A quantum computer is a
hypothetical machine that would
exploit the principles of quantum
mechanics that govern the
subatomic world, in order to
solve certain problems much
faster than we know how to solve
them with any computer today.
Quantum mechanics has been the
basic framework for almost all
of physics for nearly a century.
What is says is that if you don't
know what state a system is in -
like you don't know if an electron
is in its ground state, its lowest
energy or in the next higher
energy - well the issue is in
quantum mechanics the different
places where the particle could
be, or the different paths that
it could take to reach a certain
final position can all interfere
with each other. And if that
happens then these different
paths can cancel each other out.
So then if some are positive and
others are negative then maybe
you won't find the particle at
that final place at all.
A classical computer, you know,
is of course based on bits which
are a bunch of elements that can
be either definitely zero or
definitely one. Now a quantum
computer is based on a quantum
bit, or q-bits, which can be, as
we say, in a quantum super
position of the zero and one
states. Now the way most popular
articles like to put it is that
it can be zero and one at the
same time. And the problem is
that at some point you've got to
measure the computer to figure
out or to read out an answer.
Which answer you see is
determined by these amplitudes.
An amplitude is like the square
root of a probability. Now the
key point is that the same number
can have more than one square
root. For example, "2" and "-2"
are both square roots of "4".
So corresponding to that you
can have either a positive or a
negative amplitude. So now, what
a quantum computer would be
is a computer that would exploit
this phenomenon of interference
between positive and negative
amplitudes on a massive scale.
And the goal would be that you
would try to, sort of, choreograph
things so that all of the
different paths leading to a
wrong answer would be out of
phase. Some would have positive
amplitudes. Others would have
negative amplitudes. And so they
would cancel each other out.
Whereas the paths leading to a
right answer should all have the
same sign. They should all
reinforce each other. And if you
can arrange that, then when you
look at the computer, at the end,
then you're going to see the
right answer with high probability.
Probably the most dramatic
application of a quantum computer,
the one that makes the headlines,
is that it could break almost
all of the cryptography that we
use today to protect our credit
card numbers. But that's actually,
probably not the most useful
application. Maybe its useful
if you're the first to do it and
you don't tell anyone else about
it, but it will mean that the
world will have to switch to
other cryptographic codes when
this starts to become practical.
Maybe a much more useful
application is one thats
actually the first one that the
physicists thought of back in
the 1980s. And one that is so
obvious that we barely even talk
about it. Namely you can use a
quantum computer to simulate
quantum physics. For example if
you are designing pharmaceuticals.
Or, if you're trying to design new
nano materials. If you're trying
to understand high-tempurature
superconductors or do high-energy
physics. Or do quantum chemistry.
For any of these applications,
any place where we're sort of
understanding the quantum
behavior of atoms and molecules
is relevant, well a quantum
computer sort of naturally
implements those dynamics and
so it could give you huge speed-
ups in simulating those sorts
of things. And, probably the
third application of quantum
computers is that you can try
and throw them at these np
complete problems. Like,
combinatorial optimization
problems like airline scheduling.
Or like the traveling salesmen
problem. Any problem where you
have a whole bunch of constraints
that you're trying to satisfy.
This is a huge, huge class of
practical problems that people
try to solve. But now for these
problems we don't yet know,
sort of, how much an advantage
quantum computers are actually
going to give you. If there's
some fundamental reason why you
can't build a quantum computer
then I hope that we discover that
because that would be a hundred
times more exciting than success
in building one. In principle
impossibility of quantum computers
would force us to revise our
whole conception of the laws
of physics.