Actually, there's still a snag. We can't read out these states directly.
When you observe a mixed state, it collapses into one of the
component states, with appropriate probability - third
wierdness. So suppose you prepare one million electrons, each 40%
spin-up + 60% spin-down. Now you measure the spin of each. You will
find that 40% of the electrons (on average) come out as spin up, and
60% as spin down. But it's entirely unpredictable which come out as
which.
So when we read out the result of our computation, we only get the
result of processing one of these strips. So although our computer has
done the parallel computations for free, we've lost all but one of the
results. So it might appear that we're still no better
off than with a normal computer. However, Deutsch has been able to show
that's not true. His kind of quantum computer can still get some results
faster - see pages 248-249 of Lockwood.