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NP-complete Problems and Physical Reality Scott Aaronson

Summary: NP-complete Problems and Physical Reality
Scott Aaronson
Can NP-complete problems be solved efficiently in the physical universe? I survey proposals
including soap bubbles, protein folding, quantum computing, quantum advice, quantum adia-
batic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation,
analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and
"anthropic computing." The section on soap bubbles even includes some "experimental" re-
sults. While I do not believe that any of the proposals will let us solve NP-complete problems
efficiently, I argue that by studying them, we can learn something not only about computation
but also about physics.
1 Introduction
"Let a computer smear--with the right kind of quantum randomness--and you
create, in effect, a `parallel' machine with an astronomical number of processors . . . All
you have to do is be sure that when you collapse the system, you choose the version
that happened to find the needle in the mathematical haystack."
--From Quarantine [31], a 1992 science-fiction novel by Greg Egan
If I had to debate the science writer John Horgan's claim that basic science is coming to an
end [48], my argument would lean heavily on one fact: it has been only a decade since we learned
that quantum computers could factor integers in polynomial time. In my (unbiased) opinion, the


Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)


Collections: Physics; Computer Technologies and Information Sciences