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So over the past 50 years or so, computing
power has doubled every 18 months.
And when you add that up,
it’s really pretty amazing.
The smartphone that I have in my pocket is
more powerful than a super computer from
1970.
So an actual question is where
does this ultimately lead?
Do we run into some limits,
does this stop?
Certainly there have been some signs
lately of running into limits.
Clock speeds, the number of computational
operations per second that computers can
do, actually stopped increasing
about ten years ago.
And the features sizes it seems hard
to shrink them much further,because
you can’t really make them out of
things that are smaller than an atom.
So what happens next?
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You could try to find
some kind of shortcuts,
the big example of that
is quantum computing.
Prior to quantum computing no one
really ever found any shortcuts.
The number of steps you needed to solve
a problem was not exactly the same, but
it was about the same.
Quantum computing just
totally blows that up.
I once calculated that if you took all the
silicon in Earth’s crust and converted it
into conventional computer chips, and
ran it through the age of the observable
universe the biggest number you could
factor would be about 5,000 bits.
And if you wanted to factor a 5,000 bit
number on a quantum computer that’d only
take you about two and a half hours,
if it was running at the same speed.
So it’s really a very dramatic thing.
And besides factoring numbers,
quantum computers can also be used for
certain other things like
simulating chemical reactions.
Which might help for example in designing
new catalysts to generate cheaper energy,
or to design new medical drugs.
But our question is are quantum
computers the end of the road?
The natural next place to
look is quantum field theory.
Quantum field theory is the physics
describing things where quantum mechanics
and special relativity are both important.
So quantum mechanics is important when
you’re describing small things like
particles.
And special relativity is important
when you’re describing fastings,
things that are moving close
to the speed of light.
So in collaboration with Heathly and
John Prescol, I’ve studied this question,
and what we found was that
conventional quantum computers can
emulate quantum field computers.
Anything that could happen
with quantum field theory,
you could simulate using
conventional quantum computers.
So this doesn’t provide a new,
dramatic advantage in the way
that quantum did over classical.
>>So what now?
>>Well, there is another aspect of modern
physics that you could consider as well,
namely, general relativity.
So this is Einstein’s theory of spacetime,
his theory of gravity as being
a curvature to spacetime.
And at present, it’s not really well
understood how to reconcile quantum
mechanics with general relativity.
A sufficiently small black hole would
be a place in the universe where
quantum mechanical effects and
general relativistic effects
would both be important.
So if you had a black hole where general
relativity and quantum mechanics both come
into play, could we use that as
some kind of hyper computer?
Does that give us something beyond
what even quantum computers might do?
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In recent work with Ning Bao and
Adam Bouland,
I’ve started to investigate these models,
just kind of looking at them one by one.
And saying,
what would be the computational
implications of these models?
And in a lot of models, what you have to
do to get general relativity and quantum
mechanics to fit together, is you have to
modify quantum mechanics a little bit.
And oftentimes,
when you modify the of quantum mechanics
all kind of crazy stuff happens.
You start to have signals being able
to be transmitted faster than light.
And if a signal is transmitted faster than
light from a certain reference frame,
a certain perspective, it’s actually
being transmitted backwards in time,
which can lead to all
kinds of crazy paradoxes.
And a second thing that can happen, is you
get kind of insane computational power.
So why think about these things now?
We don’t quite have
the quantum computers ready yet
to simulate quantum field theories.
And as far as building
computers out of black holes,
that’s very far from
anything we can do today.
And so today we can look at imaginary
computers of the far future,
what powers will they have?
And we hope that by thinking about this
we can not only push the limits of
computation, but we can push the limits
in terms of our knowledge of physics.
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