Re: Quantum Computers [was Read any good books lately?]

hal@finney.org
Tue, 17 Aug 1999 07:54:11 -0700

> 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.

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