Quantenalgorithmen und Implementierung - Teil 1

1. 00:00welcome
2. 00:01Back to the course Quantum Algorithms and their Implementation.
3. 00:04After I explained the theoretical basics of teleportation - dense coding to you in the last video, I would like to
4. 00:12I will now demonstrate how teleportation can actually be implemented with Qiskit.
5. 00:19Again I use notebooks with Python to build the corresponding routines I import the corresponding
6. 00:28Libraries, Qiskit, numpy and random, which I will need for the following the first thing I do is build my circuit
7. 00:38this circuit consists of three qubits and classical bits.
8. 00:45In my quantum circuit, the zeroth qubit will be the qubit that the transmitter will use for transmission
9. 00:56would like the first and the second qubit are the two interleaved qubits, which are generated by the transmitter and the receiver.
10. 01:05and which were then actually needed for the transfer then
11. 01:11So I start to implement this teleportation algorithm.
12. 01:17I interlace the first with the second qubit so I apply the Hadamard gate to qubit 1, interleave it
13. 01:27with the CNOT gate cx - one and two have been interleaved and at this point I can now decide next
14. 01:35which information I would like to transfer.
15. 01:39If the sender wants to transmit the qubit in the zero state, nothing at all is transmitted to the qubit with the number zero.
16. 01:52applied.
17. 01:53If the transmitter wants to transmit a 1, then an X gate must have been applied to the zero QuBit.
18. 02:01If a Hadamard gate is applied, then a superposition is transmitted.
19. 02:09In the code you see here, I decided that I would like to transfer a 1, a state one.
20. 02:16So I apply the has Hadamard gate to the qubit zero
21. 02:24this qubit zero, which carries the information
22. 02:29This is now entangled with the transmitter's qubit, and the Hadamard gate has been applied,
23. 02:41both qubits were measured, qubit zero and qubit one were measured.
24. 02:46And the measurement result is now transmitted to the receiver and depending on the measurement result, now applies
25. 02:55the receivers X and or Z gate to its QuBit and then measures the result
26. 03:05and as you can see here, the result of the measurement at the receiver now consists of these sequences of bit strings
27. 03:18where the bit string or the portion of the bit, the leftmost bit string the one signals the third qubit
28. 03:28so the qubit with the number two
29. 03:31You can see an example of Qiskit notation here, so it works from right to left.
30. 03:39So if I see a one everywhere on the far left, then I see aha the qubit three at the receiver is measured as one
31. 03:48so the information was actually transmitted to the recipient.
32. 03:54I can make this transfer from the one I can make something more general also
33. 03:59I now do the following in this example I don't want to transfer a trivial qubit, I want to transfer a qubit
34. 04:07transfer a state that arises from the zero from the vector pointing upward by a rotation
35. 04:16by pi quarter yes, I have created a superposition of zero and one, but not a uniform superposition but like this
36. 04:25an intermediate state so I rotate my qubit that wants to transfer with the angle pi quarter around the x-axis, the
37. 04:34is made here at this point.
38. 04:36The further procedure in the algorithm is then the same as just now - I apply the CNOT gate, the H gate, to the two
39. 04:47Qubits when transmitter and receiver interleave with each other the transmitter measures for its two QuBits, the measurement result
40. 04:56is transmitted, and from the result or depending on the result of the measurement, the receiver then applies the two gates X and
41. 05:06Z accordingly.
42. 05:08I could now at this point consider what measurement result is actually expected at the receiver when
43. 05:16this state zero rotates by pi quarter is transferred.
44. 05:21I make life a little easier for myself by reversing the rotation by pi quarters before I measure.
45. 05:28do, that is, I say, well, is the desired, the expected result actually now transferred and I
46. 05:37rotate back by the same angle, then I expect the receiver to measure the zero state, I do this at the
47. 05:45Place so I rotate back by pi quarter, then perform the measurement and look at the measurement results, again applies
48. 05:53that to pay attention to the bit on the far left.
49. 05:57On the far left there is a 0 0 0 0 everywhere That is, we actually have this non-trivial, this non-trivial condition here
50. 06:08which arises when the basis vector zero has been rotated by PI quarter.

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