Quanthoven's Fifth

You take a bite of your lunch on a cold winter’s day. It echoes with a memory of something you ate on the quayside of a sunny Mediterranean harbour while on holiday several years ago. There’s something about the texture, the taste and the smell. You can even hear the seagulls in your head; feel the sun on your face. You could try explaining this to a friend, but they wouldn’t have the same experience even if you offered them a fork full of the very same food. You had to be on that quayside.

When it comes to our conscious experiences, it doesn’t seem like you can package up what’s in your head and give it to someone else. Yet that may be possible one day according to a team of scientists recently awarded an FQXi grant of over $100,000 to explore consciousness by bringing neuroscience and quantum physics together. "It’s not as absurd or far away as you think," says team member Bob Coecke, a quantum physicist and chief scientist at Quantinuum, a new quantum computing company with offices in the UK, USA, and Japan, that is the natural progression of Coecke’s former quantum foundations group at the University of Oxford, UK. He and his colleagues are investigating natural language processing within a quantum framework and have successfully used a quantum computer to compose chart-topping music.

Along with Quantinuum physicists Sean Tull and Quanlong Wang, who are also affiliated with the Topos Institute, in Berkeley, California, and Johannes Kleiner, a mathematician and physicist at the Ludwig Maximilian University of Munich, in Germany, Coecke wants to understand conscious experiences by building a mathematical model of consciousness. Part of their FQXi grant is going towards trying to establish "mathematical consciousness science" as a well-defined field of study. They are bringing together mathematicians, physicists, neuroscientists and philosophers through a series of seminars and workshops. (Tull discusses their latest work in the FQXi-sponsored seminar below.) "We want to come in as mathematicians and get to the core principles behind the theory," says Tull.

But where do you even begin? One approach is to recognize that, as with eating the nostalgic meal, a conscious experience depends on the ability of a system to generate integrated information. The evocative feelings conjured by your lunch came from inputs including your taste buds and your memory, which are linked to different parts of the brain. "All these layers interact," says Coecke. Consciousness is a melting pot of various strands of information.

The Conscious Universe

These ideas are codified in Integrated Information Theory (IIT), which was proposed in 2004 by FQXi member Giulio Tononi, a neuroscientist at the University of Wisconsin-Madison. IIT says that the consciousness of a system arises as the result of information traveling between different parts of that system. It seeks to quantify the amount of consciousness by measuring how interconnected those different parts are. The quantity used to measure this interconnectedness is denoted by the Greek letter phi. "Most things in the universe have a non-zero phi," says Tull. Using IIT, it could be argued that even the universe itself has a degree of consciousness.

A major advantage of IIT is that having a mathematical framework enables you to decompose the individual connections within a conscious system from the whole. The wooly thing we call consciousness then becomes objectively measurable. At least that’s the theory.

But there are currently at least four other leading theories of consciousness on offer, each based on a different mathematical framework—and it has been tough to compare and contrast them. It’s possible that the ultimate theory of consciousness is some combination of them. With this is mind, Coecke turns to category theory, a branch of mathematics that is diagrammatic, and potentially easy for everyone to use. "We are sure we have the right formalism to bring them together," says Coecke. "High schoolers have used it to solve some advanced post-graduate quantum theory problems."

"Category theory is designed to study composition and relationships," explains Tull. Connections are represented by drawing arrows between objects to illustrate the ways systems interact with each other. "It would allow the different groups working on consciousness to talk to each other," says Coecke.

The team has also looked at "Quantum Integrated Information Theory," which combines the weirdness of the quantum world with the idea that consciousness stems from the exchange of information, in an effort to better encapsulate the fluid and unpredictable connections. Another area where the interactions exhibited by quantum systems have been surprisingly useful is in natural language processing (NLP), which involves analyzing and creating language and speech using computational techniques. It’s the sort of technology routinely used by smart speakers, but the team is adding a quantum twist.

Specifically the group is investigating how to do NLP with quantum computers, which in theory can harness quantum effects to outperform standard classical machines at certain specific tasks. For instance, they can exploit quantum superpositions, which enable quantum bits, or qubits, to be in more than one state at a time, and quantum entanglement, the phenomenon that inextricably links them, to better synthesise language.

Take the word "large." In a classical computer you’d have to store all the words that could go with it—house, car, planet etc—and how they may change its meaning. This takes up a lot of memory space. A quantum computer is able to store many states at once and so is more naturally inclined to this kind of task. "You get a model of language that is quantum native," Coecke says.

Music Making

The team has already had success by demonstrating how quantum computers can be programmed to classify music that conveys different meanings (arXiv:2111.06741 (2021)). For instance, it’s long been understood, though only relatively recently experimentally confirmed, that minor chords convey sadness, while major chords inspire happiness. Meanwhile, music with fast repetitive patterns can be classified as ’rhythmic,’ while music composed of irregular successions of notes forming exquisite harmonies might be categorised as ’melodic’ or ’relaxing.’ Others may fall in between.

The group developed a quantum composer—dubbed ’Quanthoven’—to compose music that can create a certain mood. The team first pre-trained their model parameters using quantum circuits on a classical machine, and then trained the output on a real quantum computer, IBM’s ibmq_guadalupe, a 16-qubit superconducting processor. Quanthoven was able to correctly classify 59 compositions from the set of 90 as either rhythmic or melodic. "As argued by Feynman, this would be exponentially expensive to do on a classical computer," Coecke says.

"Bob’s Cigar Buzz"

They then programmed Quanthoven to generate two dozen pieces of music and to save four: two for relaxing at a tea party and two aimed at inducing excitement. They then hired a professional pianist to record them. The two pieces for relaxing at a tea party were named "Bob’s Chamomile Slowdown" and "Alice’s Mushroom Trip," while the two stimulating pieces were called "Bob’s Cigar Buzz" and "Alice’s Caffeine Rush." Impressively, "Bob’s Cigar Buzz" reached number one in the SoundClick Classical Charts.

"Alice’s Caffeine Rush"

The group are on an exciting path, says Holly Andersen, a philosopher at Simon Fraser University in Burnaby, Canada, but she adds that she wants the model to become more detailed. "I think they would make a lot more progress, or make it faster, by using more features of what is being modeled to constrain the mathematical formulations in useful ways," she says. Ultimately, like any good scientific theory, it lives or dies by its ability to make testable predictions. "Any project like this is on the hook for empirical adequacy to the phenomenon being modelled," Andersen says.

Phil Maguire, a computer scientist at Maynooth University in Ireland, agrees that there’s likely some quantum element to IIT and the team is on the right track. "IIT might tell us what we can’t say about the brain and why we can’t say it," he says. "That will help us to focus with greater precision on all the things we can know."

Understanding the link between the quantum world and consciousness also has implications for the foundations of physics, of course. For one thing, observers are a famously important part of quantum theory. Take the famous Schrödinger’s Cat thought experiment in which the animal is in a superposition—both dead and alive inside a sealed box.

"Alice’s Mushroom Trip"

It is often said that the act of "looking" breaks the superposition and seals the fate of the cat one way or the other; but that is ambiguous. What if a computer ’looks’? Does that count as an observer? What about a dog? A twentieth-century interpretation of quantum mechanics attributed to Hungarian mathematician John von Neumann and Hungarian physicist Eugene Wigner says that the consciousness of an observer is what shatters the superposition. "How consciousness according to IIT relates to quantum collapse is another ongoing question," says Tull.

"Bob’s Chamomile Slowdown"

It’s an ambitious goal, but if Tull, Wang, Kleiner, and Coecke can make some headway in understanding the complexity of our consciousness, then maybe one day we’ll finally have an explanation for how atoms can combine into something that can in turn contemplate the very fact that it is made of atoms in the first place.