Could the brain be a topological quantum computer?

More than 30 years ago, Penrose's published his pioneering ideas about the quantum brain, which were back then based on the knowledge at the time (remember quantum computing was in its infancy). His ideas, which attracted a lot of public attention, received severe criticism. Nowadays, there is a common consent between physicists and neuroscientist, that his proposal is unlikely in a biological set up, especially for the brain. Therefore, the idea of a quantum brain has been dismissed by most researchers.

However, many scientific areas relevant for the understanding of brain processes have evolved enormously since then. Those fields include quantum information, nematics, active matter, neuroscience, psychology, and even philosophy.

In quantum cognition and active matter, phenomena have been described which are using the mathematical models of quantum mechanics, and low-temperature physics, or which resemble topological quantum computing.

We are aware that some direct translation from quantum physics to biology will, at this time, not hold a critical debate. However, we believed that the problem may be down to an insufficient understanding of physics, which needs to be solved. Biology may guide us (remember electrodynamics) once more to find in-depth insight into fundamental physics.

We believe that there are at least two very intriguing arguments for quantum brain computing.

Ceilidh dance of topological effects in active matter

It has been shown that topological defects in active matter can perform ceilidh dances. The defects start dancing ceilidh, when the self-motility and the activity numbers of defects will increase during the transition from laminar to turbulence.

Sending a heart pulse wave through the brain may do exactly that: the wave which comes into the brain using the main artery where flow is laminar, will transit to the brain arteries which oscillate and then water from the blood wave will start moving into the tissue. ​There it will become turbulent because it needs to cascade down. ​Without a cascading process, exchange with the metabolism may not work.

So, all looks good. Theoretically, that could work in the brain. The pulse will do the work: it not only produces defects, it also will move them around, which is needed for topological braiding.​

There are still a number of problems. Nematic defects aren’t the same as those in quantum mechanics. But the main problem is that we need so-called worldlines attached to the dots to do braiding. This is where Majorana zero modes or anyons are coming into the game. Something like them is now essential to get this to work. They are extremely difficult to find or to realize in the lab. ​

​So, the essential step forward is to find this topological phase. The defects are doing their job. A topological phase is a phase of matter where one could find anyons. It is essentially an exotic phase with long-range entanglement but no short-range entanglement.​ This is difficult to find in the lab.

In the brain, we would need unknown quantum effects to realize something like it.

We believe that we have found a topological phase in our recent paper experimentally, and even more, the phase may be synchronized with the ceilidh dance of the topological effects.

Why not trust biology. If topological defects moving around, then biology will use them.

Quantum cognition

Let us now look at the brain at work. Instead of looking at the biological side, we can now use psychology to observe the computational outcomes. Does it behave or look quantum?​

A lot of work has been done in the field of quantum cognition. There, researchers argue that they only use the mathematical formalism of quantum mechanics without assuming any underlying quantum physics.​  Many fields like decision-making, language, memory, conceptual reasoning, human judgment and perception have been considered. ​

In the light of the success of quantum cognition, we have to ask whether the computing power of the brain is sufficient to simulate quantum mechanics? It has recently been shown in simulation of simple quantum models, that quantum computers exceed the computational power of any super-computers from around 50 qubits onwards. And not only that, from this complexity onwards, the super-computer needs thousands of years for the simulation. So, the question really is; How many qubits are involved in brain processes.  Even if there are only a few, super computers exceed the computational power of human brains by far, as has been demonstrated in Chess and Go challenges between grand masters and super computers. Therefore, it is unlikely that the brain has enough classical computing power to simulate just a few qubits. And, would it make any sense to waste so much computational power, which results so often in poor decisions? Just to round that up. Imagine dodgeball, how much time do you have to make a decision; dodge or catch? How many qubits would you need, and how much time would you have to simulate it, classically?​

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