[tt] advanced nanotechnology - Possible quantum computer limits

Eugen Leitl <eugen at leitl.org> on Sat Sep 1 12:34:28 UTC 2007 
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Date: Sat, 01 Sep 2007 03:23:47 -0400
To: eugen <eugen at leitl.org>
Subject: advanced nanotechnology - Possible quantum computer limits
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[6]Possible quantum computer limits

   [7]A discussion of possible limitations on the power of quantum and
   classical computers
   It is a useful discussion of NP hard problems. My reaction to it is
   that even if his conjecture that we cannot globally solve NP hard
   problems is correct there is still commercial viability in improving
   and expanding the cases where we can solve some NP hard problems.
   I think the question of commercial viability is how often does a
   system not get stuck in local minima. Are there usable probabilities
   when the optimal solution is found over sufficiently complex problems.
   if the best alternative systems only come up with an optimal solution
   for N=4, and special cases of N=5. But the new system can fairly
   freqently get optimal solutions up to N=100 or less frequently N=10000
   then that could be a commercial advance.
   Nature's protein folding may not be perfect for solving the NP hard
   protein folding problem but it is sufficiently successful to allow
   life to form. A commercially useful solution capability.

     Intriguingly, Farhi and his collaborators proved that, on some
     problem instances where classical simulated annealing would take
     exponential time, the quantum adiabatic algorithm takes only
     polynomial time.
     we also know of problem instances where the adiabatic algorithm
     takes exponential time just as simulated annealing does. So while
     this is still an active research area, right now the adiabatic
     algorithm does not look like a magic bullet for solving NP-complete
     problems.
     If quantum computers can't solve NP-complete problems in polynomial
     time, it raises an extremely interesting question: is there any
     physical means to solve NP-complete problems in polynomial time?

   Are those problem instances sufficiently useful and widespread for
   commercial usefulness ? Google is not perfect for internet search, but
   it is commercially successful for the range of instances where it does
   provide solutions.
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  22. http://feeds.feedburner.com/~r/blogspot/advancednano/~3/150181501/fuel-scooping-variable-minimag-orion.html
  23. http://feeds.feedburner.com/~r/blogspot/advancednano/~3/149473557/two-chinese-coal-miners-lived-179-did.html
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