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0f02a28a…156c -- 356d [parent] 
|    But are they even approximately separate worlds for quantum computers? I thought that quantum algorithms
|    leveraged the interference effects for the speed up relative to classical algorithms. So to make them work well,
|    it would seem like you would want a situation where you are very far from anything that can be described as
|    separate branches of a wavefunction. If it is just small interference effects on top of parallel, classical
|    worlds, then the speed up will be tiny, no?
|    reply [1 reply]
Laan Tungir -- 356d
Without understanding many-worlds, how quantum computers work (beyond just being able to do the math) is very
hard. But with many-worlds, understanding quantum computers is (kinda) simple.

Let's do a simplified example. Imagine you have a function with two inputs and one output. You don't know what
the function does, and want to find out.

With a classical computer in just our universe, you would have to feed in every possible combination into the
two inputs:

0 0
0 1
1 0
1 1

and then you would read the output for each. Lets imagine we feed in the inputs into our mystery function and
get the follwing outputs:

Step 1: 0 0 -> 0
Step 2: 0 1 -> 0
Step 3: 1 0 -> 0
Step 4: 1 1 -> 1

After which you would know that the function you have is an AND function. It returns a 1 when input A and B are
both 1. It returns 0 otherwise.

So by using a classical computer in just our universe, it would take 4 steps, or 4 clock cycles of the computer
to put in all the possible inputs, and get all the outputs.


But when you make a computer in our universe, you are also making computers in many parallel universes. What if
you could harness those classical computers in other universes to do some of the work?

That is what a quantum computer does.

So imagine 4 universes, each with it's own classical computer. You then assign each of those computers a
different input, and run it:

Classical Computer in Universe 1: 00 -> 0
Classical Computer in Universe 2: 01 -> 0
Classical Computer in Universe 3: 10 -> 0
Classical Computer in Universe 4: 11 -> 1

So now in just 1 clock cycle, you have tested all the possible inputs of this function using 4 different
computers in parallel.

This is the same as if I had 4 classical computers on my desk, and ran them all in parallel to get the answer
quicker. I get the answer in 1 cycle instead of 4.

Okay, great, we have reduced the computer time from 4 cycles to just 1 cycle, but here is the catch: we can't
travel to these different universes and get the results from each of the computers. They are in separate
universes, and we can't go there.

BUT, these universes do "interfere" with each other. It is because of these interference effects that we know
that the other universes exist in the first place.

So what we can do with a quantum computer is that we can get back the "interference pattern" from all the
outputs together.

The interference pattern is a blend of all the outputs together, where we can't tell what each individual output
from each universe was, but we can tell the proportion of outputs that we get.

So for our simple example, what we would get back from a quantum computer would look like:

75% of the classical computers in all the parallel universes return 0.
25% of the classical computers in all the parallel universes return 1.

So in one step with a quantum computer, we can't tell for sure exactly what out mystery function is (an AND
function) but we can tell in one step some things for sure. We know the function doesn't ALWAYS return a 0. We
know the function doesn't always return a 1. We know that it isn't an OR function which would be 75% 1's, and
25% 0's.

So there are pros and cons to using many computers across parallel universes (aka a quantum computer) vs one
computer in our universe.

Once you understand what is going on via many-worlds, lots of the mysteries of quantum computers go away.

You understand how they do what they do - they just run many classical computers in parallel, and we understand
classical computers pretty well.

You understand why sometimes they don't help much with the problem you are trying to solve, and sometimes why
they help a lot.

So to understand if a quantum computer would help with your problem, all you have to do is imagine running your
(classical) computer on a problem with all the possible inputs, and getting back in one step every possible
output and the proportion of times you would get that output.

Quantum computers are great for finding the set of all outcomes. I have this function with a million inputs,
what is every possible output of this function? A quantum computer can tell you that right away, in one step. To
find that out with my classical computer would take 2^1,000,000 clock cycles ... ain't going to happen.
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