Transcript | Entanglement and Other Quantum Foundations with Quantinuum

Quantum computing is built on the ideas of giants. These so-called quantum foundations contain some complicated concepts, including entanglement. The 2022 Nobel Prize in Physics was awarded to three scientists who expanded our understanding of entanglement. Learn how this invisible link works and explore some other fascinating core ideas behind quantum information science in this episode of The Post-Quantum World. I’m your host, Konstantinos Karagiannis. I lead Quantum Computing Services at Protiviti, where we’re helping companies prepare for the benefits and threats of this exploding field. I hope you’ll join each episode as we explore the technology and business impacts of this post-quantum era.

Our guest today is the chief scientist at Quantinuum, Bob Coecke. Welcome to the show.

Hello.

I’m glad to have you on. This is going to be a different kind of episode. We’re going to touch on some fundamentals in physics — you use a different term for it: “quantum foundations” — and we’ll get to that. And today, we’re going to be talking about entanglement, but before we get to all that spooky stuff, I figured it’d be fun to tell our listeners about how you ended up at Quantinuum — what your quantum journey has been like.

I recently posted a blog post, and I got into the history there. I started my Ph.D. in what’s called quantum foundations, which is a field started by Einstein, Schrödinger, von Neumann, where they wanted to go to the core of quantum mechanics: What is quantum mechanics telling us about the world in which we live, which is in contrast to how quantum mechanics was taught when I was at university. It was taught as a bunch of cooking recipes. Literally, they used those words: “These are the recipes. This is what you do, and you don’t think about it. You don’t think about it. You don’t ask questions. You just do it.” That was like an accountant — it was some form of accountancy.

So, nonetheless, the fathers of the field — Einstein and Schrödinger and von Neumann — lots of people, when they started studying and they heard about that field, they got naturally attracted to it. Some of the best scientists are people who are more creative, who are very attracted to that field. But then, when I was doing my Ph.D. in that field, what I didn’t know until the end of my Ph.D. is, it was impossible to get any job in that field at that time — and I’m talking mid-’90s. It was not a matter of that I couldn’t get a postdoc — there was not a single one anywhere — and so I ended up unemployed. I had a reasonably good publication record, although you couldn’t get that stuff published in the top journals, of course.

So, I reinvented myself as a mathematician in the fields of category theory and logic — as a category theoretician/logician — and I had a bit of luck. I was in Belgium at the time, and one of the people who was awarding fellowships in France was a category theoretician. He liked the fact that a physicist was going to try to get into category theory, and he pushed me hard. I got a postdoc fellowship then, but then again, after that, the constellation changes, and it was again finished, and I ended up applying for things like jobs at art school, because I was also an artist.

I didn’t believe there was any hope for me. And then, out of the blue, I didn’t apply for it, but I got a job offer from Oxford in computer science, because there, the computer scientists, especially Samson Abramsky, were very interested to see whether whatever they had been doing was applicable to physics and to make quantum computing.

I got headhunted for that job, stayed at Oxford for 20 years, became a full professor there, built a group of 50 people, and then, when my stuff was starting to become used by companies like IBM and Google, I thought it’s good to connect with the industry myself. And then I got an offer which I couldn’t refuse, because starting two years ago, it was completely impossible to do this in academia — totally impossible — for many reasons.

Yes, the field owes a lot to Oxford in general. There are quite a few people there who’ve contributed to it heavily, including one guest that I’d love to have on the show: David Deutsch. Let’s talk about some of these foundations. Would you say that you ended up working with interpretations of quantum mechanics back then as well?

Well, my Ph.D. was 100% on interpretations, but it was too far ahead of its time. The physics world didn’t want to have anything to do with quantum foundations. There was a slogan going around, “Shut up and calculate,” and people doing quantum foundations were either considered crackpots or people only interested in philosophy, and nothing else. Then, what the people in philosophy were mainly doing in quantum foundations was fighting each other over interpretations, and these fights are still going on.

Nobody takes notice anymore. That’s the big difference, but it was a very bad climate. People were not career-minded, communication-minded. It was all about “my interpretation and against the others. Then, it was like you’ve got in the U.K. — two political parties, or something like that. You had four or five official interpretations, and you had to pick one of them. I ended up working in something that was not part of those five. It didn’t exist at all.

To be more concrete, there is something called Bohmian interpretation, which is an interpretation with hidden variables, where you assign extra variables to the state of the system — and these, by the way, are very closely related to this year’s Nobel Prize. You assign states to this extra variable to the state of the system, but you can only do this if they are nonlocal, so to say, and the Nobel Prize this year was for the experimental demonstration and some theoretical work toward this proof of quantum nonlocality, because that’s what it is: the nonexistence of classical probabilistic descriptions for quantum mechanics. You have to go nonlocal if you want to do anything like that.

Bohm is an example of such a theory, and that’s one where people want to put the variables. No one wants to think that the state is just there and that everything you learn in a quantum measurement is about that state. So, the variables are assigned to the state. Now, what I was working on is where the variables are assigned to the interaction of the state with its environment, which is a measurement device. But that was the idea, which brings a subjective factor into physics, the state. It’s not just all about the state — it’s also when it stays in contact with its environment. That was complete taboo at the time, and now I know that big people like Carlo Rovelli and all that, they’re actually moving in that direction now, 30 years later.

Yes, and he’s writing some pretty great books, too. They’re making it more accessible.

Yes, with Rovelli, we have a big project where using foundational stuff in quantum — two words: “quantum gravity.” We have a very nice project going on already for three years now with the John Templeton Foundation — so that’s nice.

Going back to that, how did your work challenge the Einstein-Podolsky-Rosen paper, the famous EPR paper, where Einstein brought up the hidden-variable idea?

It’s perfectly comparable with all the previous results, of course. This is what I did in my Ph.D., and then nothing happened for me, because it wasn’t very fruitful. This is an idea which actually goes back to an old paper where they come up with an equation for measurement by taking a variable, which is associated to the measurement device and moves with the symmetries of the measurement device, rather than with the symmetries of the system.

Then, the people didn’t realise that that’s what they were doing; otherwise, they would’ve rejected it as well. Once you start saying what it actually is, where some of your variables are associated to the environment rather to the system: “Oh, no, no, no, no.”

Now, I’m going to answer your question more directly: With this discovery, EPR, it was mainly Schrödinger who coined this idea of entanglement. I started to embrace the idea that the most important thing in quantum mechanics is, what happens if you compose two systems — if you bring them together? I wasn’t aware at the time, but that’s something Schrödinger had proposed in 1935 and it was never picked up by anybody. In that paper, he was already laying the foundations of quantum computing, because he came up with something called quantum steering, and that very much goes in the direction of quantum teleportation, and quantum teleportation is itself a computational model.

John von Neumann had written the book with the Hilbert space formalism of quantum mechanics, which is the standard formalism of quantum mechanics. It was published in 1932, and then, in 1935, von Neumann himself rejected his own formalism. Of course, most people are still using it, and it’s still the way quantum mechanics is taught but von Neumann rejected it on conceptual grounds. He said, “This doesn’t feel right — this doesn’t feel like a theory of physics, how it should be,” and there are things in quantum mechanics like redundancies. When you want to associate a vector to a system, you can do this in multiple ways which are equivalent, which gives your theory a bad feel.

What von Neumann fundamentally felt was — he was also a logician — we should start by assigning some logical structure to quantum mechanics which focuses on how quantum is different from classical, and he focused mainly on the concept of measurement. So, the fact that the system changes and all that changes the way we can assign logical properties to a system, and that was called quantum logic, and then that was a field which was very active for a very long time but died out in the ’80s and especially in the ’90s, because there were a few failures: They were never able to, at a conceptual level, describe how two quantum systems compose. They were always talking about single systems. But I knew this fact — the complete failure of that area of research to describe composite systems — and then I thought, “Let’s do the opposite. Let’s start with composite systems and see where we get.

I had a few failed attempts, and then, when I was at Oxford with Samson Abramsky, who’s a very famous computer scientist, we started what’s called categorical quantum mechanics, and that’s been a success story. The idea is that your main symbol is basically putting two systems together, and then we have shown that all of quantum mechanics can be formulating those terms, and measurement emerges from it.

So, showing that intuition was very right. Von Neumann was wrong — all the attempts of von Neumann to come up with a new quantum mechanics formalism were failures, but each failure generated an entirely new field of mathematics. So, they were pretty successful, in a way.

To help our listeners, could you give a good, concise explanation about what entanglement is?

Entanglement is the fact that when you’ve got two systems and you bring them together, new forms emerge. Normally, traditionally, we have the idea that when we describe two systems, you describe one and then the other. In the case of quantum mechanics, that’s not enough, typically. These situations also exist, but they’re a limit case. It’s very uncommon.

Typically, what you have is a situation where two become one whole — and I can use a good metaphor there, for example: the concept of a twin. If I tell you, consider a twin, then I can ask you, “Let’s call them Alice and Claire,” and then I ask, “Well, how does Alice look like?” You know nothing about Alice, but the thing you know is how Alice looks: Maybe she has blonde hair, and then Claire will also have blonde hair. If Alice is tall, then Claire will be tall, and so on, but you know nothing about Alice, and this is analogous to what’s called the EPR state or the Bell state, which is the most typical entangled state. Now, through a concept like quantum teleportation, you can in some way use these new states as channels. It’s as if there is some sort of bridge from Alice to Claire through which things can flow, and it’s subtle. It’s quite subtle how this all works, but that’s entanglement.

Yes, Einstein didn’t love that, because of his nonlocal nature.

Well, yes, that was the problem. Nonlocality itself is a very subtle thing, I’ll make a disclaimer: It’s not like information, like messages. But whatever happens at one side impacts what happens on the other side. So, it’s a very subtle thing, quantum nonlocality.

Yes, and people always talk about the spooky-action-at-a-distance thing, and, Einstein, it turns out, wasn’t talking about entanglement. He was talking about that when the observation is made, that was the spooky action, the collapse of the wave function — however you want to call it.

Yes, but there is no real action. There’s no action going on. So, a lot of people have started screaming against all the spooky actions at a distance being mentioned. One is to be careful with these things, because otherwise, one is violating Einstein’s theory of relativity. That’s, of course, why Einstein got a little bit annoyed. It’s almost like under the hood, maybe there is some signal, but we don’t have access to it. We can’t manipulate it or use it. That’s the image which I have.

I tell people, “Yes, it seems like you’re sending information faster than the speed of light, but in reality, it’s random. You can’t send bits that way.”

One thing you can do — and that’s what teleportation does — is, for example, send infinite data using finite means. It’s more like an amplifier. You send a few things, and suddenly, your site receives this huge message, but you only have to send a few bits. So, that’s what the quantum teleportation is.

Yes, with teleportation, you’re using these principles in a way to transfer quantum state, but you have to have a classical channel to set up that path.

Exactly, and that’s where the qubits travel. We’re talking teleportation, so this takes us to the beginnings of categorical quantum mechanics. We were able, using composition alone, to give a very generic description of quantum teleportation. Basically, in this new formalism, quantum teleportation was the most trivial thing you could imagine. In the old formalism, it took six people 60 years. That’s why, when we first started this categorical quantum mechanics, there was something clearly very promising, because it was conceptually simple.

And another thing is, this is a particular branch of category theory, which is equivalent to drawing pictures. Ultimately, what we had was a start of a purely pictorial quantum formalism. I didn’t know at the time that it was even possible to get all of quantum mechanics pictorially, but we now know that you can. All of quantum theory can fully be formalised pictorially, because these pictures are the incarnation of the idea that it’s all about composition. It’s not a spoken thing. I can’t show pictures. The most absurd thing is to talk about pictures, because pictures are supposed to be seen.

And listeners should know that you pulled it off, because after this airs, your book Quantum in Pictures will be coming out, and I got to see a digital advanced copy of that.

And it’s pretty clear: You go through it, and it’s even got a handwriting font, so the whole thing feels like you sat there and sketched it out, and you’re talking to the reader.

It does look like the kind of book that you’d want to hand to someone who’s super lost and doesn’t understand what’s going on. So, I’m looking forward to seeing a paper copy. Now, when we talk about these principles like entanglement and teleportation, it’s one of those things that people will hear about all the time on quantum computing: They hear it, they recognise it and then they know it has something to do with it, but they don’t get what it has to do with it. Do you want to explain something very basic, like, for example, you hear that with qubits, it’s two to the end. That’s how many states of information you can represent. You can represent 4, 8, 16, 32, all the states of information, by adding qubits, and this is because those are perfectly entangled qubits. Do you want to talk about how qubit entanglement works?

It’s, again, a subtle thing. If you’re looking at the number of states that you have, it’s already infinite from the start for a single qubit. But if you’re not going to start talking about, “How much can I read out of the states with certainty?” then it’s exactly the numbers you said. Now, it doesn’t mean that that’s all you have, because under the hood, you can play a lot of games in this continuous space to do very special things anyway, even though you don’t have the access.

That’s one aspect of quantum computing thing that you have this continuous space. The other one which you mentioned is, in particular, the entanglement that while typically, dimensions, classically — you have a bit and then you have another bit, you got four, and then you have eight — here, you got an exponential blowup under the hood of size in the space.

That causes a lot of problems, for example, in chemistry, which is where molecules of quantum mechanical descriptions, a simple molecule like coffee — coffee is a very simple thing — you can’t compute, and it’s not that the theory of coffee isn’t completely known. It’s completely known. Every detail, we know of. But we can’t do this with any existing compute, because of this exponential blowup of the space when you start putting quantum systems together. So, it was said that if you want to compute anything about these things efficiently, you need a quantum computer. So, that’s an old idea going back to Feynman in the ’80s.

Yes, 1981. He was concerned with having a simulator, of simulating the physical universe.

Now, there was a belief until recently that simulation was just about quantum systems. Now, during the development of this pictorial theory of quantum mechanics, we realised that this theory wasn’t only used for quantum mechanics. We realised that there was another problem in a completely different area: natural language processing. All the systems you use involving natural language, web search, translation, which is automatic, that’s natural language processing, or AI — a lot of AI today is natural language processing.

And there was another problem in natural language processing, and it is almost surprising that nobody had addressed it. If on the one hand is meaning of words and on the other hand is grammatical structure of sentences, then we, as humans, we know how they work together, because if I tell you a sentence with words you know and it’s grammatical, but you have never heard the sentence before, then you do know what I mean. You are able to take these words, put them together using the grammar, and extract the meaning of the sentence.

The mathematics for doing that was not known. There was no theory which described that. And then, I was giving a talk in 2005 on my graphical description of teleportation. In the audience — this was at McGill in Montreal — was a very famous linguist, Jim Lambek. In the ’50s, he came up with the mathematical theory of grammar. When I started to describe teleportation, he said, “Bob. This is grammar.” I said, “No, this is physics — quantum physics.” “No, this is grammar.”

I realised that exactly the same formalism, the teleportation stuff, was a representation of his latest theory of grammar, and what we had with quantum mechanics was a solution to the problem of how to combine meaning and grammar, because these days, meaning is represented by vectors: You have all these vectors and bearings like GPT-3 and all these things, and that’s all based on meaning and vectors, and so we have formalism where you’ve got vectors flowing into the wires, and wires representing grammar, and so this is now what I mainly do with my team.

Yet I continue to look for this quantum natural language processing, because mechanical quantum formalism for combining meaning and grammar, it also wants to live in a quantum computer, and that’s something we’ve been doing now since 2000 in actual quantum computers. It’s a miracle that this is not possible with quantum computers, natural language processing, and it’s thanks to this graphical formalism.

Are you hoping to expand that and do a lot of other QML-type applications based on your work, then?

I want to emphasise that this is not QML per se, because what quantum machine learning is, you take traditional machine learning, and you try to quantum enhance this. This is not what we do. We have an entirely new approach to natural language processing compared to the one which people usually use in machine learning.

We give a lot of structure. There is a lot of structure going on, while, usually, machine learning doesn’t understand any structure. It doesn’t understand any grammar. Everything has to be learned from data, and if you try to do natural language processing on a quantum computer, it’s totally impossible in that way, only data driven. It’s because we’ve got this structure, which was the grammar, and actually a lot more these days, and we use it explicitly, that we’re actually able to do something like that. Now, this structure itself, just like the quantum entanglements, is exponentially expensive. You can’t expect to do these efficiently on a classical machine ever. It’s an example where you want to do something on a quantum computer, but it’s not quantum substance.

That’s why I asked if you’re going to try to expand it to something different.

We’re not trying to expand it to general — I don’t like the word artificial intelligence. We call it compositional intelligence. Now, I don’t like artificial, because intelligence doesn’t have to be artificial — it can be just intelligence. Second, we want to give this constructive word compositional, because it’s not at all with this composing of Schrödinger and these pictures are representations of compositions, how you see the analogy with language, where you compose words together to form sentences. And these words, of course, highly entangle to each other too, because otherwise, they wouldn’t communicate to each other, and it would just be a bag of words, which is some of the meanings, and that’s not what a sentence is. It’s not just some of the meanings of the words inside.

Well, that sounds like an interesting approach. Let’s talk about the Nobel Prize this year. If you look at the last 10 years, in 2012, it was Serge Haroche and David Wineland. Their Nobel Prize was related to quantum computing, and that’s about when I got involved in quantum computing, and now, here I am. Ten years later, once again, we have a Nobel Prize that’s directly related to quantum computing. Do you want to talk about the impact of this one?

I don’t think that the connotation of quantum computing was given to the Haroche one. It wasn’t put forth like that, and this one, I wouldn’t say it’s a Nobel Prize in quantum computing, but it’s a Nobel Prize in quantum foundations. At the time that these people were doing their work, they didn’t have computing in mind whatsoever. What they had in mind was showing what I said — that there are no hidden variable theories which are local.

That was what I’ve been trying to prove over these years, starting with the EPR paper, Schrödinger, all the way through, and I know Zeilinger very well. He’s a friend, and this is quantum foundations first in the heart and soul, and in the ’90s, that was the only real quantum foundations group in the world which was sustainable, because of his stature, and because they were doing experiments on these things. I was officially the first quantum foundations professor in the world, and this was in 2006, 2007, so quite late, and the second one was somebody in Zeilinger’s group — not surprisingly, Caslav Brukner. Caslav had told me that I was the first, because he was proud to be the second.

So, the 2012 prize, the Wineland component, that’s the work that led to trapped-ion quantum computing. That’s what I meant, why that kicked it off. And now, with entanglement, as we’ve said, it’s a very major part of a quantum computer’s work.

Of course, but the point I’m trying to make is, so much quantum computing — I’ve got lots of examples — came out of quantum foundations of people doing something foundational. And if they’re spot-on, the application automatically follows. I’m a person who believes that if you go very foundational, you’re going to get a lot more applications than if you start with applications. You do the groundwork properly. Now, a lot of people have done wrong groundwork, especially this argumentation or these interpretations. You mentioned David Deutsch, and it did inspire David Deutsch to come up with this quantum algorithm. So, David Deutsch is a many-worlds person.

Yes, I am too.

If you’ve got many worlds — you know the Deutsch story — then maybe this many computations can’t take place at the same time in all these worlds, and maybe they can’t get an advantage out of it. That was his first intuition about quantum interpretation, but I don’t think that much more has come out of this particular branch. Teleportation very much came out of Schrödinger’s theory, and Schrödinger came up with this theory to show what entanglement possibly could do and show that the world is in a different place, but he was again, not thinking about computing, of course.

This is not something that was in the mind, and the work which I’ve been doing, and then, in particular, the use in quantum computing, like the graphical formalism, pictorial formalism, this came out of trying to come up with a new formalism of quantum mechanics going back all the way to von Neumann. Like I’ve said, this is what I grew up with even as a Ph.D. student, and what I wanted to work on: coming up with a new quantum formalism. That was always my main focus. The hidden-variable stuff was a deviation. It happened to be something my supervisor told me I should do for my Ph.D. I wanted to go into this new-formalism stuff, and I started in this area of quantum logic and gradually bringing in more category theory and composition of these systems, trying to make it explicit and things like that.

And now, I’ve got a slide of all the quantum companies who are now using my diagram for some practical purpose, and this is a slide with many different categories, and you’ve got 30, 40 companies I’m aware of for quantum activity that are now using that. An example is error correction and very much lattice surgery at Google. They are quite active in that. IBM is very much engaged in using it for education and things like that, and they have like two things I have discovered: I wasn’t aware of two things working on this quantum natural language processing I mentioned. Friday, they will bring a blog post about quantum natural language processing and what they’ve done following up on our work.

This talk will be out, and the blog post will be out there by IBM. And there are so many other examples, like all the photonic quantum computing companies I’m aware of, like Quandela and PsiQuantum, for example, they’re all using this diagram to understand compilation from typical quantum circuits to the photonic layers, which look very different that qubits, in fact. If you try to build quantum computing with light, where bottom architectures look very different from qubits, they also don’t work with circuits. The way you compute is not like most existing quantum computers like IBM, ours, Google’s. They use something which is called measurement-based quantum computing.

This goes back to teleportation itself, the idea that you can use observation to change systems and, ultimately, by observation only, you have a universal computer, and this turns out to be very suitable to work with light. It’s called measurement-based quantum computing, and of course, you can talk to Hans Briegel — again, a super foundational person. He came up with these ideas from very foundational thinking about quantum mechanics, and taking the collapse, which also people are still arguing about: whether this happens — taking the collapse very serious, of course.

With the work you’re doing now and everything you’ve seen, your view on the measurement problem on the collapse, has any of that changed? Do you have a different interpretation these days?

Pretty much all I’ve done is quite agnostic to which interpretation you want. Now, as we speak, I started doing research for a paper about what these pictures tell about the different interpretations. We’re basically coming up with pictorial representations for the interpretations. We’re not done yet. We’ve got a couple, and it gives an interesting view. Some are not so pretty as others — let’s put it like that. It seems that composition is at the heart of quantum — that does tell something about which interpretations are more likely from that point of view than others. You can do them all. Principally, quantum mechanics is comparable with — except the ones that are being like discarded now, like the GRW stuff, which is close to being disproved. That’s going down, of course.

I’m finding fascinating different interpretations of even what many-worlds might mean. There’s Max Tegmark’s idea of many levels of the multiverse and his mathematical universe, and then, more recently, there’s been this idea of entanglement through time — that you can measure a state through time, not like the entanglement right now, so maybe the many worlds are just five minutes from now or something. All these ideas are interesting. I nerd out on that because, like I’ve said, I love the idea of everything happening that could happen.

Yes, but anyway, my main point I repeat is that much of the development is quantum computers and the ideas came from thinking foundationally of quantum mechanics, rather than starting and add the quantum computing with a quantum computing textbook, and let’s see what we can do. That’s my main message.

Do you want to talk about how you’re hoping this will help the field overall going forward — what’s moving forward, what’s holding you back right now?

I don’t think things are holding it back. It’s, how can we make the most of it for the future? And, like I say, in my own case, this quantum natural language processing, in fact, that emerged from thinking about, what should quantum language be telling us? It’s not something you predict, and the most difficult problem in science is the unexpected — connections you never expect, new possibilities you would never expect.

And you need some sort of vehicle to get to them, and the vehicle is not just sitting there at state and the author looks, “What are the open questions now? Which is that which a lot of people have?” A lot of scientists, they have this mentality of, “What are the open questions in the field? Let’s solve them, and let’s solve them as quickly as possible.” That’s a different approach to science than what I have. I think deeply about something, what it means, and I try to form an image, and that image tells you, then, where you should go with it. That’s a different mentality, and that’s a little bit what artists do too, more than scientists. It’s a more artistic view on scientific progress, and this is where the surprises happen.

You mentioned error correction before. Did you have any plans that you want to share about where Quantinuum is going with that — like how they hope to implement that, and a hint about the road map that might implement that?

The error-correction team is no longer me, and the only error correction I’m involved in is in photonic architecture. Like I’ve said, my team is directly working with Quandela and PsiQuantum, because what I was explaining about photonics, you’ve got this different layer at the bottom than what the quantum circuits are. You use a completely different quantum computational model with these measurements, and then there is the very sophisticated intertwining, especially with PsiQuantum, of the error correction with all of the previous. It’s very interestingly intertwined with this measurement-based quantum computing.

Terry Rudolph has been leading these ideas. He’s Schrödinger’s grandson, by the way, for those people who don’t know it, and that has to be an interesting story. And this is so complicated to reason about that the diagrams are the only way forward, and they all know it. They start to do it themselves at PsiQuantum, then Terry, at some point, on a big motorcycle, came into my house and then asked for help, basically.

Yes, I had Terry on the show.

Yes, he’s a close friend. He’s quite a character.

Yes, he’s a great guy. I enjoyed talking to him. Do you want to give us one last thought about what your work is heading toward right now. What’s the next big thing you hope to do?

Like I’ve hinted before, one thing we’re busy with is going beyond language to cognitive architecture, and maybe a new forum of interpretable AI, which we call compositional intelligence, whether it is to better understand how our brains work or to better design AI or robots, things. That’s a big chunk of the activity of my team. Quantinuum has several teams. I’m chief scientist, but I’ve also got my own team in Oxford, which is the compositional intelligence team, and that’s where we focus on.

These at the same time also are the heart, probably in the entire world, of all this diagrammatic stuff, except that the head of our software team is Ross Duncan, and the biggest part of this graphical language, which is called ZX-calculus, that’s something Ross and I did in 2007, 2008, sitting next to Terry on a bus in Iran.

I remember reading about that years ago. Good luck with that. I do have a gut feeling that one of the things that might be missing from an advance in AI is quantum, so let’s see if that’s the thing that brings it together, because so far, no system I’ve seen has even come close to even being designed like the human brain works. For example, conscious, subconscious — none of that.

Exactly, and this comes back to the exponential type of blowup that one gets when one tries to think about these things and how they should be, and how the brain works. We’ve been thinking about, how do we translate language into spatial images? If I’m talking to you, you don’t perceive this as black symbols on a white background, like on a line. When I tell you something — when I talked about Terry and Ross and me in the bus, you probably saw a bus and the three of us sitting there, or imagined something like that.

So, what is this process? The latest things I’ve been working on are translations of linguistic structure to spatiotemporal visual structure. That’s, again, another example of something completely unexpected. What we came up with, in the process, is an entirely new model of language, which is not one-dimensional — words after each other — but two-dimensional, and the amazing upshot, to end with a boom, is that representation is language-independent. Different languages have different grammatical structures in terms of words, orderings and punctuation, things.

This new linguistic structure we came up with by thinking about how we think and how we translate language into images, make all languages equal, and, for example, different presentations of, say, meaning, many short sentences, long sentences, it all becomes the same. You get incredible compression of what language actually is, and so my belief is that this structure is much closer to how meaning should be represented not just for language, but also in all the other ways. That’s my belief — that we are getting a little bit closer to how we actually reason at a high level and represent things at a high level. There aren’t many papers on that, but I assume well have one out. That’s just an example.

I can’t wait.

That’s an example of something completely unexpected by thinking about something foundational. We didn’t say, “Now, let’s build a two-dimensional representation of language.” It wasn’t like that.

That’s great. I’m looking forward to reading that. Maybe I’ll have you back on after.

Thanks so much for coming, and good luck with the book, which I’m sure everyone’s going to enjoy, from what I’ve seen.

Thanks.

Now, it’s time for Coherence, the quantum executive summary, where I take a moment to highlight some of the business impacts we’ve discussed today, in case things got too nerdy at times. Let’s recap.

Bob was a professor of quantum foundations at Oxford University. For many years, those fantastical-sounding aspects of quantum physics that we hear about were being taught as an almost philosophy. There didn’t seem to be commercial use for them, but Bob saw early on at Oxford that quantum information science is a product of quantum foundations.

One of the core quantum foundation mysteries is entanglement. Without entanglement, qubits could not interact with each other to provide our quantum computers with the capabilities to actually compute. Schrödinger called entanglement the characteristic feature of quantum theory, and it has that same importance in QIS. Entanglement makes it possible to bring two systems together so that they can no longer be described separately. Such entangled entities or particles can maintain this link over vast distances too.

This seemingly violates the concept of locality: If you observe one entangled particle and see it has a quantum property of being, say, spin-up, you know that its entangled sibling particle is spin-down. This other particle could be light-years away, and the information still seems to travel instantly. Einstein was troubled by this seeming instant transfer of information that occurs when entangled particles are observed, famously calling the decoherence moment “spooky action at a distance.” In truth, such information gleaned from entanglement is purely random, so locality is never violated. Einstein’s concept of speed of light remains intact.

The 2022 Nobel Prize in Physics was awarded to Alain Aspect, John Clauser and Anton Zeilinger for their work in investigating and controlling particles in entangled states, work that QIS has greatly benefited from.

Bob has been working on using quantum computers for quantum natural language processing, or QNLP. That is different from prior quantum machine learning. Quantinuum’s compositional-intelligence team is hoping to have an impact on general AI one day. I’m looking forward to seeing what they accomplish. You can find the YouTube link to his latest talk on QNLP in the show notes.

That does it for this episode. Thanks to Bob Coecke for joining to discuss quantum foundations and his work at Quantinuum, and thank you for listening, and if you enjoyed the show, please subscribe to Protiviti’s The Post-Quantum World and leave a review to help others find us. Be sure to follow me on Twitter and Instagram @KonstantHacker. You’ll find links there to what we’re doing in quantum computing services at Protiviti. You can also DM me questions or suggestions for what you’d like to hear on the show. For more information on our quantum services, check out Protiviti.com, or follow ProtivitiTech on Twitter and LinkedIn. Until next time, be kind, and stay quantum curious.