
Solving systems of linear equations with quantum mechanics - jonbaer
https://phys.org/news/2017-06-linear-equations-quantum-mechanics.html
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lostmsu
Wait, aren't linear equation systems solvable in N^3 where N is number of
equations/variables? Why do they claim exponential improvement?

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cvoss
Exponentially better than a polynomial in N is a polynomial in log N. See the
abstract of [1] for the precise complexity claim about the algorithm mentioned
in the article. As good as N^3 sounds, it's still not great on enormous
systems.

[1] [https://arxiv.org/abs/0811.3171](https://arxiv.org/abs/0811.3171)

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bradleyjg
It's funny you put it that way. O(N^3) sounds horrific to me. Only practical
for small problems and for anything else I'd need to look for approximations
instead. O(2^N) meanwhile translates in my mind to completely impracticable.

But I guess it all depends on what kind of Ns you are looking at.

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reacweb
I use perfect matching in go tournaments. I have tested it with 1000 players,
it was less than 2 minutes -> perfectly acceptable.

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bradleyjg
One thousand cubed is one billion. Of course it depends on what the Big-O
notion is hiding, but one billion 'steps' is generally okay. But if you had
tested it with ten thousand players it would go from one billion to one
trillion -- which we'd expect to take more than a day on the same machine.
That scaling is pretty brutal. Whereas something like sorting a list with O(N
log N) would only have gone from about ten thousand to about one hundred fifty
thousand. In order to hit one trillion steps we'd need to be sorting a list of
nearly thirty billion items.

I sometimes find myself working with ten thousand 'things', but very rarely
with thirty billion.

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dkarapetyan
It takes 1 second to solve a 2x2 system? I don't see how any speed-up is going
to make it faster than just using a regular computer.

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zitterbewegung
This is more proof of concept then actual practical implementation. Its
runtime would improve the current state of art. See
[http://www.mit.edu/~aram/talks/10-invert-rutgers-
print.pdf](http://www.mit.edu/~aram/talks/10-invert-rutgers-print.pdf)

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solotronics
forgive my ignorance but doesn't this have applications for cryptography? if
so this is potentially a huge deal.

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deepnotderp
Well this is cool. And it certainly increases the practical applicability of a
quantum computer.

