Bridging Theory and Experiment in Quantum Error Correction with Liang Jiang
Welcome to the New Quantum Era. I'm your host, Sebastian Hassinger. On this podcast, we try to navigate the exceedingly complex landscape created by the emergence of technologies that are being built out of the the direct manipulation of quantum mechanical systems. Technologies like computing, communications, and metrology or sensing. We do this by talking with the researchers who are in this murky in between territory where they often need to work as both quantum physicists and quantum engineers.
Sebastian Hassinger:By that I mean, they're working as scientists following their curiosity and intuition to probe the limits of our knowledge of the quantum universe, but they also work on designing and building tools or technologies that draw directly on that knowledge. This dual path has produced incredible results. From the Endicott House Conference in 1981 where Feynman declared quantum computing to be an idea worth pursuing to the realization of a universal set of logical gates on trapped ions by Dave Weineland and Chris Monroe took fourteen years. From 1995 to Google's supremacy experiment, where they demonstrated a speed advantage over classical computing using 53 superconducting qubits, was twenty four years. Today, in 2025, just over five years after Google's demonstration, it seems the field is undergoing another phase shift.
Sebastian Hassinger:The NISC era, an acronym coined by John Prescold to denote the noisy intermediate scale quantum computers of the twenty tens, is ending. The open question during the NISC era was whether a device with dozens of physical qubits could be useful for anything other than research into quantum computing itself. The answer has been resoundingly no. Quantum computers today are very interesting. However, that interest is held only by those attempting to build quantum computers or learn how quantum computers of the future may be used.
Sebastian Hassinger:What NISC machines are lacking is a way to deal with the n in the acronym, the noise. Computing on noisy qubits is an exercise in limitations. The length of your computation, the number of gates, the complexity of your tasks are all subject to severe limitations. And very quickly, random errors pile and the entire task sinks below the surface of the random sea of noise. What everyone agrees will be required to create devices robust enough to begin to be truly valuable is a fault tolerant quantum computer.
Sebastian Hassinger:Fault tolerance can be achieved by some combination of higher quality physical qubits and techniques of error detection and correction. Everyone working on quantum hardware today is pursuing some variation on this path to fault tolerance, Designing machines that can support error correction techniques generally referred to as codes like repetition codes, surface code, floquet codes, and others. These codes are very resource intensive. For example, Google's successful demonstration of the surface code late last year, as impressive as it was, used the entire quantum processor, more than a 100 qubits to create one robust fault tolerant qubit. Making qubits fault tolerant is the overarching mission for my guest today.
Sebastian Hassinger:He's a professor at the University of Chicago where he leads a group working at the intersection of error correction theory and experimental realization, collaborating with the team's building devices to devise and test approaches to fall tolerance, attempting to accelerate the progress across the entire field. We'll talk about his collaborations and the achievements of his students in quantum memory, computing, communication, and sensing, and you'll get an idea of of the broad set of challenges that span the boundary between theory and experiment and between science and technology. Joining me today is doctor Liang Jiang.
Liang Jiang:Thanks for joining us, Leon. Sebastian. It's great.
Sebastian Hassinger:Good. Excellent. You're enjoying the conference? Yeah.
Liang Jiang:It's been
Sebastian Hassinger:exciting. So I've I've been looking forward to speaking with you because you you've got a quite a broad set of interests, I think, in your group at UChicago. But really, it feels like the unifying theory is or the unifying sort of theme is is like the boundary between theory and experiment. You're sort of pushing the limits on what, what elements of theory, theoretical approach to quantum error correction, to noise characterizations or control, you can implement in current hardware.
Liang Jiang:Is that accurate? That's right. Yeah. Well, we know, like, there are lots of exciting applications that quantum can do. And right now, the challenge is how do we overcome the practical imperfections to get the most of the Right.
Liang Jiang:Quantum power. Right. Yeah. And my group is trying to kind of close that gap Right. By, on one hand, like, figuring out what the the hardware challenges are, and try to use theoretical tools to overcome those imperfections so that we can get like a more hardware efficient kind of schemes to overcome the errors to build a robust quantum system.
Sebastian Hassinger:Right. Right. Yeah. It's so interesting. And John Presco was saying this the other day when I I recorded an interview with him that that, you know, error correction has been a theoretical topic since '95 or so.
Sebastian Hassinger:Right? Mhmm. And and it's really now I mean, the Google surface code experiment was fantastic in in December where they were able to, you know, reach the threshold and show that it scaled as well. They doubled the or they added, it was d three and d five and they added more. Yeah.
Sebastian Hassinger:And of course, AWS's own result is really promising. It it feels like we're right at this point where things that you've been thinking about, and and drawing on whiteboards. Yes. You can actually, implement on on real hardware. Is that changing how you're thinking about error correction as you start to actually do these implementations?
Liang Jiang:Yeah. Well, it's a really exciting time to work on error correction because used to be, like, if it were, like, ten years ago or twenty years ago, we're mostly thinking about it on the purely serious side. Right. And now, like, actually, hardware really took off. Right.
Liang Jiang:Right. And on different platforms, like superconducting qubits, trapped ions, cold atoms. And they all get to a really high fidelity and also the scalability for the system is also showing really promising progress. So it's actually a really good time that we're actually working very closely with the experimentalists to understand what the real errors are, errors are in the real world, and also try to come up with more efficient schemes to help to correct the errors. As you said, the error correction theory or even fault tolerance were known more than twenty years ago, And the challenge is actually it's very hardware consuming, and it takes a lot of resource to do the standard error correction for generic errors.
Liang Jiang:Now, it's actually we need to, given qubits are still very precious resource, we want to do, like, a hardware efficient quantum error correction.
Sebastian Hassinger:Right.
Liang Jiang:Yeah. And and also the errors for different platforms are not the same, so we need to learn what the errors are and the design error correcting codes to correct the relevant errors.
Sebastian Hassinger:Right. Right. Yeah. And so hardware efficient, that seems like it would be a combination of the codes themselves and also the the design of the hardware, right? There's gotta be sort of that that classic sort of co design kind of activity.
Liang Jiang:Yes.
Sebastian Hassinger:That's really interesting. And there's there's sort of I mean, I mentioned the Google announcement, the AWS announcement, also Microsoft and others have been announcing and sort of making their plans around logical qubits and error correction public over the last year or so. Is there a particular sort of experiment that you're anticipating you're going to be able to run that you're particularly sort of looking forward to? Yeah, well, I would
Liang Jiang:say like, as a series, actually I do collaborate with people working on different physical platforms. And I find this really rewarding experience because for us, it's important to know what the problems we need to solve. And by talking to experimentalists, they tell us, Oh yeah, for bosonic systems, it's a loss error you need to correct. While for other superlative platforms, maybe they decay or there could be leakage or there could be cosmic ray events, which might potentially be an issue. And that's actually kind of inspired us to think about how to design error correcting codes for the practical relevant errors.
Liang Jiang:And so that's there are multiple successful collaborations in that aspect. We designed the bosonic error correcting codes to efficiently, using single harmonic oscillator, you can correct loss errors to make the information, kind of, quantum information storage, like, longer than the intrinsic cavity decoherence time Right. And which is called the breakeven Right. In the bosonic error correcting codes. Right.
Liang Jiang:And and has been demonstrated in at Yale and also, like, at AWS also recently. And so that's kind of a really exciting platform, which actually it's both theory and experiment go very closely and kind of making advance of the field. That's really interesting. Yeah. And also for the other superimiting transmog qubits, which Google, they make a lot of efforts during the past decades or even longer.
Liang Jiang:And it's really exciting to see they actually go also go above the break even point so that their error corrected surface code actually can store information longer. Yeah. So now the next challenge is, okay, what can we do with these memories? Can we really do quantum gates with high fidelity and also in a more scalable way? And I think that's a very exciting time to, okay, to also, like, working on these directions.
Sebastian Hassinger:You've also worked on QLDPC codes as well. Right? Which I think I mean, there's been sort of early experiments, but but they're really I mean, IBM's chip is really designed around QLDPC, I think. The the new one that they're working on, they've they've written a couple papers about. Yes.
Sebastian Hassinger:And I think that's it's a biplanar chip with something like 288 physical qubits and 12 logical qubits. Yes. That would be a totally different approach to, control and programming than than a surface code or bosonic code platform, right?
Liang Jiang:Yes, yes. Actually related to QRDPC that part of the reason that we actually get interested into is it's parallel to the IBM effort. I was also talking with researchers working on neutral atom array experiments, in particular, like Michel Luching's group at Harvard. And we were kind of like, he was showing me these really nice results, that you can shuffle atoms around, do all these coupling gates, and as they emerged from that discussion, we said, yeah, because you can have these long range couplings, there are lots of bigger family of error correcting codes that one can have, which leads to the clear DPC code. So there was actually a code design of the error correction in a sense that, well, given we can have these longer range coupling gates, and moreover, some of the operations are easier, like column swapping or row kind of exchanges.
Liang Jiang:So those actually, like, inspired us to further look into a particular family of KLDPC codes. Then when and also come up with efficient simulating the performance of a system to show, like, at least on the theory level, we can get to a good threshold with a much reduced resource overhead compared to the traditional surface code platforms. Yeah. And that actually, we're still continuing, like working on this direction, which is related to like, okay, can we it's not just the physical hardware efficiency, we also need to have the temporal aspects. We can also do gates with kind of like shallower circuit depth, so that we don't need to wait for a whole month for the calculation to complete.
Liang Jiang:Hopefully within a few hours, we can get the result. And which is also another important aspect for the quantum error correction and code designing. Right.
Sebastian Hassinger:And you mentioned sort of implementing gates in that that fault tolerant regime. That's something that I don't think people think about very much, because we're used to over the last, you know, let's say ten years, almost ten years, sort of directly programming gate by gate on physical qubits. That's not gonna be the case once you have these error corrected logical qubits, you're gonna have to do much more intricate sort of
Liang Jiang:operations to implement gates, right? That's right. Yeah, one of the major challenge for doing gates at the logical level is that you want to make sure that the imperfection of these individual physical gates does not lead to logical error. And they require some design called fault tolerant design, so that one sufficient condition for fault tolerance is any physical gates error would not cause multiple physical gate error within a coding block.
Sebastian Hassinger:I see.
Liang Jiang:And with that design, is a certain set of gates one can achieve. But unfortunately, with a certain design, like say transversal gates, we cannot do universal computation. There was a no go theorem proved by Eastern and Kaneo earlier, and people come up with different ways to overcome that no go theorem. There are different paths. One is something called the magic state injection.
Liang Jiang:Yeah, you kind of prepare a certain quantum resource states, and then you teleport it into a quantum circuit that allow you to do something that transversal gates cannot do. And the other is called code switching. You can switch between different error correcting codes. Oh, wow. And some codes can do certain subsets of gates.
Liang Jiang:Nice. The other can do the other sets. And when you put together, you actually come up with a universal set. That's interesting.
Sebastian Hassinger:Yeah. And I mean, I've heard, a couple of different codes, specifically able to protect Clifford gates, but not to Foley Gates. Is is that generically the case, or is it a different subset as you were just describing? Yeah. It's a different subset for each code.
Sebastian Hassinger:Yes. That's really fascinating. Is there I mean, I'm sure there's a reason for that, but is there a reason that's explainable without a bunch of math? Yeah. That sounds like I mean, why is that a no go theorem?
Sebastian Hassinger:That that once it's error corrected Mhmm. You can't get universal computation.
Liang Jiang:Yeah, because when you do these transversal gates, it turns out that there is a kind of like, number of gates you can do it is countably many, while the other, you want to do a universal set, which is a kind of continuous set of gates. I see. And that's kind of from discrete to that continuum. I see. There is a gap which prevents us from just using transversal gates to do universal computation.
Sebastian Hassinger:And I mean, when I think about, as you described, like, you know, magic state injection or these code switching things, it feels like that's going to inevitably drive more abstraction from in the in the opera in the in the job of programming a quantum computer. Like, no one's going to be hand coding these things anymore. And it's almost like the beginning of the the process of abstraction that happened happened in classical computing when there was, you know, initially sort of hand setting registers. And then, you know, eventually assembly language and all these these layers of abstraction. Is that something that you sort of you think ahead about, like what are those abstraction layers going to look like?
Liang Jiang:Yeah, well I think that a lot of researchers are also thinking along these lines, that how do you efficiently compile a quantum circuit using discrete set of gates which we know how to do it for tolerantly. And I think there are lots of research going on there because it definitely how to say there are exponentially many possibilities and or maybe you can come up with different gadgets of gates which might be able to do it more efficiently. Right. Yeah. And more related to kind of QR DPC code, there's also a question about you have essentially a really good quantum memory stored many qubits in the coding block.
Liang Jiang:How do you efficiently access those individual qubits to do the quantum operation? And the straightforward way is you extract or teleport out the qubits from the memory, do quantum gates and put it back. But that limitation is that you do gates one by one, which slows the circuit down. And on the other hand, with my student, former student, Qianxu, who actually found out the idea, we actually can teleport the gate into the memory and you can do a lot more things in the future. Interesting.
Sebastian Hassinger:So the gate operations happen in the memory as opposed to bringing the value out and trying to tell it. Yeah. Yes. That's interesting. And I mean, quantum memories are often also sort of the center topic around quantum communication.
Sebastian Hassinger:And that's another area where you're fairly active, right? And and Yes. So how do you think of those two sort of problem sets differently, communication versus computation? Or is it sort of one continuous set of challenges in your mind?
Liang Jiang:Yeah, well, they're definitely very closely related. In some sense, that the memory, for communication, the challenge is that how do you kind of put more information into your quantum channel and not suffer from the imperfection of the channel. The goal is to achieve the channel capacity of the communication channel. And this is very similar to what happened to our classical communication, that kind of Shannon proved there's a kind of channel capacity, and it took people half more than half a century to come up with our five g network, which almost achieved the capacity now. Right.
Liang Jiang:Right. Yeah. And so so quantum case is in some sense similar. There is some channel capacity, which we we depend on the channel, we may or may not know the exact value of the capacity or the range of the capacity, but we are also looking to, like, a quantum error correcting codes to achieve this channel capacity. For example, for quantum communication channel, if we do the fiber communication, we're also sending information using wave packets.
Liang Jiang:And each of the wave packets, can think of the bosonic mode, which suffer from the excitation loss error. Right? And for that channel, there is a capacity we know. And the question is, okay, how do we design arithmetic codes to achieve that channel capacity? And we actually look into these arithmetic codes and turns out that people more than twenty years ago come up with a really clever set of codes called the Cartesmann Kiteff Preschool codes for people working on error correction.
Liang Jiang:These are three, like, really, like, well known researchers. And they come up with a really smart code, and it's actually then we used these codes, and it took us, like, multiple years and two generation of students to show that these codes actually can saturate the channel capacity for lost channels. Wow. Yeah. Which is actually a really nice thing that, okay, probably we okay.
Liang Jiang:Maybe we don't take more than half a century, but maybe within 2,000 years, can show, like, okay, this is a code which we sort of know how to do the construction to achieve the channel communication capacity for a practically relevant channel.
Sebastian Hassinger:GKP has been implemented in superconducting qubit regimes, right, for computation. Is that work sort of directly transportable over to communication context, or do you have to sort of re engineer the implementation of GKP for communication?
Liang Jiang:Yeah, so GKP code actually has recently been experimentally demonstrated using, one is trapped ion, the motion of the ion, and the other is superconducting qubits bosonic cavity modes. So in Michel DeVriel's group, they actually demonstrate the above breakeven performance. Using GKP code, can correct information, correct, protect information and longer than the cavity intrinsic without error correction. And with that technique, in principle, if we have a good quantum transduction, converting information between microwave modes and optical modes, then we can actually directly extend the GKP code from microwave to the optical domain and potentially use it for quantum communication in the optical fiber network.
Sebastian Hassinger:But that's a really big if, if I understand correctly. Transduction from microwave frequencies to telecom frequencies is really challenging, right?
Liang Jiang:Yes. It's definitely highly nontrivial. Yeah. One aspect Highly nontrivial, yes. In one aspect, may say, like, our theory, it's just converting from another electromagnetic field to another one.
Liang Jiang:Sure. It's just that the frequency is so different, which means that, okay, they need to handle the things very differently. Right. For example, in the microwave domain, it's a superconducting device you're dealing with, and they actually are usually not compatible with optical field. Even if there's some scattered photon gets to the superconducting device, it actually would cause extra decoherence or thermal noise.
Liang Jiang:And that's why we need to be extra careful to make sure when you want to couple between microwave to optical, we need to make sure you don't scatter photons around to contaminate on the microwave side. Moreover, on the optical side, it's also challenging because you have optical pumps and the signal photon is just a few gigahertz away from the optical pumps. And you need to make sure you filter the pump and get a useful signal photon out without causing significant loss. But people are making a lot of progress in the past decade in this field, and there are already at least two experiments demonstrating you can transfer information or generate entanglement between microwave and optical modes. And those are, like, really promising for the whole field.
Liang Jiang:And at least okay. Maybe, like it's only, like, in the past one or two years, we show there is a quantum channel between the microwave and optical modes. Wow. Yeah. So now the challenge is that, okay, can we improve the efficiency?
Liang Jiang:Can we reduce the added thermal noise? Right. So that we can really, like, have an efficient, reliable channel to convert quantum information from microwave to optical and the other way around. Right.
Sebastian Hassinger:And I guess that's that's also most likely a key ingredient in sort of scaling up computation as well, because there'll be limits to, the size of any one quantum computer based on modality and other characteristics. So linking one fridge to another or one trap to another, that's gonna need some sort of transduction as well. So even before we get to long range communication, by quantum means, there's sort of quantum linking between quantum computers so they can act as a larger scale device, right?
Liang Jiang:Yes, yes, I think that's very important, because it's maybe in the microwave domain, it's probably hard to put all your qubits on the same wafer. And we need to have the interconnect between different wafers. Those interconnect could be microwave links. Or if you want to further distance, you need to do the microwave to optical, then optical to microwave to connect the remote devices. And even for an atom array or trapped ions or neutral atom arrays, one way to scale up is to have optical links between the different traps of atoms or ions.
Liang Jiang:And that will also enable people to scale up. Even for computation, that's kind of very helpful to have a systematic way to use a modular architecture to scale up the computation. And for communication, that's also important to connect to local processors or distribute the sensors to have such
Sebastian Hassinger:a link. Do you look at sort of the potential future challenges of programming that kind of distributed computational system as well, sort of there's a notion of almost a system architecture where, you know, this is more for long term storage, or this is your entanglement factory, this is your, you know, where the gate operations have, and that sort of distributed quantum computing is part of what you're thinking of?
Liang Jiang:Yeah, yeah, there are actually like many aspects. We can have this distributed and modular quantum computing. In one aspect is, okay, we can scale it up with a distributed subsystem. The other aspect is maybe we can modularize the functionality of different parts of the device. Maybe certain parts are memory, certain parts are processors, and maybe certain parts are kind of like an interface for different devices.
Sebastian Hassinger:Right. How do you spell Von Neumann machine with a Q? That's the only Some names don't lend themselves to the Q injection. It's really fascinating. I mean, you know, again, when we when we talked earlier, you sort of said you're a theorist who works very closely with experimentalists.
Sebastian Hassinger:And that's really apparent. I mean, you have a very broad and deep knowledge of what all of these the limits of the the experimental aspects of these modalities and the various challenges they're facing. It's really interesting to hear you sort of mapping that to theory. And it's that seems like do you think of that in terms of almost like system design or system architecture? Is that meeting of design and error or theory and experiment?
Liang Jiang:Yeah, well, I would say like in terms of the co design, it's an important aspect to know what the hardware challenges are and the hardware capabilities are to design error correction. And the other aspect is also thinking about what is the application you want to do. Is it for computation, communication, or sensing, or like transduction? One can come up with a kind of a more targeted design of error correction schemes, so that it will be more efficient to implement those applications.
Sebastian Hassinger:Where's sort of the upper limit of that application specific? Do you think at the level of almost like specific algorithm may have a unique approach to error correction?
Liang Jiang:Yeah, for computation, you can think there are different algorithms. Maybe certain error correcting codes will be more applicable. And another example is for quantum sensing. The question is, can error correction help with sensing? So it's slightly different from computation, because the computation you do not, you can choose whatever logical space you like to encode the information and do the computation.
Liang Jiang:However, for sensing you need to choose a logical space which is sensitive to the signal you want while to correcting the noise. And it's actually there's no guarantee that one can achieve both tasks at the same time. And that was actually kind of one of the achievements that my former student, Sisu Zhou, she accomplished, which she basically addressed the question that John Pasquale asked more than twenty years ago, how can error correction help sensing? So the setting is that you suppose you have the of very generic kind of white noise, and whether or not you can correct those white noise while sensing a particular signal associated with the Hamiltonian. And it turns out there's no guarantee it may work, but there actually developed a necessary sufficient condition that error correction can correct noise while sense the signal with the Heisenberg scaling.
Sebastian Hassinger:So almost like a roadmap. If you're going to try to build a sensing device, then you have to, as you said, fulfill those minimum requirements to be able to, if those requirements are fulfilled, you do have a guarantee that you can achieve it, or is there still no guarantee?
Liang Jiang:So actually it's a necessary sufficient condition, which in theory, it says that if that condition is satisfied, we can come up with error correcting codes to correct errors while doing the same thing with Heisenberg scaling. Otherwise, we have a proof from Fisher information that it cannot be done. And that actually addresses, because people do find successful and unsuccessful cases, and that kind of unifies, say, why and it's not it's a very easy criteria you That's can fantastic.
Sebastian Hassinger:And is there any, was she looking at a particular aspect of sensing when investigated that,
Liang Jiang:or was it just a purely theoretical process? Yeah, so the project started with kind of we were thinking about whether we can use error correcting codes to help, like, a gravitational wave detection. And actually, the bosonic codes was kind of the cat code was demonstrated breakeven slightly above breakeven performance in 2016 in Rob Shilkopf's group at Yale. And at a similar time, the LIGO, gravitational wave events, around a similar time. Yeah.
Liang Jiang:And that was kind of motivating us, like, to, including John Prescott, we said, okay, can we use error correction to help sensing? Yeah. And actually, like, so we figured out that actually doesn't work for that particular case.
Sebastian Hassinger:I see.
Liang Jiang:And we just wanted to understand why it's what's going on and then she further kind of like developed the framework to find the necessary sufficient condition.
Sebastian Hassinger:Is it, given her her necessary sufficient condition, is it possible to, I mean, at least on paper, no one want to do this, but redesign the LIGO
Liang Jiang:experiment. Yeah. So so so there's a actually there's a slight difference between CV and experiment because the experiment, there are many knobs people can turn. For example, you want to increase the laser power, and that actually can give you a better sensitivity. I see.
Liang Jiang:Right? And on the other hand, there are also certain aspects that actually certain theoretical design can inspire new generations of experiments. And related to that, there's also some recent very interesting work from, like, Professor Sunwang Choi's work at MIT. He was actually, like, with his collaborators, Robert Huang and Eichtron, they were coming up with some scheme called algorithmic based quantum metrology. So they want to do some dark matter search over a wide range of frequency range, And it's actually not easy to scan everything slowly.
Liang Jiang:And they come up combining the idea of a Grover search with the quantum sensing that can give extra speed up from the quantum Grover search. Wow. Yeah. And they can show that if you don't do that, you will not achieve that extra Interesting. Speed
Sebastian Hassinger:Yeah. That's fascinating. I mean, I've heard people talk about how, you know, computation and sensing are sort of On paper, it seems like they're a natural pair. Like you're In order to efficiently process quantum signal from quantum sensing device, you're going to need quantum processing. So you can So that's that's sounds like the first sort of practical example of that.
Sebastian Hassinger:That's really exciting.
Liang Jiang:Exactly. I think there are a lot of advances in those directions because we know quantum computer is really good at processing quantum signals. Right. Where does the quantum signal come from? Quantum sensor is definitely a very promising source of getting lots of good quantum signals.
Liang Jiang:Of course, are non trivial steps of how to make those quantum signals to be a good quantum oracle for your global search. And also there could be quantum simulators which could also give input for quantum processors to process. Interesting. And I think there are also nice work looking to like how to do the quantum learning from quantum data. Right.
Liang Jiang:And potentially we can also get like a big speed up with a quantum advantage.
Sebastian Hassinger:That's fantastic. It sounds like, across the board you are motivated by impatience you're
Liang Jiang:trying to figure out.
Sebastian Hassinger:And I think, I mean, I'll speak for myself, but I think everybody shares that impatience. We all want to see the fastest path to getting, you know, useful and and exciting results out of these devices. So, thank you very much for joining me today. It's been really fascinating.
Liang Jiang:Yeah. It's been fun to chat on these exciting topics. Excellent. Thank you. Yeah.
Sebastian Hassinger:Thank you for listening to another episode of the podcast, a production of the New Quantum Era hosted by me, Sebastian Hassinger, with theme music by OCH. You can find past episodes on www.newquantumera.com or on blue sky @ newquantumera.com. If you enjoy the podcast, please subscribe and tell your quantum curious friends to give it a listen.
