Summary: NP­complete Problems and Physical Reality
Scott Aaronson #
Abstract
Can NP­complete problems be solved e#ciently in the physical universe? I survey proposals
including soap bubbles, protein folding, quantum computing, quantum advice, quantum adia­
batic algorithms, quantum­mechanical nonlinearities, hidden variables, relativistic time dilation,
analog computing, Malament­Hogarth 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 NP­complete problems
e#ciently, 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 e#ect, 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 science­fiction 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