Einführung in das Quantencomputing - Teil 1

1. 00:01Welcome ladies and gentlemen to the Fundamentals of Quantum Computing one course.
2. 00:06In this video we look at the difference between a classical bit and a quantum bit. But where are we
3. 00:13in the agenda of the whole course?
4. 00:18Here,
5. 00:19It's about the difference between a classical bit and a quantum bit In both cases, a bit is the smallest
6. 00:27unit of a classical computer, the smallest information carrier, and
7. 00:34the quantum bit is the smallest unit of a quantum computer, the smallest information carrier.
8. 00:42How do the two differ?
9. 00:47A classical bit, and you know that, I'm telling you now properties that classical bits have, maybe boring
10. 00:54because you already know them. Properties that are normally not said in a big way either, because they naturally
11. 01:01are.
12. 01:01But I will still discuss them, a classical image is an object that can take on two values at are most often denoted by
13. 01:09zero or one, so the state of a classical bit is zero or one.
14. 01:16For example, you can think of a lamp being off or on or a wire carrying current or not.
15. 01:25You can also imagine you only have pointing, which has only two possible positions zero horizontally or one vertically.
16. 01:35If you are a photographer, you can also imagine a light particle coming horizontally or vertically.
17. 01:45Now what are the properties of the classical bit?
18. 01:49It has two properties that are really never mentioned because they are self-evident.
19. 01:53The first property is when you read out the classical bit, so you sort of look at what its value is,
20. 02:01then this fact does not change the value.
21. 02:03So when I look to see if the wire is carrying current, then I measure that and then for the still current or if
22. 02:13the clock hand is horizontal, I look at it and it is still horizontal.
23. 02:16Reading out does not change the state of a bit, which is a property that physicists call realism,which is
24. 02:23not normally said.
25. 02:26The second property is when you change an image, it cannot happen that the change in one can immediately
26. 02:37change another image.
27. 02:40Of course, it could be that if I change something here on the image, the wire then connects the two and then
28. 02:47current flows over here and then the other bit also changes but that takes time, it takes time, at least as much
29. 02:56as the light takes to flow from one bit to the other image, so for example when they connect through wire
30. 03:02then current has to flow, it takes as long as the light.
31. 03:06It is not possible with classical bits that if I change something here, the situation elsewhere will also change immediately.
32. 03:17A property that physicists call locality, which means properties are local.
33. 03:22If I change something here, then something doesn't change somewhere else.
34. 03:27Clearly classical algorithms have this property
35. 03:36How do they work now?
36. 03:39A step in a classical algorithm is the modification of a bit can then result in modification of a
37. 03:46whole register, but actually a classical algorithm is to change bit by bit and thereby at the end the
38. 03:53solution is created.
39. 03:56Furthermore, classical algorithms are deterministic, deterministic means If I start with the same initial conditions
40. 04:04and run the algorithm again, then the same result comes out Classical algorithms are like this.
41. 04:16So far, so clearly you know.
42. 04:19What, on the other hand, are quantum bits?
43. 04:23A quantum bit or Q bit for short, is an object that can take on two values, the values zero or one, two different values.
44. 04:35values, which are designated with a vertical line, zero and then a pointed bracket, respectively.
45. 04:42Vertical line one and then such a point bracket.
46. 04:48There's a reason they're called that, but it's not important for now.
47. 04:52You just see this is an object
48. 04:54The quantum bit that can take two well distinguished values zero or one or something in between or something in between,
49. 05:03a classical bit cannot, that is the effect of the super position.
50. 05:12That is, if you have imagined the classical picture as a clock hand, which can be horizontal or vertical, then
51. 05:18the quantum bit can be a clock hand that is horizontal or vertical or anywhere in between.
52. 05:28If you remember school.
53. 05:29There was the plane X Y plane, so here is the X axis, there is the Y axis.
54. 05:35And then core you could address any point by saying, kind of often along the X axis and still
55. 05:41kind of often on the Y axis.
56. 05:43And so you can also address quantum bits, says somehow often alpha on the zero axis and then still plus somehow
57. 05:53often on the one axis.
58. 05:55So quantum bits are, zero or one or somewhere in between.
59. 06:03What properties do they have now,
60. 06:14The first amazing property is read out measurement of the quantum bit, mostly changes the state of the quantum bit
61. 06:23when measuring, the result is always zero or one, i.e. horizontal or vertical.
62. 06:30So if the quantum image had a state before which is somewhere in between
63. 06:35it now changes its state horizontal or vertical.
64. 06:41You can think of quantum bit as a voter.
65. 06:44the voter goes to the voting booth and says what do I want, do I vote for the party?
66. 06:49There are two parties, there are parties zero and the the party one.
67. 06:55I'm unsure, I don't know yet. And then he is in the voting booth reading cross this cross that.
68. 07:05Now he has voted for the party say zero,
69. 07:11Before in a superimposed state it was this or that, and now, after he has voted, you can clearly say it is
70. 07:18a voter of party zero, by the way, you can't tell from the ballot paper how much he hesitated before.
71. 07:27Another nice picture is Frisbee falls through the hole, there's a Frisbee arriving, and here's the hole cover, and the
72. 07:33Frisbee somehow gets on it like this,
73. 07:35and now there are two possibilities either it falls in or it stays on it. But if
74. 07:41it falls through, then it must move in such a way that it falls through the hole cover.
75. 07:47So reading out a quantum bit changes its value - no realism.
76. 07:54The second spectacular property of a quantum bit is
77. 07:59if you change a quantum picture, here, then at the same moment it can change the properties of another quantum bit
78. 08:09that is removed from it. At the same moment means faster than it takes light to flow from one quantum image to the other.
79. 08:19Experimentally proven to be at least 10,000 times the speed of light
80. 08:27this is an effect Einstein called spooky action at a distance.
81. 08:34Is it possible to change something here?
82. 08:38spatially, without us knowing how, somewhere else in the room something also changes.
83. 08:44In fact, no one understands how the quantum bits do it, photons do it, ions do it, how the quantum particles do it,
84. 08:53nobody knows. But the fact is, they do measure again and again.
85. 09:02The effect can perhaps be compared to a married couple, one is in Europe, the other is
86. 09:08is in Australia, they have a joint account and the one in Europe is now withdrawing money from the account and at the same instance the partner in
87. 09:16Australia is also poorer.
88. 09:21Yes, we know this from human life, but that non-living matter behaves like this is very strange but
89. 09:29the quantum bits do,
90. 09:33Now that means for the algorithms for the quantum algorithms one step in a quantum algorithm is not the change
91. 09:41of a single quantum bit, but can be the change of the whole system.
92. 09:47It could be that they all interact with each other.
93. 09:50If you like the picture with the voters, a quantum it becomes a voter, then a register of quantum bits is a
94. 09:57whole village that votes.
95. 10:01If you do election advertising now, you wouldn't go to every single voter, rather you would try to
96. 10:06influence those leaders in the village to vote for your party and on their networking in the system.
97. 10:17That's also how quantum algorithms work.
98. 10:19You kind of tweak the system, make changes in very specific places, and hope that the system as a whole
99. 10:27behaves in such a way that it solves the given problem.
100. 10:31So one step in quantum algorithms is to change the overall system abruptly, and that's what quantum does
101. 10:36algorithms so fast.
102. 10:40for those of you who know it, if you don't know it, it doesn't matter,
103. 10:45Quantum algorithms work probalistically, which means that chance plays a role, and chance is used.
104. 10:51If that doesn't mean anything to you now, it doesn't matter, but you should have heard that once,
105. 10:57I would like to give you another intuition now.
106. 11:00Another intuition why quantum algorithms are so fast
107. 11:05For this, let's look at a cube.
108. 11:08So imagine a normal three-dimensional cube with 8 corners.
109. 11:18Three-dimensional cube has eight corners and we now imagine that our cube has a little glass sphere at each corner.
110. 11:25the glass sphere has a volume of one.
111. 11:30And in one of the glass spheres there is liquid completely full, so one litre of liquid is there for example, the other glass spheres
112. 11:36are empty, now at the edges of the cube.
113. 11:42There are glass tubes, the liquid can get through, can't stay in there.
114. 11:47I suppose it looks a bit like the Atomium in Brussels.
115. 11:51Here the spheres and in between like this, the corridors, but only at the edges of the cube, not somehow across or something.
116. 11:56So the setting, what you can do with this cube now is you can shake it,
117. 12:03you can shake it either to the right, to the left, or to the top, to the bottom or to the front back, as these three kinds of keys
118. 12:11When you shake right, left, that is along the right-left edge
119. 12:19you shake until the liquid is completely distributed.
120. 12:24If you were to shake it to the right and left, for example, half of the liquid would be in here.
121. 12:33Now the task is for them to distribute the liquid evenly over all eight balls, so one litre.
122. 12:42That is 18 litres in each of the eight spheres, with as little shaking as possible
123. 12:51the question is how does that work?
124. 12:55So how do you do that with as few shakes as possible, where a shake is to shake until
125. 13:01liquid is evenly distributed.
126. 13:04If you like, turn the video off for a moment and think about it before I give away the solution.
127. 13:13Here is the solution, It goes in three shakes, each in one direction, because if you shake right left first
128. 13:21then you have already distributed the liquid evenly between this sphere and that sphere.
129. 13:25If you now shake the top and the bottom, for example, then you will have the liquid evenly distributed through these four balls.
130. 13:30here and quarters towards the first quarters and now at the front at the back, then the liquid is evenly distributed,
131. 13:41that's fast.
132. 13:43Three steps changed eight values, classical computers need to change
133. 13:53eight values by all of at least eight steps.
134. 13:57You have to go to each value at least once to change it.
135. 14:03Quantum computers can shake, reach three steps to change eight values, so as an intuition
136. 14:12of the last slide.
137. 14:13Again the summary for you a classic picture looks like this, one might look like this

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