# Re: quantum computing and the brain

From: hal@finney.org
Date: Sun Oct 07 2001 - 20:53:13 MDT

Miriam writes:
> I don't understand how a quantum computer can work, but I read a little
> time back that it can do multiple calculations simulataneously. That is, if
> you have 2 qubits they can perform 4 calculations at once by simultaneously
> experiencing (in some way I can't begin to understand) all possible state
> combinations at once. Similarly that 3 qubits "feel out" 8 states, 4 qubits
> 16 states, and so on.

Don't forget, with an ordinary computer 3 bits can hold any one
of 8 states, four bits can hold any one of 16 states, and so on.
The difference with the QC is that it can operate on multiple states
simultaneously. You can put your 3 bits into all 8 possible states
at the same time, and then perform some operation on each of these 8
possible states, ending up in a superposition of all 8 possible results.

> This would be a pretty impressive computer if I have that right. Would that
> make it possible to handle all the computations of all the neurons (10^12)
> and synapses (perhaps 10^3 per neuron) of the brain even taking into
> account about 1,000 levels of exciteability for each synapse... with just
> 60 qubits!!?
>
> That can't be right... can it?

I don't think it is quite right. Accepting your figures, you don't just
multiple 10^12 times 10^3 times 10^3 to get the number of possible brain
states, and then take the log base 2 to get the number of qubits needed.

Rather, to represent a single synapse state you would need 10 bits for
10^3 possible states. Then you would need to replicate those 10 bits,
10^15 times. So the total number of bits needed to represent a single
brain state is 10^16, not 60.

If you had a QC with 10^16 qubits, it could represent all possible
brain states at once. So it could in principle simulate all possible
brain experiences with one calculation.

> It must require at least one qubit to store an item of information, even if
> calculations can be made in different ways simultaneously on that one bit
> of info, it is still just one bit.

Yes, this is a better instinct. You can have quantum parallelism but
you still need enough qubits to represent the individual information
units that you are operating on in parallel.

> Even if each bit can be a single atom (one day in the future) that still
> makes a tiny human mind -- using 10^18 atoms for storage. The entire mind
> would not be that small of course because you still need some way to
> shuttle the info around inside it, but even if the the means of moving data
> around required 100,000 atoms for each storage atom the entire thing is
> still just a sixth of a mole of material! If the "brain" used
> nanostructures of pure carbon for instance then that would be a device
> weighing just 2 grams (Avogadro's constant puts 6*10^23 atoms of carbon at
> 12 grams).

This reminds me of Robin Hanson's "Lilliputian Uploads". Robin used
similar reasoning to compute that the brain could be miniaturized to just
about fit someone who was 1/4 inch tall. Also, the degree of speedup
due to the nanotech brain could be matched to the mechanical speedups
appropriate to a being of this size. I can't find the full article but
Robin has a short essay at http://hanson.gmu.edu/lilliput.html.

Hal

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