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Article 6077 of comp.ai.philosophy:
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>From: clarke@acme.ucf.edu (Thomas Clarke)
Newsgroups: comp.ai.philosophy
Subject: Re: Quantum computing
Message-ID: <1992Jun4.125253.13040@cs.ucf.edu>
Date: 4 Jun 92 12:52:53 GMT
References: <1992Jun3.153327.22422@sei.cmu.edu>
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Organization: University of Central Florida
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More thoughts from sci.physics:

In article <1992Jun3.153327.22422@sei.cmu.edu> firth@sei.cmu.edu (Robert Firth)  
writes:
> In article <1992May29.194627.20577@hellgate.utah.edu>  
tolman%asylum.utah.edu@cs.utah.edu (Kenneth Tolman) writes:
> 
> >  Does quantum computing make sense?  Is not the essence of computing 
> >deterministic transitions from state to state, which is at the far end
> >of the court opposite quantum mechanics?
> 
> I believe the essence of computing is the processing of information.  A
> computer with a finite set of discrete states is one tool for doing this,
> but by no means the only tool.  Indeed, for some problems, it's not a very
> good tool.
> 
> Let me offer an example from a course I used to teach on system design.
> You have a maze, with one entrance, one exit, at least one path between
> entrance and exit, and a whole lot of branches, loops, dead ends and so on.
> Question: how difficult is it to compute the length of the shortest path
> through the maze?
> 
> The answer is obvious: if you made a loud noise at the entrance, so the
> sound reverberated through the maze, you would hear the sound at the
> exit after time
> 
> 	(length of shortest path) / (velocity of sound)
> 
> So, in physical reality, the complexity of the problem is linear in the
> length of the shortest path.  I think that's what we call "trivial".
> 
> Since Deutsch's Universal Quantum Computer is an accurate model of
> physical reality to the best of our current knowledge, it should be
> able to solve this problem, on an encoded representation of the maze,
> with the same linear behaviour.  As indeed it can: start a quantum
> mouse at the entrance, and, whenever it has to make a choice, have
> it make both choices, casting itself into a superposition of states.
> The first element of the superposition will exit the maze in time
> 
> 	(simulated length of shortest path) / (simulated velocity of mouse)
> 
> The class exercise was to write such a mouse, as a parallel process,
> and have it spawn copies of itself at every decision point.  Could
> we but run the mice truly in parallel, we would have the optimal
> solution; alas, we had to interleave them.
> 
> This is one example of a whole class of trivial problems which a
> computer equivalent to a mere Turing machine is spectacularly bad
> at solving.

--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu


