00:00:00.000 A theory of computation within any laws of physics

00:00:03.600 is the theory of how you can use physical objects

00:00:07.480 to represent abstract objects.

00:00:09.920 So you want to represent the integers, 1, 2, 3,

00:00:14.720 and you can use physical objects like fingers.

00:00:16.680 So that will be 1, and that's called 2, that's called 3,

00:00:19.200 and so on.

00:00:20.120 And the computers are ways of instantiating abstract objects

00:00:26.800 and their relationships in physical objects

00:00:29.920 and their motion.

00:00:31.720 So now what happens with quantum computers

00:00:35.480 is that we simply take the deepest physical theory.

00:00:37.760 We have quantum theory, and we say, what kind of information

00:00:42.080 processing does quantum theory in general allow?

00:00:45.320 And what does it not allow?

00:00:46.520 And that's the theory of quantum computation.

00:00:48.080 And when you do that, what do you find

00:00:50.400 compared with a classical computer

00:00:53.080 when you make this quantum computer?

00:00:55.680 You find a number of similarities

00:00:59.880 and we find the reasons why the Turing theory worked

00:01:04.120 as well as it did.

00:01:05.400 And then you find a number of dramatic differences

00:01:08.280 between the quantum computers and classical computers.

00:01:13.840 The one that's got the most attention

00:01:16.520 is that for certain types of calculation,

00:01:19.640 quantum computer can perform it exponentially faster

00:01:23.480 than any classical computer.

00:01:25.600 So you could have, people haven't built quantum computers yet,

00:01:29.160 but we hope that they soon will.

00:01:30.920 And when a quantum computer is built,

00:01:33.320 a small quantum computer with a few thousand cubits

00:01:37.640 that that's the quantum analog of bits.

00:01:40.080 Compared to the billions of bits

00:01:41.520 in our normal desktop, in the middle of the left,

00:01:43.480 or even our mobile phones.

00:01:45.360 Yeah, right, right.

00:01:47.480 In other words, a very, very weak, comparatively weak

00:01:50.480 quantum computer could perform more computations

00:01:54.000 simultaneously than could be performed

00:01:56.400 by the entire visible universe.

00:01:58.360 If it was all made into computers,

00:02:00.560 in fact, when I say more, that's an understatement.

00:02:02.520 It exponentially more than that.

00:02:05.200 But only for certain types of computation.

00:02:08.560 Under the