OK, I should be preparing a talk, but it is late and my mind is wandering, so it’s not going to happen tonight. Instead, I’ll pose this puzzler: If quantum computers are more efficient than classical ones then why didn’t our brains evolve to take advantage of quantum information processing?
I have a vague recollection of seeing this question on a physics blog somewhere before, and it does have a family resemblance to Scott’s infamous post, albeit a more politically correct version.
There are a number of assumptions behind this question:
- Evolution usually does a very efficient job of coming up with information processing devices. As evidence for this note that the best algorithms we have for some tasks simply imitiate nature, e.g. neural networks, simulated annealing, etc.
- Some functions of the brain, such as the ability to solve math problems, are best understood by regarding the brain as a kind of computer. Note that we don’t need to say that the brain is merely a computer, only that it can be regarded as such for understanding some of its functions, i.e. we don’t need to get into a big philosophical debate about conciousness and artificial intelligence.
- Further, in these respects the brain is a classical computer and not a quantum one. It certainly seems that the information processing function of neurons can be understood in classical terms, i.e. neural networks again. There is a small minority of experts who believe that quantum mechanics plays an essential role in the information processing functions of the brain for whom my question is nonsense.
Here are all the possible explanations I can think of.
- The set of problems in BQP, but not in P does not include anything that would have conferred a significant survival advantage for our ancestors. Admittedly, efficient factoring could be useful for surviving high-school math class, as well as for cracking codes, but this wouldn’t have mattered so much to cave-people. This would be disappointing, although not devastating, news for people trying to come up with new quantum algorithms.
- There is some big problem with building a stable quantum computer of any appreciable size, and so present day experimentalists will eventually run into the same problems that nature did.
- Dumb luck. Evolution tends to find local minima in the landscape of all possible species. Having a quantum brain is indeed a lower minimum than our current classical brain, but we never got a big enough hit to get over the mountain separating that solution from ourselves.
The first two explanations seem like the most interesting ones. If the third explanation wasn’t a possibility then there would have to be a tradeoff between the amount of progress possible in developing quantum algorithms and the amount possible in actually building a quantum computer. Given that much quantum computing funding is predicated on the idea that massive progress is possible in both areas, I’d say we should thank Darwin for dumb luck!