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Quantum computers are very efficient at solving combinatorial problems, way much more efficient than any non-quantum computer. If human brains were able to use quantum computing, they would be very efficient at this type of tasks, too. However, classic Turing machine type computers beat every human being at such combinatorial tasks as chess, go, etc. Ergo: human brains can't use quantum computing.

Do you see any flaws in this reasoning?

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    The original computers of 1950-s were also Turing machine type, but much slower, and they could not play chess very well (or at all). That quantum computers theoretically can be more efficient at certain types of tasks does not mean that every implementation of them is. A better argument against quantum mind is Tegmark's, that the brain is too “warm, wet, and noisy” to maintain quantum coherence at the relevant time scales, but even that is not ironclad, see Pereira's Quantum Mind/Classical Brain Problem.
    – Conifold
    Dec 15 '17 at 0:38
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    @Conifold, "That quantum computers theoretically can be more efficient at certain types of tasks does not mean that every implementation of them is." - if a quantum computer can't solve combinatorial tasks much better than any classic computer, what makes it different then?
    – user626528
    Dec 15 '17 at 0:40
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    A computer is called "quantum" based on the physical mechanism of its work, not on what it can do. Currently implemented (artificial) quantum computers can barely do arithmetic on a handful of qubits.
    – Conifold
    Dec 15 '17 at 0:49
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    Effective? Or Efficient? I'd appreciate seeing some references here to help frame the question. Most of your argument (and @Conifold touches on this) is based on speed of processing, rather than actual output. Add to that that many combinatorial problems can be framed in different ways; that means that the programmatic approach can also have a massive impact on the result, as can the organisation of the latent data being used to frame the combinatorial question in the first place.
    – Tim B II
    Dec 15 '17 at 0:51
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    @Conifold, the main difference of quantum computers is their ability to operate with "bits" that are in a superposition of states rather than a single definite state. The physical mechanism can be different (as well as for classic computers that can use electricity, photons or even liquids) and it doesn't really matter.
    – user626528
    Dec 15 '17 at 1:16
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You reasoning seems to be something along the line of:

  1. efficiency(QC) > efficiency(non-QC) > efficiency(Human).

  2. therefore efficiency(QC) > efficiency(Human).

  3. therefore. QC ≠ Human.

However, the power of a computational device isn't measured solely by its efficiency. A trivial example is the following:

A hand calculator is much more efficient at multiplying 34612342342349287423 * 4372834021347826340234 than a human mind is, yet the human mind can solve a wider class of problems than hand calculators.

"Quantum mind" arguments usually center around the idea that the human mind can solve a wider class of problems than classical computers (see undecidable problems) or that human consciousness has properties that can't be explained with classical computing models (i.e Turing machines). It is then argued that Quantum computers might be able to solve these problems or duplicate these properties that classical computers can't, and therefore the mind must be a Quantum computer.

The real problem with quantum mind arguments is that the consensus among computer scientists is that Quantum computers cannot solve any of the problems that classical computers can't. They are likely more efficient that non-QC, but that's it, they can't solve any of the undecidable problems. So if a human mind is indeed more powerful that a classical computer, quantum computing isn't the answer.

See this answer for more details about one of the more prominent quantum mind arguments.

As Conifold points out in the comments, beside the computer theoretical considerations I mentioned, there are physical arguments against Quantum mind theories (See Max Tegmark's argument against Quantum brains).

Interestingly enough, Max Tegmark seems more recently to seriously explore the notion that concsiousness is a state of matter, so I don't where he stands exactly on the question nowadays.

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  • Winged animals can travel faster than animals without wings.
  • If a penguin were able to use wings, they could travel very fast too.
  • However, non-winged animals such as cheetahs, deer, and antelope travel faster than penguins. Hence penguins cannot use wings.

That X can be faster doesn't imply everything that uses X must be faster.

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  • penguins cannot fly, indeed.
    – user626528
    Dec 17 '17 at 17:04
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There are some misconceptions here.

First, we do not know whether quantum computers are better at some stuff than classical computers. There are problems where we know quantum algorithms that are faster than all known classical algorithms, but so far noone has been able to prove that are no equally fast classical algorithms.

Second, there are many computational tasks humans are very bad at, despite the tasks being very easy. A core aspect here is that for something like combinatorics calculations, we are using concious, higher level style reasoning. A "hardware" implementation in our brains might have been much better, but just never evolved (being good at combinatorics is probably not strongly selected for). So from us not being good at something we cannot conclude that the basic computational machinery of our brains is not suited for that task.

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