Vom Bit zum Qubit

1. 00:01Hello and welcome to the next video in the course from bit to qubit. In this video we deal with the idea of classical
2. 00:10Computer, how to get from that idea to the idea of the quantum computer,
3. 00:17the idea of the classical computer is quite old and is mainly based on the ideas of Alan Turing algorithms
4. 00:25That is, computational rules about how to compute something had been around for a long time, and the question was: if you had a computing machine
5. 00:33that can run an algorithm like that, do you need a special machine for every algorithm or
6. 00:42is there also a machine that can execute all algorithms?
7. 00:48If so, are there machines that are better or worse?
8. 00:54And one of those computational models, so to speak, is the Turing machine.
9. 00:59This Turing machine is relatively simple: you only need a few ingredients for it, namely a memory
10. 01:08tape on which we can store information with the help of a so-called alphabet which can of course be normal letters.
11. 01:16A B C, but it is enough to have an alphabet with only two different symbols, for example, zero and one and after the
12. 01:27Turing Theorem, it doesn't really matter which alphabet we use.
13. 01:31For example, we can store all the letters from A to Z using six bits. We just need a little bit more
14. 01:39Memory Tape. The little bit more memory tape is in the case, we need six bits to store one letter
15. 01:47that means that scales linearly
16. 01:51in addition we also need a read and write head, with which we can read out, so to speak, what is written to
17. 01:57this tape and write new information on it, then we still need a program and a control state, that means
18. 02:05that says for example: read the first bit on the memory tape, if the first bit is zero, then go to the second memory-
19. 02:13tape and write a 1 on there, that's sort of the basic idea of a computer, and whether we have a computer now
20. 02:24with just one memory tape or two memory tapes, whether we're using a different alphabet or something, I can any computer,
21. 02:35simulate any classical computer with a simple Turing machine like that and the effort just scales like a polynomial,
22. 02:45so with our letters it was like this: we need six times as much memory, and that's just what our
23. 02:53today's classical computers,
24. 02:57that is, if we go into a little more detail.
25. 03:00As I said, we have our bits, so we can then represent different numbers, for example, such as
26. 03:07here The five, can be written as once four, so once two to the power of two plus zero times 2, so 0 times two to the power of one
27. 03:18plus once one, two to the power of zero.
28. 03:23If we add that up, that gives us five again
29. 03:25If we now just store these front coefficients, then we can represent the number five in the bit representation
30. 03:32as 101 And if now we want to do arithmetic operations, we want to calculate what five plus four gives with the help of our
31. 03:44data that we have stored in bits, then we need some operation, and one of these basic operation is
32. 03:52the so-called NOT gate, the NOT gate simply changes the state of the bit, that is, if it was previously in the state zero
33. 04:02we apply the NOT gate, then afterwards we are in the state one would have been before in the state one, then afterwards we are in the
34. 04:09state zero.
35. 04:12Now we not only need logic gates acting on a single frame, but we also need two bit operations
36. 04:20and an example For such a 2-bit operation the so called XOR is the exclusive one or we pack two bits again.
37. 04:30In the association for example 00 and then have a bit what comes out the exclusive or is one exactly when one of the
38. 04:40both input bits are one that means 01 gives as output 1 10 also gives as output one not two single in, pack
39. 04:51so 11 then the output is zero again and the great thing is that now it doesn't matter if I want to add or multiply or some
40. 05:02other operation I can do all these tasks with only the help of a few basic operations.
41. 05:10That is, one and two bit operation are enough to perform any algorithm and that is to say so
42. 05:19The idea of the classical computer and will soon see that the quantum computer is also based on these basic building blocks
43. 05:30We also said these bits we have to store somewhere.
44. 05:34In the past, for example, these bits were stored with the help of punched cards, that is, you could see them with the naked eye.
45. 05:42what was stored there and again later, for example, data was stored on optical data carriers such as CDs.
46. 05:51There one needed now already microscope around to see whether we stored a 0 or a 1 and if now ever more data on ever more
47. 06:00smaller and smaller space, then at some point we get to this point that we're trying to store a bit into a single
48. 06:08atom or a single photon, and if we use very large materials to store our information
49. 06:17then we can describe these storage media using classical physics, but now sometime to this point
50. 06:26where we actually store information single atoms or single photons, then we have to describe the whole thing with
51. 06:34quantum physics, and in quantum physics certain things are different than in classical physics.
52. 06:44and what is a little bit different now we want to look at that first in another context, that is before you look at
53. 06:51that one could build the computer with quantum system, one did not want to go the other way first, namely
54. 06:59one wanted to simulate the quantum mechanics quantum mechanical systems with the help of classical computers, and if now
55. 07:09wants to simulate something small, as an example here we have a must, which has two sides black or white, then
56. 07:17if I have four coins here or n coins in general, then I can describe that with n bits.
57. 07:26But if now have four atoms or n atoms here in the case.
58. 07:31Now the simply Borsche, the Borsche atomic model is called, the red one is the nucleus and then we have such an electron which is around the
59. 07:39nucleus, so to speak, we consider the electron that can either stay relatively close to the nucleus or further away
60. 07:47away that's kind of like the classical bit.
61. 07:50So for example if the atom is close to the nucleus is zero is further away from the nucleus then it is a 1 The problem is just in
62. 07:59the quantum mechanical system, the electron can not only be in state zero or in state one, but I
63. 08:09can only say with a probability that the electron is close or farther away, that is, if I have so
64. 08:16a system of n atoms, then I must store two high in probabilities and the whole so to speak
65. 08:25and that makes the whole thing very time-consuming, that is, if I try to describe a quantum mechanical system with a
66. 08:33classical computer, I run into problems pretty quickly and that's also what two great physicists have stated
67. 08:43one of them was Richard Feynman who said at a symposium in 1982 that if we simulate nature in particular quantum-mechanical
68. 08:56systems from nature, then it is quite difficult with the classical computer.
69. 09:03That is, what we could do better is We could try to describe in a system that we want to do better.
70. 09:11Using a quantum mechanical system to simulate, that is the idea is I did in 1980, it was found that
71. 09:20you already had a better and better grip on single atoms, single photons, be it I can now build a small system for myself
72. 09:28with a few atoms, with a few photons, and then I can sort of manipulate that in that way, there's another system that is
73. 09:36I want to investigate, just simulated.
74. 09:40That is, there was no universal computer was, but the idea was actually to use special systems
75. 09:47special quantum mechanical systems to simulate a certain other system.
76. 09:54Shortly after that came second physicist German, and he said So how we can build in classical computer
77. 10:04which is universal, which can do any computation, so we can also build a universal quantum computer, which can do universal
78. 10:14Quantum algorithms can execute.
79. 10:17And Turing had said, yes, that in a classical computer it doesn't matter exactly what of alphabet we use
80. 10:27how much memory-
81. 10:28Bender We use that it sort of The effort scales as in polynomial.
82. 10:34And the prediction was just that with a Turing machine like that, we can't simulate a quantum computer any more efficiency
83. 10:44that this quantum computer can then do things that a classical computer just can't do, and that's what we want to look at in
84. 10:54this course in more detail.

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