From: hal@finney.org
Date: Tue Aug 17 1999 - 08:54:11 MDT
Robert J. Bradbury, <bradbury@www.aeiveos.com>, writes:
> If, the superimposed states collapse, and *we* get the "result",
> what do the other universes get? I.e. if we get the factors
> of the number and they get all the other states (i.e. the
> non-results), then what good is the method?
Damn good question, Robert, which shows very clearly why the many
worlds interpretation is not well suited for describing the situation
with quantum computers.
What happens, in the MWI, is that the "other universes" all merge back
into one (or at least a small number) when we do our measurement.
In the one (major) universe, it gets the result of the calculation.
If it is a probabilistic calculation which is not guaranteed to succeed,
there may be other universes in which they do not get the result and they
have to try again. But these computations are set up so that ideally
there will be only one universe at the end which has the result.
This points up an ambiguity in the MWI, which is, when do other universes
exist? That is, when does the universe split? You can give two answers.
One is that it splits whenever there is an alternative which is explored
in the quantum realm. The other is that it splits whenever there is
a measurement which causes what would conventionally be called wave
function collapse.
A photon goes through a double slit diffraction experiment. It has a
certain probability (technically, "amplitude") to take one slit and
a certain probability to take the other. In conventional QM we say
it takes both slits and produces interference. In the first version
of the MWI above (which I think is the one Deutsch subscribes to) we
would say that there are two universes, one where it takes one slit and
one where it takes the other. Then when the photon hits the detector
(film, or whatever) the two universes interfere and combine. In other
versions of the MWI, there is no split until the photon is measured.
The passage through two slits happens in only a single universe.
Quantum computers are similar to this. We put the quantum computer into
a superposition of states. Does this cause the universe to split into
multiples? By Deutsch's interpretation, yes, which is why he makes the
claim about QC implying MWI. By other interpretations, no, since no
measurements have been done yet.
If we were to then measure the system without doing anything fancy, the
measurement-based MWI would say that the universe splits at that point.
But we don't do that. Instead we do a complex series of manipulations
designed to put the system into a state where we can measure it and get
a good, deterministic result. At that point the measurement ideally
does not cause a split because there is no uncertainty in the result.
In short the MWI as applied to quantum computers either does not shed any
light on the question (if you assume that universes split when measurements
are made), or else it requires universes to recombine at the end of the
calculation, meaning that the "split" was somewhat tentative.
Hal
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