The New Quantum Era

The New Quantum Era, a podcast by Sebastian Hassinger.

And Kevin Rowney.

Welcome back. Today on the New Quantum Era, we're interviewing Martin Savage, who is a professor of nuclear theory and quantum informatics at the University of Washington. He runs a research team there exploring how quantum computing systems can investigate subjects in high energy physics and quantum chromodynamics. He also runs the incubator at University of Washington on quantum simulation. Interesting guy.

Yeah. Really interesting, Kevin. I met Martin where he gave a talk actually at a workshop at University of Washington that I attended, earlier this year, where he highlighted, the results that are published on a paper on the archive titled quantum simulations of hadron dynamics in Schwinger Model Using 112 Cubits, and it was kind of breathtaking actually because it's the scale of the experiment. He used the IBM's Heron chip, which is a 133 cubits, used most of those cubits where most experiments on on quantum computers these days, tend to be in the sort of under 10 qubit kinda range on average.

Yeah. Yeah.

Right. Exactly. So you used over a 100 qubits and, really, a staggering circuit depth and length of of job. So it was one of these really rare instances where the the work had scientific merit in and of itself and also pushed the limit of what you can do on quantum computers today. So I I immediately said, oh, we need to have them on the podcast to

learn more. Good stuff. That's gonna be good.

Welcome back to the podcast. We're joined today by doctor Martins j Savage from University of Washington, professor of physics. Also, the the PI for the incubator for quantum simulation, which is a really fascinating center that's hosted up at University of Washington. Welcome, doctor Sabet. How are you?

Yeah. Good. Thank you very much for hosting me.

Welcome on, man. Yeah.

Very glad to have you with us. So if if you don't mind, we'd love to hear just a bit of your journey to quantum computing. You're you're in nuclear physics, I believe. Right? And and you sort of jumped more recently into quantum computing.

Yeah. So so, I I made the transition around about 2017, 2018, and it coincided with a few things lining up. But I thought I'd tell you roughly where I came from and then how we go, if that's okay. Awesome. Yeah.

So, so I did my undergraduate work in Auckland, New Zealand, and my master's thesis was in experimental nuclear physics. They had an accelerator there, and it was a great education. And I came to do my PhD at Caltech, and my and I started as a nuclear experimentalist and switched into theoretical particle physics. So my advisor was Mark Wise. We worked on beam meson decays.

And this was in, starting in the mid 19 eighties. I was at 85 to 90 at Caltech. And Feynman was, had given, was giving lectures on quantum computing at that time. But, I didn't pay much attention. It seemed a little exotic, and I was really focused on on yeah.

And and Murray Gell-Mann was giving lectures on, and information also. I took that class, and I I found it fascinating. And Seth Lloyd was there as a post doc at the time. So that was the beginning, but I really didn't engage and pay attention. I was focused on high energy high energy theory.

And so then, I became I was a post doc at Rutgers University and a doc at UC San Diego, and we were working on sort of low energy effective theories, strongly interacting systems. And then I was assistant professor at Carnegie Mellon University in particle theory. And then University of Washington came along and said would you like to return to nuclear physics? And so in 1996, I said, yeah, gladly. And I came to UW.

I was a nuclear theorist working on effective field theories. And then we got to this point in developing these theories where we realized that in order to really go further and get the precision we needed to have impact, we had to go to large scale numerical simulation. And so I switched to that point with, you know, 2, 2 or 3 others. We we formed the NPR QCD, Lattice QCD collaboration. So it was nuclear physics with Lattice QCD.

And, largely against the advice of all of our colleagues and friends, we, put in significant effort to compute strong interaction processes using lattice QCD multinuclei and nuclei, and we made really good progress. And so then I was involved in the exascale, process and evaluating the resources required for nuclear physics to get to where we needed to go. And so this was around 2017 and, and we realized there was classes of problems that exascale and even beyond exascale, we're just not going to get to. Right. And, and these were problems that were finite densities of variant of fermions and also dynamics.

And so there is a sort of moment, in that period where it's like, okay, we need to do something else here. And it was also at that moment that IBM's devices would come in online. So those two things lined up well. And so we'd said, okay, can we do this? And that was pretty much the beginning of the transition, at least for me and for others.

And the before you before we get into the quantum computing part, I'm just curious. The idea to use numerical simulation for, particle physics and nuclear physics, was there any, sort of inspiration or borrowing of techniques from computational chemistry in that? Or or was what was the impetus around there? Around that?

Yeah. So so great question. I mean, from from the high energy physics point of view, large scale simulations have been going on at least at the fundamental level since the early 19 seventies

Mhmm.

With Lattice QCD. So this was, Wilson, Kreuz, and others that really, you know, laid down the foundation very shortly after the formulation of QCD itself. And there's been through that evolution and and interchange of techniques, between fields. Right? So one way quantum field theory is a little peculiar because it really is dealing really complex numbers are critical.

You know, the the I in I squared equals minus 1 is really central to what we do.

Doubtless.

And so the techniques are similar and there's been a lot of sharing, quantum chemistry, many body systems, condensed matter systems, and high G physics and nuclear physics. And that's continuing, and sort of accelerating even a little bit on the quantum side.

Right. Right. I mean, that's that's sort of where I I was wondering if there is a connection because computational chemistry is also finding these sort of bottlenecks and blockers where even exascale and beyond, methods are not going to yield results. And quantum computation actually has a potential path forward if we can improve the hardware fast enough.

Yeah. That's right. So so, you know, dynamics is one area which is sort of globally Right. One of one of these global areas where quantum computing is gonna make the difference. It's it's gonna be the only path forward to get to some of the things we gotta get to.

We've heard

that say that same theme in the past interviews. Right? Is it that for many people who are, you know, the cutting edge of science, the the the variation of dynamics is is wildly challenging in terms of your classical numerical methods. There's really almost no other way forward besides, quantum computing. Is that is that a fair characterization in your mind?

Yeah. Yeah. Yeah. Yeah. Yeah.

I mean, it's you're really from the techniques we have to use, high school computing, we're really stuck. They just don't take us to where we need to get to.

Right. Right. So that that makes you a pretty early adopter of quantum computing. I mean, IBM system on the cloud is about the first chance most people have ever got to get their hands on, virtually, their hands on a quantum computer. So you've been doing this now for that's, you know, as close to 7 years or something.

That actually makes it, it gives me more context for the the simulation that I saw you describe at the the workshop at University of Washington, which I guess was this past December. Right? It was quite a huge step forward from what I've seen with with other other similar efforts.

Yeah. So the the original calculation where, we're actually brought in, by people at Oak Ridge. So we we formed a team at Oak Ridge in 2017, and the first calculation that we did they did they did the calculation looking at the ground state of the deuterium. And the work that we were involved in here at the University of Washington was actually the shringer model on 4 cubits. And and this and this was a natural place to go.

The Innsbruck team on on, 4 qubits of trapped ion systems had done the first calculation, and that was basically, you know, the light turned on and it's okay. This is where we gotta go. And the work that we did, in December, so there there was there's been a long path. Right? And and so we've sort of roughly have a, well, I mean, pretty good idea where we need to get to, but it's a case of somewhat a mercenary approach.

Like, okay, we can do this now. Okay. We can now do this. Okay. This is And we did a calculation in August where we, built on some algorithms that had been recently developed and developed scalable algorithms.

So our problems have a lot of symmetry that basically discretely translationally invariant And we came up with circuits in such a way that you could actually tune them up on modest sized classical computers and then scale them out to arbitrary large on a quantum computer. And so we demonstrated that to prepare the vacuum to quantum vacuum of the Schwinger model. And then what we did in December, late December, and I'll come back to one particular point, was to then start doing dynamics. So we created a lump of energy, and then we let and then we could time evolve it forward for a significant number of time steps and then watch actual these composite particles form and then propagate out. So we saw a light so we saw a light cone of composite particles in this in this system, which is very much on the path of where we wanna go for strong interactions in quantum chromodynamics.

So with the size of the system, the simulation we did was a 112 cubits, and we ran 14 time steps. And that largest one was required 14,000 CNOT gates and a set a depth of 370. It was a beast. It was a beast of a calculation.

Yeah. Yeah. No kidding. I mean, the the IBM, 100 by 100 challenge was just issued, I think, earlier last year, maybe in the spring, where, when they released that system that you ran on the Heron 132 qubit chip, they were calling for somebody to to try running a a 100 qubit, circuit or a circuit using a 100 qubits with a 100 circuit depth, and you blew the doors off at the first attempt. That's impressive.

How did you manage to run that many CNOT gates?

Quite easily, it turns out. Well, no. I'm being facetious. So the the the part of the key here was, firstly, the error the the medic error mitigation that we used, there was it was, a variant in what had been used before and turned out to work very well here. But also the fact that our, our system again has this translational invariance.

And so there's a lot of, I mean, there's similarity in the correlation as you step from 1, from plus infinity to minus infinity. And so that helps enormously. So it's not, it's not, it's very much not an arbitrary quantum circuit. It's a very structured quantum circuit. So that helps significantly enable, in being able to do this.

And so, you know, we we ran a 150,000,000 shots. Yeah. And, and and applied, yeah. It was a significant resource. And what made this possible is in fact that, for the, you know, we've all run on large scale, compute systems, and they always go pretty quiet between Christmas and New Year's.

And, we were ready. And so that's what happened.

That's really funny.

Interesting. So so, yeah, the decoherence issues and maybe the the errors on on gates themselves, you largely were to cement that by the symmetry of the problem and perhaps that the amount of, runtime required was just, minimal relative to the the result objective?

Yeah. So the so we constructed, the circuits had a lot of periodicity to them. You know, they're they're translationally invariant by, you know, 1 unit each time. And so when you stack the circuits on top of each other to to, implement one layer and, and adapt VQE algorithm, then in fact, you can do a lot of cancellation and and there's a lot of compression. So the first layer was was as dense as it could be.

The second layer was was very dense. It wasn't wasn't, it wasn't perfectly dense, but it was very dense. And so there was a lot of compression, that happened. And and so the 14,000 CNOT gates compressed down to 33, you know, 3370.

Right.

And and so that's sort of where the some of the magic was that happened here. Yeah.

Yeah. And

If we'd have had to stack them out arbitrary deep, it would have just not worked. Right.

Right. Right.

It would have been a total failure.

And did I did I hear you correctly? So there's a this is essentially a VQE algorithm at its core?

So, yes and no. So, we use we use the VQE algorithm, the Adept VQE algorithm to build the operator structure using classical computers. So we tuned up that circuit. Because it's localized, we can actually tune it up on a classical computer and get these angles to be exponentially close to where they need to be. And so once you have those angles, then because we'd set up operator operator structures that could be extended to arbitrarily large without changing those angles, then we're able to actually blow out the entire, quantum register, but without having to do an iterative VQE on the quantum.

Interesting.

Because of the the the circuit scaled up. The the right? Yeah. That's right. Okay.

Got it. Got it. Yeah. So once you once you approximate got a good approximation on the classical VQE simulation, you're able to apply that to the scaled up circuit on the entire

Absolutely. Absolutely. Yeah. It's again, because, you know, these theories are confining. So when you look at how charges correlate as you move them apart, then once you're outside a few confinement radius confinement lengths, then all the correlations drop to 0 exponentially.

And so you really only have to worry about a small volume and get that right. And you can do that with exponential precision, and that's what you do on the classical computer. That's where the VQE part is, and you can do that classically. You know, that that will change as you start going towards continuum. You'll have to then go you can then tune up on a smaller quantum computer to scale to a bigger one, but you're still in you're still having this great simplification.

So I it's a problem ideally suited to the the current era of of QC. Yeah. Yeah.

Yeah. So, so I I agree exactly. I think that there's a chance that these these these one dimensional systems, which is where we're looking at now, the, you know, these, if you perform scattering, so I take 2 energy, clumps of energy and I collide them together, Computing what happens is is beyond classical computation. And but that but, it could be that within, you know, a reasonable period of time, like 2 years, you could actually do that on a quantum computer with today's quantum computers. I I think it's it's close.

That's amazing. And am I right in thinking, I mean, you just described it as 2 clumps of energy colliding, so that's the type of work that normally experimentalists do in, say, the Large Hadron Collider, for example. Right?

Exactly. Yeah.

So you're you're replacing this enormous piece of lab equipment that's buried under the ground in Geneva with with, something that can fit in a DILF fridge in a data center?

I would never say that. Fair enough.

But but but perhaps one day you have hopes.

You know, so one of the things you if you if we look at study how Lattice QCDs evolved, you know, so quantum simulations are comparable to where Lattice QCD on classical computing was in the early 19 seventies. I mean, right around its creation. And in fact, the classical computers then were a little bit more capable. But and, so there there was a lot of development period, and it's only recently, I would say in the last 10 years, that the latest QCD simulations have been able to provide results that are better than what can be obtained from experiment. But there's classes of things that are better.

I mean, we're learning things about, weak interactions because we can do strong interactions, factors of 3, 4, 5 better than you can do with from experiment. But replacing experiment, I think, is not the right way to think about it. It's not it's supplementing and complementing. That's how I view these things. Right.

Right. And guiding future ones.

Bad choice of words in my place. I mean, I mean, in this particular experiment, you were accomplishing something something that otherwise you would have needed to try to simulate or to to do experimentally with some large piece of paper.

Yeah. I mean, I yeah. It's very much a complimentary and supplementary activity. It's not a replacement. Yeah.

Yeah.

So I totally understand. But still, I mean, it's a provocative line of inquiries. And to sort of at least try to compare what you're currently doing with, say, the past history, the long 100 year history, right, of of colliders, accelerators, etcetera. Is that is that a fair comparison? And if so, I mean, what's what's what era of experimental technology have we reached by simulation in in a QC, do you think?

Yeah. So this is a great question. Right? And and so on the QCD side of thing and where we're aiming for, you know, with the quantum simulations area is to be able to, you know, you basically verify the technology and prove that the your numerical simulations work with high precision, you can make predictions, which then you do experiments and they're born out. And then you can take the simulations and go to environments where you can't do the experiment, like in the core of a neutron star or when you, right.

And so it's to go to places that you can't go. Right. Either through observation or terrestrial. That's, that's the objective. But, you know, the experiment you need to do the verification stage, and that's critical to be able to make sure you have your errors right and you can make predictions.

Yeah.

Is that something that that that work, the theoretical work is sort of underway where you're you're the community is starting to build kind of a a model for what the interior of a neutron star might be so that you can actually perform experiments in that in that theoretical context.

Yeah. There's a lot of effort to try and do I mean, these are remarkably complicated environments and well, yeah.

Sounds like it.

And so for instance, when a supernova collapses, enormous energy is released. And to, you need to understand what's there, but you also get a large production of, for instance, neutrinos. And neutrinos have long wavelengths associated with them and they can change their flavor and they can interact with each other. And that's something again, that's really, that's again a beyond exascale challenge. That's something so people are looking to simulate the dynamics of neutrinos coherently scattering with the shell, which is fundamentally quantum mechanical is to try and get a better handle on what's going on in those extreme environments.

So that's so that's something else that that's also being done in parallel to what we're doing.

Yeah. That's true. I I sometimes have a habit of, asking our guests to a little bit speculate on on the future here. But, I mean, I just I'm trying to maybe brainstorm with you a little bit permission, please. But there are numerous, you know, theories in physics that are, you know, deep, deep in the range of theory that many people criticize as being essentially untestable given, you know, just the amount of power and energy available, you know, in just the solar system.

Right? It's just it's just that so much extreme energy is is required. But could it be the case that perhaps some of these techniques could push the boundary, right, of, computation based experiment in ways that could test, at the limits, some of these rather out there, theoretical projections.

Yeah. Absolutely. I mean, it's giving when quantum simulations get to the point where, you know, they take you beyond classical, you gotta be able to probe ideas and environments that you just can't do any other way.

Right. Wow. Yeah.

So, I I some of the theories I think will remain beyond, the boundaries, but Yeah.

Civilization. Yeah.

But but, but it's it's definitely gonna help in pushing that type of research forward. Yeah.

Really interesting. And can you can you perhaps bottom line that some more? I mean, what what what are the major, you know, large theories of everything do you think perhaps could be probed successfully with with these methods?

Yeah. No. I mean, I think I'm not gonna venture down that pathway, right now. It's setting myself up for, but I appreciate the question.

And so, I mentioned the incubator for quantum simulation, which I guess that's NSF funded. Right? The the primary No.

It's actually DOE funded through the Office of Nuclear Physics through Quantize. Yeah.

Right. That makes sense. Yeah. And so, this would be the the work that you've done is sort of fits obviously under that, that umbrella. Are are there other areas within you actually bring quite a disparate group together in that incubator, and they sort of have, quite a creative kind of mixing, don't they?

Yeah. Absolutely. So so the the incubators got really sort of 3 different functions. So we had the local research is one of them. Another important component is the is the workshops we run.

So so I took a leave from the Institute For Nuclear Theory where I was a member there for a long time. And we work together. So the incubator holds 1 month 1 month year of programs, so basically 2 2 week programs. And we bring together people from all the different areas and in particular focus topics. And so from quantum, engineering people from tech companies, universities, national labs, to focus on something that would benefit from having people sit here and talk to each other and present for an extended period of time.

And we hold those in the Institute For Nuclear Theory. And, you know, they're very lightweight. It's it's a think tank environment. Excuse me. And it they and all of them have been, you know, really I don't wanna say surprisingly successful.

They're working as we'd hoped, but they've really been special in the sense that after somebody in the elevator said, one of the attendees said, you know, we arrived as fermions and left as bosons. Be because the 1st week, people from different areas don't quite know each other's language, and they've not met each other before sometimes. And and then it takes about a week, and then in the second week, people start really it starts gelling. And it's really exciting to see. Yeah.

Do you think that that in a sense, the quantum information science is is almost acting as a a lingua franca that's that's sort of crossing the boundaries between these different disciplines within physics and other physical sciences?

It's absolutely it's it's starting to. That's right. So so this is something that's new, sort of where it is today. It's sort of new in high energy physics, new in nuclear physics, new in the domain sciences to some extent. And the, you know, the some of the ideas and concepts have been in the fields, but they haven't been sort of formalized and put together.

But now with the with quantum information now becoming, you know, prominent and recognized as central to making advances in these areas, it's really starting to come together like that. And so so, the concepts of information that are now coming into high energy and nuclear physics are are actually changing how we think and allowing us to do things that we wouldn't have been able to do before. I mean, it's really making a difference. And then also conversely, and this is kind of also part of the point of the workshops is that we have technology, for instance, in nuclear physics, the nuclear many body technology. So some of the nuclear models that have been studied since the 19 sixties are also, for instance, have Hamiltonians that are used for spin squeezing on programmable quantum sensors for an ex as example.

So we we have a lot of, you know, technology we developed for specialized problems that have more general applicability, and that's now also being dispersed within the community. That was just one example. Yeah. So so so there's really really, an increasing exchange of information and ideas that's really beneficial to everybody in the advancement of the of multiple fields.

Multiple fields. Yeah. It's so exciting.

Yeah. It does seem perhaps indicative of a trend where more and more it's the case the quantum information sciences become sort of core to pedagogy for students of high energy physics and similar,

I I think it's I think it's gonna become one of the themes that allows you to understand what not only what you understand experimentally, but how you understand how the theories are working and how to make advances in problems that were, you know, I don't want to say too challenging, but where progress has been slow.

Yeah. I

mean, this is bringing in new ideas and new concepts. Absolutely. Yeah.

Yeah. Yeah. It's it's

really an exciting time. I mean, really exciting time.

Really is.

Yeah. It really is. We live in miraculous times. Yeah.

Yeah.

Yeah. Yeah. It's, it is remarkable every time I think about how on the nose Feynman was in 1981 with that keynote. If if he could only see where we come to now, it's it's pretty extraordinary progress for that amount of time. So so when you look ahead, Martin, just as as a as a maybe a wrap up question, do you do you have sort of targets in your mind or accomplishments that you're sort of working towards that that you can share?

Because obviously, you don't wanna you don't want somebody to scoop your your research, results. But

Yeah. Absolutely. I mean, at least nuclear and high geophysics is a number of number of sort of large scale objectives. They're all, you know, the ones we're sort of focusing on on the at the moment are sort of these non equilibrium questions of what is the nature of matter under quite extreme conditions and, you know, when you tries to compress it or heat it rapidly, what does it do? And we don't know how to answer these questions really.

For me, we are we are sort of chasing how to do QCD and strong interaction physics, the dynamics at high energies. I'd say that sort of captured it. So you know, what we talked about before, if we could start from say 2 very high energy protons, collide them together into that, these large showers that you see in the colliders, we can make progress towards and, you know, making postdictions and then making predictions, I mean, that would be phenomenal.

Yeah. Really amazing.

And and at least in one d, I think we're making some progress. 2 d and 3 d is harder, but 1-D is real we're learning a lot and we're making progress. So yeah.

Well, I there's no other way to characterize the result from that that paper that you that you released, I guess, in early January other than progress. I mean, that was a huge step forward in terms of, of, an actual result. So, my hat is off to you. It's really quite impressive.

Well, You know, these things were made possible by having, you know, great teams. You know, this is Of course. I have to mention, you know, we have these great postdocs and students and junior faculty here that are contributing, you know, in all in very special ways. So, that work was made possible by good teamwork. They've been good collaborators.

Fantastic. For sure.

Great story. Yeah. Good stuff. Awesome. We're so grateful for your time, Albert Snipes.

Thank you.

Well, thank you very much. It was a pleasure. That's great.

Wow. Another fascinating interview. I love these, conversations with, people in the science is using quantum computers, right, to explore, you know, actual frontier questions in in the higher sciences. I mean, just just amazing stuff. You know, this is probably one of the biggest frontiers where there's actual real applicability, right, of, and and value for a high volume quantum computer setup.

So, yeah, just just amazing stuff they're doing on that

team. Absolutely. It it we've said it before, but this really is the culmination of of Feynman's vision from that keynote in 1981. Right? I mean, these are Feynman machines.

We're now getting to the point where we're simulating quantum systems that you can't otherwise simulate in in classical classical settings.

Yeah. I mean, he really just, you know, lit it out plain. It's like essentially for, I mean, any of these computational problems that he's dealing with. There's there's no way, a classic computer could could get on top of this question. Right.

So yeah.

It's just Yeah. And super I mean, you know, you you you asked some probing questions there, Kevin, that that, that Martin didn't wanna make, you know, a committed answer to for obvious reasons, but I hope the question was really I

hope I hope he didn't have any pissed off by that one. Yeah.

No. I'm sure he didn't. I mean, the, you know, the the implications of what he's talking about is if there is a path forward with quantum computers that extends the the computational approach to higher energy physics,

Yeah.

He's going they are that community is gonna start to be able to do things that otherwise would be, you know, need a a huge amount of investment, capital investment in a collider or an accelerator, or potentially wouldn't even be possible in those settings. Right?

Yeah. You you could do encode what only could be done on a a cyclotron. So kinda cool. Right. Right.

Well and and eve you went even further and asked him, are there any particular, you know, areas where you think there might be, you know, progress towards, like, a theory of everything kind of

Well, or or at least at least being able to run some of the experiments that are needed to, you know, falsify or endorse, right, some of these theories of everything that that require just, you know, absurdly fantastic energies beyond any hope of, you know, of real realization as a real world experiment. So, you know, it's kinda cool. And and, of course, you politely step back

from

speculating on this one, but I did, I did have to ask.

Of course. You gotta be the rabble rouser. I I thought it was also really notable. Some really interesting characteristics that were specific to Martin's workload here or use case. One, it touches on one of our themes for this year, which is we're sort of questioning whether there is any value that's gonna be realized from variational textings, VQE in particular

Yes.

You know,

sort of be being pronounced dead in 2023. In one sense, this is another you know, a lifeline for VQE because he actually did use VQE in a classical setting before running the experiment on the actual quantum computing, system, which I thought was really interesting.

Yeah. Really interesting. Yeah. But but just an amazing tour de force of his entire team. And it was just great to hear him acknowledge.

It was a gigantic suite of talent required to produce this result. Yeah. So, it's just fascinating science, really.

Yep. Absolutely. And I think, you know, there's certainly more to come from that group. And I'm I'm also looking forward to seeing how these sorts of, you know, he he sort of referred to the the techniques and the technologies that the higher energy physics and particle physics and other subdomains of physics are are developing and sharing among one another. And I think that's, you know, we're we're going to see acceleration almost, you know, necessarily out of these types of efforts across the board.

Yeah. Yeah. And in closing, I just it was really just thrilling for me to hear how he's acknowledging openly, right, that the pedagogy and higher energy physics and and these subjects I mean, necessarily, we'll more and more have to embrace, you know, programs of quantum information sciences Yeah. In order to fully, you know, realize the possibilities of of the current era. So just, just great insights.

Very, very

It really was. Alright.

Okay. That's it for this episode of The New Quantum Era, a podcast by Sebastian Hassinger and Kevin Roney. Our cool theme music was composed and played by Omar Costa Hamido. Production work is done by our wonderful team over at Podfi. If you are at all like us and enjoy this rich, deep, and interesting topic, please subscribe to our podcast on whichever platform you may stream from.

And even consider, if you like what you've heard today, reviewing us on iTunes and or mentioning us on your preferred social media platforms. We're just trying to get the word out on this fascinating topic and would really appreciate your help spreading the word and building community. Thank you so much for your time.