here. I was supposed to be at some extremely boring theory meeting in Washington, but I came home because Premi had to go and get her eye fixed, so anyway… Anyway, have a good time. She's extremely boring.

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Rm 330: DOE meeting. I did actually meet my program manager, so that was the most important. Okay. Good. Oh, very nice.

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Rm 330: Very looking forward to your talk. Awesome. Let's double fact check. Okay, yeah. So…

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Rm 330: Who is your PhD advisor at Funa? Mukun Leila. I got it. Okay, good. You didn't work with Dan Row. No, I didn't. He was on my committee, though. He was on the committee?

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Rm 330: Oh, that'd be good. She might be watching.

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Rm 330: which is great if you're doing, you know, if you want to be in coffee, but they are not doing that, so it's just like, just touch, and I'm actively trying to go through with not trying to do it on a group basis, so again.

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Rm 330: Well, I'll tell… I'll, I'll send you a short notice.

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Rm 330: It's not that big. It doesn't, you know, it's not a place.

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Rm 330: Oh, sorry. Sooner.

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Rm 330: Yeah, yeah.

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Rm 330: Now we have to go back to doing that.

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Rm 330: That's the nearest high quality vision. So the vision is nothing about…

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Rm 330: Yeah, but that… I'm not. I was at the theory, DOE Theory Investigators meeting until yesterday morning. I had to come back and take it.

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Rm 330: And I'll just decide.

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Rm 330: I told you to talk to that.

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Rm 330: Let's see if they… I think it'll be okay.

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Rm 330: And you have to, like, pasta or something? Yeah. This is, like…

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Rm 330: I know the rules, but it doesn't help. And it's very simple.

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Rm 330: Yeah, that's right. Each time you measure the link plus 0.

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Rm 330: Yeah, that's true.

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Rm 330: No, they just stopped working.

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Rm 330: Not a mayor.

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Rm 330: Is it working, yeah? And this way in advance. Yeah, it was working, it's just working.

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Rm 330: That's another challenge. Yeah, no, it's just like… Tested it before.

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Rm 330: Is there a talk on that, Hank?

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Rm 330: I… Is your talk on the memory stick? I, don't try again.

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Rm 330: Yeah, sorry.

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Rm 330: Be as efficient and as contractually complicated you are.

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Rm 330: It's fine. Oh, it's working out, why about it? It's good.

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Rm 330: Got 2 more minutes for me.

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Rm 330: Don't read that prompt.

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Rm 330: There's 19 people a month.

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Rm 330: Reporting in progress.

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Rm 330: You cannot go to China, young man.

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Rm 330: You cannot give a talk on your mortgage idea, you've got… you've got too much Ministry of War support.

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Rm 330: One moment.

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Rm 330: There's also under 20 additional people online already. Okay, amazing.

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Rm 330: We're gonna update.

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Rm 330: They're gonna monitor the questions.

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Rm 330: Eric?

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Rm 330: I'm here too, I can help you. Go do that, okay.

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Rm 330: they can hear me, but I guess they can, yeah. All right, well, welcome to the second of our Colloquium series. Last week, Ananda Roy told us about theoretical aspects of information.

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Rm 330: And, this week, it's my great pleasure to introduce you to, Srivatsan Chakram.

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Rm 330: I sent to most of us, who is going to continue this theme.

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Rm 330: He's an experiment… for those of you who don't know, Batson is an experimental, physicist working here at the intersection of quantum information, quantum optics, and condensed matter physics.

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Rm 330: he did his PhD at Cornell University, where, fun fact, he almost became a theoretical physicist. But he saw the light, and ended up looking to…

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Rm 330: Buckley Tory, and then went on to, University of Chicago, where he was a post office with David Schuster, and we were lucky enough to pick him up as a junior faculty member here at Rutgers.

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Rm 330: And, what he's been doing since he came here to Rutgers is to build up, at least to me, it looks very impressive, a multi-mold superconducting, cavity platform

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Rm 330: And, he has microwaves bouncing around inside this platform, and, he can manipulate the photons, and, this gives and opens up ideas and possibilities for quantum memories.

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Rm 330: But error correction and, many-body physics with photons.

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Rm 330: So, I mentioned that he almost became a theorist, but in my opinion, this perhaps explains why he has such a talent for building beautiful experiments.

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Rm 330: And to address deep theoretical problems.

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Rm 330: And so it's a great pleasure to welcome him today. He's going to tell us about programming quantum, oscillators, computation, and simulation with random access memory. And one more thing before I finish. Next week, we are going to switch fields, and we're going to learn about, dark matter and dark energy, so please put that on your,

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Rm 330: put that on your list, and let me hand over Batson. Welcome, Batson. Thank you, Piers for such a kind introduction. It's really my pleasure to give this Colloquium and tell you all about what we've been up to in the last several years.

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Rm 330: So, this talk is going to proceed in two acts.

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Rm 330: I can figure out my laser pointer. Okay. Yes, so the first act will be sort of telling you a history of superconducting quantum systems through the lens of the second quantum revolution, putting it in the broader history of the development of engineered quantum systems.

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Rm 330: And the second act will be about how we use supernatural quantum technologies to build and program new kinds of quantum processors with random access memory.

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Rm 330: So,

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Rm 330: As all of you probably know, last year was the centenary year of the birth of the modern theory of quantum mechanics. We had a beautiful lecture, Colloquium in spring, from Piers sort of describing this remarkable period of history between 1925 and 1927, starting with Heisenberg's work in Helligoland, where he.

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Rm 330: figured out that observables should be represented probably by matrices. We probably didn't know what they were at the time. Pascal Jordan and Max Vaughan, then put forth

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Rm 330: the theory of matrix mechanics, and along with Dirac, they figured out that there are certain observables, like position and momentum, that do not commute, and now we say that X and B have this commutator that is IHR.

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Rm 330: within a short period afterward, Schrodinger put forth this famous equation for wave mechanics, and also showed that it was equivalent to the matrix mechanics perspective, and then Max Bond put forth the statistical interpretation of the

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Rm 330: Wave function, and with that, within a period of 3 years, we had quantum mechanics in close to its final form.

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Rm 330: Of course, this work didn't happen in isolation. It was the culmination of 50 years of experiments that we learn about in a modern physics class that pointed out that there is new physics beyond classical physics.

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Rm 330: And in the years that followed after the birth of quantum mechanics, quantum mechanics was put through its bases and tested with more and more precision.

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Rm 330: This includes experiments done with atomic and molecular beams by Rabi and Ramsey. This gave birth to nuclear magnetic resonance and development of atomic clocks. By 1967, the cesium-133 hyperfine transition was the standard for time.

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Rm 330: Quantum mechanics was also applied to increasingly complex systems, it was applied to molecules, to the work of Pauling and others, and then it was applied to solitary physics with great success, with the development of band theory, which explained metals and semiconductors, and that indirectly led to the classical computer

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Rm 330: revolution, quantum mechanics was also applied to

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Rm 330: Macroscopic quantum phenomena, like superconductivity and superfluidity, and in the latter half of the 20th century, quantum mechanics was combined with special relativity to give forth the standard model of particle physics that explains all of the fundamental forces in nature.

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Rm 330: Yet, despite this remarkable predictive success, there was always doubts about quantum mechanics, doubts about the regime of validity of the theory, doubts about what it all means.

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Rm 330: And some of these questions were raised by the founders themselves. Schrodinger was perplexed about what would happen if we applied these quantum principles that worked so well with atoms to the macroscopic scale, and put forth this famous Schrodinger-Kat paradox.

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Rm 330: Heisenberg had similar misgivings.

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Rm 330: Einstein had issues with the randomness that was baked into the heart of quantum mechanics, and also probably was one of the first people to realize that quantum mechanics was incompatible with local realism, as Ananda pointed out in his Colloquium.

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Rm 330: last week.

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Rm 330: So in the years that followed, with all of the successes and the developments of modern atomic physics.

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Rm 330: These thought experiments that were put forth by, the founders began to be, realized in experiments, and

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Rm 330: Slowly, it became possible for us to control, isolate, and manipulate and measure individual quantum systems. Ananda talked about this, Wells inequality test, which pitted local realism against quantum mechanics and quantum mechanics1.

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Rm 330: And this, was awarded the 2022 Nobel Prize.

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Rm 330: the work with atomic beams and all of that ultimately led to the development of ion traps, which, along with the atomic beam work, was awarded the 1989 Nobel Prize, and this is the… forms the basis of now our current,

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Rm 330: That tie on quantum computers.

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Rm 330: And there was also,

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Rm 330: Okay, again.

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Rm 330: I think I have to probably switch to using the…

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Madhu Venkadesan: Mouse click on the slide once, and that'll fix it.

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Rm 330: Oh, amazing.

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Rm 330: Oh, thank you.

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Rm 330: Okay, There was also, all of this work also,

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Rm 330: People also use this technology, to,

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Rm 330: Use lasers to cool atoms down, to very low temperatures, like,

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Rm 330: microkelvin to nanoKelvin, and this ultimately led to the development, or the, discovery of the creation of a Bonsai condensate in the lab, and this is sort of set forth the modern field of, ultra-cold atomic,

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Rm 330: gases?

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Rm 330: Through all of this work, there was also a lot of progress on the control of single ions

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Rm 330: And photons and later atoms. This was recognized with, a 2012 Nobel Prize to Serge Harosh and David Weineland,

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Rm 330: David Weineland used lasers to control the electronic states and the emotional states of trapped ions in a ball trap. In some sense, Serge Harosh did the dual experiment where he used atoms, Rydberg atoms, which are basically atoms that are promoted to a very high principal quantum number, to control the quantum state of light stored in a microwave cavity. In some sense, the experiments that we do

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Rm 330: descendants of these experiments done by, Serge Harosh. And with these experiments,

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Rm 330: these two gentlemen were able to create Schrodinger-Kat states for the first time. They were able to create an entanglement state between an atomic degree of freedom and a macroscopic classical state.

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Rm 330: Sergeant Roche was able to watch this cat state decay. He did the first experiment that used the cavity field as a meter to measure the quantum state of the atom. He was also able to observe quantum jumps in photon number in this cavity.

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Rm 330: And by the 80s and 90s, it became clear that these systems were not just useful for fundamental tests for quantum mechanics, but could be used to build a new kind of quantum computer based on quantum logic, as Madhu talked about in his Colloquium.

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Rm 330: There was also a parallel line of research that was started by Tony Leggett, who sadly passed away earlier this year, but he posed the question that these superconductors and superfluids, which are macroscopic quantum systems.

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Rm 330: Is there a way in which we can use them to test the limits of quantum mechanics? So, this here is a levitating superconductor. It has 10 to the 23 electrons.

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Rm 330: about a billion of them form Cooper pairs. These Cooper pairs are bosonic, and they all condense into one macroscopic quantum wave function. And importantly, this

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Rm 330: condensate is protected by the fact that there's a gap to single particle excitations, which you can only create if you break a Cooper pair. And for aluminum, which is the metal that we most use.

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Rm 330: This gap is around 82 GHz, so you have to provide that much energy in order to create a single particle excitation, and because you don't have single particle excitations, largely, this condensate, its dynamics can be

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Rm 330: Very low loss.

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Rm 330: So,

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Rm 330: You can create intense… interesting dynamics of this condensate. Probably the most interesting thing you can do is to build what is called a Josephson junction. This is two pieces of superconductor separated by a thin insulating barrier. We make this out of aluminum. The insulator is a thin layer of aluminum oxide, typically around a nanometer.

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Rm 330: Now, the coherence length of the Cooper pairs is much larger than that, so you can have these Cooper pairs tunnel across this Josephson junction. So this is the tunneling Hamiltonian, where N is the number of… number difference of Cooper pairs across the two islands.

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Rm 330: So this should be familiar to anyone who's taken a solid-state physics class. This is basically the type binding model, and you can find the eigenstates of this. They are just the plane wave states. So, phi is a state of well-defined phase. It's a superposition of all possible numbers, number differences of Cooper Pairs.

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Rm 330: This should also remind you of the relationship between

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Rm 330: position eigenstates and momentum eigenstates in quantum mechanics. So, if you take phase and you promote it to an operator, and you promote charge to an operator, then phase and charge are canonically conjugate observables, just like position and momentum.

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Rm 330: And now you can write down this Phani Hamiltonian in the phase basis, and you get that the Hamiltonian is minus EJ cosine phi, so the energy goes at the cosine of the phase difference across the Josephson junction. And then you can write Newton's equations

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Rm 330: for this Josephson junction, which is, like, n dot is, like, you know, endless, like, momentum, so this is P dot equals to the gradient of the potential, so if you do this, then you get that the current goes as the sign of the phase difference, so this is…

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Rm 330: Just as an effect, which is magical, that you… if you have two pieces of superconductor, if you just have a phase difference across them, there's a persistent current without you applying a voltage. And interestingly, if you apply a DC voltage, then you get an AC current. So this is a highly interesting nonlinear object.

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Rm 330: And it's a macroscopic manifestation of quantum mechanics, but Leggett pointed out, that this really doesn't help you test whether quantum mechanics really applies in the macroscopic scale. In order for you to do that, you actually have to create a CAP state of this phase coordinate, or at the very least, what you should try to do is to see paneling of the space coordinate across some classically forbidden region.

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Rm 330: And this is… yeah. Why isn't it?

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Rm 330: Face-coherent superconductor, already some kind of…

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Rm 330: macroscopically quantum coherent state. It is a macroscopically quantum coherent state. Why can't we use… we can't just… can't use the word cat. Why not? Well, so it is a, like, in some sense, it is like, like, if you just have a, like, a BCS state, it's kind of like a coherent state, so it's like a classical state.

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Rm 330: So if you want to create, like, so that's like a coherent state in a cavity, right? So if you want to create a CAD state, you need a superposition of two coherent states, and that's kind of the point that Leggett was making.

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Rm 330: And yet, A state with a well-defined face can be regarded as a superposition of

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Rm 330: states with well-defined particle number. That is totally true, but… But why don't we call that a CAP statement? Well, I guess,

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Rm 330: It is a… a CAD state is a superposition of two

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Rm 330: classical states, right? So, the coherent state is a state, if you look at the Wigner function of, right, it is, it doesn't have any negativity. It's very much like the vacuum state that's being displaced, right? So, that's the sense in which the current state is a classical state, right? It has no negativity in the Wigner function, whereas if you now make a superposition of two coherent states, you get Wigner function negativity, which is a sign of

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Rm 330: non-pascal, but that's the sins of the beach.

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Rm 330: Right, so,

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Rm 330: It's not just about superposition, but it's more about non-classical nature. Yeah, absolutely, yeah. So, there's a laser, if you shine a laser, that's also a coherent state. That's right, yeah. And, so in a coherent state.

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Rm 330: I would argue is a classical state, even if it has a few photons, and I'll show you such states here.

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Rm 330: Okay, so, so John Clark, along with Michel Devery and John Martinez, went ahead and tried to see, this macroscopic quantum tunneling, and they were… did these, seminal experiments in 1985 that was recognized with the 2025 Nobel Prize, which is,

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Rm 330: for the discovery of macrocopic quantum mechanical tunneling and energy quantization in an electrical circuit. So, this is the experiment that they did. So, they took a Josephson junction, which is represented by this X over here. The Josephson junction also has some innate capacitance, because it's just two pieces of superductor separated by a gap. There's some dissipation around, so there's some resistance, so this is how you should represent

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Rm 330: the circuit for a justice injunction. What they did is they basically applied both a DC and an AC current to this system. I argue to you that,

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Rm 330: Joseph's injunction on its own forms a cosine potential for the space coordinate. If I now apply a current bias, what I then get is a tilted washboard potential, and the metastable well over here can have quantized energy levels.

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Rm 330: So, what they did is that they took this tunnel junction and they cooled it down. So, at high temperatures, the space coordinate can just

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Rm 330: thermally activate onto this barrier and just roll down the hill. And when it rolls down the hill, it gets, like, some expectation value of phi dot, and through the… through Faraday's law, that leads to a macroscopic voltage. So, they were able to detect, the…

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Rm 330: escape of this phase by just measuring a macroscopic voltage in the circuit. And what they found is that if they cooled the circuit down to very, very low temperatures, at some point, there was still

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Rm 330: tunneling that they observed. And this is this macroscopic quantum tunneling.

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Rm 330: The other experiment that they did is that they controlled the circuit parameters so that the circuit cannot tunnel from the bottom-most level, or the tunneling rate was highly suppressed, but it would tunnel if you excited it to some

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Rm 330: intermediate level in the valve. So then what they did is they irradiated the circuit with microwaves, and found that, the circuit had quantized energy levels, so it would… it would physically excite the phase coordinate to some higher level, and then it could escape.

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Rm 330: So, this, really gave birth to the entire field of supernuting quantum computing.

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Rm 330: And now, in the intervening 40 years, we have made many, many different types of superconducting qubits. In some sense, all superconducting qubits with one degree of freedom can be represented by a circuit of this type, consisting of a Josephson junction, an inductor, and a capacitor. The first superconducting qubit that was made was the Cooper pair box.

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Rm 330: But now we have many, many of them.

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Rm 330: And this is kind of like our periodic table. These different circuits have different physical qubit states, and more importantly, different sensitivity to various environmental noise sources that makes it so that certain qubits are better than other qubits.

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Rm 330: The most widely used Supernatural qubit is the transform. So the transform is basically, Josephson.

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Rm 330: along with the capacitor. So this has an additional external capacitor that we add. I argued to you that the energy of a Josephson junction goes as the cosine of the phase, so this is kind of like the inductive energy associated with the Josephson junction. There's also an energy associated with the capacitor, so EC over here is the energy associated…

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Rm 330: one electron's worth of charge difference across the capacitor. So this is the total Hamiltonian for this very simple superducting circuit.

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Rm 330: Again, number and phase are canonically conjugate over here.

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Rm 330: So you can see over here, this is a tiny Josephson junction, but you have two capacitor pads over here that have been added.

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Rm 330: And the phase differences are macroscopic single particle quantum degree of freedom. So this Hamiltonian is actually identical to the Hamiltonian of a quantum rotor, so this phi is a compact degree of freedom. EJ cosine phi is basically a gravitational field, so it's really a rotor in a gravitational field.

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Rm 330: But it can have quantum fluctuations. So, this capacitance essentially controls the moment of inertia of the rotor. So the original Cooper pair box that had a very small capacitance is a very light rotor. They're just free to fluctuate all over the place.

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Rm 330: This gate charge, you can think of as, essentially, if I have a flux tube that is going along this axis, and if this rotor were charged, then I just get this as the Hamiltonian. So, if the phase fluctuations are large, you can see that the spectrum

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Rm 330: depends very sensitively on the gate charge, and that's bad. So, one of the morals of the last 40 years is that charge noise is bad.

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Rm 330: You know, so what they did is they made a circuit that was completely insensitive to charge noise, so if you make the rotor heavy, it only can fluctuate above the minimum, and as a result, it is… the spectrum is insensitive to gate charge, and now this is just a particle in a cosine potential. It's just a weakly anharmonic oscillator. In fact, it's the quantum problem that was being solved by

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Rm 330: Heisenberg in Heligoland, just an anharmonic oscillator.

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Rm 330: And the honesty is not that large, it's about a few percent, but that's enough for us to use the lowest two levels

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Rm 330: as a qubit. So the transition between G and E is different from the transition between E and F, and you can prepare an arbitrary quantum superposition of G and E by just shining microwaves. So this is the block sphere of this, of this two-level system. If you just had a classical bit, it would just be either the south pole or the north pole of the block sphere.

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Rm 330: But an arbitrary quantum state is any point on this block sphere, and you can reach there with just shining one microwave tone and turning it on for the right amount of time. If you adjust the phase, then you can, you know, sort of change the axis of this rotation. This is called an Rabi oscillation.

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Rm 330: So, another thing I want to point out is that this artificial atom that we have, you know, is very simple. You can maybe object to calling it an artificial atom. It doesn't have fine structure or hyperfine structure and so on. But, you know, it has anharmonic quantized energy levels.

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Rm 330: It also has a very large dipole moment. Because it's two capacitors separated by a macroscopic distance, its dipole moment is about 10 million times the dipole moment of a hydrogen atom. So as a result, it couples really strongly to electromagnetic fields, and if it were just out in the open, it would

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Rm 330: radiatively decay very, very quickly, right? So it wouldn't have only a lifetime of a few hundred nanoseconds. However, you can borrow techniques from atomic physics and tailor the vacuum that,

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Rm 330: the atom sees. And this is what Serge Harosh did in his experiments. He put an atom in between two mirrors, forming a Fabi-Perot resonator, and the only wavelengths of the vacuum that were allowed were the ones which fit within the cavity, right? So as a result, you can now control the radiative decay rate of the atom. You can bring it into resonance with one of the modes and enhance the decay.

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Rm 330: Or you can move it further away and suppress the decay. This is called the Purcell effect.

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Rm 330: So…

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Rm 330: We can do the same thing by coupling our supernatural qubit to a resonator. This gave birth to the field of circuit quantum electrodynamics, which is another great innovation that pushed our field forward. I think it also should be recognized for the Nobel Prize at some stage, which is my opinion.

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Rm 330: So here, what you have is a coplanar waveguide resonator. You can think about this as a two-dimensional version of a coaxial cable. There's a center pin and ground, and there's some electric field across it. And here, you have a superconducting qubit. So these are two Josephson junctions, and this is a tiny island of superconductors. So this is actually a Cooper pair box, so this is actually a terrible qubit, but this is the first qubit where

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Rm 330: people short-circuit QED, and because this dipole moment, is really large,

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Rm 330: You know, it couples to the environment, but you can control the environmental density of states.

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Rm 330: This also, though, importantly, allows you a much better scheme for reading out the quantum state of the qubit.

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Rm 330: So, circuit QVD is essentially cavity QED with a macroscopic atom, and with the optical cavity replaced with a microwave cavity. The Hamiltonian for this system is described by this James Cummings model. So what's shown in the red is the Hamiltonian for a harmonic oscillator, what's shown in blue is the Hamiltonian for a qubit, and what's shown in green is the coupling between them. This is the dipole coupling

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Rm 330: between a qubit and an oscillator.

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Rm 330: And this is called the James Cummings coupling. And by virtue of the fact that,

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Rm 330: The… an artificial atom is so big, you can have very strong coupling between the qubit and the oscillator, and the coupling rate can be on the order of, like, 5-10% of the frequency itself.

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Rm 330: If you bring the qubit into resonance with the cavity, so here I can tune this qubit and bring it into resonance with the cavity, so then the qubit in the cavity hybridizes and forms these polaritons. In this limit, which is the resonant limit of the James Cummings model, you can have

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Rm 330: photons exchange between the qubit and the cavity. This is what's called a vacuum Rabi oscillation, a single photon being exchanged.

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Rm 330: And,

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Rm 330: You can also look at the same physics in the limit where the qubit and the cavity are far off resonant. In this case, if you have this atom in this optical cavity, the atom

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Rm 330: cannot absorb the photon, right? And the cavity… and the atom cannot emit into the cavity, but still, the atom can impact a phase shift to the light. So, it's kind of acts like a bead of glass whose refractive index depends on the spin state. So, as a result, the cavity's frequency depends on

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Rm 330: The qubit's state. This is actually what we use to read out the quantum state of the qubit.

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Rm 330: Another way you can look at it is that the qubit's frequency, what's in front of sigmaZ, depends on the photon number in the cavity.

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Rm 330: So, this is us creating a coherent state in the cavity and doing spectroscopy of the qubit, and you can see that we can count individual photons that make up that coherent state. And the splitting in each of these cases is what is called the dispersive shift.

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Rm 330: And, the kind of cavity QED systems that you can make in circuit QED are, in some sense.

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Rm 330: much better than atomic cavity QED systems. Like, one figure of merit is what is called the cooperativity, like, how much is the coherent coupling in comparison to the decoherence of the cavity and the atom? So this number for atomic cavity QED experiments is, like, 100 or something like that, but with our kind of circuit QED systems, you can make this

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Rm 330: Like, something like a million to a billion.

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Rm 330: And, this is the same physics that we harness for bosonic control of our many cavity boards. So these are basically the ingredients for superlacting quantum information. We have macroscopic artificial atoms, which have very large dipole moments, a million times that of hydrogen, sorry, the hydrogen atom.

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Rm 330: You can read out and control these systems with microwaves using the machinery of certain quantum electrodynamics. The qubit frequencies that we typically operate with are in the 5 to 10 GHz range. You can convert this into temperature, and that's around

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Rm 330: 250 to 500 millie Kelvin.

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Rm 330: So, what we do is, in order to see quantum mechanics, we have to cool these systems down in a dilution refrigerator, and the base stage of our dilution refrigerator gets down to 8 minike kelvin. So, if you just bolt it to the bottom of this dilution refrigerator, this circuit is initialized in a good approximation to the quantum ground state. And then you can prepare arbitrary quantum states by shining microwaves on it, as if it's an atomic system.

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Rm 330: And this is your lab in this building. Sorry, is this your lab in this building? Yeah, this is our lab in this building, yes, this is the 162 lab, yes.

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Rm 330: Yeah, it's new and shiny dilution refrigerator. Yes.

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Rm 330: So, with all of these advances over the past 20 years, there's been rapid progress, and now we have a bunch of companies that are building quantum processors with 100 qubits or so. Nanda talked about this in Colloquium. Most of the qubits that are being built in these companies are lattices of these transpond qubits that I talked about.

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Rm 330: And, they are not perfect, they're still noisy.

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Rm 330: And we certainly need quantum error correction to build, like, truly useful quantum computers, but already, people are asking interesting questions in quantum simulations, quantum chemistry, and quantum optimization. And also, importantly, there's been a lot of progress in experimental demonstrations of quantum error correction. The most widely used code is this surface code. Recently, Google had a very important result, where

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Rm 330: they stored

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Rm 330: a logical qubit, one qubit's worth of information, redundantly across many, many physical qubits, and show that that logical qubit

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Rm 330: performed better than the physical qubit that it was made of. It was better by a factor of two, but, you know, this is beyond break-even. And the goal is… importantly, they also showed that things got better as they scaled the size of the system up, which makes you think that if you make… build bigger and bigger systems, you can lower the error rate, and maybe one day achieve fault-tolerant quantum computing.

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Rm 330: And all these advances have happened because of the fact that the coherence time of these superconducting qubits have steadily improved over the past 20 years. The first qubit that showed Rabi oscillations, the Rabi oscillation lasted for a nanosecond. It's a Cooper pair box. Now we have, even in our lab.

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Rm 330: Qubits which last for 50 to 100 microseconds, and we have these cavities which last for, several milliseconds.

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Rm 330: These advances have happened because there have been advances in, making different styles of qubits, that are… have reduced sensitivity to noise. It's happened because of improvements in shielding and filtering. It's been… it's happened because of improvements in

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Rm 330: our understanding of the material science. Now, at Princeton, Andrew Hawke and Natalie DeLeon's group have 1.7 millisecond

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Rm 330: transplants made out of tantalum. But what I want to show over here is that the best core enzymes still belongs to these microwave cavities, kind of like this,

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Rm 330: like, Hirosh-style cavities, which are also made out of niobium. And we, I was involved in an experiment where we have, a 20 millisecond,

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Rm 330: A cavity with a 20 millisecond photon light, right?

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Rm 330: So this kind of informs, the kind of architectures that we build. We use microwave cavities as quantum memory. This is good because they have long single photon lifetimes, as I advertised.

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Rm 330: But also, each of… each cavity mode… each cavity has many modes, and each of them is a harmonic oscillator, and a harmonic oscillator has many levels, so it has a built-in redundancy that a qubit does not have.

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Rm 330: You can make these cavities out of mini form factors, like the dumbest thing you could do is to make a coffin cavity like this, like, kind of like a clamshell. You can also make these kind of coaxial cavities, which is basically… you should think of this mode as the mode of a cantilever, lambda by 4 mode. And this is nice, because then you can… it doesn't matter how you see the top.

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Rm 330: And all of these cavities can be coupled to a superducting qubit, and the zero-point electric field of that cavity mode can couple to the dipole moment of our transponse antenna, and we can get some coupling. And this can be done also in various cavity geometries.

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Rm 330: The other reason why cavities are good is that this redundancy of the FARC levels makes it so that you can have much more hardware-efficient quantum error correction. In the case of qubits, you need at least 5 physical qubits to make a logical qubit, but in the case of a cavity, you can make a logical qubit even in a single oscillator, partly also because

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Rm 330: of the restricted decorance channel that a cavity has, and a perfect cavity only has photon loss. So this is an example of such a quantum error correcting code. So what I'm showing here is a picture of the quantum state of the cavity. This picture has all the information about the quantum state. It's what's called the Wigner function, so it's kind of like a quasi-probability distribution in phase space, a classical state, as we discussed, like a core state.

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Rm 330: only has positivity, but once you have negativity, it's a sign of you've made a non-classical state. So, this arithmetic encode has two logical states.

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Rm 330: one logical state is Fox state 2. The other logical state is a superposition of 0 and 4. These two states are orthogonal, they have the same mean photon number, so if they… if you lose a photon, then you… you get to a state like this.

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Rm 330: Importantly, the coefficients did not change, so the quantum information is still there. And then I can detect, does the cavity have an even number of photons or a non number of photons? That's our error syndrome, so with that, I can tell that an error has happened without knowing any information about the nature of the superposition. So…

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Rm 330: with this kind of approach, there have been many other error correction codes, like the FAT code and the GKP code. This GKP code also showed beyond break-even quantum error correction. Very recently, they… by about the same factor that the Google experiments achieved, about a factor of 2.3 or so.

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Rm 330: All right, so, I guess this motivates the kind of quantum architectures that we build.

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Rm 330: We use quantum memory. We're also inspired by how classical computers look like. A classical computer has

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Rm 330: memory hierarchy, various layers of memory. You're really only controlling a few bits that are in the CPU register, and you have various layers of memory all the way down, and as you go down this pyramid, you increase your access time and increase the capacity, but as you… and if you go up this pyramid, you increase the cost per bit.

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Rm 330: The control is also highly multiplex. You don't have a control line for every bit in your classical computer, right? So… so we think a quantum computer should also have memory.

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Rm 330: And we build our memories using very low-loss microwave cavities.

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Rm 330: Build random access quantum memories, where we can have multiplex control of tens of quantum bits of information just using a few control lines, with the advantage that it's

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Rm 330: hardware efficient, you have a large, high-covariance tailored space. The first kind of architectures I'm going to talk about is one where we have a supernatural gene qubit that now is acting like an ancilla. A trans bond is an ancilla that controls tens of, you know, cavity modes.

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Rm 330: This is our first generation of architecture. Our second generation actually starts to look more like a memory. We have a main memory and a cache memory, and a tunable coupler that's coupling between them.

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Rm 330: So, let me just tell you about my program overall. We sort of

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Rm 330: build modular quantum processors using random access quantum memory. We think about ways in which you can best control these systems, how we do quantum error collections with these systems. Now that we have good control, we're starting to think about interesting quantum simulation experiments that we can do. Some of the things we think about are

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Rm 330: probing measurement-induced phase transitions, or using them for quantum chemistry, or maybe even lattice gauge theories at some stage. And we also use them for quantum sensing. We use our systems to measure thermalization of various dielectric materials at very low temperatures, which actually

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Rm 330: places a fundamental limit on decoherence of qubits, and we also use them to study interesting quantum materials, like moinary materials, in collaboration with Eva's group.

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Rm 330: So here's the outline of the reminder of my talk.

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Rm 330: So, yeah, so I'll talk to you about our first generation device, which is a weakly coupled multi-mode Podic memory, and I show how we can do fast operations in the system, how we can do state preparation, preparing target states, and do Podic encodings.

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Rm 330: I'll talk about how we've also used these techniques to control really high coherence, like, tens of daily cycling cavities in collaboration with Fermilab, and I'll talk to you about a new control scheme that we have developed that sort of is actually

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Rm 330: answering a question that was raised in the initial tappedion experiments of David Weineland, how do you use the James Cummings interaction to prepare or implement an arbitrary unitary? And we've actually demonstrated the first practical scheme for doing this.

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Rm 330: And then I'll talk to you about development of new next-generation random access memories and applications to quantum simulation and machine learning.

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Rm 330: So this is how we make our cavity. So if you want to… so, if you want to make… the simplest cavity you can make is a rectangular waveguide cavity. So the… so this is basically a box with vacuum in it, right? And inside it, you can have a necromantic mode that's basically the mode of a two-dimensional drum.

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Rm 330: So, it has, nodes at the end, antinode at the middle. So the wavelength of this cavity mode is about twice the size of this cavity. So now you can imagine if I drill a hole, this hole is much, much smaller than the wavelength.

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Rm 330: So, this field cannot leak out. Then you can imagine that I can actually make the entire cavity by drilling offset evanescent holes. This is nice because I can take a monolithic block of superconductor and just drill holes and define a cavity volume, and thereby eliminate one source of loss which arises from

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Rm 330: making it out of two pieces, you'll always have some resistive glass at any joint.

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Rm 330: And we can make this cavity much longer, and we can tailor the mode spectra. So here's a longer multi-mode cavity. Here's the fundamental mode of such a cavity, where you have one antinode. You can see that you've tapered the shape so that the field gets lensed on one side. This is the fifth mode of the cavity. All the modes have, like, some electric field at the end, so we can just stick our transform at the very end.

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Rm 330: And we'll get some dipole coupling with all of the cavity modes.

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Rm 330: This is the first device that we built, in Chicago when I was postdoc.

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Rm 330: And if you… so it's basically two such, flute-style cavities. So if you just slice it at the middle, you can see that we have one long waveguide over here, and one smaller waveguide, and in between, you have a transmog

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Rm 330: qubit. So this is, like, two capacitor pads that act like antennae that couple to the zero-point electric field, and in between, you have this tiny Josephson juncture.

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Rm 330: So it's now basically a single artificial atom that's coupled to many cavity modes, and we can make the cavity modes have a lifetime of a few milliseconds.

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Rm 330: This realizes a James Cummings model, except that we now have multiple cavity modes, so this is a multi-mode version of the James Cummings model. You can actually do a back-of-the-envelope calculation of the coupling strength that you can get, because it's basically… the dipole moment is a Cooper pair separated by a millimeter. The zero-point electric field, you can calculate by calculating the total energy in the electric field and setting it equal to h-bar omega by 4.

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Rm 330: So from this, you can just calculate what this G should be from post principles. It's around, like, 50 to 100 megahertz.

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Rm 330: We typically operate this Hamiltonian in the dispersive limit, where the qubit and the cavity are far off resonant, and we get this multi-mold version of the dispersive Hamiltonian, which we can use for control. So if we just have a harmonic oscillator, and if I just apply a microwave drive to it.

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Rm 330: because the energy levels are all evenly spaced, this can only allow me to make a classical state. So here, I'm plotting the Wigner function of this cavity, so you should think of this as position, and this as momentum, and I've scaled the X and Y axis by the scale of the zero-point fluctuations. So this here is the, you know, the size of the Gaussian wave packet that is, you know, the ground state. So if I apply a microwave drive.

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Rm 330: to this, all you can do is kind of push this blob around. That's the only thing that you can do. But if you couple it to a qubit, it turns out that you can implement an arbitrary unitary in this cavity.

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Rm 330: So all we have to do is couple it to a qubit and shine microwaves on both the qubit and the oscillator, and actually we can apply

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Rm 330: do this universal control in a variety of ways. I'll just tell you the canonical approach first, like, it's what's called the snap displacement gate set. So, essentially, one of the knobs I have is that I'll apply this microwave drive to the cavity and prepare

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Rm 330: current state, so this is just a displacement operation in phase space I can do. I can displace it anywhere in phase space. The other thing I can do, though, is the… is that I can resolve photon numbers, right? So I can do… so this is me doing spectroscopy of the qubit, and seeing that the qubit frequency is different depending on the photon number in the cavity.

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Rm 330: So what this means is that I can do a lobby rotation on the qubit, conditioned on the cavity having one photon, 0 photon, whatever. So if I now do that, then I essentially put a minus sign just to Fox stage 0. So if I do an operation where I displace the cavity, just put a phase shift to Fox stage 0, and displace back.

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Rm 330: then you can see that I have now prepared a state that has a dominant peak at one photon. So, this is the way in which we have prepared FOC1.

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Rm 330: So there are many ways in which you can use a coupled qubit to do universal oscillator control. The only thing I'll say is that the first two methods rely on this dispersive coupling being large, so in some sense, they are descendants of the Serge Harosh style of doing cavity control.

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Rm 330: The last two, can still do fast gates when the coupling is very weak. And in particular, the one that we have made a lot of progress on is in the James Cummings gate set.

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Rm 330: The James Cummins interaction is also the interaction that you can have between the electronic state of a trapped ion and the emotional mode of the trapped ion. So in some sense, this is kind of a descendant of the Wineland style of control.

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Rm 330: So, I mean… I mean, this all sounds great. The main thing is that, you know, our cavities are extremely pristine. They can have tens of milliseconds of coherence, but our ancilla, our control circuit, is typically much more lossy. So the name of the game is, like.

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Rm 330: Can you do fast operations while not destroying the coherence of the cavity? So there's a bit of a trade-off here. If you couple strongly, then you can get a large dispersive coupling, but that can also… that'll also mean that the cavity will inherit more of the transbound circuits loss.

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Rm 330: But if you now couple weekly, then maybe your gates will become slower, and then you'll have errors that'll happen during the gate. So,

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Rm 330: these are things to keep in mind. The other thing to keep in mind is that the circuit is nonlinear, so if you couple it to a whole bunch of cavity modes, the cavity modes will inherit that nonlinearity. So you can get, like, Hubbard-like interaction between the photons, and that is maybe fun for quantum simulation, but generally bad when you're operating a quantum computer.

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Rm 330: So, we are trying to address these challenges, in many different ways.

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Rm 330: So, one strategy is to weaken the coupling and still do fast gates, the other is to improve the ancillor score and style, and then the new architecture that I told you about. So, this is the first device that we built, so…

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Rm 330: Here we have, same architecture. This is our multi-mode cavity. This is a readout cavity. This is a transform. Transform has about 50 microseconds of lifetime. The cavity mode has millisecond lifetimes. We have lowered the coupling now to about a factor of 10 below what we had in our Chicago experiments.

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Rm 330: So now, how do we do control?

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Rm 330: So what we do… what we use is the fact that the cosine potential leads to aquatic nonlinearity. So we… essentially, you do formid mixing experiments.

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Rm 330: So what you can do is you can pump the system and essentially activate this kind of a Feynmann diagram, where you can have two photons in the transpond coupled to one photon in the resonator by driving at the appropriate frequency. So, here is the Hilbert states of the system. So, I have a cavity and a transpond. The cavity can have states 0, 1, 2, and 3. The transpond states are given by G, E, and F.

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Rm 330: So, if I drive the system at the difference frequency between the second excited state of the transpond and one photon at the resonator, then in that rotating frame, these two states become resonant. Those two states don't directly couple to each other, but there… there's a,

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Rm 330: F couples to E, and G also couples to E. This coupling is from the microwave drive that we apply. This coupling is from the James Cummings interaction. So now you can have a virtual harp

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Rm 330: between the second excited state of the transform and one photon in the cavity, and this is essentially our Swiss Army knife that allows us to do any operation. So this allows us to realize a tunable Chains-Cummings interaction, except that our qubit is the ground state and the second excited state of the transform, and you can exchange that with the photon in any of the cavity modes.

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Rm 330: Crucially, this operation can be made faster than the dispersive coupling state by a factor of 25, or something like that. So, if I drive the system at the difference frequency between the second excited state of my circuit and any of the cavity modes, I can drive this kind of a

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Rm 330: vacuum Rabi oscillation. So this is a single photon being exchanged between the circuit and any of the cavity modes. So we can do this with, let's say, 7 cavity modes, and the rate is about

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Rm 330: 25 times faster than the CAI.

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Rm 330: Kai is the dispersing shit.

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Rm 330: So this allows us to put a single photon in any of our moors, but can we do more than that? The answer is yes. We can use this to climb up the FARC ladder, so I can… I can go to F, go to G1, but then I can just…

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Rm 330: Keep doing that climbing.

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Rm 330: The James Cummings interaction, at higher photon numbers has a square root of n enhancement. This is called the bosonic enhancement, just comes from, you know, if you take at A on n, you get a square root of n plus, you know, square root of N, right? It's just that factor. So if I now do spectroscopy of the

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Rm 330: this F0G1 transition, I get something like this. Basically, I prepare the circuit in F, and drive this, and see that if I drive at the right frequency, I can go into the one state, and I can do this for,

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Rm 330: higher and higher photon numbers, and so now I can drive Rabi oscillations across different photon number sectors. I can do F0 to G1, F1 to G2, and, you know, the rate goes is squared to A.

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Rm 330: So we can do this, this, single photon, we can add up to, let's say, 15 photons in any of our 10 cavity modes. So this is a very large Hilbert space that we can control.

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Rm 330: So, if you want to now use this to prepare an interesting state. Let's say I want to prepare a superposition of,

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Rm 330: FOC 0 and FOC2, I can basically, you know, we… a lot of our experiments, we sort of doodle out the kind of control sequence that we need to use. So this is, again, this joint Hilbert space.

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Rm 330: I can take, prepare a superposition of G and E by just driving

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Rm 330: that transition, take it to F, and then I do this trick where I can move one branch of the superposition into the E state. So the E state is transparent to the sideband process that we use. So with this, now we can basically

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Rm 330: Prepare a superposition of 0 plus n.

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Rm 330: And, you know, I can measure it by doing photon number resolved qubit spectroscopy. So here you can see that this state is 0 and 1, 0 and 2, 0 and 3, and 0 and 4, and I can also fully characterize the quantum state of the system by using Wignet tomography. So, essentially, what we do is we use this Ramsey sequence to do what is called a parity measurement. So, essentially, we…

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Rm 330: put the qubit in a superposition, and the phase that it gets depends on the photon number, and we tune it so that all the even states go to one end of the block sphere, and the odd states go to the other end. So then, if you do a second pi over 2 pulse, it maps this phase information into population. So this is a way in which you can map the parity of the quantum state into the

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Rm 330: transmon G and E state, and this alone is, you can show, is sufficient for doing, Wigner, you know, fully characterizing the quantum state. We can extend this to

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Rm 330: doing operations across multiple modes, so here is an example of something where we prepared what is called a noon state, so this is a superposition of n photons in the left mode and n photons in the right mode. The sequence kind of looks the same, I won't explain it, but essentially, it requires you to do sideband operations on… alternating sideband operations across the two different modes.

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Rm 330: And, the same techniques that we use to characterize a single mode can be extended to characterize two modes. So, this is multi-mode Wigner tomography. We can use this to then fully reconstruct the density matrix. So this is an example of a bell state that we prepared between the two modes, and you can also make a two-mode moon state.

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Rm 330: So, we put a paper out on this in March. It came out in PRX in March, where we sort of worked through a set of schemes that allow you to go beyond state preparation to demonstrate a class of unitary operations, not complete unitary control, but just a class of encoding operations. One trick is the shelling trick, the other trick is the fact that

330
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Rm 330: You can control the detuning of this,

331
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Rm 330: Of this, sideband pulse in order to

332
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Rm 330: activate a pi rotation on one photon number and a 2 pi rotation on some other photon number, and this alone allowed us to

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Rm 330: do a whole bunch of encoding, right? So here's an example of us encoding a qubit's worth of information into the binomial code. So, the binomial code, the down logical is, is,

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Rm 330: is, you know, 0 plus 4, the arch logical is 2, and this is the superposition of that. So what this gate sequence does is that it can take an arbitrary superposition that I load into the transform and put it into this error-correcting code. And this is a completely analytic sequence that we figured out.

335
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Rm 330: And it works reasonably well. After post-selecting on the transplant being in the ground state, we can get this operation to happen in about,

336
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Rm 330: in, with, 96% fidelity, I'm sort of…

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Rm 330: We'll be running low on time, so I'm just going to say that these,

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Rm 330: control schemes that we have developed also work for these very, very high-Q accelerated cavities, which we have done in collaboration with a group at the SQMS Center at Fermilab. So, this is basically cavities with 20 millisecond coherence, and they used the sideband control techniques that we developed and extended them. In particular, they used mid-circuit measurements and feed-forward to prepare

339
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Rm 330: Essentially, FOC states up to FOC 20, so this is actually some kind of a record for the fidelity of a FOC 20 state, like, 95% fidelity.

340
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Rm 330: And this scheme can also be extended to do multi-mode operations, so what I talked about is this F0G1 sideband, but if I run this detuned, then I can actually use the F state as an intermediate state and just go between

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Rm 330: G10 and G01. So this is what we would call a beam splitter operation, and this beam splitter operation actually works reasonably well. We can do this beam splitter operation with approaching 3 nines fidelity.

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Rm 330: Okay, so now let me tell you how we can extend these kind of control schemes to prepare to implement arbitrary unitary operations. So essentially, I want to program an arbitrary unitary in the oscillator. So how I'm going to do this is with an ANSAC that essentially consists of

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Rm 330: Transbound rotations and James Cummings interactions. That's all I'm allowed to do. I'm just going to alternate them, okay? So, as I've told you before, like, the James Cummings interaction couples these levels together, right? And the qubit rotations can be used to couple these levels.

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Rm 330: So, what we do is we play a trick where we turn the James Covey's interaction on only for just long enough that it does a two-pie notation over here.

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Rm 330: So now you can see that this set of pulses that I have makes it so that the dynamics is completely closed within this subspace, right? So you can ask the question.

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Rm 330: With this closed dynamics, can I implement an arbitrary unitary? And the answer to that is yes.

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Rm 330: The other advantage of this is that, you know, because we use the G and the F state, if FTKs to E, I can flag that error and post-select it out. So I can kind of detect transmond relaxation errors and get rid of them.

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Rm 330: Also, this is a bit of a detail, but the dispersive shift still plays a role, and it can speed up the gates.

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Rm 330: So now, you know, we put this into an optimizer, or Jordan put this in an optimizer, and asked the question, can I pick angles for these transform adaptation and these James Cummings gates to prepare an arbitrary unitary? Here is a… the unitary is what's called a shift gate, so 0 goes to 1, 1 goes to 2, 2 goes to 0. So this is an example of a cube print.

350
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Rm 330: Clifford Gate.

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Rm 330: So, you can see that, actually, we do this, basically a version of gradient descent to figure out the angles that will allow us to implement this unitary, and turns out that if I want to do an arbitrary unitary with

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Rm 330: dimension B, so I've… I have this oscillator Hilbert space. I've cut it off at some D, and I'm asking the question, can I do an arbitrary D-dimensional unitary? The answer is yes, and the depth of this AMSAT scales as D squared, which is kind of what you would expect if you did parameter counting. What's interesting is that

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Rm 330: I'll skip this dispositive shifts cleanup, but I guess, you know, the,

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Rm 330: The fact that there is a dispersive shift makes it so that the gate is actually faster than without.

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Rm 330: If you use the detuning as a control knob. And one of the interesting things about this is that it's not that much more difficult to do a random gate than to do a Clifford GET.

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Rm 330: And so, we actually implemented this in the lab. It's actually took us quite a while, because we had to kind of stabilize our lab temperature to about 0.1 degrees or something for this to work, which we were not able to do.

357
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Rm 330: So we went around it. But, I guess if you… if you have, like, such a shit kit, you know, you can prepare all possible input states, so this is

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Rm 330: Fox state 0, Fox State 1, Fox State 2, these are arbitrary superpositions. If I now run this pulse sequence, this innocuous, simple-looking pulse sequence, I can take 0 to 1, 1 to 2, 2 to 0, etc.

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Rm 330: And we can also do more complicated non-Clifford gates. This is an example of what is called a Givens rotation. So it's doing something… doing a rotation in a 0-1 subspace while leaving 2 unaffected. So you can also do that.

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Rm 330: Just by changing the pulse like this.

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Rm 330: And we can fully characterize the state by what is called process tomography, so you put all possible inputs, measure the outputs along all possible axes, and then reconstruct

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Rm 330: what is the yur tree that I made? So with this, we… this is such a process matrix, it's kind of hard to interpret these, but you can, from this, get a fidelity for the gate, and the gate fidelity for these operations is actually decent. It's like 95% on a… or 96% on average across the entire set of

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Rm 330: cubed gates that we applied. This includes Clifford gates and non-Clifford gates.

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Rm 330: All right, so there's a paper out on this. So, in the remaining time that I have, I'll just tell you about our next generation of memories that we're building. So, this is the architecture that I told you about. Trans mode, coupled to many cavity modes. I've shown you single and few mode sideband control.

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Rm 330: What did you say before that in the lab, you had to stabilize the temperature to 0.1 degrees, and you couldn't do it, so was that not experimental data? No, that is experimental data, so what I meant is that, like, I guess the… and maybe I, you know, we pump the system really strongly, so we have a very large stark shit.

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Rm 330: That stop shift depends very sensitively on the power, so if the electronics amplitude changes by 0.1%, that stop shift shifts a lot.

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Rm 330: So what we did is we put all our electronics in a server rack, so that allowed us to get it down to one degree. But then what we eventually did is that we just used the stark shift as our calibration. So we just changed the power and kind of stabilize it so that the start shift is always the same. We had to do these things. Thanks, Vikrush.

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Rm 330: Yep.

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Rm 330: So, so our first architecture is one where we have a transpond coupled to all of these cavity modes, and that's…

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Rm 330: You know, I showed you a single and few more control, not a quantum computer, because, you know, I didn't show you an operation on one mode, irrespective of what is stored in all of the other modes. So it's not even a good memory, actually. So what we want to do is we want to get to a stage where we can have gate fidelities that are not 99%, but 10 to minus 3 and 10 to the minus 4, and also reduce these many-body crosstalk errors, and this is something that we've

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Rm 330: we have a solution for. This is what's called the Cascaded Atom Access Quantum Memory Architecture. It was actually an experiment that I started at Chicago in 2019, and could not finish it, but one of our undergrads, Ish, actually went and joined Stanford, and he finished the experiment, so this gives me a special kind of pride, actually. So, this architecture actually consists of, now you have your storage cavity coupled

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Rm 330: to, cache memory, and… which is in turn coupled to the transport. So here, the transform is coupled to all the cavity modes.

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Rm 330: What we have instead is a buffer layer, and the buffer layer alone is coupled to the transform, and with this, you can reduce crosstalk errors by a factor of, like, 10 to the 5, or something like that.

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Rm 330: And then what we have is a tunable coupler that is also a superducting circuit, but it plays a very different role. It's something that just mediates interactions between cavity modes. It doesn't, like, actually ever have a photon.

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Rm 330: So what we do is we swap it into the buffer, do a gate, and then put it back. That's the gate operation that we do. So we've actually implemented this also in our lab, thanks to work from Chalm and Pratu and Andre.

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Rm 330: like, you know, it took us 2 years to do this. So this is basically how it looks like. This was made by our Rutgers Machine Shop. If I, look at how it looks like on the inside, this is our multi-mode cavity, this is our cache memory, and then in between, we have the superconnecting circuit. There is a… it's not a transmond, it's special, it has, like, a small Josephus injunction in parallel with

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Rm 330: And what's interesting is that this is not a particle in a cosine potential, it's this particle in this, like, weird potential that has… that breaks inversion symmetry, breaks phi to minus 5 symmetry, so you can have a cubic nonlinearity.

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Rm 330: And as a result, you can pump this circuit at a different frequency between two cavity modes and drive a beam splitter operation. One of the main challenges that we had to face is that our entire cavity is superconductor, and we have to tune this by applying a magnetic field, and, you know.

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Rm 330: there's a Meister effect, so that's bad. So how we do it is that we have a little loop that, you know, we… there has to be some piece of it that is copper, because, you know, that's how you apply the magnetic field. The copper can't get too close to the cavity molds, because then it'll destroy the currents. So what we have is this tiny pickup loop, where if you apply a magnetic field, there's a persistent current that comes in this pickup loop, and it's that persistent current that drives

380
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Rm 330: The flux that sheds the squid that tunes its properties.

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Rm 330: So this is, how the device looks like. This multi-mode cavity has many modes between 5 and 7 GHz. The storage cavity has modes between 4.2 and 4.7, which is what we pick. In between, we have this

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Rm 330: snail circuit that's a tunable coupler, which is tuned with this DC coil, and then you have a transpond that's, like, coupled, isolated from the memory, it's far away. It's just only coupled to the buffer, right? So, if you want to now do an operation, you have to swap it into the buffer, and then do the gate with the highly nonlinear transpond.

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Rm 330: So, if we tune the flux through this snail circuit, then you can see that it tunes, and it has avoided crossings with all of the modes, similar to the avoided crossings that I showed you before. And we biased the snail circuit at one particular point.

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Rm 330: It took us a bunch of effort, but now we have pretty state-of-the-art values for a CAIC device with a tunable coupler added to it. We again have millisecond coherence.

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Rm 330: And we can drive the… if I now want to do a… if I… so if I want to load and unload from the memory, I have to take a quantum state in one of these modes and bring it here, and I can do that by just driving this circuit at the difference frequency.

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Rm 330: So, here's us making it work. So, I loaded a photon into the buffer cavity using the sideband process that I showed you, and then I can load it into the storage mode.

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Rm 330: So it works reasonably well. Still not perfect, but we can do these swap operations between our main memory and our cache memory in a few microseconds. One thing that we are trying to figure out is why is the… why the fidelity is not as good as we expect it to be. The fidelity is in the 98% to 99% range, and this is, comes from not the bare coherence of the cavity, it's really good. It comes from

388
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Rm 330: new physics that you see when you have, like, a Josephson circuit that you strongly drive, so where, like, my students are getting very good at, like, doing

389
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Rm 330: like, flow-K Markov simulation, like, strongly driven connecting circuits, how you deal with them. So you can… this is… this, 1001 exchange, one thing we can do is we can kind of do a single-shot measurement at the end, and ask, was it in 0, was it in 01, or 1-0? And then I can force…

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Rm 330: whether it was in the 1001 subspace, and this usually leads to improvements, but it only leads to marginal improvements for us, and it kind of tells us what we are limited by. We are limited by kind of defacing. So this is what we are trying to figure out. Our plan for scaling this up is that we build these kind of

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Rm 330: you know, single modules, but then we couple them together. We have an ongoing experimental collaboration with, Wolfkan, Pfaff, Angela Ku, and Cham, where we are, doing this kind of,

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Rm 330: remote entitlement experiment involving two multi-mode cavity modules. The module itself is this kind of cascaded RAM that I told you about. We really want to control it with what's called a fluxonium circuit. We've made good progress on this. I cannot tell you about that. And eventually, once you have

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Rm 330: two fluxoniums across a cable that are remotely entangled, then you can use that as a resource to do gates between the two cavity modes. So this is the experiment that we are trying to do.

394
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Rm 330: And with these devices.

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Rm 330: I guess, now that it's kind of working, we're sort of starting to think about what kind of interesting quantum summation experiments that we can do. Certainly, we think that

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Rm 330: There are many quantum simulation problems that are more efficiently, expressed in terms of qubits, sorry, in terms of… with oscillators rather than with qubits. This is, of course, true for bosons, because Boson is a… is a cavity mode, but you can also use

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Rm 330: two cavity modes to encode a spin much more efficiently, like in, the, many of you may be familiar with this Schreiner boson mapping that allows us to encode a spin in two oscillators.

398
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Rm 330: And we're using these kind of mappings to start to think about doing quantum chemistry simulations with strongly coupled rotational and vibrational degrees of freedom, and moving towards slowly

399
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Rm 330: spin models, or large cage series, and so on. We're also, you know, our systems also allow us to do fast mid-circuit measurements, and this really allows us to

400
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Rm 330: simulate phenomena that are not found in nature. So one of the things that we've looked at in collaboration with Jed is to look at measurement-induced space transitions in Podonic systems, and there we see some new physics that's not seen in the qubit version of this.

401
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Rm 330: We're also using these systems for,

402
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Rm 330: starting to use these systems to try and ask machine learning kind of questions. So, you can have some classical data, and you can take this classical data and encode it in a cavity state, and, like, let's say it's 0 and 1,

403
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Rm 330: So, the 0 and 1 can be encoded in some cavity state, and then you can run that cavity state through a quantum circuit, and at the end, do some measurement. It could be a measurement of the qubit, or it could be a measurement of photon number, and this circuit can actually also learn to tell whether what I fed in was a 0 or a 1.

404
01:05:03.710 --> 01:05:05.530
Rm 330: You know, it does it, of course.

405
01:05:05.580 --> 01:05:18.749
Rm 330: Much worse than a classical neural network at this stage, but there are actually interesting, speedups that people are talking about with classical… even classical machine learning that you could potentially do with a quantum computer.

406
01:05:18.750 --> 01:05:34.619
Rm 330: And our goal, this is a collaboration with, Victor Batista and Chen Wang. Victor Batista is at Yale and Chen is at… now at Toronto. But the goal is to use this kind of system to learn molecular properties, like, you know, like the, you know,

407
01:05:34.620 --> 01:05:51.690
Rm 330: atonization energies and so on, and also use these to build new kinds of variational eigensolvers, which, you know, you can do with qubit-only systems, but you can sort of… this is a much larger Hilbert space that you can traverse in interesting ways, and as a result, I expect that there are questions that you can solve better with systems like this.

408
01:05:52.230 --> 01:06:12.050
Rm 330: All right, so with that, I would like to thank my wonderful group, and, Jordan led the experiments on the weekly coupled memory, with assistance from Tom and also from, from Ethan. Tom and Andre and, Pratu are working on the cascaded Random Access Memory Device.

409
01:06:12.050 --> 01:06:15.760
Rm 330: Shiv is the student working on the measurement-induced phase transitions.

410
01:06:15.760 --> 01:06:26.709
Rm 330: And, Rahul and Ying-Ting are implementing the Fluxonium in the 3D cavity. And also, many thanks to Misha Gershenson, who really, like.

411
01:06:26.710 --> 01:06:41.190
Rm 330: without him, we would not be anywhere near where we are at the moment. And, I mean, we actually do part of our experiments in his lab, so maybe one day he will still come back, you know?

412
01:06:41.350 --> 01:06:49.079
Rm 330: Hasn't happened yet. And also, I want to thank all of our… my collaborators, past and present.

413
01:06:49.270 --> 01:06:53.889
Rm 330: And I'll flash at the conclusions and be happy to take any questions.

414
01:07:01.040 --> 01:07:02.170
Rm 330: Questions?

415
01:07:06.760 --> 01:07:08.660
Rm 330: Yeah, go ahead.

416
01:07:10.570 --> 01:07:20.700
Rm 330: So, you show these graphs at some point, things change over time. How often do you have to look into it and

417
01:07:20.790 --> 01:07:32.520
Rm 330: move it back to where it should be. In other words, correct? You mean, like, the quantum state itself, or, you mean just our classical control stuff? Both.

418
01:07:32.770 --> 01:07:57.010
Rm 330: So, in the case of our classical control, it's actually… I mean, we do have these temperature fluctuations that we have to worry about, but once we fixed it, it's actually remarkably stable. Like, I mean, I come from an atomic physics background, and my advice is just to say, every atom is the same, right? But your apparatus is not the same. Whereas here, every qubit is different, you know? There's many two-level systems that one qubit has that the other doesn't, but it's remarkably stable.

419
01:07:57.100 --> 01:08:06.130
Rm 330: And as a result, you know, we can afford to do experiments where we do our experiment at home and run the dilution fridge over here, you know.

420
01:08:06.130 --> 01:08:17.549
Rm 330: And regarding the quantum errors, like, I guess it's set by the cavity lifetimes and such, so I didn't really show this. Maybe this is a good opportunity to

421
01:08:17.550 --> 01:08:24.479
Rm 330: show you some extra slides that I have, like, we have, we've done these experiments where we have sort of,

422
01:08:24.660 --> 01:08:25.860
Rm 330: like,

423
01:08:25.860 --> 01:08:45.410
Rm 330: like, basically done the analog of, you know, I told you how we made a bell state, but we can also kind of stabilize the bell state. So, what we do is, in between, we run a measurement that measures a syndrome, like, doesn't… you shouldn't… I shouldn't ask the question, is the cavity in the left… is the photon in the left cavity or the right cavity? But I can ask.

424
01:08:45.410 --> 01:08:54.379
Rm 330: is there a photon in this space, right? And if I ask that question, then I can then do… use the fact that I also have systems that are fairly

425
01:08:54.380 --> 01:09:10.040
Rm 330: high loss, so you can engineer the dissipation to sort of do autonomous stabilization. So here's an experiment where we had, you know, the noon state that I told you about, like, we make the noon state, and this is a Ramsey fringe of the noon state.

426
01:09:10.040 --> 01:09:20.950
Rm 330: And, you know, it lasts for a long time, lasts for a few milliseconds. But then, in between, what we can do is we can just do this kind of stabilization experiment that's asking the question, was it…

427
01:09:20.950 --> 01:09:22.659
Rm 330: Is that an error?

428
01:09:22.660 --> 01:09:40.970
Rm 330: Then, if there is an error, let me do an operation that prepares the bell state and then cools it into the target state, just completely autonomously, and with this, we can sort of raise the lifetime of the cavity stage, but we have to do it on the timescale of the T1 of the system. Yeah.

429
01:09:40.990 --> 01:09:44.729
Rm 330: It's almost catches you. Yes. Every so often, you just…

430
01:09:44.730 --> 01:10:09.550
Rm 330: Well, so, I guess, like, I mean, so far, actually, we are not really doing error correction mid-circuit yet, right? So, like, we run a gate, at the end of it, you know, we check if the transplant has an error, and I know that we can throw that out because of how we have constructed the gate. So we are only doing it at the very end at the moment. So, you know, we are not yet doing these measurements where, in between, I do a

431
01:10:09.550 --> 01:10:33.070
Rm 330: error correction check, and then do a correction, you know, maybe in the future. Does anyone do that? Yes, I mean, I guess, like, I mean, I would say, like, it's not the case that people really use error correction at this stage, you know, on a quantum processor. There certainly are mid-circuit measurements that can be done in a whole host of systems. We can also do mid-circuit measurements, and we do.

432
01:10:33.070 --> 01:10:36.229
Rm 330: But it's just that we haven't used it yet for anything.

433
01:10:36.900 --> 01:10:38.289
Rm 330: particularly cool.

434
01:10:38.430 --> 01:10:40.640
Rm 330: But, yeah, yeah.

435
01:10:40.820 --> 01:10:45.289
Rm 330: Sang has a question online. Sang, can you, unmute and ask your question?

436
01:10:46.010 --> 01:10:56.640
sangc: Okay, that's a very nice talk. I have a simple question. Your aluminum plug, aluminum plug you used?

437
01:10:56.850 --> 01:11:01.569
sangc: Is it single crystal, polycrystal, or do you have…

438
01:11:01.570 --> 01:11:02.060
Rm 330: myself.

439
01:11:02.060 --> 01:11:10.700
sangc: Do you do some kind of a purification? Can you get more than 5 knives? And any kind of impurity has any impact?

440
01:11:11.330 --> 01:11:27.609
Rm 330: Yeah, no, it does have, in fact, so we make it out of a block of financed purity aluminum, so, you know, when you machine such a thing, it machines like butter, you know, and if you look at the surface of it, actually, you can kind of see domains, so it is kind of, like, single crystall-y, like…

441
01:11:27.850 --> 01:11:33.659
Rm 330: I mean, it's not one crystal, but, you know, you can kind of see facets,

442
01:11:33.690 --> 01:11:58.580
Rm 330: And yes, like, it is the case that, like, what is still limiting the coherence to a millisecond is the fact that our surface of the inside of the cavity has some oxide on it, and that oxide has, like, sort of atomic two-level kind of systems that can absorb in the gigahertz lane, so they take energy away. In some sense, like, the… all the advances that people have made in Fermilab accelerators is, like, really

443
01:11:58.580 --> 01:12:18.689
Rm 330: understanding niobium oxide and managing, you know, they do this surface preparation that gets rid of the oxide, and then they put the qubit in while maintaining vacuum so that oxygen doesn't get in, right? So you have to do things like that. But, and I guess, yeah, so we are so far not really yet moving in that direction, because our

444
01:12:18.690 --> 01:12:29.140
Rm 330: 1 millisecond cavities are plenty enough for us, because our coherence is actually limited by our circuits, but, you know, soon we will have to start to look at how to make better cavities,

445
01:12:29.240 --> 01:12:35.870
Rm 330: Yeah, and probably we will follow also the NioBM cavity route, because it's been shown to work.

446
01:12:36.240 --> 01:12:37.060
Rm 330: Yeah.

447
01:12:37.060 --> 01:12:46.770
sangc: I see. So, I believe niabium, the highest security you can give 6 nines. Aluminiums are probably 5 nines, isn't that what you have?

448
01:12:47.330 --> 01:13:11.549
Rm 330: Yeah, so aluminum is finites, and yeah, I guess I don't know if it is to… I don't… I think they get it to be as pure as possible, but I don't think it is actually limited by the purity, but more the oxide. And in general, yeah, I mean, I think the bulk metal is only so good, so there's been actually a lot of good work on so-called micro-machine cavities, where you take a piece of silicon, and you etch the silicon.

449
01:13:11.550 --> 01:13:26.949
Rm 330: And then you evaporate metal on top. And evaporated metal can be much purer, right? So you can, you can get fairly high, like, cavities with, like, very low surface-to-volume ratios that have fairly high coherence that way.

450
01:13:26.950 --> 01:13:27.790
Rm 330: Yeah.

451
01:13:27.790 --> 01:13:36.780
sangc: I see. So, you know, I am not familiar with aluminum, but, for example, like, copper, CU.

452
01:13:37.060 --> 01:13:43.909
sangc: If you make a single crystal, you know, if you expose copper to air, moisture, it oxidates surface.

453
01:13:44.280 --> 01:13:48.270
sangc: But somehow, if you grow a single crystal of copper.

454
01:13:48.490 --> 01:13:53.370
sangc: Oxidation is an absolute minimum, if it's through a single crystal.

455
01:13:53.510 --> 01:13:59.190
sangc: Oh, interesting. So, there may be some window opportunity for aluminum, rear crystal.

456
01:14:00.630 --> 01:14:18.940
Rm 330: Yeah, it would be awesome to actually talk to you more about this. I mean, I think, actually, there's a lot of progress in the field happening now, because, like, actually, real, you know, kind of scientificists and material scientists are involved now, and trying to, you know, improve the material science of it. Yeah.

457
01:14:18.940 --> 01:14:21.739
Rm 330: Yeah, it would be awesome to talk to you more about this, yeah.

458
01:14:22.000 --> 01:14:23.849
sangc: Okay, okay, thank you.

459
01:14:30.020 --> 01:14:31.209
Rm 330: Any questions?

460
01:14:35.530 --> 01:14:36.799
Rm 330: Nothing more online?

461
01:14:37.500 --> 01:14:38.950
Rm 330: Nothing more online.

462
01:14:39.790 --> 01:14:40.940
Rm 330: Let me ask him.

463
01:14:41.740 --> 01:14:44.099
Rm 330: More general question. How is…

464
01:14:44.360 --> 01:14:59.959
Rm 330: you really do quantum mechanical manipulations in a machine. Right. And you came to that at some point when you'd learned quantum mechanics. How has it changed your view of quantum mechanics? This is a wonderful question. I mean, one thing is that, actually, I think

465
01:14:59.960 --> 01:15:12.059
Rm 330: I really have, actually, nice discussions with my students on this, you know, and it is something that, you know, I think more people should think more about, right? I guess, like, in terms of how it is

466
01:15:12.060 --> 01:15:15.070
Rm 330: changed it, right? Like, I mean.

467
01:15:15.200 --> 01:15:31.360
Rm 330: I guess, definitely have this, like, in some cases, we have, like, kind of a more trajectories kind of picture, you know, of quantum trajectories kind of picture for various kind of, like, all these experiments where you have an error happening and so on.

468
01:15:31.360 --> 01:15:53.820
Rm 330: I would say, in terms of, like, interpretations, like, I don't know, I'm still, like, probably, like, a more of a modern Copenhagen kind of person, you know? So, yeah, I guess, like, it's… I had really fun discussions with people in the math department about pilot wave theory, for instance, which we are certainly not, you know, using to think about it, but, you know.

469
01:15:54.800 --> 01:16:09.769
Rm 330: I think that there's still, very much a mindset of this kind of, that one shouldn't think about these questions, but we really can ask these questions, you know? There have been nice experiments, like, from, I think, maybe the most

470
01:16:09.900 --> 01:16:20.699
Rm 330: The very nice experiment from Michel DeV group, like, like, sort of, catching a quantum jump and reversing it, sort of…

471
01:16:20.700 --> 01:16:30.750
Rm 330: approaching, sort of, fundamental questions that you can ask, about quantum measurement in these kinds of systems. yeah, certainly,

472
01:16:32.100 --> 01:16:37.349
Rm 330: very interested in these questions, but, you know, we… I guess we haven't really done anything,

473
01:16:37.780 --> 01:16:51.600
Rm 330: profound about it yet, you know? So you can still… you still feel happy using a Copenhagen-type picture of everything you're doing? Well, yeah, I mean, like, I guess we, we,

474
01:16:51.860 --> 01:16:57.910
Rm 330: I still very much think about it as, like, we have a, I guess, definitely functionally.

475
01:16:57.910 --> 01:17:15.789
Rm 330: we just have a Copenhagen approach many times, right? Like, we have this qubit that's coupled to our cavity, and, you know, we apply a microwave dye to our cavity, and the cavity makes this bell state, this sort of cat stake, where you have, like, cavity-free

476
01:17:15.790 --> 01:17:23.790
Rm 330: one coherent state entangled with up and down and so on. So all that stuff we know is happening, but in the end, we still kind of,

477
01:17:23.870 --> 01:17:28.550
Rm 330: you know, think about it as a projected measurement that we do, right?

478
01:17:28.710 --> 01:17:46.640
Rm 330: So, yeah, I guess, yeah, there's also interesting things that you can do where you don't need to have a strong projected measurement. You can, sort of have a weak measurement that's always on. There's nice work that's going on from that perspective as well, yeah. But I would say,

479
01:17:47.030 --> 01:18:00.349
Rm 330: Yeah, that's, I mean, we… I'm, I'm at least functionally, like, almost, a Copenhagenist, you know? All right.

480
01:18:00.800 --> 01:18:02.380
Rm 330: Any other questions?

481
01:18:03.150 --> 01:18:12.640
Rm 330: I have some students who have strong opinions about this that, you know, that should feel free to speak up. We'll ask another question. Any ask questions?

482
01:18:14.670 --> 01:18:17.199
Rm 330: Okay, let's tag Bhusan one more time.

483
01:18:33.400 --> 01:18:34.930
Rm 330: I didn't want to ask you.

484
01:18:35.320 --> 01:18:59.559
Rm 330: Yeah, exactly. Yeah, yeah. So, like, yeah, so we need it. I got a focal point here.

485
01:18:59.560 --> 01:19:03.390
Rm 330: Can you remind me, did you ever call us?

486
01:19:03.560 --> 01:19:19.110
Rm 330: Yeah, yeah, so we just, measure the structure, and then obviously…

487
01:19:19.110 --> 01:19:40.330
Rm 330: Yeah, and we do that, like, every, like, every, like, millisecond. I'm saying here is that…

488
01:19:40.330 --> 01:19:53.559
Rm 330: No, because it's something that we kind of figured out the correct atomic physics itself.